Advances in Electronics and Electron Physics, Volume 77

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS

VOLUME 77

EDITOR-IN-CHIEF

PETER W. HAWKES Laboratoire d’Optique Electronique du Centre National de la Recherche Scientifque Toulouse, France

ASSOCIATE EDITOR

BENJAMIN KAZAN Xerox Corporation Palo Alto Research Center Palo Alto, California

Advances in

Electronics and Electron Physics EDITEDBY PETER W. HAWKES Laboratoire d’Optique Electronique du Centre National de la Recherche Scient@gue Toulouse, France

VOLUME 77

ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers Boston San Diego New York London Sydney Tokyo Toronto

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90 91 92 93

9 8 7 6 5 4 3 2 1

CONTENTS CONTRIBUTORS TO VOLUME 77 . . . . . . . . . . . . . . . . , . . . . . . PREFACE. ............... .,................

Active-Matrix Thin-Film Transistor Liquid-Crystal Displays SHINJIMOROZUMI I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Evolution and History of Thin-Film Transistor-Addressed Liquid-Crystal Displays . . . . . . . . . . . . . . . . . . . . . . . 111. Key Factors in Thin-Film Transistors for Liquid-Crystal Displays . . . . , . . . . . . . . . . . . . . . . . . IV. Characteristics of Different Types of Thin-Film Transistors and Thin-Film Transistor Liquid-Crystal Displays. . . . . . . . V. Driving Schemes for Thin-Film Transistor Liquid-Crystal Displays . . . . . . . . . . . . . . . . . . . . . . . VI. Color-Image Thin-Film Transistor Liquid-Crystal Displays . . VII. Performance of Liquid-Crystal Displays Based on Alternative Technologies. . . . . . . . . . . . . . . . . . . . . . . VIII. Applications of Thin-Film Transistor-Addressed Liquid-Crystal Displays . . . . . , , . . . . . . . , . . . . . . . . IX. Concluding Remarks . , . . . . . . . . . . . . . . . . . . , . . . . Acknowledgement. . . . . . . . . . . . , . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . , . . . . , . . . . . . . .

vii ix

2 12

17 28

47 57 65 69 74 77 77

Resonators, Detectors, and Piezoelectrics JEAN-JACQUES GAGNEPAIN

I. Introduction.

,

....,.........,.............

84

11. Fundamental Equations of Elasticity and

............................ ................,......... IV. Crystal-Lattice Anharmonicities (A Brief Review) . . . . . . . , V. The Resonator: Simple Linear Model . . . . . . . . . . . . . . . VI. Nonlinear Properties . , . . . . . . , . . . . . . . . . . . . . . . . Piezoelectricity

111. Material Constants

VII. Sensitivities to External Perturbations and the Design of Detectors . . . . . . . . . . . . . . . V

..........

85 93 98 103 112 125

vi

CONTENTS

VIII. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

132 132

Scanning Electron Microscopy in the Petroleum Exploration Industry J . M . HUGGETT I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Reservoir Petrography and Diagenesis . . . . . . . . . . . . . . . V . Paleontology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. Qualitative Pore Studies . . . . . . . . . . . . . . . . . . . . . . . VII. Petrophysics and Reservoir Production . . . . . . . . . . . . . . VIII . Future Developments. . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

140 140 150 156 185 185 192 201 202

Signal Analysis in Seismic Studies J . F . BOYCEAND L . R . MURRAY I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. The Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . . . I11. Wave Propagation across Plane Interfaces . . . . . . . . . . . . . IV. Preprocessing and Prestack Deconvolution . . . . . . . . . . . . V . Velocity-Field Determination and Stacking . . . . . . . . . . . . VI . Migration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII . Amplitude Variation with Offset . . . . . . . . . . . . . . . . . . . Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

INDEX

.....................................

210 214 229 244 263 277 298 308 316 316

319

CONTRIBUTORS The numbers in parentheses indicate the pages on which the author’s contributions begin.

J. F. BOYCE(209), Wheatstone Laboratory, King’s College London, The Strand, London WC2R 2LS, England J. J. GAGNEPAIN (83), Centre National de la Recherche Scientifique, Laboratoire de Physique et Metrologie des Oscillateurs, 32, Avenue de l’observatoire, 25000 BesanCon, France J. M. HUGGETT (139), The British Petroleum Company p.l.c., BP Research Centre, Chertsey Road, Sunbury-on-Thames, Middlesex, TW 16 7LN, England S, MOROZUMI (l), Seiko Epson Corporation, Fundamental Technology Research Department, 3-3-5 Owa, Suwa, Nagano, 392, Japan L. R. MURRAY (209), Wheatstone Laboratory, King’s College London, The Strand, London WC2R 2LS, England

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PREFACE The four chapters that make up this volume cover several fields of electronics and electron physics. The opening survey, by Shinji Morozumi, provides a broad survey of the history and present status of one of the most important of the newer display technologies, the so-called “active-matrix” type of liquid-crystal display. For many decades the cathode-ray tube (CRT) has dominated the display field, especially where high-resolution, large-area images are involved and particularly where full-color information is required. Although a variety of new displays have gained acceptance during the past 10 to 15 years, for example gas plasma, electroluminescent, and liquid-crystal types, inherent limitations make it unlikely, except for limited application areas, that any of these will seriously challenge the CRT. However, by integrating an array of thin-film transistors with a corresponding matrix of liquid-crystal elements, a versatile new form of display has emerged that overcomes many of the limitations of these other displays, offering the possibility that images with picture quality comparable to that of cathode-ray tubes can be produced. In addition, such displays have the added advantages of being in the form of a flat panel whose size may vary from a few centimeters to more than a meter. It is thus likely that these new displays will be of major importance during the coming decade, not only for television but also for computer and industrial applications. The second chapter is concerned with a topic that is of considerable practical importance: piezoelectricity and its applications in resonator and oscillator design. The range of applications of piezoelectric devices is very broad, too broad for all of them to be covered in a single chapter, and JeanJacques Gagnepain has chosen to concentrate on resonators. The treatment is detailed and his account is virtually an up-to-date monograph on the subject. A short but important section is devoted to non-linear properties, for “nonlinearities . . . are at the origin of some of the most fundamental properties of the materials.” The third chapter is a further member of a series of occasional articles on particular applications of the transmission or scanning electron microscope (SEM). Here, the role of the scanning instrument in the, at first sight, unlikely field of petroleum exploration is explained in great detail by J. M. Huggett. In fact, the SEM has been in use in the petroleum industry for almost as long as the instrument has been in existence for the examination of core samples. The modes of operation employed have expanded over the years, and specimen ix

X

PREFACE

preparation techniques have increased beyond number. This wide-ranging chapter covers both the techniques and their applications in detail. As in so many other branches of microscopy, analytical methods are rapidly increasing in importance. Cathodoluminescence is of particular interest here. Despite the specialized nature of the information sought, it is fascinating to see how all the resources of the SEM contribute to solving the petroleum engineer’s problems. The final chapter, by J. F. Boyce and L. R. Murray, is also concerned with earth science but a very different kind of tool is now employed: the analysis of seismic signals. The behaviour of acoustic signals within the Earth, detected at several sites on the surface, provides three-dimensional information about the Earth’s interior. The task of translating the information acquired at the detector sites into a model that is in accordance with the geological facts is extremely complex and the authors give a clear account of some of the ways in which the problem is solved and of the difficulties that beset the seismographer. It only remains for me to thank all the contributors to this volume most warmly and to list forthcoming reviews in this series. P. W. Hawkes

Parallel Image Processing Methodologies Image Processing with Signal-Dependent Noise Pattern Recognition and Line Drawings Bod0 von Borries, Pioneer of Electron Microscopy Magnetic Reconnection Sampling Theory Layered Synthetic Microstructures as Dispersive Devices for the Extreme Ultraviolet Finite Algebraic Systems and Trellis Codes Electrons in a Periodic Lattice Potential The Artificial Visual System Concept Corrected Lenses for Charged Particles A Gaseous Detector Device for ESEM The Development of Electron Microscopy in Italy

J. K. Aggarwal H. H. Arsenault H. Bley H. von Borries A. Bratenahl and P. J. Baum J. L. Brown P. Chakraborty H. J. Chizeck and M. Trott J. M. Churchill and F. E. Holmstrom J. M. Coggins R. L. Dalglish G. D. Danilatos G. Donelli

xi

PREFACE

The Study of Dynamic Phenomena in Solids Using Field Emission Amorphous Semiconductors Median Filters Bayesian Image Analysis Phosphor Materials for CRT Emission Electron Optical System Design Statistical Coulomb Interactions in Particle Beams Number Theoretic Transforms Tomography of Solid Surfaces Modified by Fast Ions The Scanning Tunnelling Microscope Applications of Speech Recognition Technology Spin-Polarized SEM The Rectangular Patch Microstrip Radiator Electronic Tools in Parapsychology Image Formation in STEM Low-Voltage SEM Languages for Vector Computers Electron Scattering and Nuclear Structure Electrostatic Lenses CAD in Electromagnetics Scientific Work of Reinhold Riidenberg Metaplectic Methods and Image Processing X-ray Microscopy Applications of Mathematical Morphology Focus-Deflection Systems and Their Applications Electron Gun Optics Thin-Film Cathodoluminescent Phosphors Electron Microscopy and Helmut Ruska

M. Drechsler W. Fuhs N. C. Gallagher and E. Coyle S. Geman and D. Geman T. Hase, T. Kano, E. Nakazawa, and H. Yamamoto V. P. Il’in G. H. Jansen

G. A. Jullien S. B. Karmohapatro and D. Ghose H. Van Kempen H. R. Kirby I(.Koike H. Matzner and E. Levine R. L. Morris C. Mory and C. Colliex J. Pawley R. H. Perrott G. A. Peterson F. H. Read and I. W. Drummond K. R. Richter and 0. Biro H. G. Rudenberg W. Schempp G. Schmahl J. Serra T. Soma et al.

Y. Uchikawa A. M. Wittenberg C. Wolpers

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Active-Matrix Thin-Film Transistor Liquid-Crystal Displays SHINJI MOROZUMI Seiko Epson Corporation Fundamental Technology Research Department Suwa. Nagano. Japan

I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . A . Historical Background . . . . . . . . . . . . . . . . . . . . B. Basic Twisted-Nematic Liquid-Crystal Display Cell . . . . . . . . . .

2 2 4 6

C. Multiplexed Twisted-Nematic Liquid-Crystal Display Cells and Their Limitation D . Advantages of Active-Matrix Liquid-Crystal Display Panels . . . . . . . I1 . Evolution and History of Thin-Film Transistor-Addressed Liquid-Crystal Displays A . Early Work on CdSe Thin-Film Transistors and Silicon-on-Sapphire Transistors B. Transistor Arrays Based on Single-Crystal Silicon and Diode Arrays . . . . C . Emergence of Silicon Thin-Film Transistors and Diodes . . . . . . . . . I11. Key Factors in Thin-Film Transistors for Liquid-Crystal Displays . . . . . . A . Fundamental Physical Arrangement and Operation of the Thin-Film . . . Transistor Liquid-Crystal Display . . . . . . . . . . . . . . . . B. Electrical Requirements . . . . . . . . . . . . . . . . . . . . C. Structural Requirements and Fabrication Processes . . . . . . . . . . IV. Characteristics of Different Types of Thin-Film Transistors and Thin-Film Transistor Liquid-Crystal Displays . . . . . . . . . . . . . . . . . . . . A . CdSe Thin-Film Transistors . . . . . . . . . . . . . . . . . . B. Amorphous Si Thin-Film Transistors . . . . . . . . . . . . . . . C. Polycrystalline Si Thin-Film Transistors . . . . . . . . . . . . . . V . Driving Schemes for Thin-Film Transistor Liquid-Crystal Displays . . . . . . A . “Point-at-a-Time” Data Transfer Method . . . . . . . . . . . . . . B. “Line-at-a-Time” Data Transfer Method . . . . . . . . . . . . . . C. Input-Signal Modification for Grey-Scale Operation . . . . . . . . . . D . Large-Scale Integration Drivers and Their Connection to the Liquid-Crystal Display . . . . . . . . . . . . . . . . . . . . . . . . . E. Integrated Thin-Film Transistor Drivers . . . . . . . . . . . . . . VI . Color-Image Thin-Film Transistor Liquid-Crystal Displays . . . . . . . . . A . Structure . . . . . . . . . . . . . . . . . . . . . . . . .

1

9 12 13 14 15 17

18 21

23 28 29

31 39 47 48

50 53 54 55 57 58

.

Copyright 0 1990 by Academic Press Inc All rights of reproduction in any form reserved. ISBN 0- 12-014677-0

2

SHINJI MOROZUMI

B. Color Filter Fabrication. . . . . . . . . . . . . . . . . . . . C. Backlighting. . . . . . . . . . . . . . . . . . . . . . . . D. Driving Scheme for Color Liquid-Crystal Display Panels . . . . . . . . VII. Performance of Liquid-Crystal Displays Based on Alternative Technologies . . . A. Comparison between Thin-Film Transistor and Diode-Controlled LiquidCrystal Displays . . . . . . . . . . . . . . . . . . . . . . B. Comparison between Directly Multiplexed and Active-Matrix Displays . . . VIII. Applications of Thin-Film Transistor-Addressed Liquid-Crystal Displays . . . . A. Television Applications . . . . . . . . . . . . . . . . . . . . B. Computers . . . . . . . . . . . . . . . . . . . . . . . . IX. Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . A. Comments on the Status of Liquid-Crystal Displays Relative to Displays Based on Other Technologies . . . . . . . . . . . . . . . . . . . . B. Present Problem Areas in Thin-Film Transistor Liquid-Crystal Displays . . . C. Future Expectations of Thin-Film Transistor Liquid-Crystal Displays . . . . Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61 63 64 65 66 61 69 69 13 14 14 15

16 17 71

I. INTRODUCTION A . Historical Background

Liquid-crystal displays (LCDs) have a much shorter history than that of cathode-ray tubes (CRTs) and are relatively new compared to other flat-panel display devices such as plasma display panels (PDPs) and electroluminescent displays (ELDs). Despite their recent emergence, LCDs have come into widespread use and are expected to replace many of the older displays in many applications because of their unusual combination of low power consumption, thin structure, light weight, and relatively low cost. Organic materials identified as liquid crystal were already known in the 19th century. Such materials are characterized by the fact that over some temperature range of their liquid state, the molecules exhibit a degree of long-range order making the material somewhat similar to a crystal of solid material. The elongated liquid-crystal molecules also possess a dipole moment, allowing them to be oriented by an external field; and this together with their optical anisotropy allow them to be used for electrical control of light transmission. The possibility that liquid crystals could be used in a display device was first demonstrated in 1968 (Heilmeier et al., 1968a and 1968b). In this early work, the dynamic-scattering mode (DSM) was used in which a thin layer

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

3

of nematic-phase liquid crystal, one of the several forms of liquid-crystal materials, was employed (de Gennes, 1974). When an electric field was applied across this material, it was shifted from a clear to a milky (scattering) state, blocking the transmission of direct light. Upon removal of the field, the material reverted to its initial clear state. Unfortunately, the use of this phenomenon in practical applications was limited by various factors, such as degradation of the material by the electrical current passing through it, poor viewing characteristics, and the somewhat high voltage levels required for operation, e.g., 25 volts, making it less than ideal for use with low-voltage semiconductor drivers. A few years later, in 1971, an improved method of operation for nematic liquid-crystals was devised (Schadt and Helfrich, 1971). Referred to as the twisted-nematic field-effect mode (TN or TN FEM), this method provided significant advantages over the earlier DSM type. Due to its much lower voltage operation, enabling it to be used with low-voltage complementary metal oxide semiconductor (CMOS) circuits, which appeared at about the same time, the way was opened for the extensive use of liquid-crystal displays in watches and calculators in 1973. Since then, as a result of the progress in large-scale integration (LSI) technology, many electronic instruments have become more compact and lightweight by taking advantage of the availability of low-power and lightweight LCD screens. Simple displays containing relatively few TN elements could be made with each element controlled by a separate semiconductor driver. However, in the case of displays with a large number of elements, it was recognized that some form of X-Y addressing, which had already been employed for PDPs and ELDs, was desirable to reduce the large number of drivers. This approach has enabled satisfactory liquid-crystal displays with a limited number of rows of elements to be made. However, as discussed below, the particular characteristics of TN liquid-crystal cells seriously reduce the contrast ratio and viewing angle obtainable as the number of rows is increased. During the late 1970s, when no satisfactory thin-film transistor (TFT) or active-matrix technology was available, directly multiplexed T N liquid-crystal displays provided the only means to satisfy the need for larger displays with a large number of pixels. For example, in 1978, a 120 x 160-elementblack-andwhite LCD T V screen based on direct-drive multiplexing was developed (Kaneko et al., 1978). Although this technology is still employed and such a LCD TV has actually been marketed, problems of poor viewing quality remain. The portable personal computer (PC)is an example of another application requiring large-area liquid-crystal displays with high-quality images. Whereas early units employed relatively small liquid-crystal displays with 32 x 120 picture elements, the latest ones are 10 inches in diagonal and have 400 x 640

4

SHINJI MOROZUMI

elements. These are also directly multiplexed displays making use of the T N or the more recent supertwisted birefringence effect (SBE) liquid-crystal mode (see Section 1.C). Although the latter provides somewhat improved viewing characteristics, the overall viewing quality is still considered inadequate. The continuing need for compact LCD TVs (Morozumi et al., 1984a) and laptop computers with desirable viewing characteristics has thus stimulated the research and development of active-matrix LCDs in which an active element is incorporated at each picture cell (pixel). Although various types of active elements have been explored, the greatest interest has been in TFT elements, particularly those based on amorphous and polycrystallized silicon TFTs. Although such TFTs have already been incorporated in pocket LCD TVs, the screen size is still too small for more general applications. Present activity is thus being directed at developing large-area TFT LCDs for largersize TVs and computer screens with picture sizes of more than 10 inches in diagonal. In the following sections of this chapter, liquid-crystal displays based on such TFT elements (TFT LCDs) are discussed at length. In addition to the material aspects of TFT elements and their performance characteristics, the design, structure, and operation of complete TFT LCDs will be discussed. Also included are the electrical driving schemes used and the application areas of these displays.

B. Basic Twisted-Nematic Liquid-Crystal Display Cell The operating principle of a TN-LCD cell is shown in Fig. 1. As indicated in Fig. la, in the absence of an applied electric field, the elongated liquidcrystal molecules (assumed to be in the nematic phase) orient themselves parallel to the glass plates confining the liquid-crystal layer, whose thickness is less than or equal to 10 micrometers (pm). With suitable surface treatment of the plates, the molecules contacting the upper plate are made to align in a direction which differs by 90" from the molecules contacting the lower plate. Because of the ordering effects within the liquid-crystal medium, successive molecular layers are twisted with respect to their neighbors as shown. Also as shown in the figure, polarizers are provided on the outer surface of the glass plates, with the polarizing axes corresponding to the liquid-crystal molecules at the respective plates. Because of the gradual twist, when the structure is illuminated from below with unpolarized white light as shown in Fig. la, the polarized light entering the liquid-crystal layer will have its plane of polarization twisted 90" by the liquid-crystal molecules and emerge through the upper polarizer. However, if a voltage is applied across the transparent electrodes of the liquid-crystal

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

5

Conductor (a) (b) FIG.1. The principle of the twisted-nematic liquid-crystal display (TN LCD):(a) without an electric field, incident light can pass through the cell; (b) with the applied voltage, the light is blocked.

layer, as shown in Fig. lb, the molecules are forced into a position parallel to the electric field because of their dielectric anisotropy so that their long axes become perpendicular to the plates. The polarized light entering the liquidcrystal layer is now no longer rotated and is blocked by the upper polarizer. Instead of the above arrangement, where the polarizers of the glass plates are positioned with their axes perpendicular to each other (crossed polarizer method), the parallel polarizer method, in which the axes of both polarizers are parallel, is also possible. In this case, the optical effect of the applied voltage is inverted. An example of the light transmission as a function of voltage for the crossed polarizer method is shown in Fig. 2. As indicated, the application of as little as 3-4 volts is sufficient to switch the cell from ON to OFF. Of importance to note in Fig. 2 is the fact that the change in light transmission depends strongly on the viewing angle, and this may be a serious problem when displaying an image with grey scale. This dependency is caused by the partial tilt from parallel to perpendicular of the molecules at intermediate voltages. For instance, when a voltage intermediate between the O F F and ON state is applied to the cell, tilting the molecules by 45" with respect to the plates, the curves of light transmission viewed respectively at 60",90°,and 120"to the glass plates differ from each other, since the molecules have varying orientations with respect to the polarized light. If, however, a voltage sufficient to fully shift the molecules to the perpendicular state is applied to the cell, light is completely blocked and a good black state may be achieved over a considerable range of viewing angles.

6

SHINJI MOROZUMI

0

1

2

3

4

5

Voltage ( V ) FIG.2. Optical response of a twisted-nematic (TN) cell with crossed polarizers to applied voltage: cell exhibits a viewing-angle dependency in light transmission; a smaller angle gives a steeper characteristic; in the case of parallel polarizers, these characteristics are inverted with respect to applied voltage.

C . Multiplexed Twisted-Nematic Liquid-Crystal Display Cells and Their Limitation

Because of the voltage threshold characteristics of the TN liquid-crystal cells, they allow a large number of pixels to be addressed by means of X - Y orthogonal strips of transparent conductors. Using an electrode arrangement such as shown at the top of Fig. 3, with a continuous layer of liquidcrystal material confined between the two sets of transparent electrodes, the individual cells or picture cells (pixels) are defined by the crossover regions of the electrodes. Since the pixels may be activated by applying suitable voltages to these electrodes (data and scan lines) in a time-sequential manner, a much smaller number of driving circuits is required than if each pixel were addressed separately. As indicated in Fig. 3, during successive fields the polarity of all the addressing pulses is reversed. This procedure prevents any DC voltage from appearing across the liquid-crystal elements during continuous scanning, which could cause deterioration of the liquid-crystal cells. In a positive field, successive rows of elements are addressed sequentially at a sufficiently rapid rate to avoid image flicker. Addressing a single row is accomplished by

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS Di Dz

7

DN

Scan Lines

S> s2

\Data

Lines

Positive

k

Field

Negative I

1

ield

FIG.3. Electrode configurationand drivingwaveforms for direct-drive dot-matrix TN LCD: each frame consists of a positive and negative field; on voltage for one pixel when selected is kV,, and OFF voltage is (k - 2) V,.

applying a pulse voltage ‘‘kVO”to the row of elements connected to one of the scan lines S,-S,, while for the remaining nonaddressed rows a voltage level “V,” is maintained. During the addressing time of this row, a voltage “2V0” is applied to the vertical data lines of the OFF elements, resulting in a voltage “(k - 2)V0” across them. At the same time, a “0” voltage is applied to the data lines of the ON elements, resulting in a voltage “kV,” across them. This process is then repeated for successive rows until all the elements of the array have been addressed. This addressing method, referred to as direct-drive multiplexed operation, has been widely used for TN liquid-crystal displays containing, for example, up to about 100 scanning lines. Typical applications are portable computers, copy and other office machines, communication instruments such as telephones, and pocket TV sets. However, as explained below, as the number of

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SHINJI MOROZUMI

scan lines is made larger to increase the resolution of the display, the effective voltage difference between ON and OFF pixels is reduced and the viewing quality of the displayed information becomes poorer. This results from the fact that the optical response of the liquid-crystal cells is determined by the rms voltage, i.e., the integral of the square root of the voltage applied to them over the time required to scan all the rows. In terms of the rms voltage, the ON voltage V,, of a pixel can be expressed as (Alt and Pleshko, 1974):

V,, = J { k 2 V ; / M }

+ {(M - l)V$M},

(1)

where M is the number of scan lines. For an OFF pixel, the rms voltage V,,, can expressed as:

V,,,

= J{(k

+

2)'Vi/M) { ( M - l)Vi/M}. The resulting ratio of V,,,/Kff, expressed by C, is then given by: -

C = Jk2

+ V t / ( k - 2)2 + V i .

(2) (3)

It can be shown that the maximum value of this ratio, C,,, is given when

k=&G+I.

(4)

If this condition is satisfied, the maximum voltage ratio ,,C, cmax

=

J(JM+ I)/(&

- 1).

becomes: (5 )

From Eq. (5), it can be seen that as the number of scan lines M increases, becomes progressively smaller and approaches unity. As an example, if a value of M = 200 is inserted into Eq. (9,a voltage ratio ,,C , of 1.152 is obtained. Assuming that the magnitudes of the ON and OFF voltages allow them to fall on the steeply sloping portions of the curves of Fig. 2, the resulting optical contrast ratio will be only 2.5 at a viewing angle of 60", whereas at larger viewing angles, the contrast ratio will be reduced to a much lower level. In order to alleviate this problem, attempts have been made to develop new TN liquid-crystal materials as well as to optimize the cell structure and fabrication process (e.g., surface alignment of molecules) to obtain cells with a sharper threshold. However, it appears that for practical purposes, images with acceptable contrast cannot be obtained for direct-drive dot-matrix TNLCD arrays with more than about 100 scanning lines. Recently, other solutions have been proposed using a new phenomenon in nematic liquid crystals, the supertwisted birefringence effect (Scheffer et al., 1985) as well as new materials in the form of ferroelectric liquid crystals (Clark and Lagerwall, 1980). Although these approaches have advantages, they still present some problems such as limited speed of response, difficulty in producing a good grey scale, and difficulty of fabrication of the display as a result of the more critical cell spacing.

,,C ,

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

9

D. Advantages of Active-Matrix Liquid-Crystal Display Panels

In the active-matrix approach, a suitable “active” circuit element is incorporated at each pixel to overcome the limitation of direct-drive multiplexing. These active elements may consist of thin-film field-effect transistors as shown in the configuration of Fig. 4, or they may consist of diode elements as shown in Fig. 5. In Fig. 4, each pixel consists of a TFT and an associated pixel electrode on the lower glass substrate and a common electrode on the upper glass plate. The picture cell (pixel) is defined by the liquid-crystal material contained between the pixel electrode connected to the TFT ar.d the common electrode. Since the resistivity of the liquid-crystal material is relatively high, it acts as a capacitive circuit element. Each of the horizontal gate lines, which correspond to the scan lines in Fig. 3, is connected to the gate electrodes of a row of TFTs. When a suitable pulse is applied to a gate line, it switches the corresponding row of TFTs from the O F F state (high resistance) to the ON state (low resistance). If, during this time, voltages corresponding to the data to be displayed are applied to the data lines, the liquid-crystal elements, i.e., the pixel capacitors, are charged up through the selected TFTs of this line to the applied voltages. After the pulse on the selected gate line is terminated and the TFT elements of this row revert to their OFF state, the charge on the liquid-crystal elements may be stored if the OFF resistance of the TFTs is sufficiently high. Usually, the storage time is required to be more than one frame time, i.e., more than 1/60 second. In this case, the voltages across ON elements of the liquid-crystal

rode

‘TFT

’Pixel Electrode ‘Glass

(a) (b) FIG.4. Configuration of TFT LCD: (a) thin-film transistors (TFTs), pixel electrode, gate lines, and data lines are fabricated on lower glass substrate; upper glass plate has transparent common electrode; the liquid-crystal material is confined between both plates; (b) LC material acts as capacitor in each pixel.

-

10

SHINJI MOROZUMI

Scan Line

-Glass -LC Material

.Glass

\

Data Line

\

Pixel Electrode

\

Diode

(a)

I

Data Line

-------1

Diode I

I

-I------J

Pixel

Pixel Electrode

(b)

(C)

FIG.5. Configurationof diode LCD: (a) thin-film diodes, data lines, and pixel electrodes are fabricated on lower glass substrate; upper glass has stripe transparent electrodes as scan lines; (b) each pixel consists of a bidirectional diode in series with a liquid-crystal element connected between a scan line and data line; (c) current-voltagecharacteristicof bidirectional diode.

material are, in effect, subjected to a static drive signal during the entire frame time. At the same time, the high resistance of the OFF TFTs of the array eliminates cross talk, that is, it prevents signal voltages from building up across liquid-crystal elements of other rows when they are not being selected. Due to the above storage action and cross-talk-free operation, a high optical contrast ratio can be obtained in accordance with the curves of Fig. 2, avoiding the limitation of VJEff signals imposed by Eq. (5). In the arrangement of Fig. 5, each data line is connected to a set of bidirectional diodes that are in series with the pixel electrodes of a column of liquid-crystal cells. In order to enable positive and negative signals to be applied to each pixel during successive fields, diodes having a bidirectional characteristic are employed. In this structure, a layer of liquid-crystal material

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

11

is confined between the pixel electrodes and the scanning electrodes oriented horizontally. Operation of this type of display structure depdnds on the availability of diodes that have a well-defined threshold in their currentvoltage characteristic and a steep slope beyond the threshold. During addressing, the signals applied to the array are somewhat similar to those employed for the array of Fig. 3. In the case of Fig. 5, however, the diodes serve to prevent voltage from appearing across the liquid-crystal elements that are not being addressed. In the case of elements being addressed, the combined voltage across the data line and the scan line is assumed to exceed the voltage threshold of the diode, allowing these liquid-crystal elements to be charged. As in the case of the TFT array, if the OFF resistance of the diodes is sufficiently high, a charge established across a liquid-crystal element may be retained for a long period after the moment of addressing, thus permitting high-contrast images to be obtained. Aside from the high contrast ratio and wide viewing angle that can be achieved by using the active-matrix concept, this approach allows the design of display panels with a relatively large number of scan lines, e.g., 500 or more. Also, since liquid-crystal elements without a sharp electro-optical characteristic and small C,,, in Eq. ( 5 ) can be used in order to attain high contrast ratio, other phenomena and materials than those associated with the twistednematic effect may be used. In addition, the active-matrix approach allows images with a much better grey scale to be produced than is possible with direct-drive multiplexed operation. Early arrays of TFTs employed cadmium selenide (CdSe) as the semiconductor for the conductive channel of the TFT. At present, the main efforts are based on polycrystalline silicon (poly-Si) or amorphous silicon (a-Si) for this purpose. Although the image quality of the TFT-type active-matrix LCD is much higher than that of conventional direct-drive multiplexed LCDs, the use of active-matrix addressing presents other difficulties. Display panels with TFTs are inherently more complicated than those using the direct-drive multiplexing method because of the added steps involved in TFT fabrication. In practice, it is quite difficult to produce a TFT array with an acceptably low number of defects. Since diodes in the form of thin-film elements involve a simpler fabrication process than TFTs, active-matrix LCDs with diodes are also receiving considerable attention. Typical of such diodes are metalinsulator-metal (MIM) bidirectional elements and dual amorphous Si pn diodes. Since their current-voltage characteristics are not quite ideal, the actual grey-scale performance presently obtained with diodes may be somewhat restricted. Though the emphasis in this chapter will be on LCDs employing TFTs, a comparison between active-matrix LCDs with TFTs and diodes will be discussed further in Section VI1.A.

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SHINJI MOROZUMI

11. EVOLUTION AND HISTORY OF THIN-FILM TRANSISTOR-ADDRESSED LIQUID-CRYSTAL DISPLAYS

The active-matrix liquid-crystal display was first proposed in 1969 (Lechner et al., 1969) with emphasis on the diode type. This concept was presented again with further refinement in 1971 (Lechner et al., 1971),at which time the idea of the twisted-nematic liquid-crystal display was also proposed. Thereafter the emphasis on active-matrix LCDs gradually gained momentum. The developmental history of active-matrix LCDs is indicated by the number of papers on active-matrix LCDs presented at the Society for Information Display (SID) Symposia shown in Fig. 6. In the cradle period from 1973 until 1975, the basic approaches to activematrix LCDs made used of CdSe TFTs and silicon-on-sapphire (SO'S) transistors. In this period, the potential and possibility of realizing a dotmatrix display with a large number of pixels and good viewing characteristics were proven. However, at the same time, the difficulties and limitations involved in achieving active-matrix LCDs, particularly the active element fabrication, were also recognized. In the second period (1976-1981), SOS TFTs were superseded by metal oxide semiconductor (MOS) transistor technology with the aim of reducing these active-matrix LCD problems. This resulted in black-and-white video

S i Thin-Film

u-

(,

0

poly& Amorphous)

L 0)

n E

z

5

Varistor,MIM amorphous Si

0

'73 '14 '75 '76 '77 '70 '79 '80 '01 '82 '83 84 '05 '86

Year

FIG.6. Number of papers presented annually at the Society for Information Display (SID) Symposia on active-matrix LCDs: TFT types are classified into CdSe and Te, MOS, and Si thinfilm categories; since 1982, papers on Si TFTs have received the most attention.

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

13

display panels based on MOS transistors. However, they appeared not to have a high potential for practical use, because these LCDs had viewing limitations due to the opaque substrate. In parallel with this work, diode elements were proposed as active-matrixelements in order to solve problems associated with the difficulty of transistor fabrication. In the third period, from 1982 to the present time, a remarkably large number of papers on arrays of Si TFTs appeared because of their ease of fabrication and excellentcharacteristics.Furthermore, the demonstration that full-color images could be achieved with Si-TFT technology greatly stimulated the further development of active-matrix LCDs. This period exhibits a flowering of the active-matrix LCDs with a long-term effort since 1971. Actually, the commercial application of active-matrix LCDs to pocket TV receivers has already begun. A. Early Work on CdSe Thin-Film Transistors and Silicon-on-Sapphire Transistors

Initial research on thin-film transistors made use of evaporated polycrystalline CdSe and, to some extent, cadmium sulfide (CdS) thin films. The CdSe TFTs were used for the scanning circuits of photoconductor arrays (Weimer et al., 1966,and Waxman, 1968).Subsequent to this, CdSe TFT active-matrix arrays were studied for use with ELDs (Fischer, 1971). The first transistoraddressed LCDs using such CdSe TFTs consisted of a 6 x 6-inch character and graphic display with 20-lines-per-inchresolution (Brody et al., 1973)and a 30 x 50-element video display with 50 elements per inch (Lipton and Koda, 1973).These were followed by work on LCDs based on SOS transistor arrays used in a 1 x l-inch video display (Lipton et al., 1975).Although such LCDs were at a quite primitive stage, these efforts demonstrated the effectiveness of the TFT-addressed active-matrix LCD for achieving high resolution and excellent viewing characteristics. In the above work, all the layers for the CdSe TFTs, namely the CdSe channel material, the gate insulator, and the gate electrodes (such as aluminum), were fabricated by evaporation in a vacuum chamber. Since the CdSe layer has a high carrier mobility (approximately 100 cmZ/Vsec) allowing a high ON current as well as sufficiently low OFF current, TFTs based on this material exhibited satisfactory electrical characteristics for use in active-matrix LCDs. However, instability problems made their practical application difficult. These problems were caused by the nature of the interface between the CdSe channel material and the gate insulator as well as by the gate insulator itself. The realization of a highly stable interface and insulator was quite difficult with the evaporation equipment available at that time because of poor vacuum.

14

SHINJI MOROZUMI

The use of SOS technology avoided these problems, since it involved fabrication of the transistors on a single-crystal sapphire substrate with a high-qualitygate insulator and related interface like an MOS transistor on a Si single-crystalwafer. But the epitaxial growth of Si films on sapphire substrates was not so easy, and, additionally, the cost of such transistor arrays and their limited area precluded their exploitation for general purposes. B. Transistor Arrays Based on Single-Crystal Silicon and Diode Arrays

In the next generation, explored during the 1970s, the use of MOS transistors (instead of SOS technology) fabricated on a silicon single-crystal wafer was investigated for small video LCD devices 1-2 inches in size (Lipton et al., 1977). Such MOS transistors could be easily fabricated by means of ordinary integrated-circuit (IC) technology, unlike SOS transistors. However, since the silicon crystal substrate is not transparent and therefore prevents a second polarizer from being positioned under the lower electrodes, the TN mode (see Section LB), which produces the highest contrast ratio of all the liquid-crystal operating modes, could not be applied. Initially, the dynamicscattering mode was employed (Yanagisawa et al., 1981),but this resulted in problems of material degradation (see Section 1.A). Subsequently, the guesthost mode (Heilmeir and Zanoni, 1968a),which involved use of a dye material in addition to the liquid-crystal material, was employed for active-matrix LCDs with MOS transistor arrays (Hosokawa et al., 1981, and Yamasaki et al., 1982), since this eliminated the need for a rear polarizer. However, this approach also had size and cost limitations similar to those of the SOS technology. Furthermore, since the full-color display technique made possible by the transmissive mode cannot be used, this approach has been almost discontinued at the present time. During this period, diode-type active elements were explored as an alternative to transistors in active LCDs because of the difficulties in transistor fabrication of the active elements and the limitations of display quality such as contrast ratio. The object of such efforts was to achieve a simpler and easier fabrication procedure than that associated with TFTs. The use of diodes also seemed to present less of a stability problem than TFTs. One example is the “varistor” diode array produced on a sintered zinc oxide (ZnO) substrate (Castleberry, 1979).However, since the ZnO diodes required as much as 200 volts for driving and the ZnO substrate was opaque, problems similar to those of the MOS-array LCD emerged and this work was not entirely successful. In another approach, a MIM bidirectional diode array was fabricated on a glass substrate (Baraff et al., 1980). The diodes used here consisted of tantalum-

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

15

anodic oxidized (Ta,O,), and chromium. These had quite stable electrical characteristics, a sufficiently low threshold voltage to drive the TN liquidcrystal material, and were easily fabricated on a large-area glass substrate, making possible active-matrix LCDs that exhibited excellent display quality. At the present time, MIM LCDs remain one of the promising solutions to realize large-area, high-quality, and low-cost liquid-crystal displays. As an example, small-size video LCDs (220 x 220) and large-size graphic LCDs (400 x 640) have been developed with MIM elements(Morozumi et al., 1983b, and Niwa et al., 1984).Aside from MIM diode arrays, developmentalefforts on other diode-type active-matrix LCDs have been relatively small compared to the efforts on TFTs. C . Emergence of Silicon Thin-Film Transistors and Diodes

In the early 1980s,the direction of research on active-matrix LCDs shifted to the use of silicon thin films in the form of amorphous Si (Snell et al., 1981) and polycrystalline Si (Depp et al., 1980),mainly for use as TFTs. Research on Si thin-film materials and TFTs grew rapidly because of the availability of deposition systems that can fabricate well-controlled p and n layers of amorphous Si and because of progress in Si IC technology involving device fabrication, device design, evaluation, etc., all of which are involved in activematrix technology. In addition, market requirements for high-quality displays accelerated the development of active-matrix LCDs. The results of this are shown by the increasing number of papers presented annually on this subject beginning in the early 1980s as shown in Fig. 6. Usually, the silicon film is deposited by means of the decomposition of silane (SiH4)gas. For this purpose, both thermal decomposition at a relatively high temperature and decomposition at a low temperature with the assistance of a glow discharge can be used. Since the crystallization temperature of silicon is relatively high, a low-temperature-deposited silicon film has a noncrystallized, i.e., amorphous, state. Such amorphous materials have been studied (Madan et al., 1976) for the purpose of film fabrication at low temperature. In 1975, the epoch-making work by Spear and Le Comber appeared, showing that the control of p- and n-type properties of amorphous silicon films could be accomplished by doping with hydrogen in addition to acceptor and donor impurities through the glow discharge decomposition of SiH, gas. This stimulated research on amorphous Si devices such as transistors, photovoltaic cells, and photoconductor-coated drums for copy machines, all of which required the low-temperature deposition of silicon on glass or similar substrate. The first practical application of amorphous silicon films was in the field of solar cells. Since such devices had a relatively simple structure and

16

SHINJI MOROZUMI

small area, they were suitable vehicles for the study of the properties of amorphous silicon films and enabled the optimization of the deposition systems required for them. Resulting from the accumulated experience with the deposition technique developed for producing amorphous silicon p-n diodes for such solar cells, systems making use of plasma-enhanced chemical vapor deposition (P-CVD) became available for production use. P-CVD equipment allows a highly controlled amorphous silicon film to be fabricated on a large-area substrate. Building on this background, the first suggestion for amorphous silicon TFTs (Le Comber et al., 1979) led rapidly to the successful research and development of active-matrix LCDs. N-channel amorphous silicon TFTs based on electron conduction (in which an electron mobility of around 0.1-1.0 cm2/V sec was obtained) were selected at the very start. Initially, the OFF current was too high because a thick film of 1 pm was employed. However, this problem was later corrected by reducing the film thickness to below several hundred angstroms (Sunata et al., 1985). Although the electron mobility of the amorphous silicon was relatively low, films of this material exhibited an extremely high dark resistance. The resulting TFTs thus had an extremely low OFF current as well as an ON/OFF current ratio sufficiently high to make it useful as an activematrix element. In early test samples of amorphous Si TFTs, their electrical characteristics were lacking in reproducibility and shifted considerably in a short time. Efforts to reduce this instability constitute the major element in the history of the development of amorphous silicon TFTs. However, recently, with the use of the continuous deposition method, whereby the gate insulator of the TFT and the amorphous silicon semiconductor film are deposited during a single pump-down, the stability has been improved sufficiently to allow the practical use of such TFTs. In addition to efforts to develop amorphous silicon TFTs, diode-type active elements based on amorphous silicon, such as amorphous silicon p-n diode rings (Togashi et al., 1984), were proposed and explored. These were developed for the purpose of avoiding the stability problems associated with amorphous silicon TFTs by making use of the symmetrically bidirectional electrical characteristics achieved with groups of series or parallel diodes. Aside from the succession of developmental efforts on amorphous silicon films mentioned above, the fabrication method and properties of poly-Si films were studied at around the same time. In the mid-70s, most of the MOS transistors used in integrated circuits employed silicon gate technology in which a doped poly-Si film made by the thermal decomposition of SiH4 gas was utilized for the gate electrode material. This fostered the investigation of various aspects of poly-Si films such as the grain size, grain boundary properties, grain growth, and carrier mobility (Seto, 1975, Baccarani et al., 1978, and Mandurah et al., 1979). During this period, low-pressure and low-

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

17

temperature-CVD (LPT-CVD)systems were developed for LSI production to deposit silicon, silicon nitride, and silicon oxide films with high throughput and quality. Since at pressures lower than atmospheric, silicon grains grow even at low temperatures around 6WC, these systems made it possible to deposit high-mobility poly-Si films at these low temperatures. Such materials thus became of interest for TFTs having a structure similar to that of the MOS transistor, whose stability had been investigated previously. Aside from their potential use as active-matrix elements, the comparatively high mobility of poly-Si films and the excellent switching characteristics of TFTs based on these films suggested the possibility that poly-Si TFT driver circuits, as well as active elements for the display itself, could be fabricated on a single substrate. Both amorphous and polycrystalline Si TFTs have desirable features compared to materials used in earlier TFTs. Since a silicon film consists of a single type of atom as opposed to a chemical compound such as CdSe, whose stoichiometry may be upset in processing, its controllability and reproducibility are quite good. In addition, deposition systems for silicon films capable of high uniformity and throughput are readily obtained. Also, since silicon, a nontoxic material, is commonly used as the semiconductor in the production of ICs, the associated device technologies, design software, and production equipment could easily be diverted to the Si TFT technology. The most important factor in the production of active-matrix elements is the yield, determined by the number of defects caused by nonoperable TFT elements and open- and short-circuited metallization lines. Techniques for minimizing the number of defects also profited from the production techniques developed for LSI and very-large-scaleintegration (VLSI) used for such products as the high-yield 256K-bit and the 1M-bit dynamic random access memories (DRAM). As an example, the optical-projection system developed for photo-exposure patterning in LSI and VLSI production is also very effective for the fabrication of TFT arrays with a minimum of defects. Active-matrix displays based on TFT arrays utilizing silicon thin films have thus become the main stream of LCD development. Since 1984, such LCDs with full color capability have been in commercial use for pocket-size TV sets.

111. KEYFACTORS IN THIN-FILM TRANSISTORS FOR LIQUID-CRYSTAL DISPLAYS The TFT-addressed LCD has a much more complicated structure than the direct-drive multiplexed TN LCD because of the TFT array. In realizing a TFT LCD, many factors must be taken into account. These include the TFT material, the TFT structure, and the fabrication processes involved. Although

18

SHINJI MOROZUMI

the structure, operation, and characteristics of TFTs are quite similar to those of MOS transistors fabricated on a silicon single-crystal wafer, the fabrication of a TFT array for an LCD involves, from some point of view, more technological problems. Due to the nonsingle-crystal material used in TFTs, the realization of the desired electrical characteristics becomes extremely difficult. At the same time, the required uniformity and stability present major problems. In addition, these arrays must be fabricated without defects that result in nonoperating pixels on a glass substrate much larger in area than a silicon wafer. For instance, in a 4 x 4-inch matrix display that contains 500 x 500 pixels, all 250,000 transistors must operate properly in order to obtain a defect-free display panel. In this section, the key factors associated with the TFT elements themselves are discussed. A. Fundamental Physical Arrangement and Operation of the Thin-Film Transistor Liquid-Crystal Display A cross-sectional view of the TFT LCD is shown in Fig. 7 based on the configuration in Fig. 4 (see Section LD). On the lower glass plate, the TFT array is fabricated as well as the transparent driving electrodes for the individual pixels, usually a layer of indium tin oxide (ITO). On the upper glass plate, a common electrode, also made of ITO, is fabricated. For the glass substrates, quartz, hard glass, or soda-lime glass can be used, provided they can withstand the TFT processing environment including temperature and etching solutions. The liquid-crystal material, in most cases a TN type, is ,Common

Electrode

LiquidCrystal

Glass Substrate

Sealing TFT

To Data Line

'Pixel Electrode

Semiconductor 0 Pixel Electrode

Insulator I

Gate FIG.7. Cross-sectional view of TFT LCD: the liquid crystal is driven by a voltage applied between the common electrode on the upper glass plate and the pixel electrode connected to the TFT; in the usual case where twisted-nematic (TN) liquid-crystal material is employed, polarizers (not shown here) are placed on the outer surfaces of both glass plates.

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

19

contained between the glass substrates as a layer 5-7 pm thick. In operation, the liquid-crystal elements are driven by AC voltages (accomplished by polarity reversal of drive voltages of each field) applied between the pixel electrodes and the common electrode. It should be noted that for proper operation, the electrode surfaces must be suitably treated to appropriately align the liquid-crystal molecules, and polarizers must be provided on the external surfaces of both glass plates. The circuit arrangement of the complete TFT LCD is shown in Fig. 8. As indicated, there are (N x M) pixels addressed by N data lines and M gate lines. The drive circuits for these lines may be located outside the display and connected to these lines, or they may be integrated along the edges of the display substrate, fabricated from TFTs based on the same semiconductor if suitable characteristics can be obtained. In operation, the gate lines are sequentially activated during a frame time, turning on successive rows of TFTs. During the time a row of TFTs is turned on, the signal voltages corresponding to that row are transferred from the drive circuits to the pixel electrodes through these TFTs. After this row of TFTs is turned off, the capacitive charges stored on the pixel electrodes (i.e., across the liquid-crystal elements) may be retained until this row is addressed again if the OFF resistance of the TFTs is high enough (assumingthe leakage through the liquid-crystal elements is small). The equivalent circuit for one pixel is shown in Fig. 9. The liquid-crystal material is represented as a resistor Rlq in parallel with a capacitor Clq

FIG.8. Circuit arrangement of TFT LCD: usually, the column and row drivers are positioned along the four edges; gate lines correspondto scan lines, and display data is transferred through the data lines to each pixel.

20

SHINJI MOROZUMI

VG

Line Pixel Electrode VP

I Data Line

Common Electrode

FIG.9. Equivalent circuit for one pixel of a TFT LCD: the liquid crystal is represented as a resistor Rlq and a capacitor Clq; the TFT has parasitic capacitances, Cgs and Cgp, between the gate and data line, and between the gate and pixel electrode, respectively; if necessary, the capacitor Ca is added; usually, a constant voltage is applied to the common electrode.

between the pixel electrode and common electrode. As indicated, the TFT as a switching element has parasitic capacitances Cgs and Cgp between the gate line and data line, and between the gate line and pixel electrode, respectively. To prevent signals from the gate line capacitively coupling to the liquid-crystal elements, Clq should be much larger than Cgp. In some designs, an additional capacitance Ca is incorporated to avoid this problem. For a given O F F

positive field

negative field

Time

FIG.10. Driving waveforms for TFT LCD: one frame consists of a positive and negative field. The input signal on an activated data line, e.g., D1,has a voltage swing V,; similar signal voltages are applied to the other activated data lines in accordance with the picture content; the gate line voltage is zero when nonselected, and V, when selected; V,,, is the signal voltage appearing across the liquid crystal.

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

21

resistance of the TFT, such a capacitance also serves to increase the charge storage time of a pixel. Figure 10 shows an example of the driving waveforms and the resulting signal on the pixel elements, V, is the amplitude of the gate signal and f V, represents the signal voltage (whose polarity is reversed for each field) applied to the data line. V,,, is the resultant pixel electrode voltage, with AV, being produced by the capacitive coupling through Cgp of Fig. 9. By reversing the polarity of the signal voltage each field, a DC voltage, which would considerably shorten the life of the material, is prevented from appearing across the liquid crystal. Although signal voltages of equal magnitude are applied in each field, a large value of AV, (which is always of the same polarity) may generate an undesirable asymmetry in the pixel voltage. In addition, such a AVp may cause a large leakage current through the TFT due to the increase in the voltage difference between the data line and pixel electrode. Therefore, in addition to the reasons mentioned above, a small value of Cgp compared to the total pixel capacitance is required. B. Electrical Requirements

When driving the liquid-crystal elements with alternating polarity signals, a complete image is scanned at twice the frame frequency. Generally, the human eye can easily detect flicker below 25 Hz, so the minimum frame frequency must be more than 30 Hz. For perfectly symmetrical pixel voltages during the positive and negative fields, a frame frequency of 30 Hz would be acceptable from the point of view of flicker. However, since the usual pixel voltages are not perfectly symmetrical, a frame frequency of more than 30 Hz is generally chosen to avoid any visible flicker. This requires that storage time of a pixel for retaining 90% charge be at least 16 msec, which, in turn, requires the OFF resistance of the TFT ( R X f f )determined , by the RC time constant of the pixel, to be: R K f f> 10 x 16 x 10-3/Clq.

(6)

It is assumed here that the time constant of the LC material itself, Clq x Rlq, is also larger than 16 msec. The National Television System Committee (NTSC) TV standard signal uses 525 scan lines with interlacing of the even and odd fields at a rate of 60 Hz. The period for one scanning line is thus 1/30 x 1/525 sec, about 64 psec. Consequently, assuming that the pixel is charged to 90% of the input signal voltage, the ON resistance R T,, required to charge the liquidcrystal element is; RT,, < 1/2.3 x 64 x 1OP6/Clq.

(7)

22

SHINJI MOROZUMI

From Eqs. (6) and (7), the switching ratio, R = RT,,,/RT,,, must therefore be: R > 1 x 104.

(8) This is the minimum requirement for proper operation of the TFT LCD. In practice, a value for R of more than 10’ is necessary, since in extreme environments, involving high temperature or high ambient light, the O F F current of the TFT easily increases by a factor of 10 or more. Also, the ON current might be degraded by aging of the TFT. Figures l l a and b show typical characteristics of a poly-Si TFT. They exhibit close similarity to the “gradual” model (Grove, 1967) for the conventional MOS transistor governed by the following formulas: Id

= p{(VG - VTH)VD

Id

=

/?(V,

-

- Vi/2}

(unsaturated region),

VTH)~/~

(9)

(saturated region),

(10)

p = p c o x W/L,

(1 1)

where V, is the gate voltage with respect to the source, V, is the drain voltage, VTH is the threshold voltage, p is the carrier mobility, Cox is the gate capacitance, and W/Lis the ratio between the width and length of the channel, respectively. Relative to the MOS transistor, the amorphous or polycrystalline silicon TFT has a smaller mobility and a higher threshold voltage because of the larger density of trapping states in the channel region. On the other hand, especially in polycrystalline material, the OFF current is larger than in the MOS transistor because of the leakage current flowing through the traps across the reversely biased p-n junction at the drain electrode. 0

a

I

3 n

v

5

4 3

2 1

0

-31-

-10

0

10

20

30 vG(v)

0

5

10

15

20

vO(v)

(a) (b) FIG. 11. Typical characteristics of a polycrystalline-Si TFT: (a) log of drain current (I,) vs. gate voltage (Vo);(b) drain current (I,) vs. drain voltage (VD).

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

23

The required voltage for controlling the liquid-crystal element depends on the material itself and its mode of operation. In the case of the typical TN liquid crystal, the optical saturation voltage, as shown in Fig. 2, is around 3.5 volts. However, a writing voltage of more than 4 volts is required on the data line to compensate for any decay in the stored charge. Since the available voltage from the usual CMOS LSI driver is about 20 volts, the breakdown voltage of the gate insulator is designed to be more than 20 volts. In addition, an excess gate voltage swing may lead to misoperation as a result of the parasitic capacitance Cgp in Fig. 9. When the TFT is turned on and off, a spurious signal, determined by the ratio of (Clq + Ca) to Cgp, (shown by AV, in Fig. 10) will be capacitively coupled to the pixel electrode. If Cgp is not small, e.g., > 1/ 10 of (Clq Ca), this spurious voltage may become a problem. The net voltage V,, between gate and source, assuming the waveforms shown in Fig. 10, is given by:

+

(12) If V, is limited to 20 volts and V, is required to be at least 4 volts, the TFT must have the required ON/OFF ratio expressed by Eq. (8), with the net gate voltage of less than 16 volts for the ON condition and 0 volts for the OFF condition, respectively. In a two-level display with only O N and OFF elements, a low degree of uniformity, for example a variation within a factor of 10 in the O N and O F F currents of the TFTs, is allowed. On the other hand, a much better degree of uniformity in TFT characteristics is required across the entire substrate for high-quality video and computer displays intended for operation with a large number of grey levels. Assuming that more than 20 grey levels are to be achieved, the pixel optical transmission must be controlled to within less than 5%. If the TFT has uniform enough characteristics in its O N and OFF currents, this may not be a serious problem. However if, for instance, one pixel is to be written to 90% and another pixel to 95% of full brightness, variations in O N current that cause a 5% difference in the written potential will cause a nonuniformity in brightness corresponding to one grey level. Such a nonuniformity may easily be recognized by the human eye. Likewise, the O F F current distribution may influence the uniformity of brightness due to the variation in the storage time constant. Thus, when a high-quality display with a large number of grey levels is desired, much more stringent requirements are imposed on the TFT characteristics than those indicated by Eqs. (6) and (7). VG,

=

VG

-

C. Structural Requirements and Fabrication Processes The production yield of the substrate with its TFT array fundamentally depends on the TFT device structure and the fabrication processes employed.

24

SHINJI MOROZUMI

These factors, determining, for example, the number of photomasks required, the number of manufacturing machines required, and the number of substrates that can be processed per unit time for each fabrication step (throughput) control the overall cost of the display. These various factors are discussed below. 1. Device Structure

Generally, two types of TFT structures are used, the staggered type and the inverted staggered type as shown in Fig. 12. In addition, a double-gate structure (Farrah and Steinberg, 1967), in which gate electrodes are provided on both sides of the thin-film semiconductor, has occasionally been investigated. Such structures enable a higher ON current to be obtained, since conductivity is induced on both surfaces. However, this arrangement has not been adopted in practice, because its fabrication is too complicated. In the two types of TFT indicated in Fig. 12, at least four layers, the channel semiconductor film, the layer from which the source and drain are fabricated, the gate insulator layer, and the gate electrode layer, are necessary. In addition, not shown in Fig. 12, a transparent conductive layer is required from which the pixel electrodes are fabricated as well as a metallization layer for the data lines and an insulating layer to separate the metallization layer from the gate electrodes. Also, additional layers may be needed if an added capacitor in parallel with the liquid-crystal pixel capacitance is necessary. In view of the numerous fabrication steps, simpler structures could make the production process shorter and increase the yield. Although a thin gate insulator is desirable to obtain high ON currents for a given gate voltage, this causes a lowering of the breakdown voltage. Such breakdown can occur as a result of defects resulting from dust or flakes of Rl

0 0

Gate Semiconductor Source and Drain Insulator

Glass Substrate (a) (b) FIG.12. Typical structure of a TFT:(a) staggered type; (b) inverted staggered type,

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

25

foreign matter incorporated during fabrication and also as a result of a discharge due to static electricity, which is a more serious problem. In practice, the thickness of the gate insulator is determined by compromising between these two factors. The nature of the contact between the semiconductor and the source and drain electrodes is another key factor in the performance of the TFT, since a high contact resistance may reduce the O N current. Generally, the use of an intrinsic or slightly doped semiconductor results in a nonohmic contact. Whether or not the TFT requires an additional intermediate layer to produce an ohmic contact is determined by the maximum contact resistance that can be tolerated between the TFT drain electrode and pixel electrode. 2. Substrate Material Since a primary requirement for the substrate is transparency, glass is usually used. There are various kinds of glasses, the choice of which depends on the processing temperature it must withstand, its acid resistivity, impurities, and flatness. For the highest processing temperatures of up to 1l W C , quartz substrates can be used. Hard glass such as Corning 7059 glass can be employed at intermediate and low temperatures of less than 600°C. Soft soda-lime glass can be used only at low temperatures. For the photolithographic process used to form the patterns in each layer, sulfuric acid, nitric acid, hydrochloric acid, etc., are used to etch away the undesired portion of each deposited layer. The glass must be resistant to such acids, otherwise it will be simultaneously etched, generating many fine cracks. Impurities, particularly alkali metals such as Na and K, affect the stability of the TFT characteristics in the same manner as in MOS transistors if they are allowed to penetrate into the channel material and insulator region. Since this is often the case, the glass surface is coated with a Silicon Oxide (SiOJ film. This prevents etching of the glass and diffusion of contaminants into the TFT. The flatness of the glass is also very important for the assembly of a satisfactory liquid-crystal cell. For a complete TN LCD, the spacing variation between the plates must be less than 0.2 pm. This requires the short-range deviation in the flatness of the glass to be less than 0.2 pm. However, a longrange warpage of more than 10 pm can be tolerated, since the flexibility of the plates allow them to be bent during cell assembly, retaining their spacing uniformity with the aid of small internal spacers distributed over the display area.

3. Elimination of Defects The problem of defects is the most important factor determining the fabrication yield and cost. Various types of defects are observed in activematrix LCDs. Some are defects in the TFT itself due to breakdown of the gate

26

SHINJI MOROZUMI

insulator that cause the TFT to remain permanently ON or OFF. Others arise from short circuits at cross points between the gate and data lines, caused by damage from an electrostatic discharge or from defective patterns produced during photolithography. Also, open circuits caused by defective photolithography may arise in the data and gate lines. During the photolithographic process, several photomasks are used to produce the TFT and active-matrix substrate patterns. Figure 13 shows the three types of photolithography that can be used: contact, proximity, and projection. During optical exposure, defects may arise as a result of the detachment of photoresist material from the substrate and transfer to the photomask, dust on or in the photoresist, dust and flakes on the substrate, and transfer of other small particles from the substrate to the photomask. Once such materials come in contact with the photomask, they are hard to remove, since brushing the surface of the photomask may cause new damage. After repeated use, defects on the photomask gradually accumulate if the mask is in contact or near the substrate. To avoid such defect generation in the mask, projection exposure is preferred, since the mask never touches the substrate. With the employment of this method, it has been shown that defects generated during photolithography can be greatly reduced. Usually, during deposition, the film is deposited not only on the substrate but also on areas around the substrate, such as substrate holders, electrodes, chamber walls, etc. This material may fall on the substrate as flakes, causing defects. Therefore such flake generation has to be considered when choosing the deposition system. For example, P-CVD systems for producing amorphous Si films easily generate flakes and require an appropriate design or other means to suppress them. Photoresist

0 Patterned Layer

Photo-Mask

I

I

(a) Contact ( b ) Proximity (c) Projection FIG. 13. Three photolithography methods. (a) Contact: the photomask contacts the substrate; (b)proximity: the photomask is positioned close to the substrate; (c)projection: pattern on the photomask is projected onto the substrate through a lens.

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In any case, all the fabrication processes including the final liquid-crystal cell assembly must take place in a clean environment. In practice, it is quite difficult to realize a complete process that results in a perfect TFT LCD with zero defects. However, for many applications, no defects can be tolerated. In these cases, some redundancy technique must be used. For instance, multiple TFTs may be used for each pixel, enabling the removal of the defective TFT by laser-beam trimming (Takeda et al., 1986).

4. Environmental Problems In many cases, LCDs must endure harsh environmental conditions, such as high or low temperature, high humidity, and strong ambient light. These conditions may cause problems with the TFT itself or the liquid-crystal material. In some cases, the LC material limits the temperature-operating range. At low temperature, the response time of the LC material may become too long, whereas at high temperature, the RC time constant may be dgraded because of the decrease of its resistivity. In addition, the LC material may suffer from high humidity if it is not completely protected from the outside environment. In fact, moisture may penetrate into the LC material through the edges of the display panel where the glass plates are sealed together, requiring the choice of a suitable moisture-resistant LC material. Since the metallization layers and other layers associated with the TFT may be damaged by moisture, causing open circuits in the data and gate lines as well as a shift in the TFT characteristics, they may have to be covered with some kind of passivation layer. Usually, at high temperature or under strong ambient light, the OFF current of the TFT increases. In such cases, the leakage current through the TFT must still satisfy Eq. (6). For example, the leakage current of the TFT doubles with every 10-degree rise in temperature, assuming the activation energy of the semiconductor film to be about 0.6 eV. If the TFT LCD is required to operate up to 6 0 T , the leakage at room temperature must then be less than 1/10 of the value indicated by Eq. (6). Generally, if the LCD is viewed in the reflective mode, it may be placed in direct sunlight. On the other hand, if it is viewed in the transmissive mode with back lighting, the illumination level of the backlight will have to be about ten times greater than sunlight if the display is designed to be visible in sunlight. However, the actual intensity of the backlight reaching the TFT will be a half or a quarter of the full backlight level because of absorption by the rear polarizer as well as the internal color filter layers (see Section VI) if the display is designed for color. The leakage current I, induced by light is determined by the photo-generated carriers created in the channel region, I , = W/Lnqp E/hvz{ 1 - exp( - at)} V , ,

(13)

28

SHINJI MOROZUMI

where Wand L are the channel width and length respectively, n is the quantum efficiency (chargecarriers produced per absorbed photon), q is the unit charge of an electron, p is the mobility of the carriers (one of which is assumed to be mobile), E is the light power, v is the average frequency of the light, z is the carrier lifetime, a is the optical absorption coefficient, t is the thickness of the semiconductor film between source and drain, and V, is the drain voltage relative to the source. As indicated by Eq. (13), channel-region semiconductor films with small values of a and t have a smaller photo-induced leakage current. It is therefore obvious that a very thin semiconductor film is useful to reduce such current. In cases where the photo-leakage current is too large, a light shield in the form of a metal film may be deposited over each TFT to reduce this current to an acceptable level. 5. Reliability Problems

Conventionally, the reliability of MOS transistors on a Si single-crystal wafer is evaluated by means of the bias-temperature (BT) test, in which maximum-rating DC voltages are applied at elevated temperatures between gate and drain and between source and drain. Under these conditions, the activation energy for the transistor degradation at different temperatures is calculated. From this, the lifetime at room temperature can be determined. The lifetime may be defined as the time required for a specific shift of the electrical characteristics to occur, for instance a 2- 3-volt shift in the threshold voltage, a several-times increase of the OFF current, or a similar decrease of the ON current. The lifetime of a TFT can similarly be determined. In the operation of the TFT LCD, the TFT is always driven by a pulse signal. If the pulse-temperature (PT) test is used instead of the BT test, the measured lifetime becomes much longer. However, it is not clear which method is most accurate. The required lifetime of an LCD depends on the application. Typically it is more than 1,000hours, but in some cases, it may be more than 10,000 hours. IV. CHARACTERISTICS OF DIFFERENT TYPESOF THIN-FILM TRANSISTORS AND THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

Presently available thin-film transistors (TFTs) can be divided into three categories in accordance with the semiconductor material used: CdSe, amorphous Si, and polycrystalline Si. In this section, their different structures, fabrication processes, and electrical characteristics will be discussed as well as their performance in complete LCDs.

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A . CdSe Thin-Film Transistors 1. Structure and Fabrication Processes

Of the three types of TFTs, those based on CdSe were, until 10 years ago, the most thoroughly investigated. Films of this material exhibit a high electron mobility and are easily fabricated by vacuum evaporation without requiring any complicated deposition system. Both the staggered type and inverted staggered type (see Fig. 12) have been employed in accordance with the location of the gate electrode. In some cases, a double-gate structure with gate electrodes provided on both surfaces of the semiconductor channel material (Chen and Luo, 1981, and Luo et al., 1981) has also been explored in order to improve the electrical characteristics and stability of the CdSe TFTs. The typical structure of an inverted staggered CdSe TFT is shown in Fig. 14. For the gate insulator, sputtered or evaporated SO2, aluminum oxide (A1203),and Ta,O, films have been used. The source and drain electrodes are generally made of aluminum, chromium, or other metals that enable a low-resistance or ohmic contact to be made with the CdSe film. The CdSe film is deposited by vacuum coevaporation from separate sources of Cd and Se or from the CdSe compound. The CdSe TFT with a tantalum (Ta) gate electrode and a Ta,O, gate insulator provides a good example of the inverted staggered type (Moersch et al., 1984). During fabrication, the gate electrode made of Ta film is formed first. In this process, a Ta film is deposited on a glass plate, and undesired areas are etched off with the aid of photolithography (see Section 111. C. 3). Then a 1500-A-thick Ta20, film is formed by anodic oxidation of the Ta in an acid solution. The resultant oxide film is very stable, and its thickness and other properties are easily controlled by the voltage applied during oxidation. Next, Source

Drain

Gate Glass

,.;.,.., ... .. ... ..

1777771 0

CdSe A1

S i O z , TazOs Ta or A l FIG. 14. Typical cross-sectional view of a CdSe TFT with inverted staggered gate. Al203,

30

SHINJI MOROZUMI

a 500-A-thick CdSe layer is deposited by vacuum evaporation after sputtercleaning of the Ta,O, surface in order to improve the interface between the Ta,O, and CdSe. Finally, an aluminum layer is deposited, forming the source and drain electrodes by the lift-off method. In this process, the surface is first coated with a thick photoresist layer, which is then removed everywhere except in the channel region by photoexposure through the transparent glass substrate. Following this, an aluminum layer is evaporated. Removal of the remaining thick photoresist then removes the aluminum except in the source and drain regions that are self-aligned with respect to the gate. In an alternative fabrication process not requiring the use of a photolithographic process, a shadow-mask method was tried (Luo and Hester, 1980).In this case, each layer is evaporated through a suitable metal shadow mask, with all the layers being formed in one pump-down. Since in this method the pattern required for each layer does not require a complicated photolithographic technique, the entire TFT fabrication process becomes much simpler. However, because of other problems that arise, such as insufficient pattern accuracy, short shadow-mask lifetime and susceptibility to defects, this method is seldom used today. 2. Characteristics The conductivity of a CdSe TFT can be understood by means of a model involving a polycrystalline semiconductor with grain boundary trapping (Levinson et al., 1982).Here, it is assumed that the current flowing through the film is governed by thermionic emission above the barrier height formed at the grain boundary. For small drain voltages, this model applied to the TFT has exhibited good agreement with experiment. The field-effect carrier mobility reported for CdSe TFTs is slightly different from publication to publication, but in each case, the ON/OFF ratio reported was more than lo4. In one example, the mobility was found to be in the range of 40-100 cm2/V sec when the thickness of the CdSe film was about 500 A (Lee et al., 1983). Generally, CdSe TFTs have had poor reliability. For example, with a DC bias gate voltage, the electrical characteristics of CdSe TFTs tend to shift in a short time. However, in the early work on the uniformity and stability of this material under the accelerated life test, it was concluded that CdSe exhibited adequate stability and uniformity for display devices (Brody et al., 1975). The OFF current stability was investigated using an 80-100-&thick CdSe semiconductor with a double-gate structure using a 1000-A-thick A1203 film together with a 3000-A-thick SiO, film for the top insulator and a 4000-A-thick A1203 film for the bottom insulator (Luo et al., 1981). The leakage current in the O F F state of this TFT was 2.5 x lo-', ampere, giving an ON/OFF current ratio of 2.7 x lo'. DC and dynamic life

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

31

tests in the O F F state showed that this TFT performed better under actual operating conditions than under DC conditions. 3. Performance of CdSe TFT LCDs In the early 1970s,a liquid-crystal display panel based on CdSe TFTs with a 6 x 6-inch area and 120 x 120 lines (Brody et al., 1973)was built and tested. This produced images with a 25: 1 contrast ratio using the TN liquid-crystal mode with crossed polarizers (see Section l.B) when operated at the normal (30 Hz) TV frame rate, thus allowing about 60 psec writing time for one scan line. In subsequent work, CdSe TFT LCDs with 1 x 1-inch and 5 x 5-inch size, both with a 50-lines-per-inch resolution, were produced by a hybrid process using a combination of an evaporative shadow mask and photolithography for forming the patterns in each layer (Luo and Hoesly, 1982). Later, a largearea LCD for portable computers with 400 x 640 pixels and a 10 x 7-inch display area was developed (Luo et al., 1985). The TFT array here was fabricated on a Corning 7740 glass substrate using five photomasks. These TFTs had a 7: 1 channel length to width ratio, producing a 1-pA ON current with 20 volts on the gate and a source to drain potential of 10 volts, while exhibiting a 100-pA OFF current with a gate voltage of zero. Using parallel polarizers instead, allowing O N elements to be transmitting, a contrast ratio of over 20:l was obtained as well as a viewing angle cone of more than 45". The image quality of this TFT LCD was excellent and was clearly far superior to that of directly multiplexed TN LCDs of those days. In other efforts, CdSe TFT driver elements for the X and Y lines of the display were fabricated on the same substrate (Malmberg et al., 1986). The switching speed of these TFTs in generating a 5-volt pulse across a 100-pF load capacitance was 2.5 psec or less. To provide redundancy, separate driver circuits were provided at both ends of each X and Y line instead of at a single end. In this case, when a defective drive circuit was found in either driver, the defect-free driver was selected, greatly improving the yield of the drive circuits. With such an integrated panel design, the number of external connections was reduced from 2084 to 232. B. Amorphous Si Thin-Film Transistors

1. Structure and Fabrication Processes Most of the activity on amorphous Si thin film and related devices can be traced back to the work in 1975 by Spear and Le Comber (Spear and Le Comber, 1975). They found that hydrogen doping of the amorphous Si film resulting from the glow discharge in SiH, gas was effective in controlling

32

SHINJI MOROZUMI

whether the resultant film was p or n type. In 1979,the possible application of amorphous Si TFTs to matrix-type LCDs was presented (Le Comber et al., 1979).Following this, many attempts were made to realize such active-matrix LCDs. In detail, these structures are different from laboratory to laboratory, but typically they can be classified by the structure type of TFT used, i.e., either the staggered gate type or the more common inverted staggered gate type (see Section 1II.C.1). Silicon oxide films were initially employed as the gate insulator film, but recently silicon nitride films have been used in order to obtain high electrical stability and reliability. Usually, the gate insulator film is continuously deposited just after or before the deposition of the amorphous silicon film by a change of the reacting gases or reacting chamber without exposure to atmosphere so as to prevent generation of unstable interface states between the gate insulator and amorphous Si film. The gate electrode of amorphous Si TFTs is made of metal, such as aluminum, chromium, or tantalum. Since the amorphous Si film is quite sensitive to light, the surface opposite to that covered by the metal gate electrode may require a light-shield layer external to the TFT. The need for the light-shield layer, however, may be avoided by using a very thin amorphous Si film, for example, 300-500-A-thick (Sakai et al., 1985), since such films produce a relatively small number of photo-generated carriers. The metal contact to the intrinsic amorphous Si layer used for the TFT usually exhibits a nonohmic Schottky diode property and relatively high resistance. In some cases, this contact resistancemay be higher than that of the TFT channel. If the contact resistancecan be ignored, as in displays requiring no grey scale or operated at a slow frame rate, aluminum, chromium, or I T 0 (indium tin oxide used for the driving electrodes of the liquid-crystal matrix) may directly contact the amorphous Si, serving as the source and drain electrodes (Ugai et al., 1984). However, video displays generally require a uniform and low contact resistance in order to control the generation of a large number of grey levels. Therefore, an n + layer of amorphous Si is sandwiched between the source or drain electrode and the amorphous Si film to reduce the contact resistance. If the I T 0 layer directly contacts then' layer, the contact resistance may not be sufficiently low, since the I T 0 film exhibits semiconductor rather than metal properties. In this case, an additional intermediate metal layer may be required. The typical fabrication process for a staggered-type TFT is as follows (Yanagisawa et al., 1985).First a 1000-A-thickchromium layer is deposited as a light-shield layer. After this is patterned into small elements by photolithography, an insulating layer of silicon nitride is deposited to serve as electrical separation of the light-shield layer from the TFT. Then, the I T 0 elemental areas used for the liquid-crystal driving electrode as well as the data

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

33

lines that connect to the TFTs as source and drain electrodes are also formed by photolithography with a first photomask. After the ohmic contact layer is formed, a 3000-A-thick intrinsic amorphous Si layer and a 5000-A-thick silicon nitride gate insulator film are consecutively deposited by plasmaenhanced CVD. Then, the through holes in the gate insulator and amorphous Si layer are opened with a second photomask in order to form a direct contact region between the I T 0 data line and aluminum connection pad. Following this, an aluminum layer is deposited and patterned with a third photomask to form the gate electrode and gate lines. Then the gate insulator and amorphous Si layer are etched off except under the remaining aluminum layer to form the same pattern as that of the aluminum layer. The complete TFT is thus formed with three photomasks, excluding the light-shield mask. 2. Characteristics The characteristics of the amorphous Si TFT are mostly determined by the threshold voltage and the mobility of the semiconductor. The threshold voltage, which is about 1-5 volts, is determined by the thickness of the gate oxide, interface state density in the region between the gate insulator and the amorphous Si layer, and the density of states within the semiconductor film. The mobility,determined by the electrical properties of the amorphous Si film itself, is almost the same for measurements by different laboratories; 0.10.3 cm2/V sec. The OFF resistivity is quite high-more than 1014ohm cm. In most cases, the ON/OFF current ratio is around lo6,which is sufficient for use in active-matrixLCDs as discussed in Section 1II.B. Theoretical analyses were made on the state density in hydrogenated amorphous silicon (a-Si:H) films (Kishida et al., 1983,and Suzuki et al., 1982).According to the work of Kishida et al., reduction of the gap-state density near the conduction band edge is necessary in order to obtain a high ON/OFF current ratio. In an early paper (Snell et al., 1981),the characteristics of the amorphous Si TFT and its application to LCDs were investigated. Figure 15 shows the structure of this device. An I T 0 layer is deposited on the Corning glass and then patterned by photolithography to provide transparent conductive pixel electrodes for driving the liquid-crystal element. A chromium film is then evaporated and undesired areas are etched away to form the gate electrode. Next, a 5000-A-thick silicon nitride film and an amorphous Si film are deposited in sequence by means of an RF gIow discharge, and the unwanted areas are etched off. Finally, an aluminum metallization layer is evaporated and patterned to form the source and drain electrodes and data lines. In this structure, no light shield was employed. The channel length (source-to-drain distance) was 500 pm and the width of the source and drain electrodes was 40 pm. The transfer characteristics of this transistor, indicated by the drain

34

SHINJI MOROZUMI a-Si

FIG. 15. Design of a-Si field-effect transistor element: (a) section through device; (b) FET in part of the matrix array (ITO: indium-tin-oxide squares, G: gate electrode, D: drain electrode, S: source electrode, A: contact hole etched through sillicon nitride film). (Figure 1 from Snell et a!., 1981. Copyright 0 1981 Springer-Verlag.)

lo-'

d

10-6

-

10-0

-

10-10-

10-12 -10

I 0

10

VC

20

30

40

(v)

FIG. 16. Transfer characteristics of a-Si FET elements: the drain current I , is plotted against the gate voltage V, for three drain potentials V., (Figure 2 from Snell et al., 1981. Copyright 0 1981 Springer-Verlag.)

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

35

current I , as a function of gate voltage V, for 2, 10, and 20 volts of drain voltage V,, are shown in Fig. 16. As indicated, the OFF current at zero gate voltage is below lo-" ampere, the ON/OFF current ratio is about lo6, and the threshold voltage is around 5 volts. Calculations indicate the field-effect mobility to be around 0.4 cm2/V sec. The effects of photoconductivity on the amorphous Si TFT are shown by the transfer curves of Fig. 17 (Sugata et al., 1983).For this TFT, a 0.3-pmthick silicon nitride film was used as a gate insulator. The amorphous Si layer was 0.2 pm thick, and a 0.1-pm n + layer was used to make ohmic contact. These layers were deposited in succession by means of a glow discharge. The gate electrode, and source and drain electrodes consisted of 0.1 and 0.5-pm-thick aluminum, respectively. The channel length was 16 pm and the width was 4800 pm. The threshold voltage was 3 volts and the mobility was 0.3 cm2/V sec. At zero gate voltage, under illumination with a 2,500-lux tungsten lamp, the O F F current without a light shield was more than lo3 lo+,

lo-"

I

I

I

10

0 VG

I

1

20

(v)

FIG. 17. Characteristics of a-Si TFT:dotted curve represents the characteristics of TFT with a light shield under illumination from a 2500-lux tungstenn lamp; solid curve shows characteristics in dark. (Figure 2 from Sugata et al., 1983. Permission for reprint, courtesy Society for Information Display and the Institute of Television Engineers of Japan.)

36

SHINJI MOROZUMI

times higher than in the dark state. However, by employing a light shield, the photo-induced current increased less than 10 times as shown in Fig. 17. By using a very thin amorphous Si film, it was shown that the light-shield layer could be eliminated (Sakai et al., 1985, and Sakai et al., 1986). Figure 18 shows the structure and characteristics of such a TFT. First, a 50-nm-thick gate electrode of chromium is sputtered. A 300-nm-thick silicon nitride film and 40-nm intrinsic amorphous Si layer are then deposited by plasmaenhanced CVD. Following this, the source and drain electrodes are formed using a 10-nm-thick n + intermediate layer and a 100-nm-thick siliconcontaining aluminum layer. The channel length was 8 pm and the width was 30 pm. In Fig. 18b, the drain current ID as a function of the drain-to-source voltage V,, is shown for gate voltages V, of 0 and 20 volts. This TFT exhibited a threshold voltage of 3-5 volts and a mobility of 0.5 cmZ/Vsec. As shown in Fig. 18, by employing a very thin amorphous Si film, an O N / O F F current

(a) ID(A)

1E-05

decade /div

1E-13 00.00

20.00 VDS 2.000/div(v)

(b)

FIG. 18. Structure and characteristics of a-Si very-thin-film transistor: (a) cross-sectional view of device with thin 40-nm a-Si layer; (b) typical electric characteristics of device; curves (1) and (2) show OFF characteristics in the dark and when illuminated with a fluorescent lamp of 10E4 lux, respectively. VDS is drain to source voltage. (Figures 1 and 2 from Sakai et al., 1985 Copyright 0 1985 IEEE.)

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

37

ratio of more than lo4 was obtained under illumination of a 10,000-lux fluorescent tube. Although the initial characteristics of amorphous Si TFTs measured just after fabrication are good enough for use in an active-matrix LCD, their uniformity and stability present major problems. The uniformity depends mainly on the manufacturing equipment, but the stability is associated with an undesirable physical property of the amorphous state semiconductor. In studies of amorphous Si TFTs (Powell, 1983), it was shown that charge trapping in the silicon nitride gate insulator layer caused a shift only in the threshold voltage, but not the mobility, as a result of changes in the voltage bias condition. For example, at a gate voltage of 12 volts, and at 70°C, Powell observed more than a 3-volt shift of the threshold voltage within 5 seconds. This shift did not exhibit a simple log-time dependence, but was a more complicated function of time. It was concluded that such instability was caused by the injection of electrons from the semiconductor channel into the gate insulator with an activation energy of 0.3 eV. In other work (Ast, 1982),a similar instability was observed by trapping electrons in the amorphous Si and gate insulator, and detrapping by the light. Here, the illumination dependency of the drain current decay due to such trapping was shown. In the dark condition, drain current decay of up to one order of magnitude was observed within 100 hours using the 10% duty cycle pulse measurement. In the illuminated condition, the drain current decay reached a maximum of only 113. 3. Performance of a-Si TFT LCDs In 1982, the first successful developments of monochrome displays based on a-Si TFT LCDs were described (Kawai et al., 1982,Le Contellec et al., 1982, and Okubo et al., 1982).In this early period, display size and resolution were relatively limited as shown, for example, in Okubo's paper describing a 240 x 240-pixel array with a 96 x 96 mm active area. In 1983, another developmental display with 220 x 240 pixels and 44 x 60 mm in size (also monochrome) was described. This used a TN liquid-crystal for graphic images and a guest- host liquid-crystal for TV applications. These panels were capable of 40:l and 3.3:l contrast ratios, respectively (Suzuki et al., 1983). A more sophisticated display using amorphous Si TFTs, capable of producing color video images, appeared in 1986 (Hotta et al., 1986). In this display panel, the picture elements have red, green, and blue color filter layers of differing thickness. This is referred to as the multigap liquid-crystal cell spacing method (Nagata et al., 1985)with parallel polarizers (see Section 1.B). The cross-sectional view of such a TFT LCD is shown in Fig. 19. Usually, in the TN mode, the optical transmission has a wavelength dependency because

38

SHINJl MOROZUMI Polarizer

Counter Electrode I T 0

Aligning L a y e r

FIG. 19. Cross-sectionalview of full-color multigap LC TV panel:liquid-crystallayer thickness, e.g., dRand d , of red and green cells, is optimized for the best color transmission.(Figure 1, from Hotta er at., 1986. Permission for reprint, courtesy Society for Information Display.)

of the effect of rotatory dispersion. In the parallel polarizer method, this dependency appears in the OFF state of the liquid-crystal cell in which realization of neutral white becomes more difficult than in the cross-polarizer method. In order to eliminate such undesired effects that may be noticeable in the OFF state, the liquid-crystal cell thickness must be adjusted to have optimal spacing between its upper and lower electrodes for the particular range of wavelength involved (Gooch and Tarry, 1975).This is accomplished by varing the thickness of the color filter layers. With this multigap method and the addition of a black matrix to block the light passing between the pixel electrodes, the contrast ratio was enhanced due to an improved black state. Furthermore, the color pixels were arranged in a triangular pattern to obtain the best image definition with the given number of pixels. The display had an area of 45.6 x 60.4 mm (3-inch diagonal), containing 240(V) x 378(H) pixels. In operation, it produced a contrast ratio of more than 30:l over an included viewing angle of 30"(V) and 50"(H), and had a response time of less than 40 msec. Such panels were shown to be capable of displaying good color TV images with RGB-peak-enhanced-typefluorescent backlight. Another full-color LCD with a very thin amorphous Si film was described by Sakai et al. (1985). This contained 220 x 240 pixels in an area of 34.1 mm(V) x 45.6 mm(H), producing a contrast ratio of more than 30: 1 in the TN mode. Figure 20 shows a photograph of a picture produced by this color LCD. As of the present, amorphous Si TFT LCDs of more than 10-inchdiagonal size have already been demonstrated. One of these has a picture size of 134.6 x 21 1.2 mm and contains 408 x 640 pixels (Sakamoto et al., 1986).This produced images with a contrast ratio of more than 20:l. Another panel (Takeda et al., 1986)has been built with 480 x 640 pixels and a 256 x 192 mm

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

39

FIG. 20. Black-and-white photograph of a TV picture displayed on full-color LCD with very thin 40 nm a-Si layer: the number of pixels is 220 x 240, and the contrast ratio is more than 30:l. (Figure 4 from Sakai et al., 1985. Copyright 0 1985 IEEE, and courtesy Seiko Instrument and Electronics Ltd.)

picture area (12.5-inch diagonal). Production yield may become a problem in such large-area and high-resolution LCDs because of defective elements. In order to overcome this problem, in the latter panel, a redundancy technique was employed in which two TFTs were provided for each pixel, with one TFT being disconnected by laser beam if it was defective.

C. Polycrystalline Si Thin-Film Transistors 1. Structure and Fabrication Processes The properties of polycrystallized silicon films have been studied since the time of the development of the silicon gate MOSFET (Faggin and Klein, 1970).The physics of poly-Si films were thus comparatively advanced prior to their application to TFT LCDs. Most poly-Si TFTs of the staggered type have fabrication processes and a structure similar to those of MOS transistors fabricated on a Si single-crystal wafer. In poly-Si TFTs, instead of a bulky Si single crystal, a polycrystalline Si thin film is deposited on an insulating substrate to form the semiconductor. For the deposition of the poly-Si film, the (LPT-CVD)method, in which SiH4 gas is decomposed at around 6WC, is usually employed.

40

SHINJI MOROZUMI

There are two types of poly-Si TFTs, depending of whether they are subsequently processed at high or low temperature. The former employ a thermally grown oxide and are fabricated at 800°C or higher on a quartz substrate although a novel glass substrate capable of withstanding 800°C has also been employed (Troxell et al., 1986).The latter employ a CVD-deposited SiO, film as the gate insulator and are fabricated at less than 600°C on a hardglass substrate, such as Corning's 7059. Figure 21 shows the fabrication steps employed in making a hightemperature-processed poly-Si TFT, using four levels of photomask to complete the TFT. This process is quite similar to that used for the Si-gate MOSFET and is also easily performed, since all the manufacturing equipment used for LSI production can be employed. A 1500-3000-1&thick poly-Si film is first deposited. The undesired areas are then etched away by photolithography with a first photomask, leaving the source, drain, and channel regions. Following this, the gate insulator layer is grown in a dry 0, atmosphere. The poly-Si film for the gate electrode is then deposited and removed except in the Poly- Si

,-Gate

Electrode

Source and Drain Regions Insulator (SiOZ)

(C

1

FIG. 21. Fabrication process of a high-temperature-processed poly-Si TFT: (a) poly-Si film is deposited by LPT CVD on the quartz substrate and patterned; (b) after thermal oxidation of the first layer of poly-Si, a second poly-Si layer is deposited and patterned to form the gate electrode. Following this, self-aligned source and drain regions are formed in the first poly-Si layer by ion implantation; (c) after a second SiO, deposition, contact holes are opened to the source and drain regions; (d) I T 0 is sputtered and patterned to form the data line and pixel electrode.

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

41

area of the gate electrode with a second photomask. Phosphorous ions are then implanted in the source and drain regions to form a low resistance layer and to enable ohmic contact to be made to the external conductors. In this process, the poly-Si channel region below the gate electrode is shielded from the phosphorous ions. Next, a 5000-8000-A-thick Si02 film is deposited by CVD, and contact holes are opened to the source and drain regions with a third photomask. Finally, the I T 0 layer used to form the pixel electrode and data line is sputtered and patterned by photolithography with a fourth photomask. Because of the self-aligningprocess used in fabricating the source and drain electrodes, whereby the gate electrode acts as a shield for the phosphorous ions, there is minimum overlap between these electrodes and the gate, reducing the parasitic capacitances between these electrodes. The structure of a low-temperature-processed poly-Si TFT is shown in Fig. 22. This is also carried out with four photomasks (Morozumi et al., 1986b). First, a 1500-A n+ layer of polycrystalline Si is formed on the hard-glass substrate with a first photomask. Then, a 100-500-A-thin undoped poly-Si layer is deposited by LPT CVD, and undesired areas are etched away except for the channel region and the source and drain contact regions to the n+ poly-Si layer, using a second photomask. Next, a 2000-&thick I T 0 layer is sputtered and patterned with a third photomask to provide the pixel electrodes and data lines. After cleaning the surface of the poly-Si layer, the gate oxide is deposited by CVD. Finally, the I T 0 layer for the gate electrodes and gate lines is sputtered and patterned with the fourth photomask. Other low-temperature methods to fabricate poly-Si TFTs making use of molecular-beam deposition (MBD) and electron-beam gun (E-gun) evaporation for the growth of the poly-Si film have also been developed. In the MBD method (Matsui et al., 1980),the silicon film was deposited under ultrahighvacuum conditions on the order of Torr. The film could then be easily undoped poly-Si +

I TO (to Data Li

poly-Si (Source, Drain) ixel Electrode)

\

glass FIG.22. Structure of low-temperature-processed poly-Si TFT: a hard-glass substrate can be utilized since the maximum process temperature is 600°C; contact resistance between the channel under the gate electrode and the nf poly-Si layer is small, allowing high ON current to be obtained.

42

SHINJI MOROZUMI

polycrystallized even at 500°C and exhibited a carrier mobility as high as 10 cm2/V sec. In the E-beam method (Oana et al., 1983), a poly-Si film with a field-effect mobility of more than 10 cm2/V sec was obtained at 550°C in high vacuum (1 x lop6Torr). 2. Characteristics In general, the electrical characteristics of amorphous Si or poly-Si films are determined by the states or traps in the band gap of the semiconductor material itself. According to the analysis of field-effect phenomena in poly-Si films (Kamins, 1972), the gap-state density near the Fermi level (deep defect levels) is the dominant factor in determining the threshold voltage. On the other hand, it is obvious that the electron mobility is influenced by the scattering of the free carriers by the gap states near the conduction band edge. Comparing the gap-state density between the a-Si:H (Suzuki et al., 1982) and the poly-Si films (de Graaff et al., 1982), it has been found that the a-Si:H film has much higher density near the conduction band edge than near the Fermi level, whereas the poly-Si film has a relatively uniform distribution of gap states within the forbidden gap. Here, the Fermi level is almost the same as the intrinsic level, because the semiconductors for TFTs employ undoped or lightly doped films. With respect to amorphous Si films, such densities in polySi films are lower near the conduction band edge, and higher near the Fermi level. As a result, the poly-Si film has much higher mobility, over 10cm2/Vsec, and relatively higher threshold voltage, 5-7 volts, than the amorphous Si film. As mentioned in Section IV.B.2 in connection with a-Si TFTs, the threshold voltage can be affected either by interface states between the semiconductor film and gate insulator or by charges trapped in the gate insulator. The above-mentioned gap states of poly-Si films, which determine the TFT characteristics, result from the properties of the grain boundaries. Investigations of this subject (Depp et al., 1980, and Levinson et al., 1982) have shown that the trap density located at the grain boundary influences the carrier mobility as well as the threshold voltage of the TFT. In both investigations, the drain current of poly-Si TFTs was calculated by using models with appropriate trap density, resulting in good agreement with experiments. Although the poly-Si film has a higher carrier mobility, more than 10 cm2/V sec, compared to the amorphous Si film, its OFF resistance in the dark may be too low because of its small band gap and large carrier density as compared with the amorphous Si film. However, in the illuminated condition, poly-Si TFTs have a much lower photo-induced leakage current than amorphous Si TFTs. Whereas the energy band structure of amorphous Si corresponds closely to the direct transition type in accordance with measure-

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

43

ments of the optical absorption coefficient (Carlson and Wronski, 1979), that of polycrystalline Si seems to be of the indirect type as in the case of singlecrystal Si. These authors found the absorption coefficient .of amorphous Si films to be more than an order of magnitude larger than that of crystalline Si, consistent with the fact that the polycrystalline Si films exhibit an indirect transition (Moss et al., 1973).This explains why the photo-leakage current of poly-Si TFTs is much smaller than that of amorphous Si TFTs. In order to reduce the OFF current in the dark to the required low level, a thin poly-Si film of less than lo00 8 has been used as well as a dual-gate structure as explained below. Both approaches are also effective in reducing the photo-leakage current of poly-Si TFTs to the level where they can be used without a light-shield layer. The typical characteristics of poly-Si TFTs prepared by both the hightemperature and low-temperature processes described in Section 1V.C.1 are shown in Fig. 23. The thickness of the poly-Si films is 650 8 and 250 8,

. Vos=4V Single

Dual

!I

-c.'

C

e l L I 3 0

High Temperature Process Single Gate, Dark Dual Gate,Dark __---Dual Gate,100,000lux

n

-12

I Dual Gate, Dark

I

- 1 4 1 " " " "

-10

0

10

20

30

Gate Voltage VCS(V) FIG.23. Typical characteristics of high-temperature and low-temperature-processed poly-Si TFTs: the effect of the dual-gate structure on the OFF current both in the dark and under illumination is also shown in the figure.

44

SHINJI MOROZUMI

respectively, with the gate oxide thickness being 1500 A for both. In both dualgate TFTs, with a channel length of (15 pm + 15 pm) and a channel width of 10 pm, the ON currents exceed 1 pA, whereas the OFF currents are below 1 PA, resulting in an ON/OFF current ratio that reaches lo6. Even when illuminated with 100,OOOlux,the poly-Si TFT has a ratio of more than lo5.It is thus clear that the dual-gate TFT is effective in reducing the O F F current compared with a single-gate TFT of the same total channel length, especially when a large negative gate bias is applied to the TFT. As shown in Fig. 23, in the dual-gate structure, two TFTs are connected serially and their gate electrodes connected together. In the case of n-channel TFTs, for example, a p-type accumulation layer is formed at the surface of the channel when a negative gate voltage is applied. In this condition, lateral n-p-n junctions are induced, assuming n-type source and drain electrodes. If positive drain voltage relative to the source is applied, the O F F current is determined by the leakage current through the reverse-biased p-n junction at the n-type drain electrode. Because of the large trap density in the poly-Si film, the leakage current through the reverse-biased p-n junction increases exponentially with the applied drain voltage. The dual-gate TFT arrangement thus results in a tenfold decrease in the O F F current at a negative gate voltage of 10 volts due to halving the applied drain-to-source voltage across the TFT section (assuming the total length of the channel region is fixed). The thickness of the poly-Si film has much to do with the drain current of poly-Si TFTs. Such thickness dependency is shown in Fig. 24(Morozumi et al., 1985). As the film becomes thinner, the OFF current decreases in both the illuminated and dark conditions due to the decrease of cross-sectional area and corresponding leakage carrier generation. At the same time, the O N current increases because of the reduction of the threshold voltage, which changes from 8 volts at a thickness of 1000A to 5 volts at 500 hi. The reason for this is as follows. The threshold voltage is defined as the gate voltage required to capacitively induce free carriers at the semiconductor channel surface and space charge in the body of the semiconductor through the gate insulator to turn on the TFT (Kamins, 1972). Although the number of surface carriers is determined by the gate potential and independent of the semiconductor film thickness, the number of space charges depends on the semiconductor film thickness where this thickness is smaller than the space charge depth. Thus, as the thickness of the poly-Si film decreases, the required space charge depth to turn on the TFT also becomes smaller and the threshold voltage is subsequently reduced. Accordingly, an ON/OFF current ratio of more than 10' in the dark can be obtained with a thickness below lo00 A. Laser crystallization (Juliana et al., 1982), laser recrystallization (Nishimura et al., 1982), and hydrogenation (Kamins and Marcoux, 1980) of the poly-Si film are all effectiveapproaches to improve the ON current of the polySi TFT. In the laser-recrystallization method, grains in the poly-Si film are

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS 10-~

-5

1o - ~

45

L ON Current

10-8 * S W

: lo-' 3

V

C ._

2

L = (15+15)u rn W = lOum vDS=4v tox = l500A

OFF Current

0

lo-" 10-1*

.,-I3

1U

Poly-Si thickness ( 8 , ) FIG.24. Dependence of poly-Si TFT characteristics on film thickness: with a thickness of less than 1,OOO A, the ON current is drastically increased due to the space charge reduction in the poly-Si film; the OFF current is also reduced by the thinner poly-Si film.

fused and regrown to a larger size when scanned with a CW argon laser beam, resulting in a much higher electron mobility of up to 300 cm2/V sec. By employing hydrogenation, in which the poly-Si film is treated in a hydrogen plasma to reduce the number of grain boundary defects, the field-effect mobility has been increased up to 34 cm2/V sec and the threshold voltage decreased to 8 volts. Generally, the stability and reliability of a TFT are determined by the semiconductor film, gate insulator film, and the associated interface. In the case of the poly-Si TFT, the properties of both the gate oxide and the interface between the gate oxide and the poly-Si film are the dominant factors determining the stability, since the poly-Si film itself is stable at room environment due to its monoatomic structure and high crystallization or recrystallization temperature, which is assumed to be more than 600°C. Usually, the instability of the electrical characteristics is caused by a short- or

46

SHINJI MOROZUMI

long-term shift of the density of states in the oxide and at the associated interface. Such a shift is strongly related to carriers being trapped or released from the traps. In the case of high-temperature processing, where a thermally grown oxide is used as a gate insulator, poly-Si TFT has a stability (Morozumi et a]., 1983a)similar to that of the conventional MOS transistor fabricated on a Si single-crystal wafer, since such oxide has a state density much smaller than that of other gate insulator films. In the case of poly-Si TFTs fabricated by the low-temperature process, the deposited oxide has a higher state density, especially at the interface. However, with careful deposition of the oxide so as to almost maintain stoichiometry, as well as using a suitable cleaning treatment for the surface of the semiconductor just before the deposition, a lifetime of four years at 60°C with DC bias has been obtained (Morozumi et al., 1986a). 3. Performance of Poly-Si TFT LCDs The first successful full-color video LCD was developed using a poly-Si TFT array made by the high-temperature process with a thermally grown gate oxide (Morozumi et al., 1983a). This display, with a size of 43.2 x 32.4 mm, had 240 x 240 pixels and exhibited an excellent contrast ratio of more than 40: 1 using a TN liquid crystal. Subsequently, the display size was increased to a 4.25-inch diagonal with 480 x 480 pixels, producing full-color images with excellent viewing characteristics (Morozumi et al., 1984b). At the same time, a 1.51-inch diagonal 210 x 180 pixel full-color LCD made by the hightemperature process with full integration of all the drivers on the same substrate was developed. Using the low-temperature process, full color LCDs have also been fabricated with 440 x 480 pixels and 5.13-inch diagonal active area (Morozumi et al., 1986a). For this LCD, LPT-CVD equipment was used to fabricate the poly-Si film and gate oxide. A photograph displaying the image produced on such a display is shown in Fig. 25. Another low-temperature display with 240 x 360 pixels and a size of 24 x 36 mm has been developed (Oana, 1984)in which the TFTs were fabricated by electron-beam evaporation in high vacuum at 520°C. The mobility of these TFTs was 15 cm2/V sec and their threshold was 8 volts. In this display, the gate drivers were also integrated on the same substrate. Using laser-recrystallized poly-Si TFTs, a 120 x 160 pixel black-and-white TFT LCD with an active area of 30 x 40 mm was fabricated (Ishizu et al., 1985). Here, the TFTs fabricated on a quartz substrate had a mobility of 320 cm2/V sec and an ON/OFF current ratio of lo8. In general, because of the high mobility and ON current of the poly-Si TFTs, integration of the driver circuits on the same glass substrate as the TFTs

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

47

FIG. 25. Black-and-white photograph of image produced on a 5.13-inch color LCD fabricated with a low-temperature-processed poly-Si TFT array; the number of pixels is 400 x 480.

is easier than in the case of amorphous Si TFTs. With the advances being made in low-temperature-processedpoly-Si TFTs, TFT LCDs of much larger size and including integrated drivers are expected in the coming few years. Details of the integration of the driver circuits are discussed further in Section V.E.

v. DRIVING SCHEMES FOR THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS The basic circuit diagram for TFT-addressed liquid-crystal displays is illustrated in Fig. 8 (see Section 1II.A). In all cases, a line-by-line scanning scheme is employed, similar to that in CRT rastering, with successive

48

SHINJI MOROZUMI

horizontal lines being sequentially addressed from top to bottom to complete a single frame or field. As mentioned in Section I.C, liquid-crystal elements require an alternating drive signal to prevent degradation. Consequently, positive drive voltages are applied to the display for one scanning field, followed by drive voltages of reversed polarity during the next field. Since flicker becomes visible at frame rates below 30 Hz, the field rate, which is twice the frame rate, has to be more than 60 Hz. The pixel TFTs of one horizontal scan line are connected to a common gate line and receive display signals from the data drivers (column drivers) through each data line. Two methods are used to transfer the display signal to the pixels. One is a “point-at-a-time’’ method, in which the signals are transferred to each pixel sequentially from left to right. Another is a “line-at-atime” method, in which the signal is transferred to all pixels of a line at once during addressing. With the first method, grey scale is easily obtained, but the transfer speed is limited. For high-quality, high-resolution displays, the second method is best. However, it requires more complicated driving circuits. In both methods, there are several kinds of column driver configurations to meet the requirements of different applications. When designing the drive circuits, the scanning speed must be taken into account. For example, if the TFT LCD employs 500 data lines and has 500 scan lines, the pixel scanning rate, assuming a field rate of 60 Hz, would be 15 MHz. This is a rather high frequency for existing LSI drivers, especially when the input video signals contain grey-scale information. Therefore, when designing the TFT LCD and determining factors, such as total number of pixels, frame rate, and grey-scale capability, it is very important to consider the demands on the driving circuits from the view of scanning speed. A. “Point-at-a-Time’’ Data Transfer Method

The driving arrangement for the “point-at-a-time’’ addressing method, in which each data line is addressed point-by-point, is shown in Fig. 26. Addressing can be divided into two operations. One involves addressing of a single line, whereas the other involves addressing the entire frame. Figure 27 illustrates the waveforms associated with the former (a) and the latter operation (b). During one line time, one of the gate lines GI-GM is selected by the output of buffers BG,-BGM, causing the corresponding row of TFTs to be turned on. At the same time, the column shift register starts its operation according to shift clock CLX with the pulse STX which is synchronized with the horizontal synchronizing signal. The outputs of the column shift register, after passing through the buffer amplifier BD, -BD,, produce pulses S , -SN that sequentially turn on the gates of the sampling transistors TI- TN.

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

GI G2 G3

Gu Di D2 D3 DN FIG. 26. “Point-at-a-time” driving scheme: the switch array TI-TN and capacitors Cd comprise the sampler and holder (sampler/holder) array; signals S,-S, sequentially activate the sampler/holders in order to latch the display data on the video signal.

-

m--m

CLX

- YTS

STX

- I G

s1

- 2G

V

s2

i

d

Video

D2

0

-

positive field

0Dl- -o

e

k

--.

negative field

I(

1 trame

4

Y

0-.

(a) (b) FIG.27. Driving waveforms for the “point-at-a-time’’ method: (a) the operation for a period of one scanning line: Gate pulses S,-SN sample the video signal and hold it for full period of one scanning line; (b) the operation for one frame: One frame consists of positive and negative fields to drive the liquid-crystal material with the alternating voltage swing.

49

50

SHINJI MOROZUMI

These transistors together with their associated capacitors Cd, act as sampler/ holders and latch the instantaneous signals as voltages in the capacitors Cd. These signal voltages are stored on the data lines D, -DN until the next activation of the sampler/holders and during this time are transferred to the corresponding pixel electrodes through their associated TFTs in the ON state. The transistors Tl - TN of the sampler/holders must respond to the pulses Sl-SN, usually within a few hundred nsec, in order to charge or discharge the capacitors Cd. However, several psec are allowed to transfer the signals on the data lines through the pixel TFTs to the pixel electrodes, since this transfer can take place during an entire line time. During operation of a frame (Fig. 27b), the pulses to drive the successive gate lines GI-G, are sequentially generated by the row shift register, which is synchronized with the clock pulse CLY and started with the pulse STY. After completing the scanning of the gate lines with positive video signals applied to the data lines (producing a positive field), the scanning is repeated with video signals of reversed polarity applied to the data lines (producing a negative field) to create a complete frame. This addressing method was applied to a commercial TFT LCD for a color pocket television receiver with 240 (horizontal) x 220 (vertical) elements. The display was provided with two column-driver LSIs, each with 120 output channels, located on the upper and lower sides of the display panel, respectively, with an interlaced connection to the data lines. These driver LSIs were driven by NTSC signals. The frame rate was 30 hz and the period for one scan line was about 64 psec, resulting in a point (pixel) addressing rate of approximately 3 MHz. The +4-V video signal was applied to the data input terminal of the display, and the voltage applied to the gate lines was about 20 volts. Since this addressing scheme can be realized by a simple circuit configuration as shown in Fig. 26, as many as 120 output channels can easily be integrated on a small silicon chip less than 25 mmz in size.

B. “Line-at-a-Time’’Data Transfer Method With the “line-at-a-time” method, the data line is driven for the full period of one scan line. Operation is otherwise the same as in the “point-at-a-time’’ method. In this method, the signal is latched in a digital or analog latch array before being applied to the data line buffers. If the display requires grey scales, analog latches or equivalent circuits are used. In the case of a “bi-level”display without any grey levels, digital latch arrays are sufficient. Due to the use of latch arrays, the display signals are input to the column driver in one period of the scan line, and are output through the latch array to the data lines in the next period. Although such input and output operations require two periods, the input operation for line (rn + 1) and output operation for line (rn) are

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

51

carried out in the same time period. As a result, the total addressing time required is same as that of the “point-at-a-time” method. The “line-at-a-time” driving scheme without grey scale, shown in Fig. 28, is the simplest driving method. During the line time when gate line (m - 1) is selected, the column shift register in the column driver serially transfers the digital display data DX for line (m)with the shift clock pulse CLX. After this input is completed, all the data signals are transferred to the latch with the latch-enabling pulse LE, the display signals are output on the data lines D,-DN through the digital buffers B,-BN, and at the same time the next gate line (m)is selected to turn on the corresponding row of connected TFTs. Data signals are then transferred to each pixel of the row through their TFTs within the full period of a scan line. During the same period, the display data for line (m 1) are input to the shift register. The row-driver operation is the same as in the case of the “point-at-a-time” method. In order to provide the necessary alternating polarity drive signal for the liquid-crystal elements, the column buffers B,-BN output in a tristate, with their output, for example, being either 0 or 4 volts for positive fields and either 0 or - 4 volts for negative fields. Since all the circuits in this arrangement are of a fully digital design and the total number of transistors is relatively small due to the simple configuration, these can easily be integrated on a small silicon chip. There are two methods for obtaining a grey-scale capability with the “lineat-a-time” method. One involves the employment of an analog latch array and

+

CLX DX

Column Shift Register 1

I

I

GI G2

G3

Gu D i Dz D3 DN FIG.28. “Line-at-a-time” driving scheme without grey scale: this is the simplest method due to the full digital configuration of the row and column shift registers, latch array, and associated buffers.

52

SHINJI MOROZUMI

the other makes use of a combination of pulse-width modulator and latch array. The circuit configuration of both methods inevitably becomes complex. In the latter method, grey levels are obtained by controlling the pulse width of the display signal. The pulse width applied to the data lines determines the LC pixel voltage in accordance with the charging time of the pixel capacitor through the TFT that is turned on. Since the circuit used for this method is fully digital, there is no need to produce a variation in the driving voltage of the output channels. However, it is not realistic to apply this method to displays requiring a large number of grey levels, because the pulse-width modulator may become extremely complicated as the number of grey levels increases. This method is thus suitable for graphic displays with a few grey levels rather than a video display with full grey levels. The circuit diagram for a “line-at-a-time’’ driver with analog latches is illustrated in Fig. 29. Here the column shift register supplies successive gating pulses to the gates of transistors TII-TIN,which, together with the signal holding capacitors Csl, consist of the sampler/holders. This is exactly the same operation as the “point-at-a-time”method shown in Fig. 26 and Fig. 27.

Da Dz DJ DN FIG.29. “Line-at-a-time’’ driving scheme with grey-scale capability: the key is dual analog sampler/holders consisting of gate transistors, storage capacitors, and analog buffers incorporated serially between the video signal line and gate lines, in which the lower sampler/holder is operated as an analog latch; with this scheme, since the data lines are driven for the full time of one scanning period, a video image with a large number of grey levels can be produced.

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

53

The outputs of the sampler/holders are transferred to analog latches through analog buffers All -AlN. The analog latches, which have latching transistors TZ1- TZN,signal-holding capacitors Csz and analog buffers A2,-AZN, receive the analog display signals from sampler/holders, and transfer them to data lines D,-DN controlled by latch-enabling pulse LE. When the gate line (m - 1) is addressed, the sequentially sampled video signals are held in the capacitors C,, during one line time; these stored signals are then transferred to analog latches with the latch-enabling pulse LE to drive the corresponding data lines after the last sampler/holder is activated. Subsequently, gate line (m)is addressed, turning on the connected TFTs, and the video signal is thus transferred to the pixel electrode through the TFTs. Since the data lines here are driven for the full line scanning period, full pixel charging is achieved even if the ON current of the TFTs is slightly insufficient or the metallization resistance of the data lines is relatively high. Usually, the analog buffers consist of a voltage follower differential amplifier made of CMOS transistors and storage capacitors of a few p F integrated on the silicon chips. In such analog buffers, any deviation from linearity and variation in offset voltage must be strictly controlled in order to display a high number of grey levels with satisfactory uniformity. Since the analog buffers and storage capacitors occupy a large area of the Si integrated circuit, the number of output channels per chip may be limited. C. Input-Signal Modification for Grey-Scale Operation

As mentioned above, difficulties are involved if good reproduction of grey levels is required. In addition to problems associated with the driving scheme itself, the input signal must be modified to take into account the nonlinearity in the optical characteristics of the T N liquid crystal as exemplified in Fig. 30 by the transmission curve for an LCD using the crossed-polarizer method (see also Section 1.B). Here, the optical transmission starts to change at 2 volts; and at around 3 volts, following the steep transient, it gently slopes past 4 volts towards saturation. Unlike CRTs, LCDs have both O F F and ON saturation states that are very nonlinear near these points. If linearly divided grey levels are required, the voltages applied to the liquid-crystal cell obviously must be compensated, particularly around 3 volts. In the case of a computer display with a limited number of grey levels, e.g., 4-16, such levels can be easily obtained by means of a corresponding number of voltage levels produced with a digital-to-analog (DA) converter circuit. On the other hand, in the case of video signals broadcast for commercial TV, these signals are already modified to compensate for the nonlinear characteristic of the CRT (gamma compensation). Therefore, when precisely controlled grey levels are required

54

SHINJI MOROZUMI

0 0

1

2

3

4

5

Applied Voltage (V)

FIG.30. Typical transmission as a function of applied voltage of TN LCD with crossed polarizers: OFF state below 2 volts and ON state above 4 volts; between the saturated regions, a nonlinear transition is observed; to obtain good grey levels, the applied voltage levels must be modified to compensate for this nonlinearity.

in the LCD, the broadcast video signal must be reconverted from its gammacompensated state to an appropriate form as required by the LCD. D. Large-Scale Integration Drivers and Their Connection to the Liquid-Crystal Display

Row drivers to activate the lines and column drivers to transfer the display signal to the data lines are available, integrated on CMOS-LSI chips with multiple output channels. Usually, the driver LSIs have 60-120 output channels per chip and are positioned on the four sides of the display panel for connection to the LCD input terminals associated with the gate and data lines. In the case of a display with 480 x 480 pixels, for instance, two row- and two column-driver LSIs, each with 120 outputs, are connected to the LCD at the left and right sides, and at the top and bottom, respectively. The connections at opposite sides may be interlaced. The design and operation of the row drivers are less of a problem than the column drivers since all the circuits are fully digital and their operating speed is relatively low. In the case of a TV display based on NTSC standards, the total number of gate lines may be either the same or half the effective number of scan lines (about 480)of the 525-line system. Since all of these lines are scanned within 1/60 sec, the line time, i.e., one period of the shift clock, becomes 64 psec, which is relatively long. On the other hand, when designing a column-

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55

driver circuit configuration such as shown in Fig. 26 and Fig. 28, many factors, such as the integrated silicon chip size, the operating frequency, power consumption, grey-scale capability, and output impedance must be taken into account. If a TV display panel has 500 data lines addressed within 64 psec, each column driver must complete its operation within at least 128 nsec, an extremely high speed for analog operation. With respect to power consumption, since the liquid-crystal itself is essentially a capacitive circuit element, most power is consumed by the driver LSIs, especially the highfrequency data line drivers. Sometimes a pixel scanning rate of more than 5 MHz is required. In this case, each LSI with 120 driver channels consumes more than 100 mW even though a CMOS circuit is used. Since a dot-matrix-type LCD has many input terminals with a small pitch, it requires accurate and highly reliable connections between the driver LSIs and the LCD panel itself. The total number of connections and their pitch are determined by the display area and resolution, e.g., the number of gate and data lines. Here, it should be noted that the connection pitch can be halved by using interlaced connections. For example, using such interlacing, a 5-inch diagonal TV display with500 x 500 pixels requires a total of 1000connections with a pitch of 0.4 mm for the columns and 0.3 mm for the rows, respectively. For displays with such a large pitch, one can use flat-packaged LSIs assembled on an ordinary circuit board. These may be connected to the LCD by simple means such as rubber connectors with separated U-shaped gold-plated electrodes held together by the rubber material. However, when the pitch becomes less than 0.3 mm, other approaches may be required. One method is film bonding in which a flexible film such as polyimide with a copper metallization layer is used with the tiny fingers of the film directly connected to the LCD input terminals. This chip-on-glass technique is also useful for compact displays. Here, the driver LSIs are mounted directly along edges of the glass substrate of the display on which the pixel TFTs are fabricated. This may be the best solution for connecting the LCD and LSIs when the driving circuits cannot be integrated with the TFTs themselves on the same glass substrate. as described below.

E . Integrated Thin-Film Transistor Drivers One advantage of the TFT-addressed LCD compared to direct-drive LCDs is that it offers the possibility of fabricating the driver circuits on the same substrate as the display. Whereas this avoids troublesome connections between the LCD and driver LSIs, other problems, such as obtaining TFTs with the necessary speed (ON current) required for the shift registers and related circuits, and insuring a sufficiently high yield of the TFT driver circuits,

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appear. If the TFTs associated with the pixels can be fabricated with few defects, the integration of the driver circuits with TFTs may be feasible. However, since a few defects in the pixel TFTs are sometimes acceptable,but at the same time, no defects in the driving circuits can be tolerated, some redundancy technique with alternative switches is necessary. Efforts to integrate the driver circuits have been made with three types of TFTs: CdSe, amorphous Si and poly-Si TFTs. In the drive circuits using nchannel CdSe TFTs (Brody, 1984),the mobility of these TFTs is high enough to allow satisfactory operation when integrated on the glass substrate of the display. On the other hand, the mobility of amorphous Si TFTs is too low for proper operation as integrated drivers for the column electrodes, although a low-speed gate-line-integrated driver has been developed using such TFTs (Akiyamaet al., 1986).In the case of poly-Si TFTs, the mobility is sufficiently high, and full integration of the TFT drivers has been demonstrated. Figure 31 shows the frequency range of NMOS dynamic and CMOS static poly-Si TFT shift registers (Morozumi et al., 1984b). Although both can operate at a

-

lo6 -

CMOS Drivers

___---NMOS Drivers

fro-4F--'

Po'

lo5 -

10 fmin

I 0

I

10

20

supply Voltage ( V ) FIG.31. Frequency range of shift registers based on poly-Si TFT-integrated drivers: as shown, the CMOS static driver has a wider operatingfrequency range than the NMOS dynamic driver. (Figure 4 from Morozumi et al., 1984b. Permission for reprint, courtesy Society for Information Display.)

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sufficiently high frequency (more than 1 MHz),the NMOS dynamic driver has limitations in its low-frequency operation. With the CMOS poly-Si TFTs, a fully integrated display with drive circuits was successfully achieved (Morozumi, 1985). Figure 32 is a microphotograph of the integrated poly-Si TFT driver circuits. These appear very much like ordinary LSI circuits on a Si single-crystal wafer. Figure 33 also shows a photograph of an operating 1.27inch 220 x 320 pixel full-color TFT LCD with full integration of poly-Si TFT driver circuits. It has a 80 x 90 pm pixel pitch and produces images with a contrast ratio of over 40:l with rear illumination. Such a miniaturized LCD can be used for video camera monitors and projection displays as mentioned in Section VIII.A.3.

VI. COLOR-IMAGE THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS For producing full-color images, liquid-crystal displays have a significant advantage compared to other flat display panels, since a color image can be easily obtained by adding an appropriate array of color filters together with

FIG.32. Microphotograph of integrated poly-Si TFT drivers: the white region is the metallization layer made of aluminum;other regions are the IT0 and poly-Si layer; minimum line width is 5 pm.

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FIG.33. Black-and-white photograph of miniaturized TFT LCD with full integration of poly-Si TFT drivers: active display is 0.94” diagonal size with 220 x 320 pixels; such displays are used with an optical magnifier as video-camera monitors.

a related backlighting system to a monochrome LCD. Compared with the conventional multiplexed LCD with a typical contrast ratio of less than 20: 1, the TFT LCD with a contrast ratio as high as 100:1 has greater potential for producing a high-quality color image comparable to that of a CRT. The first full-color TFT LCD was demonstratedin 1983(Morozumi et al., 1983a).Since then, most TFT LCDs have been developed for use in color-TV displays, where a high-quality image is important. A. Structure

The typical structure of a TFT-controlled full-color LCD is illustrated in Fig. 34. As in the case of shadow-mask color tubes, the color filter elements in registry with their associated TFT-controlled pixels must be made sufficiently

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-Liquid-Crystal

‘Pixel Pixel Electrode ( I T 0 1

t t t t t

TF T

Light Source FIG. 34. Structure of full-color TFT-LCD: a color filter layer is formed below the upper common electrode as an addition to the monochrome-type LCD; usually, organic dyes are used to produce the red, green, and blue filter elements.

small so that they are not resolved by the observer’s eye at normal viewing distance. As shown, the color filter layer is fabricated on the inner surface of the upper glass plate, with the common electrode then being deposited on the color filter layer. Except for the filter, the display is thus exactly the same as the monochrome-type TFT LCD. As in the case of color CRTs, the color image is created by additive color generation. Since the total light absorption by the color filters and polarizers on the outer surfaces of the display is high (more than 90%), viewing the LCD by reflected light results in an image that is too dark to view in normal room light. In order to obtain high brightness, a backlight is therefore used. Different arrangements using the same number of pixels may cause different image perceptions by the observer, particularly with regard to resolution. Typically, three types of color pixel arrangements are employed as shown in Fig. 35: the stripe, diagonal mosaic, and delta arrangement. Figure 35a shows the vertical stripe type. This arrangement makes the LCD drive circuitry less complex but requires the use of more horizontal pixels than the other schemes in order to produce a given effective resolution. Figure 35b shows the diagonal mosaic arrangement, the most commonly used. The drive circuit for generating the color video signal for this scheme (described in Section V1.D) is rather complicated, but seems to produce good resolution. Figure 35c shows the delta arrangement. This produces excellent resolution, but the wiring layout of the pixels becomes somewhat complicated. If high resolution is required with the limited number of pixels, the delta arrangement is the best choice. However, if a relatively large number of pixels can be used, displays with the mosaic or stripe arrangement are easier to design and drive.

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( a ) Stripe (b)Diagonal Mosaic ( c ) Delta FIG.35. Color pixel arrangements used for full color LCDs: (a)stripe (verticalor horizontal); (b) diagonal Mosaic; (c) Delta; the stripe arrangement is easier to address,but results in poorest resolution; the delta arrangement produces the highest resolution, but results in the most difficult pixel design.

The overall light transmission of the LCD panel is determined by the LCD cells as well as by the light absorption of the polarizers and color filter layer. The transmission of the LCD cells depends on the “aperture ratio” and the optical interface losses. Since the aperture ratio, defined as the ratio of the window area of the pixel to its total area, is strongly related to the opaque areas of the transistor and metallization area (which may be relatively fixed), it is proportionate to the pixel size. A typical value of a TFT-LCD cell transmission is about SO%, assuming an aperture ratio of 70% and a pixel pitch of about 0.2 mm, and considering reflections at the optical interfaces such as between the glass and air, glass and ITO, etc. In a color filter layer, lower transmission produces higher color purity. In some color filter designs, the transmission is as low as 20%. Since the two polarizers absorb about 6070% of the incident light, the total transmission is reduced to less than 5%. Thus, in order to realize a highly graded color image, color LCD requires the use of a backlight source with a correspondingly high power consumption. An example of the color gamut of a full-color TFT LCD shown on the CIE chromaticity diagram is indicated in Fig, 36 (Morozumi, 1985). In this chart, the center point corresponds to “white” and the outer heavy line shows the locus of each wavelength that is assumed to have an infinitely narrow peak in the spectrum. Therefore, a larger triangle is desirable to obtain high color purity as close as possible to pure red, green, and blue. As can be seen, an excellent color gamut similar to that of a CRT is obtained. The slight difference in the triangle between the TFT-LCD and the CRT results from a difference in the contrast ratio of the two. The black level of a CRT represents the completely nonemissive state, whereas in the case of the TFT LCDs, there is a slight light leakage in the black state, allowing some color mixing to occur. In addition, the LCDs depend on the use of a white fluorescent tube for backlighting. The wide spectral distribution of such a tube influences the colors obtained, whereas in the CRT the colors produced depend only on the electron-excited phosphors that may have narrow emission bands.

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c

0

10

20

30

40

50

60

70

80

Values of x FIG.36. Chromaticity diagram of full-color TFT LCD: as a result of improvements in the optical properties of the LCD, color filter layer, and backlight, an excellent color gamut close to that of a CRT is obtained. (Figure 8, from Morozumi, 1985. Copyright @ 1985 IEEE.)

B. Color Filter Fabrication The first requirement for producing a high-quality color image is filter material with the proper spectral transmission curves. The second requirement of the filters is that they provide a smooth surface on which to fabricate I T 0 electrodes on the innerside of the liquid-crystal cell and thereby insure uniform cell spacing. The third requirement is dimensional accuracy in the case of a highly dense pixel arrangement. The fourth requirement is resistance to fading, especially since the display cells may sometimes be exposed to direct sunlight, whether operating or not, as well as intense backlighting, which is always used in operation. In addition, the color filters must not fade at the elevated temperatures employed during the subsequent liquid-crystal cell fabrication steps such as deposition of the I T 0 transparent conductive film. Various methods for fabricating the color filter mosaic have been developed to meet the above requirements. In one method, the elemental filter areas have beed deposited by printing, but this has not been successful so far in TFT LCDs because of the unsatisfactory spectral transmission and the poor dimensional accuracy. In another method, pigment particles are deposited by

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an electro-deposition technique on the I T 0 layer (Suginoya et al., 1983); but this aIso has not found practical use because of unsatisfactory color. Presently, organic film dyeing, which in the past has been applied to color filters for video image sensors, is the most popular way to fabricate the color filter layer. The fabrication process used in the typical dyeing method is shown in Fig. 37a-f. For accepting an organic dye, a 2-3-pm-thick organic film, either natural protein such as gelatine or glue, or a synthetic material such as polyvinyl-alcohol (PVA) is coated on the glass substrate. This film is covered with a layer of photoresist in which windows are opened in the regions that are to be dyed. The glass substrate is then dipped into red dye solution, which is absorbed in the exposed areas of the film as indicated in Fig. 37b. The photoresist is then removed, and these steps are repeated successively for the green and blue dyes as indicated in Fig. 37c and d. As shown in Fig. 37e, a passivation layer of acrylic resin, 3000-5000-A-thick, is coated on the surface of the color filter layer in order to prevent the release of dye material into the liquid-crystal material. Finally, as indicated in Fig. 37f, a common electrode in the form of an I T 0 layer is deposited by sputtering. This procedure is carried out below 200°C to prevent fading of the dyed film. Although more than 3,000 different dyes are known, a relatively small number are useful. In practice, acid dyes are used in this application because of

Organic Base Glass Substrate

(a)

(b)

Y

T

R

e

d

-

D

y

e

d Areas

C Green C C C .Dye 1 . 1

Photoresist

Blue Dye

Photoresist

(C)

. 1 C C C & J t

(d)

.....V,,

~

Overcoat I

I

FIG.37. Fabrication method of dye-type color filter: (a) a photoresist window for the red region is opened and the surface exposed to dye; (b) the photoresist is removed; (c),(d) same procedure is repeated for green and blue regions;(e) an overcoat layer is provided for passivation; (f) Common electrode mode of I T 0 is deposited.

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their resistance to fading under intense backlight and exposure to sunlight, as well as the acceptability of such dyes by the base film. The dyes and their concentration are selected in order to obtain the necessary spectrum of the color filter layer, taking into account the backlighting spectrum. Although a high dye concentration provides high color purity as mentioned in Section VLA, it results in poor light transmission. Therefore, the concentration of the dye has to be accurately controlled in order to obtain an optimal combination of transmission, chromaticity, and white balance. Figure 38 shows the typical spectrum of color filters fabricated by organic dying. In this example, the average transmission of white light is about 25%. C. Backlighting

Usually, the backlighting arrangement consists of the light source itself, a diffuser to spread the light more uniformly over the screen, and a reflector to enhance the brightness by reflecting the rear-emitted light to the front surface where the diffuser is positioned. Slender fluorescent tubes, either of the heatedfilament type or cold-cathode type, are well suited as light sources in the above configuration for use with full-color LCDs, particularly since they have a high emission efficiency and relatively long lifetime. The filament type is desirable because of its higher light emission efficiency (10-20 lumens/watt in a small tube) and excellent whiteness. Although cold-cathode tubes have a low

Wavelength (nrn) FIG.38. Transmission properties of dyed color filter layers with respect to wavelength: average transmission of white light is about 25%.

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2,

P 01 K

w

_1

n

400 Wavelength (nm)

FIG.39. Spectrum of peak-enhanced-type fluorescent tube: the peaks of the red, green, and blue bands are positioned so as to match the optical properties of the color filter elements in order to produce the desired spectral output from the display.

efficiency (a few lumens/watt), they are used for applications requiring a long lifetime. In order to obtain primary colors with sharp peaks in the spectrum, i.e., high color purity, special phosphors whose emission is concentrated in narrow bands corresponding to the red/green/blue (RGB)primaries are used in the tubes. Figure 39 shows the spectrum of such a “peak-enhanced” fluorescent tube of the filament type designed for use with a full-color TFT LCD. The color temperature of the emission is about 7,000 K, and the efficiency of the tube is 15 lumens/watt. The starting voltage for the discharge is close to 1,000 volts, and the maintaining voltage is 70 volts using an AC power source and an electronic ballast circuit. Such a fluorescent tube, with a length of 5 inches and diameter of 0.4 inches, has a power consumption of 3 watts. When used with a 3 inch color LCD, a surface brightness of 5,000 nits is obtained from the diffuser, resulting in a surface brightness of 200 nits from the display. With the tube placed midway between the diffuser and reflector, which have a spacing of 0.8 inches, there is a variation in brightness of about 50% across the panel. D. Driving Scheme for Color Liquid-Crystal Display Panels

The driving scheme for the TFT-LCD color panel is slightly different from the monochrome type shown in Fig. 26 (Section V.A), since the display data must be processed to contain R, G,and B signals that match the color pixel arrangement of the panel. As one example of the driving scheme, the circuit diagram for a color TFT LCD with pixels of each color arranged along diagonal lines is shown in Fig. 40. In operation, the commonly used composite

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FIG.40. Driving scheme for full-color TFT LCD with diagonal mosaic color pixel arrangement: video signals, Vl-V3, are composed through a 3 x 3 matrix switch triggered by a horizontal synchronizing signal; in this example, the “point-at-a-time”addressing method of Fig. 26 is employed.

TV video signal is first demodulated to obtain the normal color video signals, V,, V,, and V, through the chroma circuit conventionally used in color-TV sets. These signals are then converted to alternating-polarity video signals, V,, V,, and V,, by a video conversion circuit to satisfy the requirements of the liquidcrystal materials as mentioned in Section V and shown in Fig. 27. The amplitudes of these signals and their voltage levels are also adjusted in this circuit in accordance with the electro-optical characteristics of the liquid crystal. The R, G, and B video signals, V,, V,, and V, are multiplexed by a 3 x 3 matrix switcher to generate the V1, V 2 , and V 3 signals so that the starting pixel in each scan line shifts successively from R to G, G to B, and G to R. The matrix switch is controlled by the horizontal synchronizing signal, switching once per scan line. In the case of the delta arrangement of color pixels, a similar driving scheme is used. In the case of a vertical stripe filter arrangement, however, there is no need for a rotator or multiplexer. BASEDON VII. PERFORMANCE OF LIQUID-CRYSTAL DISPLAYS ALTERNATIVE TECHNOLOGIES Although TFT-controlled liquid-crystal displays have many desirable features, for some purposes diode-controlled LCDs as well as directly multiplexed LCDs may have certain advantages. To better understand the

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relative merits of these other technologies compared with TFT LCDs, they are discussed in the sections below.

A. Comparison between Thin-Film Transistor and Diode-Controlled Liquid-Crystal Displays

Important points of comparison between TFT and diode LCDs are in the ease of the active element fabrication and the display performance. For use as thin-film diodes, MIM elements based on Ta,05 or SIN films (Suzuki et al., 1986) as well as amorphous silicon elements in the form of so-called p-n diodes have been developed. The former have bidirectional current-voltage characteristics within a single element, in which the electrons flow through traps in the thin Ta,O, film and exhibit the Poole-Frenkel-effect current (Baraff et al., 1980). In one form, p-n diodes have been employed using the “diode ring” configuration, in which a pair of p-n diodes of opposite polarity are connected in parallel utilizing the nonlinearity in the forward characteristic of each diode to obtain bidirectional characteristics (Togashi et al., 1984). In an alternative form, a “back-to-back” diode configuration has been studied with a connection in series employing the nonlinearity of the reverse characteristics (Szydlo et al., 1983).In the fabrication process for such diodes, 2-4 photomasks are required for their fabrication, whereas TFTs generally require 4-9 photomasks, making the large-area fabrication process with thinfilm diodes simpler than that for TFTs. However, in the case of diodes, the nonlinearity characteristicsbetween two terminals connected in series with the liquid-crystalelement directly influences the ON/OFF ratio. By comparison, in the case of TFTs, the ON/OFF current ratio is selective in accordance with the gate voltage swing, being independent of any nonlinearity in the currentvoltage characteristic between the source and drain. Unfortunately, the diode nonlinearity factors, which, up to now, are almost the same among the various thin-film diodes (Howard, 1986), are not sufficient to enable complete frame storage operation to be obtained in an active-matrix LCD. This differs from the case of TFT-type active-matrix LCDs. Whereas most TFTs have an ON/OFF current ratio greater than lo5, the ON/OFF ratio for diodes is around lo3 or lo4 at best because of the poor nonlinearity factor. It is thus difficult for diodes to satisfy the requirements indicated in Eqs. ( 5 ) and ( 6 ) of Section 1II.B. This leads to contrast ratio degradation and limited grey-scale capabilities unlike the situation with TFT elements. In addition, since the spread or distribution of electrical characteristics of diodes as well as their shifts with temperature directly degrade the display uniformity, strict control is absolutely required in the fabrication of the diodes to insure sufficient uniformity of their characteristics. Accordingly, at the present time, the TFT

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LCD is the most promising device for the realization of high-quality images, whereas the diode-type LCD is more suitable for large-area displays with limited or no grey-scale capability, although directly multiplexed LCDs are also competitive for such applications. Using thin-film diode elements, a number of LCDs have already been fabricated. For practical applications, full-color pocket TV sets based on MIM LCDs are already being mass-produced with 2.6 and 3.3-inch diagonal sizes. For test purposes, 6.7-inch MIM LCDs with 440 x 640 pixels capable of displaying full-color video images have also been built (Maezawa et al., 1987). For portable computer displays without grey scale, 9-inch diagonal monochrome MIM LCDs with 400 x 640 pixels have been developed (Morozumi, 1985). Using amorphous Si diode rings, full-color LCD panels containing 480 x 720 elements with an area of 122.4 x 120 mm have also been developed (Togashi et al., 1986). In any case, as long as the TFT elements present difficulties for large-area fabrication, thin-film diodes will remain a potential challenge to TFTs for large-area, high-quality displays. B. Comparison between Directly Multiplexed and Active-Matrix Displays

As mentioned earlier, active-matrix LCDs, whether controlled by TFTs or diodes, have an image quality close to that produced by steady-state or staticdriven liquid-crystal cells. The active-matrix LCD can have a contrast ratio as high as 100,depending on the specific design. On the other hand, the contrast ratio achievable in practice with the direct-drive multiplexing method is currently limited to less than 20:l if more than 200 scan lines are used. However, since the directly multiplexed LCD requires no active-element fabrication, it is easy to realize a large-area panel without concern for the defects that tend to occur in active matrix LCDs. The comparison below will be made in specific terms for displays used in presenting computer data or producing video images. In the case of a large-area data display that may require a complete absence of defects such as those used for existing portable computers, direct multiplexed LCD may be a better choice than active-matrix LCDs of either the TFT or diode type, despite the limitations in contrast ratio and viewing angle of the directly multiplexed LCDs. In fact, at the present time, directly multiplexed LCDs with 400 x 640 pixels with a diagonal size of 9-12 inches are being used in portable computers and word processors. Most such largearea LCDs now employ either the SBE liquid-crystal technology (Scheffer et d., 1985) with 270-degree twist-angle or supertwisted-nematic (STN) arrangement with a twist-angle range between 180 and 240 degrees (Akatsuka

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et a!., 1986) instead of the conventional TN arrangement. Although the SBE LCD has a serious problem resulting from the displayed image being colored because of birefringent effects, this has been solved by adding a liquid-crystal color-compensating layer that cancels or neutralizes the birefringent effects (Watanabe et al., 1988). This removes the color and produces an enhancement of the contrast ratio. Such neutralized STN LCDs with a contrast ratio as high as 15:l have been achieved by a 400 x 640-pixel LCD driven from both the top and bottom half of the column lines at a multiplexing ratio of 1/200. Although the image quality and the response time (as slow as 100-400 msec) of such panels (Kawasaki et al., 1987)are still inferior to those of active-matrix LCDs, they are suitable for some limited applications such as portable computers. However, these displays may be inadequate in the future when higher resolution and color images with a high number of grey levels are required. For directly multiplexed displays, the new ferroelectric LCDs (Clark and Lagerwall, 1980) may offer advantages of higher contrast and greater viewing angle; but their grey-scale capability, response time, and stability of molecular alignment are factors that are still unclear. If much higher performance is required in the future, such as a contrast ratio as high as 100:1, a viewing angle up to i50 degrees, a resolution of more than 1,000 x 1,000 pixels, and a grey scale with more than 16 levels, TFT active-matrix LCDs are likely to have the highest potential. The diode type may also be a candidate to satisfy these requirements if the nonlinearity factor of the diodes can be sufficiently improved as discussed above. In the field of video displays, both directly multiplexed and active-matrix LCDs have been used for 2- 3-inch diagonal picture-size small TV receivers, so-called pocket TVs. For high-quality color-TV receivers, active-matrix LCDs using polycrystalline-Si TFTs, amorphous Si TFTs, and MIM diode arrays of around 240 x 240-380 elements have been employed. On the other hand, for lower-priced receivers, directly multiplexed TN LCDs with around 1 10 x 380,220 x 240, or 220 x 320 elements have been used. Both types seem to have established their position in the market, and this situation will probably not change for a while, since their quality and price satisfy separate parts of the market. At the present time, since such small TV sets with a screen size of less than 3-inch diagonal are used for temporary entertainment as compared to ordinary home CRT receivers, the image quality is not very significant as long as the price is commensurate with quality. However, in the future, as the screen size becomes larger and larger, image quality may become more important and may be required to approach the quality of ordinary home TVs. Therefore, in the future, the active-matrix LCD may dominate over the directly multiplexed LCD unless there is a giant breakthrough in image quality of the latter type.

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OF THIN-FILM TRANSISTOR-ADDRESSED VIII. APPLICATIONS LIQUID-CRYSTAL DISPLAYS

The ultimate target of LCDs, particularly the TFT-addressed type, is to replace CRTs in application areas such as television and computers. As already mentioned, for television applications, small-sizecolor TFT LCDs are being marketed, with the display size expected to increase year by year. Activematrix LCDs for computer displays have not been utilized yet and are still under development. Although CRTs are obviously not about to be replaced by TFT LCDs, the practical use of TFT LCDs has already been established in a number of new applications or as replacements for CRTs in some special applications. Such applications of TFT LCDs are discussed below. A. Television Applications

There are three application fields of interest for TFT-LCD full-color-TV displays. The first is for pocket- or portable-TV use with a 2-6-inch display size as already indicated, or even up to 10-inchdiagonal size in some cases. The second is for wall-size TV, in which case the diagonal size is, for example, more than 20-inches,and may be up to 40 inches for high-definition TV using more than 1,000 scan lines. The third is for projection TV, in which the image produced by a small-sized TFT LCD is projected onto a large screen. 1 . Pocket TV Pocket color-TV receivers with 2-inch and 2.5-inch diagonal picture size containing 220 x 240 and 220 x 320 poly-Si TFT arrays, respectively, were already marketed by Seiko Epson in 1984 and 1985. Also a 3-inch color TV receiver with an array of 240 x 378 amorphous Si TFT elements was marketed by Matsushita and Sharp in 1986 and 1987,respectively. Following these TVs, 4-inch and 5-inch color TV sets have been marketed by several Japanese consumer electronics companies. A black-and-white photograph of the 2-inch TFT-LCD color-TV set made by Seiko Epson is shown in Fig. 41. The color pixels here are fabricated in a diagonal arrangement with the filter elements made by the organic dye method. Using the conventional twistednematic liquid crystal with crossed polarizers, a contrast ratio of more than 50: 1 is obtained. Although the image has some viewing-angle dependency because of the type of liquid crystal employed, in a pocket-type TV receiver viewed by one person this is not a serious problem. A single pencil-type hotcathode fluorescent tube with a power consumption of about 1 watt is used as the backlighting source, producing a 50-ft lambert brightness at the viewing

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FIG.41. Black-and-white photograph of a 2-inch pocket-type full-color LCD TV receiver:it employs a 220 x 320 poly-Si TFT array and exhibits excellent viewing characteristics.

surface of the display panel. The total power consumption of the set is closed to 1.8 watts, allowing it to be operated for more than three hours with four AA dry batteries. The outside dimensions are 128.6 x 76.6 x 30.7 mm, resulting in a compact pocket receiver that can be viewed almost anytime anywhere. At present, the size of such displays is limited by their cost, which is almost proportionate to the display area. However, the cost of TFT LCDs is expected to be reduced year by year, with commercial displays being enlarged to 6-inch to 10-inch diagonal size. Aside from their use for receiving broadcast TV signals, such displays will no doubt find applications in viewing or monitoring images produced by video cassette recorders, video discs, as well as portabletype video cameras. 2. Wall-type Flat T V

Large-sized flat TV displays that can be mounted on the wall are the ultimate target for every flat-display technology. At the present time, TFT

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LCDs for color video displays up to around 12 inches in diagonal size (Takeda et al., 1986, and Sakamoto et al., 1986) have already been fabricated for test

purposes but not for commercial use. However, achieving the most desirable size, e.g., more than 30 inches diagonal, is very difficult even for developmental evaluation because of the lack of suitable fabrication equipment. Even though the current techniques, available for a diagonal size of less than 12 inches, could be applied to the fabrication of such large-size display panels, the production cost would be extremely high due to the very poor yield caused by defects as well as the very low productivity, i.e., the very small ratio of production capacity to required investment. For example, the step-and-repeat projection aligner used in existing photolithography machines, which is quite common for the current production of TFT substrates, costs more than one million dollars. At best, this can process 30 1-foot-square glass substrates per hour to form a fine pattern for a single layer with a minimum number of defects. In effect, this would require over 30 projection aligners to be installed in order to produce only the photolithographic pattern for 10,000 pieces of 40-inch diagonal TFT-LCD arrays per month, resulting in quite a high production cost. Besides, in such large-size displays, the image quality (which is determined for example, by contrast ratio, grey-scale reproducibility, viewing angle, and brightness) must be better than or at least equal to that of CRTs, unlike the case of small-size display panels. This requires further technical improvements in the panel itself. In view of the extensive efforts being presently directed toward the development of large-size, high-definition TV systems based on more conventional display technologies, it is expected that progress in this area will further increase the demand for 30 or 40-inch-size wall-type TV displays. Of importance is the fact that, in the case of TFT LCDs regardless of the display size, no significant differences in the fundamental technology is required. More important, as mentioned, are the improvements in the manufacturing technique and related equipment necessary to achieve a large productioncapability/equipment-investment ratio for large-size substrates, as well as improvements in the TFTs to obtain the necessary high uniformity in electrical characteristics and low-metallization resistance.

3. Projection TV At the present time, there is much interest in projection systems for producing large-screen color images. Such systems, generally making use of multiple CRTs, are costly and bulky and have limited light output. The use of TFT LCDs instead of CRTs for projection provides an attractive alternative approach and presently seems to be a more realistic method for containing a large-size image compared to attempting to obtain a large wall-type TV

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display with its attendant difficulties mentioned above. Although a package as compact as that achieved by a small direct-view TFT LCD cannot be obtained with this method, nevertheless a video projector based on TFT LCDs can be assembled in a relatively small box and may create new applications for largearea video displays. A configuration example of a TFT-LCD projection display is shown in Fig. 42 (Morozumi et al., 1986b). Here, three TFT LCDs are used, each one serving as a light-valve imaging device for one of the primary colors. As shown, a single halogen lamp source, whose white light is separated into three primary colors by the dichroic mirrors, is used. After passing through the three TFT LCDs, the three color images are combined by the dichroic prism and projected onto the viewing screen through a common optical system. Since each TFT LCD can be very small, the entire system can be compact and lightweight. Using special optics, the distance between the screen and the projection unit may also be short, allowing a 30-40 cm overall depth of the system for a projected image of 40-inch diagonal size. In the initial system, 1.3-inch diagonal LCDs with a 220 x 320-element poly-Si TFT array and a 300-watt halogen lamp produced a 50:l contrast ratio and a maximum brightness of 70 ft-lamberts; on a viewing screen with a gain of six. The number of pixels was subsequently increased to 440 x 480, and a contrast ratio as high as 70:l was obtained (Aruga et al., 1987). At the same time, the light source was changed to a 250-watt xenon arc lamp in order to

V i e w i n g Screen Mirror

7

7

Hal -

Ref l e c t o r Dichroic Mirror \Dichroic Prisms

FIG.42. Basic structure of color projector using three TFT LCDs: due to its simple structure, the projector is small and lightweight. (Figure 1 from Morozumi et al., 1986b. Permission for reprint, courtesy Society for Information Display.)

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obtain an increased screen brightness and higher color temperature image as well as to extend the lifetime of the lamp. With this system, an image with 300-ft-lambert brightness was obtained on a 40-inch diagonal front-projected screen having an optical gain of 19. An example of such a color image is shown by the black-and-white photograph in Fig. 43. B. Computers

At the moment, the application of liquid-crystal displays in computers is limited to portable-type units that require a flat compact panel and frequently low power consumption. For these applications, directly multiplexed TN or STN LCDs are used rather than TFT LCDs because of the relatively early stage of development of the latter displays. Present computer displays of this type are 9-12 inches in diagonal size and contain in the range of 200 x 480 to 480 x 640 pixels. Although they have either none or a limited number of grey scales, producing only monochrome images, these characteristics are adequate

FIG.43. Black-and-white photograph of a color image projected on a 40-inch screen using the TFT-LCD full-color projector: brightness is 300 ft-lamberts, and contrast ratio is 50: 1 .

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for many portable-computer applications. However, as mentioned earlier, the viewing characteristics of such displays is relatively poor, and efforts are thus being made to develop suitable active-matrix LCDs for this application. Since cost competition in this application is severe, the diode-type active-matrix displays, being probably less expensive than the TFT type, may provide sufficient improvement for these applications where strictly controlled grey scales are not necessary. Alternatively, directly mu1tiplexed ferroelectric-type LCDs, despite their lack of grey scale, may be a strong candidate in the near future for this application because of their improved contrast ratio. However, even a portable-type computer will ultimately require a flat display panel with much higher resolution, more grey levels and color, requiring the use of TFTLCD technology. Nevertheless, until TFT LCDs come into more general use for large-area wall-type color-TV applications, it is not likely that such displays will be economically competitive for portable or desk-top-type computer applications.

REMARKS IX. CONCLUDING A. Comments on the Status of Liquid-Crystal Displays Relative to Displays Based on Other Technologies During the past 15 years, direct multiplexed liquid-crystal displays not employing active-matrix elements such as TFTs have gained a dominant position among the various other types of flat-panel display devices. With the successful development of extended-area LCDs containing a large number of pixels, these panels have pioneered a new market in portable computers and word processors. In such applications (which presently can be satisfied by black-and-white images), directly multiplexed LCDs, however, are still not fully satisfactory in terms of their viewing quality, contrast ratio, and viewing angle. Although electroluminescent displays (ELDs) have the best viewing angle and contrast of the different flat-panel displays, they are also the most expensive, whereas LCDs with the lowest viewing quality have the lowest cost. Plasma display panels (PDPs), providing another alternative for these applications, are located somewhere between the ELD and LCD displays in terms of cost and viewing characteristics. Although directly multiplexed LCDs have an advantage in battery-operated applications because of their much lower power consumption compared to both PDPs and ELDs, it is expected that LCDs and PDPs will be major competitors in portable-computer applications for some time to come. To obtain improved performance in these applications, while still competing costwise with the CRT, directly multiplexed LCDs making use of the STN liquid-crystal materials or ferroelectric-

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type liquid-crystal materials are likely to come into wide use. Possibly the diode-type active-matrix LCDs may find use in this area if fabrication costs can be kept sufficiently low. In the case of TV applications,full-color capability and good grey scale are essential requirements.Here other flat-panel display technologies have serious limitations. In the case of electroluminescent displays, for example, obtaining sufficient brightness (aside from very high costs) is a serious problem. In the case of plasma display panels, problems of limited brightness and low efficiency as well as cost have not been overcome. For such applications, the TFT-controlled liquid-crystal display is the leading contender, both in terms of image quality and cost. This is especially the case for large-size TV displays where images with increased resolution are desired. In the long-term future, it is expected that computer displays will increasingly require color and greyscale capabilities.The success of the TFT LCD in television applications may thus result in its further dominance in the computer field.

B. Present Problem Areas in Thin-Film Transistor Liquid-Crystal Displays Much of the fundamental development of TFT LCDs has already occurred. Present and future problems relate mainly to questions of how to increase the size and resolution of the displays while maintaining a reasonable cost. In order to achieve an acceptable production cost for large-area TFTLCD panels, new manufacturing systems capable of handling large-area substrates with an acceptable ratio of manufacturing capacity to investment amount will have to be developed, since the throughputs of the existing thinfilm deposition, pattern-forming, and related equipment are insufficient to satisfy these requirements. In addition, problems relating to the reduction or elimination of defects must be solved. This has much to do with the specific production equipment used and the manufacturing environment involved. However, these problems may be minimized by the use of satisfactory redundancy techniques incorporated in the panel structure, where each pixel contains multiple TFTs instead of one (Ogura et al., 1986).The integration of thin-film driver circuits with the pixel TFTs on the same substrate may also reduce cost if high-yield driver circuits can be obtained, possibly making use of redundancy techniques. Since present images produced by TFT LCDs are not fully comparable to those produced by color CRTs with respect to contrast ratio, viewing angle, and grey-scale reproducibility, further development is required not only to improve the TFT characteristics but also to obtain liquid-crystal material that has a wider viewing angle and higher contrast ratio. Also color filters with

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improved chromaticity as well as backlighting systems that are highly efficient and have reduced depth are needed. In any case, since all the problems mentioned above are not associated with intrinsic limitations of the TFT LCD, it is expected that they will be solved in due time.

C. Future Expectations of Thin-Film Transistor Liquid - Crystal Displays During the next three years, TFT LCDs are expected to find use in small pocket and portable color-TV receivers, with display sizes up to about 10 inches in diagonal. The main technology employed will be amorphous Si thin films rather than polycrystalline films for the TFTs because of the relative ease of fabrication of large-area substrates with this technology using present manufacturing equipment. During this period, it is also expected that the image quality in terms of contrast ratio, viewing angle, and color purity will be continuously improved and eventually approach that of CRTs. However, since it will be difficult during this period for TFT LCDs to dominate in other applications requiring a large size and an absence of defects, such as in portable computers, directly multiplexed LCD devices, despite their limitations, will continue to be used primarily for these purposes. Within 10 years, it is expected that many of the problems mentioned above will be solved and thus enable TFT LCDs to be utilized for large-area displays up to or more than 20 inches in diagonal with a resolution as high as 1,000 lines, not only for TV but also for computer terminals. Such displays may also be used for personal applications in which a computer terminal is combined with a TV system functioning as a general-purpose color information display unit. The most advanced TFT-LCD units will have a diagonal size up to 40 inches and contain over 1,000 x 1,000 color pixel triads. It is also expected that these displays will have a contrast ratio in excess of 100: 1, a viewing cone of more than a 120" included angle, a brightness of more than 300 ft-lamberts, and a panel depth less than 4 inches, making them useful for high-definition home TV. During this period, the production of such TFT LCDs will be fully automated, and a production technique requiring no redundant elements may be established. These displays may make use of polycrystalline silicon films fabricated by low-temperature techniques such as laser-beam annealing to obtain TFTs with greatly improved characteristics, since scanning speeds and data rates much higher than the current NTSC system will be required. It is also highly likely that these display panels will be fully integrated with their drive circuits on a single substrate, minimizing the number of input leads. Although the CRT is presently considered to be the standard against which other displays are measured, within the next decade there is a distinct

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possibility that liquid-crystal displays based on thin-film transistors will not only become strong competitors to CRTs in many applications but will also displace them in a significant number of applications.

ACKNOWLEDGMENT The author would like to express great thanks to Dr. B. Kazan for his continuous encouragement and helpful suggestions in completing this article.

REFERENCES Akatsuka, M., Katoh, K., Sawada, K., and Nakayama, M. (1986). Electro-optical Properties of Super-twisted Nematic Display Obtained by Rubbing Technique (Japan Display ’86). Proceedings of the 6th International Display Research Conference, 400-403. Akiyama, M., Dohjo, M., Higuchi, T., Toeda, H., Suzuki, K., and Oana, Y. (1986). An ActiveMatrix LCD with Integrated Driver Circuits Using a-Si TFTs (Japan Display ‘86). Proceedings of the 6th International Display Research Conference, 212-215. Ah, P. M. and Pleshko, P., (1974).Scanning Limitation of Liquid Crystal Displays. I E E E Trans. Electron Devices ED-21,146-155. Aruga, S., Araki, R., Kamakura, H., Shinozaki, J., and Morozumi, S. (1987).High Resolution FullColor Video Projector with Poly-Si TFT Array Light Valves. S I D 1987 International Symposium, Digest of Technical Papers, 75-78. Ast, D. G. (1982).Materials Limitation of Amorphous Si: H Transistors. Conference Record of the 1982 International Display Research Conference, 152- 160. Baccarani, G., Ricco, B., and Spadini, G. (1978). Transport properties of pol ycrystalline silicon films, J. Appl. Phys. 49,5565-5570. Baraff, D. R., Long, J. R., MacLaurin, B. K., Miner, C. J., and Streater, R. W. (1980). The Optimization of Metal-Insulator-Metal Non-Linear Devices for Use in Multiplexed Liquid Crystal Displays. 1980 Biennial Display Research Conference, 107-109. Brody, T. P., Asars, J. A,, and Dixon, G. D. (1973).A 6 x 6 Inch 20 Lines-per-Inch Liquid-Crystal Display Panel. I E E E Trans. Electron Deuices ED-20,995-1001. Brody, T. P., Luo, F. C., Szepesi, Z. P., and Davies, D. H. (1975). A 6 x 6-in 20-lpi Electroluminescent Display Panel, IEEE Trans. Electron Deuices ED-22,739-748. Brody, T.P.(1984).The Thin Film Transistor-A Late Flowering Bloom. IEEE. Trans. Electron Devices ED-31, 1614-1628. Carlson, D. E., and Wronski, C. R. (1979). Amorphous Silicon Solar Cells. In “Amorphous Semiconductors” (M. H. Brodsky, ed.) Topics in Applied Physics 36, p. 293-294. SpringerVerlag, Berlin. Castleberry, D. E. (1979). Varistor-Controlled Liquid-Crystal Displays. Proceedings of the S l D 2015, 197-201. Chen, I., and Luo, F. C. (1981). I-V characteristics of thin-film transistors, J . Appl. Phys. 52, 3020-3026. Clark, N. A., and Lagerwall, S. T. (1980). Submicrosecond bistable electro-optic switching in liquid crystals, Appl. Phys. Lett. 36, 899-901.

78

SHINJI MOROZUMI

De Gennes, P. G. (1974).Dynamical Properties of Nematic. In “The Physics of Liquid Crystals,” pp. 151-207. Clarendon Press, Oxford. De Graaff, H. C., Huybers, M., and de Groot, J. G. (1982). Grain Boundary States and the Characteristics of Lateral Poly-Si Diodes. Solid-state Electronics 25,67-71. Depp, S . W., Juliana, A,, and Huth, B. G. (1980). Polysilicon FET Devices for Large Area Input/Output Applications. International Electron Devices Meeting, Technical Digest, 703-706. Faggin, F., and Klein, T. (1970).Silicon Gate Technology, Solid-state Electronics 13,1125-1144. Farrah, H. R., and Steinberg, R. F. (1967).Analysis of Double-Gate Thin-Film Transistor, IEEE Trans. Electron Devices ED-14,69-74. Fischer, A. G. (1971). Design Considerations for a Future Electro-luminescent TV Panel, IEEE Trans. Electron Devices ED-18, 802-804. Gooch, G. H., and Tarry, H. A. (1975).The Optical Properties of Twisted Nematic Liquid Crystal Structures with Twist Angle < 90”,J. Phys., D 8, 1575-1584. Grove, A. S . (1967) In “Physics and Technology of Semiconductor Devices,” pp. 317-333. John Wiley and Sons, Inc., New York. Heilmeier, G. H., and Zanoni, L. A. (1968a).Guest-Host Interactions in Nematic Liquid Crystals: A New Electro-Optic Effect, Appl. Phys. Lett. 13,91-92. Heilmeier, G. H., Zanoni, L. A,, and Barton, L. A. (1968b). Dynamic Scattering: A New Electrooptic Effect in Certain Classes of Nematic Liquid Crystals. Proc. IEEE. 56, 1162-1171. Hosokawa, M., Oguchi, K., Ikeda, M., Yazawa, S., and Endo, K. (1981). Dichroic Guest-Host Active Matrix Video Display, SID 1981 International Symposium, Digest of Technical Papers. 1 14- 1 15. Hotta, S., Nagata, S., Miyata, Y., Yokoyama, K., Adadachi, K., Chikamura, T., Yoshiyama, M., Nishikawa, A,, and Kawasaki, K. (1986). Full Color Multi-Gap LC-TV Display Panel Addressed by a-Si TFTs. S I D International Symposium, Digest of Technical Papers, 296-297. Howard, W. E. (1986). Active-Matrix Techniques for Displays. Proceedings of the S I D 2714 (Fourth Quarter), 313-326. Ishizu, A., Suzuki, Z., Matsumoto, T., Miki, H., Onishi, Y.,Nishimura, T., Akasaka, Y. (1985). An Active-Matrix LCD Addressed by Laser-recrystallized Poly-Si TFTs. Proceedings of the S I D 2614 (Fourth Quarter), 249-253. Juliana, A., Depp, S. W., Huth, B., and Sedgwick, T. (1982). Thin-Film Polysilicon Devices for Flat-Panel Display Circuitry. S I D 1982 International Symposium, Digest of Technical Papers, 38-39. Kamins, T. I. (1972). Field-Effects in Polycrystalline-Silicon Films. Solid-State Electronics 15, 789-799. Kamins, T. I., and Marcoux, P. J., (1980). Hydrogenation of Transistors Fabricated in Polycrystalline-Silicon Films. IEEE Electron Device Letts. ED-1, 159-16. Kaneko, E., Kawakami, H., and Hanmura, H. (1978). Liquid Crystal Television Display. Proceedings of the SID 1912 (Second Quarter), 49-54. Kawai, S., Takagi, N., Kodama, T., Asama, K., and Yanagisawa, S. (1982). Amorphous Silicon Thin-Film Transistor for Liquid Crystal Display Panel. S I D 1982 International Symposium, Digest of Technical Papers, 42-43. Kawasaki, K., Yamada, K., Watanabe, R., Mizunoya, K. (1987).High-Density Performance Black and White Supertwisted Nematic LCD. S I D 1987 International Symposium, Digest of Technical Papers, 391 -394. Kishida, S., Naruke, Y., Uchida, Y., and Matsumura, M. (1983). Theoretical Analysis of Amorphous-Silicon Field-Effect-Transistor. Japan J. Appl Phys. 22,511-517.

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

79

Lechner, B. J., Marlowe, F. J., Nester, E. O., and Tults, J. (1969). Liquid Crystal Matrix Displays. 1969 International Solid-state Circuits Conference, Digest of Technical Papers, 52- 53. Lechner, B. J., Marlowe, F. J., Nester, E. O., and Tults. J. (1971). Liquid Crystal Matrix Displays. Proc. IEEE 59, 1566-1579. Le Comber, P. G., Spear, W. E., and Ghaith, A. (1979). Amorphous-Silicon Field-Effect Device and Possible Application. Electron. Lett. 15, 179-181. Le Contellec, M., Morin, F., Richard, J., Coissard, P., Morel, M., and Bonnel, M. (1982). Amorphous and Polycrystalline Silicon TFT for Addressing Display Devices. S I D International Symposium, Digest of Technical Papers, 44-45. Lee, M. J., Judge, P. C., and Wright, S. W. (1983). Electrical Properties of CdSe Transistors Prepared by Photolithography. SID 1983 International Symposium, Digest of Technical Papers, 152-153. Levinson, J., Shepherd, F. R., Scanlon, P. J., Westwood, W. D., Este, G., and Rider, M. (1982). Conductivity behavior in polycrystalline semiconductor thin film transistors. J. Appl. Phys. 53,1193-1202. Lipton, L. T., and Koda, N. J. (1973). Liquid Crystal Matrix Display for Video Applications. Proceedings of the SID 14/4 (Fourth Quarter), 127-130. Lipton, L. T., Meyer, M. A,, and Massetti, D. 0.(1975).Liquid Crystal Television Display using a Silicon-On-Sapphire Switching Array. S I D 1975 International Symposium, Digest of Technical Papers, 78-79. Lipton, L. T., Stephens, C. P., and Lloyd, R. B. (1977). Fully Integrated MOS Liquid Crystal Video Rate Matrix Display. SID 1977 International Symposium, Digest of Technical Papers, 64-65. Luo, F. C., and Hester, W. A. (1980).Design and Fabrication of Large-Area Thin-Film Transistor Matrix Circuits for Flat-Display Panels. IEEE Trans. Electron Devices ED-27,223-230. Luo, F. C., Chen, I., and Genovese, F. C. (1981). A Thin-Film Transistor for Flat Panel Displays. IEEE Trans. Electron Devices ED-28,740-743. Luo, F. C., and Hoesly, D. (1982).Hybrid Processed TFT Matrix Circuits for Flat Display Panels. SID 1982 International Symposium, Digest of Technical Papers, 46-47. Luo, F. C., Patterson, J., Braunstein, T., and Leksell, D. (1985). A 640 x 400 CdSe TFT-LC Display Panel, S I D 198.5 International Symposium, Digest of Technical Papers, 286-288. Madan, A,, Le Comber, P. G., and Spear, W. E. (1976). Investigation of the Density of Localized States in a-Si Using the Field Effect Technique. Journal of Non-Crystalline Solids 20, 239-257. Maezawa, S., Yazawa, S., Niwa, K., Ushiki, T., Takano, T., Wakai, Y., Baba, H., Suzuki, M., and Koide, K. (1987). MIM LC-TV Using New Drive Method. S I D 1987 International Symposium, Digest of Technical Papers, 54. Malmberg, P. R., Patterson, J. G., Braunstein, T. H., Snoke, C. R., and Luo, F. C. (1986). ActiveMatrix Liquid-Crystal Display with Integrated Scanner Electronics. S I D 1986 International Symposium, Digest of Technical Papers, 28 1 - 284. Mandurah, M. M., Saraswat, K. C., and Kamins, T. I. (1979).Phosphorus doping of low pressure chemically vapour-deposited silicon film. J. Electrochem. SOC.126, 1019-1023. Matsui, M., Shiraki, Y., Katayama, Y., Shintani, A., and Maruyama, E. (1980). Polycrystallinesilicon thin-film transistors on glass. Appl. Phys. Lett. 37,936-937. Moersch, G.,Lueder, E., Kallfass, T., and Koger, K. (1984).High-Voltage TFTs for Addressing of Light Valves and EL Displays. S I D 1981 International Symposium, Digest of Technical Papers, 320-323. Morozumi, S., Oguchi, K., Yazawa, S., Kodaira, T., Ohshima, H., and Mano, T. (1983a).BjW and Color LC Video Display Addressed by Poly-Si TFTs. S I D 1983 International Symposium, Digest of Technical Papers, 156-157.

80

SHINJI MOROZUMI

Morozumi, S., Ohta, T., Araki, R., Sonehara, T., Kubota, K., Ono, Y., Nakazawa, T., and Ohara, H. (1983b). A 250 x 240 Element LCD Addressed by Lateral MIM (Japan Display ’83). Proceedings of the 3rd International Display Research Conference, 404-407. Morozumi, S., Oguchi, K., and Ohshima, H. (1984a). Latest developments in liquid crystal television displays. Opt. Eng. 23,241-246. Morozumi, S., Oguchi, K., Misawa, T., Araki, R., and Ohshima, H. (1984b). 4.25-in. and 1.51-in. B/W and Full Color LC Video Displays Addressed by Poly-Si TFTs. S l D 1984 International Symposium, Digest of Technical Papers, 316-319. Morozumi, S . (1985). Active Matrix Addressed Liquid-Crystal Displays. Conference Records of the 1985 International Display Research Conference, 9- 13. Morozumi, S., Sonehara, T., Kamakura, H., Ono, T., and Aruga, S. (1986a). LCD Full-Color Video Projector. SID 1986 International Symposium, Digest of Technical Papers, 375-378. Morozumi, S., Araki, R., Ohshima, H., Matsuo, M., Nakazawa, T., and Sato, T. (1986b). Low Temperature Processed Poly Si TFT and Its Application to Large Area LCD (Japan Display ‘86). Proceedings of the 6th International Display Research Conference, 196- 199. Moss, T. S., Burrel, G. J., and Ellis, B. (1973).In “Semiconductor Opto-Electronics,” pp. 297-300. Butterworth & Co., Ltd., London. Nagata, S., Ogawa,T., Adachi, K., Hotta, S., and Yoshiyama, M. (1985).Twisted-Nematic LiquidCrystal Full-Color Display Panel with Reduced Rotatory Dispersion. SID 1985 International Symposium, Digest of Technical Papers, 84-85. Nishimura, T., Akasaka, Y., and Nakata, H. (1982).Characteristics of TFT Fabricated in LaserRecrystallized Poly-Si for Active LC Display. SID 1982 International Symposium, Digest of Technical Papers, 36-37. Niwa, K., Maezawa, S., Suzuki, M., Takeuchi, T., and Kamikawa, T. (1984). LCTV Addressed by MIM Devices. SID 1984 lnternational Symposium, Digest of Technical Papers, 304-307. Oana, Y., Kotake, H., Mukai, N., Ide, K. (1983). Electrical Properties of Polycrystalline Silicon MOSFETs on Glass. Proceedings of the 14th Conference on Solid State Devices, Tokyo, 1982, Japan J Appl. Phys. 22 (Suppl. 22-1), 493-496. Oana, Y. (1984). A 240 x 360 Element Active Matrix LCD with Integrated Gate-Bus Drivers Using Poly-Si TFTs. S l D I984 International Symposium, Digest of Technical Papers, 312-315. Ogura, H., Kunigita, M., Suekane, M., Imaji, N., Enoki. S., Yuki, M., and Muto, R. (1986).Active Matrix Color LCD Fabricated by Using Redundancy and Repair System (Japan Display ‘86). Proceedings of the 6th International Display Research Conference, 208-2 11. Okubo, Y., Nakagiri, T., Osada, Y., Sugata, M., Kitahara, N., and Hatanaka, K. (1982). LargeScale LCDS Addressed by a-Si TFT Array. S l D 1982 lnternational Symposium, Digest o j Technical Papers, 40-4 1. Powell, M. J. (1983).Charge Trapping Instabilities in Amorphous Silicon-Silicon Nitride ThinFilm Transistors. Appl. Phys. Lett. 43,597-599. Sakai, T., Shimbo, M., Suzuki, M., Yamazaki, T., and Sakami, R. (1985).A Color LC Panel Using a Very Thin Film Transistors (V-TFT). Conference Record on the 1985 International Display Research Conference, 30-31. Sakai, T., Motte, S., Tanaka, H., Ohta, M., Takahashi, K., and Yamazaki, T. (1986). An Active Matrix-Addressed Color LCD Using VZ-TFT, Japan Display ’86. Proceedings of the 6th lnternational Display Research Conference, Paper PD-3. Sakamoto, H., Hayama, M.,Takasago, H., Sugiura,T., Yamane, K., Arai, H., Tokutomi,Y.,Ando, T., Watanabe, K., Miki, H., and Onishi, Y. (1986). A 10-Inch Diagonal Active Matrix LC Display Addressed by a-Si TFTs (Japan Display ‘86). Proceedings of 6th lnternationai Display Research Conference, PD-10. Schadt, M., and Helfrich, W. (1971). Voltage-Dependent Optical Activity of a Twisted Nematic Liquid Crystal, Appl. Phys. Lett. 18, 127-128.

ACTIVE-MATRIX THIN-FILM TRANSISTOR LIQUID-CRYSTAL DISPLAYS

81

Scheffer, T. J., Nehring, J., Kaufmann, M., Amstutz, H., Heimgartner, D., and Eglin, P. (1985). 24 x 80 Character LCD Panel Using the Supertwisted Birefringence Effect. SID 1985 International Symposium, Digest of Technical Papers 120- 123. Seto, J. Y. W. (1975).The Electrical Properties of Polycrystalline Silicon Films, J. Appl. Phys. 46, 5241- 5254. Snell, A. J., Mackenzie, K. D., Spear, W. E., and Le Comber, P. G. (1981). Application of Amorphous Silicon Field Effect Transistors in Addressable Liquid Crystal Display Panels. Appl. Phys. 24,351-362. Spear, W. E., and Le Comber, P. G. (1975). Substitutional Doping of Amorphous Silicon. Solid State Commun. 17,1193-1 196. Sugata, M., Okubo, Y., Osada, Y., Kasugayama, Y., and Nakagiri, T. (1983). A TFT-Addressed Liquid Crystal Color Display (Japan Display '83). Proceedings of the 3rd International Display Research Conference, 210-212. Suginoya, M., Kamamori, H., Terada, Y., Kato, N., and Iwasa, K. (1983). Multicolor Graphic LCD with Tri-Colored Layers Formed by Electrodeposition (Japan Display '83).Proceedings of the 3rd International Display Research Conference, 206-209. Sunata, T., Yukawa, T., Miyake, K., Matsushita, Y., Murakami, Y., Ugai, Y., Tamamura, J., and Aoki, S. (1985).A large Area, High Resolving Power Active Matrix Color LCD Addressed by a-Si TFTs. Conference Record of the 1985 International Display Research Conference, 18-23. Suzuki, K., Aoki, T., Ikeda, M., Okada, Y., Zohta, Y., and Ide, K. (1983). High-Resolution Transparent-Type a-Si TFT LCDs. SID International Symposium, Digest of Technical Papers, 146-147. Suzuki, M., Yoyama, M., Harajiri, T., Maeda, T., and Yamazaki, T. (1986). A New Active Diode Matrix LCD Using Off-Stoichiometric SiNx Layer (Japan Display '86). Proceedings of the 6th International Display Research Conference, 72-74. Suzuki, T., Hirose, M., and Osaka, Y. (1982). Influence of Gap States on Basic Characteristics of a-Si:H Thin Film Transistor, Japan J. Appl. Phys. 21, 315-311. Szydlo, N., Chartier, E., Perbet, J. N., Proust, N., Magarino, J., and Hareng M. (1983). Integrated Matrix Addressed LCD Using Amorphous Silicon Back to Back Diodes (Japan Display '83). Proceedings of the 3rd International Display Research Conference, 416-418. Takeda, M., Ogo, S., Tamura, T., Kamiura, H., Noda, H., Kawaguchi, T., Yamashita, I., Ando, D., and Kuroda, H. (1986). 12.5" LCD Addressed by a-Si TFTs Employing a Redundancy Technology (Japan Display '86). Proceedings of the 6th International Display Research Conference, 204- 201. Togashi, S., Sekiguchi, K., Tanabe, H., Yamamoto, E., Sorimachi, K., Tajima, E., Watanabe, H., and Shimizu, H. (1984). A LCTV Display Controlled by a-Si Diode Rings. SID 1984 lnternational Symposium, Digest of Technical Papers, 324-325. Togashi, S., Sekiguchi, K., Tanabe, T., Okigami, T., Okamoto, M., Sorimachi, K., Yamamoto, E., Sugiyama, O., Ishimori, S., Kikuchi, M., Suzuki, A.,Tajima, E.,and Aoyama, T. (1986).A Full Color 6.7" Diagonal LCTV Addressed by a-Si Diode Rings (Japan Display '86). Proceedings of the 6th International Display Research Conference P D 4 . Troxell, J. R., Harrington, M. I., Erskine, J. C., Dumbaugh, E. H., Fehlner, F. P., and Miller, R. A. (1986). Polycrystalline Silicon Thin-Film Transistors on a Novel 800°C Glass Substrate. IEEE Electron Device Letts. ED-7, 591-599. Ugai, Y., Murakami, Y., Tamamura, J., and Aoki, S. (1984). A 7.23-in.-Diagonal Color LCD Addressed by a-Si TFTs. SID 1984 International Symposium. Digest of Technical Papers, 308-311 Watanabe, H.,Okumura,O., Wada, H., Ito, A., Yazaki, M., Nagata, M.,Takeshita, H., Morozumi, S. (1988).Full-Color LCD with Neutralized STN (NTN). SID 1988 International Symposium, Digest of Technical Papers, 416-419. Waxman, A. (1968).Thin-film transistors don't have to be drifters. Electronics (March 18),88-93.

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Weimer, P. K., Sadasive, G., Meray-Horvath, L., and Homa, W. S. (1966).A 180-StageIntegrated Thin-Film Scan Generator. Proc. IEEE. 54,354-360. Yamasaki, T., Kawahara, Y., Motte, S., Kamamori, H., and Nakamura, J. (1982).A Liquid Crystal TV Display Panel with Drivers. SID 1982 International Symposium, Digesr of Technical Papers, 48-49. Yanagisawa,T., Sakai, K., Adachi, T., Kasahara, K., Ide, K., and Hori, H. (1981). A MOS Array with Platinum Display Electrodes for Reflective Dynamic Scattering LCDs. S I D 1981 lnternational Symposium, Digest of Technical Papers, 110-1 11. Yanagisawa, T., Kasahara, K., Okada, Y., Sakai, K., Komatsubara, Y., Fukui, I., Mukai, N., Ide, K., Matsumoto, S., and Hori, H. (1985).A 3.1-in. TFT-Addressed Color LCD. Proceedings of the S I D 26/3,213-216.

Resonators. Detectors. and Piezoelectrics JEAN-JACQUES GAGNEPAIN Laboratoire de Physique et MPtrofogie des Oscillateurs du C.N.R.S. UniversitP de Franche-Cornti-Besanron Besanron. France

I . Introduction . . . . . . . . . . . . . . . . . . . . I1. Fundamental Equations of Elasticity and Piezoelectricity . . . A. Initial and Final States. Displacements . . . . . . . . . B. Strains . . . . . . . . . . . . . . . . . . . . . C . Mechanical Forces and Stresses . . . . . . . . . . . D . Electrical Forces . . . . . . . . . . . . . . . . . E. Conservation Laws . . . . . . . . . . . . . . . . F . Equilibrium Equations in the Material State . . . . . . . I11. Material Constants . . . . . . . . . . . . . . . . . . A . Elastic Constants . . . . . . . . . . . . . . . . . B . Piezoelectric, Electroelastic and Electrostrictive Constants . . C . Dielectric Constants . . . . . . . . . . . . . . . . IV. Crystal-Lattice Anharmonicities (A Brief Review) . . . . . . A. Specific Heat . . . . . . . . . . . . . . . . . . B. Acoustic Wave Attenuation . . . . . . . . . . . . C . Heat Conductivity . . . . . . . . . . . . . . . . . D . Thermal Expansion . . . . . . . . . . . . . . . . V. The Resonator: Simple Linear Model . . . . . . . . . . A . Bulk-Acoustic-Wave Resonator . . . . . . . . . . . B. Surface-Acoustic-Wave Resonator . . . . . . . . . . V1. Nonlinear Properties . . . . . . . . . . . . . . . . . A . Propagation and Resonance of Finite-Amplitude Waves . . B. Propagation in a Prestrained Medium . . . . . . . . . VII . Sensitivities to External Perturbations and the Design of Detectors A . Temperature . . . . . . . . . . . . . . . . . . . B. Forces and Pressures . . . . . . . . . . . . . . . . C . Accelerations . . . . . . . . . . . . . . . . . . D . Electric Field . . . . . . . . . . . . . . . . . . E. Miscellaneous Detectors . . . . . . . . . . . . . . . VIII . Conclusion . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . .

. . . . .

84 85 86 87 . 87 88 89 . 92 93 94 . 95 91 . 98 100 . 100 102 102 . 103 . 103 . 108 112 . 112 . 118 . 125 125 127 129 129 131 132 132

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Copyright 0 1990 by Academic Press. Inc All rights of reproduction in any farm reserved ISBN O-I?-014677-0

84

JEAN-JACQUES GAGNEPAIN

I. INTRODUCTION

Piezoelectricity was discovered by Jacques and Pierre Curie (1 880). This new effect was presented as the property of crystals, with particular symmetry rules, to develop electric charges on their surface when squeezed or pulled by mechanical forces. This was the direct piezoelectric effect. The converse effect was reported by Lippman (1881) soon after and verified by the Curie brothers, but it was only during World War I that Langevin (1918) applied the piezoelectric effect to the emission and detection of underwater sound waves using large quartz crystal plates. This was the very beginning of underwater acoustics. The development of resonators started with the works of Nicholson (1919)and Cady (1921),who showed how it was possible to drive electrically a piezoelectric crystal (the first experiments were made by using plates of Rochelle Salt and quartz crystals) near its mechanical resonance frequencies. Cady demonstrated that such a resonator could be used for controlling the frequency of an oscillator. Frequency control was born. The vibrations of the piezoelectric crystals near their resonance frequencies were represented by simple equivalent electrical circuits by Van Dyke (1925), Dye (1926), and Mason (1943). These circuits were applied to transducers, oscillators, and filters. An important milestone was also the use of a quartz oscillator for stabilizing the frequency of a radio transmitter (around 1926). New piezoelectric materials were needed. If quartz is one of the oldest and still today one of the most widely used, materials with a high electromechanical coupling factor were developed. Ammonium dihydrogen phosphate (ADP) and piezoelectric ferroelectrics appeared during the 1940s. In the early 1950s, the important discovery of the piezoceramic lead zirconate titanate (PZT) was made (Jaffe et al., 1971). Today piezoceramics are still very important for transducer applications. Single crystals, also with high coupling factors, were developed during the 1960s (for example, lithium tantalate, and lithium niobate). And more recently, research has started on the synthesis of aluminum phosphate (berlinite). Even semiconductors, when they are piezoelectric like gallium arsenide, can combine electronics and acoustics on the same substrate. Alternatively, AIN or ZnO piezoelectric thin films can be used on silicon substrates. Quasiamorphic materials like polymers (PVDF) can be made piezoelectric after mechanical and electrical polarization. It is important to notice that anisotropy is the key property of all these materials (isotropic crystals cannot be piezoelectric, and a sufficient lack of symmetry is necessary). This anisotropy makes it possible to control the characteristics of devices by choosing appropriate orientations of the material. Since the applications of the piezoresonator, this technique has been used to reduce the sensitivity of the devices to different physical quantities. Great efforts have been made to compensate the temperature dependence,

RESONATORS, DETECTORS, AND PIEZOELECTRICS

85

leading to various quartz crystal cuts (AT, BT, CT, DT, FT, GT, etc., and more recently to the SC-cut). This last cut simultaneously compensates static and dynamic temperature sensitivities (the dynamic temperature sensitivity being related to the stress sensitivity). Similar studies have been made, and are still in progress, on the compensation of changes due to acceleration, stress, electric field, etc. Since the early works of the Curies, Langevin, Cady, and many others, the application of piezoelectrics has spread in many different fields. Piezoelectric devices find applications in ultrasonic emission and detection, nondestructive testing, microscopes, frequency control and signal processing, acoustoelectronic and acousto-optic components, physical and medical acoustics. In frequency control, efforts are made to reduce the sensitivities of piezoelectric resonators to temperature, force, pressure, acceleration, etc.; by contrast, it is also possible to increase the sensitivity selectively with respect to a given physical quantity for applications using the resonator as a sensor. Piezoresonators are widely used in consumer products, like wrist watches, TV and radio sets, games, and in communication and military systems (for example, in frequency standards, radars, sonars, etc.). The present chapter does not pretend to cover exhaustively all aspects of piezoelectricity, and the focus will be essentially on resonators, their properties, and their various applications. Among the variety of piezoelectric materials, monocrystals and in particular quartz, lithium niobate, and lithium tantalate will be presented in detail. Particular emphasis will be given to nonlinear effects, because the characteristics and the performances of the devices today are mainly limited by the nonlinearities of the crystals. Nonlinearities, as it will be shown, are at the origin of some of the most fundamental properties of the materials. 11. FUNDAMENTAL EQUATIONS OF ELASTICITY AND PIEZOELECTRICITY

In the approximation of infinitesimal deformations, the general equations reduce to their linear form, and the mechanical constitutive equations correspond to Hooke’s law. There is no distinction made between the coordinate system before and after deformation. But for finite-amplitude deformations, the exact equations must be considered, which are no longer linear but involve nonlinearities of two different kinds. The solid itself does not follow linear laws, because of the nature of the interatomic forces and potentials. These nonlinear characteristics are at the origin of anharmonicities in solids, which define basic properties such as acoustic attenuation, thermal expansion, and finite-heat conductivity. In macroscopic models, the same anharmonicities appear as fundamental constants of higher order, and contribute to the nonlinear terms of the

86

JEAN-JACQUES GAGNEPAIN

constitutive equations. These kinds of nonlinearity depend on the crystallographic orientation and can be called intrinsic nonlinearities. On the other hand, any deformation modifies the volume and the surface of a solid. As a consequence, the specific mass, the stresses, and the strains are changed, and the equilibrium and constitutive equations again become nonlinear. This second kind of nonlinearity is the same for all materials, and it can be called an induced or geometric nonlinearity. The two kinds of nonlinearities have the same order of magnitude, and both contribute to the nonlinear behaviour of a solid. The general equations of elasticity and piezoelectricity will now be summarized. More details can be found in the works of Thurston (1974)for the elastic and thermoelastic parts, of Tiersten (1971) for the general thermoelectroelastic problem, and of Nelson (1979). Solving these equations and applying them to the nonlinear propagation of waves or the propagation in prestrained media will be the subjects of the next sections, with the applications to resonators and detectors. A . Initial and Final States, Displacements

In an orthogonal reference system (Fig. 1) let a, be the coordinates of a material point M of the solid in the initial state, i.e., at rest. Under deformation, the point undergoes a displacement and takes a new position M' with coordinates x j , denoting the final state. Initial and final coordinate systems are also respectively known as material and spatial, or Lagrangian and Eulerian coordinate systems. The components of the mechanical displacement are noted

FIG.1. Coordinates before and after deformation.

RESONATORS, DETECTORS, AND PIEZOELECTRICS

87

The instantaneous velocity of a particule is 0.

=

-.dxj dt

B. Strains Let dl, and dl be the distance between the points M ( a i ) and P(a, + da,) before deformation, and M'(xj) and P'(xj dxj) after deformation

+

dlo = daidai,

dl

= dxjdxj.

(3)

The strain tensor qij is defined as

d12 - d l i = 2qijdaidaj,

(4)

which by means of the relation dxj = (axj/aa,)da,can be written

By substituting Eq. (1) into (5) the final form is obtained:

au. +au. auk au q , , = 1- L L+-L 2 aai daj aai aaj

(

1.

(6)

It must be noticed that this exact relation is nonlinear, due to the quadratic term (auk,/aai)(auk/aaj), a term which is neglected in the approximation of infinitesimal deformations. This strain expression is given with respect to the material coordinates ai. A similar expression could be established with respect to the final coordinates x j by usingda, = (aai/dxj)dxj,leading to the strains eij,

In the linear approximation, the two strains qij and eijbecome identical and are noted

C . Mechanical Forces and Stresses The solid can be subject to internal and external forces that are surface and body forces, the latter resulting from the application of an external quasistatic, electrical field. One considers in the usual manner an elementary tetrahedron (Fig. 2) with surface element dS(ABC) of normal unit component ni submitted to surface force (per unit area) Qj.

88

JEAN-JACQUES GAGNEPAIN +

x3

X1

FIG.2. Tetrahedron with surface dS ( A B C )of unit normal n submitted to a surface force Q,

The internal stresses acting on the tetrahedron are denoted by T j , where refers to the j-component of the stress vector applied to the surface with normal unit parallel to the i-axis. The static equilibrium condition yields Q. J = n.T.. I U

(9)

It can be shown that this relation is true in general, even in the presence of body forces (Thurston, 1964). Relation (9)is written in the final state of the solid. Stresses pi,. in the initial state are defined similarly. Let dAF and dAi be the components of the elementary surfaces dS, and dS before and after deformations, Obviously, TjdAi= ejdAP.

(10)

D. Electrical Forces Following Tiersten (197l), the electroelastic solid is considered as an electronic charge continuum coupled to the elastic continuum. The lattice continuum is assumed to have a positive charge density, and the electronic continuum a negative one. Relative motions of the two continua create electric dipoles. Each elementary volume element is submitted to an electric body force and a body couple C , following

C =8

h

Ei.

pi is the dipole density and Ej the quasistatic Maxwell electric field, which

RESONATORS, DETECTORS, AND PIEZOELECTRICS

derives from the electric potential

89

4,

E. = --. a4

axj

J

It will be useful to introduce the Maxwell stress tensor T ; ,

+

TE = &oEiEj &Ej - 4 ~ ~ E ~ E k 6 ~ ~ ,

(13)

and the electric displacement Di, Di = EO&+

c,

(14)

with tobeing the permittivity of the vacuum.

E. Conservation Laws Four basic conditions, known as the conservation laws, state that the mass of a solid remains constant, the rate of change of the momentum equals the resultant force, the rate of change of the angular momentum equals the resultant couple, and the rate of change of energy equals the external work done (mechanical and nonmechanical) and, in addition, the heat exchange. The conservation laws are established using the integral form. By considering an arbitrary element of volume (and surface), the integral forms are transformed into a local form (valid at every point of the solid), with the conditions at the surfaces of discontinuity being associated. Only the main results are given here. Details of the transformation and extensions to generalized discontinuities and interfaces can be found in various works (Thurston, 1974; Planat, 1984; Daher, 1987). 1. Conservation of the Mass

Let dVo and dV be the volume of a solid with mass dM before and after deformation, po and p the corresponding specific masses. Conservation of the mass reads podVo = p d V = dM = cte.

(15)

Introducing the Jacobian matrix of the deformation with determinant J,

Eq. (15) is written PJ

= Po.

(17)

90

JEAN-JACQUES GAGNEPAIN

The integral form corresponds to

which, after transformation, leads to the local form generally called the equation of continuity

dp avi - + p= 0. dt axi 2. Conservation of the Linear Momentum The rate of change of the linear momentum equals the sum of the surface and body forces acting on and in the solid

Q a E j / d x i )correspond to the electrical forces, and Fj are the other body forces (gravitational forces, for instance). Using Eq. (9) in (19) and applying the divergence theorem gives the local form, called the equilibrium equation

in the volume. And n,(Gj

+ TFj)= 0

(22)

on the surface, in the simpler case of a free-of-forces limiting surface. 3. Conservation of the Angular Momentum

The rate of change of the angular momentum equals the sum of the torques

=

d j v ( x j A pvj)dl.i

After transformation, the local form gives the symmetry property of the stress tensor.

Gi - T k = EiPk

- Eke.

(24)

RESONATORS, DETECTORS, AND PIEZOELECTRICS

91

This shows that in a general electroelastic solid, the stress tensor is not symmetrical. The condition of symmetry is verified only in a pure elastic medium, or in the linear approximation, since the right-hand side of Eq. (24) is nonlinear. 4. Conseruation of the Energy

The rate of change of the total energy (sum of the kinetic and internal energies) equals the rate of working of the forces and the heat exchange.

U is the internal energy per unit mass; QkUk and FkUk represent the rate of working of the surface and body forces. The electric forces are included in the stress D =

dE. dP. cAui axj + E idtL ,

and nkqkis the thermal energy flow. The local form of Eq. (25) is obtained by applying the mass and linear momentum conservation laws and the divergence theorem in Eq. (25). This yields

where 0 is the temperature and q the entropy per unit mass. The same conservation equation can be expressed in terms of the electric field and of the temperature (rather than polarisation and entropy) by introducing the enthalpy x

x = u - '10 E i 4 --,

P

This leads to

Considering axj/aam,Ei,and 0 as independent variables, and therefore

92

JEAN-JACQUES GAGNEPAIN

x = x (axj/da,.Ei&), then (30) Identifying Eqs. (29) and (30) gives the constitutive equations T .= p

ax

axi

a(axj/aa,)

z’

(3 1)

p. = - p - 82

(32)

ax q = --

(33)

aEi’

ae’

It will be more convenient to express the energy function x in terms of the strain and electric field given in the initial reference system. By using Eq. (5) for the strain and the transformation

a4 Wk -- --

auk

=

ax, _ _84 _ __ ax, aak

= -E

ax, auk

(34)

for the electric field, the constitutive equations become T.. = p

ax. ax. ax axi ax l A -+ p-Ej-, aa, da, dqmk dam aW,

ax p. = -p- ax. __ aa, dw,’ ax

q = --

ae’

(35) (36) (37)

F. Equilibrium Equations in the Material State The mechanical equilibrium equation [Eq. (21)] is written with respect to the material coordinates by using the transformation (dldx,) = (aak/ax,)(a/aak) and po/p = J. Thus,

with the boundary condition at the free surface N k P kj

= 0,

(39)

where P k j is the stress tensor in the initial state (previously introduced for its

93

RESONATORS, DETECTORS, AND PIEZOELECTRICS

mechanical part by Eq. (10)).

and

correspond to the body forces 'Fj=JFj

In a similar way, one can introduce the material electric displacement

the electric equilibrium equation

in the absence of free charges in the volume, and the boundary conditions Ag9; - 9;) = 0,

(43)

(4+ - $-) = 0

(44)

on the surface. Equation (43) assumes that there are no electric charges on the surface. Such a condition is arbitrary, but was useful for solving the problem of the propagation of a surface acoustic wave on a piezoelectric and semiconductor substrate, because without this assumption, one boundary condition would be missing. The problem was finally solved by Ancona and Tiersten (1980; 1983) by considering an exact model of the charge distribution near the interface of the solid, and more recently by Daher and Maugin (1987). 111. MATERIAL CONSTANTS

The properties of a particular solid are defined in the expression of its internal energy. For an electroelastic medium, the internal energy can be given as a series expansion of the mechanical strains and electric fields, as follows.

94

JEAN-JACQUES GAGNEPAIN

The thermal terms have been omitted in this expression. The symbols cijkr, represent the second-, third-, and fourth-order elastic constants, respectively. In this definition, the order corresponds to the power of the corresponding term in the energy expansion. Therefore, second-order terms for the energy lead to linear relations in the constitutive equations. Nonlinearities begin with the third-order terms. The symbols, , ,& cmnpare the secondand third-order dielectric constants, and emijare the regular second-order piezoelectric constants. Finally, and correspond to nonlinear thirdorder piezoconstants. They are known as electroelastic and electrostrictive constants, respectively, with the latter ones occurring even in nonpiezoelectric media. Among the large family of piezoelectric materials, which can be classified as monocrystals, ceramics, polymers, and others, only the most widely used monocrystals will be examined here (quartz, lithium niobate, and lithium tantalate). Quartz has been studied intensively, but knowledge of its constants is still incomplete, and even fewer constants are known for the other crystals. Therefore, in this section only the constants of quartz will be presented in detail, and general comments will be made for the other crystals and materials. Almost all values of the constants that have been measured can be found in the Landolt-Bornstein (1979) tables. Cijklmn, Cijklmnpq

A . Elastic Constants

The values of the second-order elastic constants are well known and are available in the form of the compliance or stiffness constants, defined at constant electric field or constant electric displacement. They have been measured for most piezoelectric materials (Landolt-Bornstein, 1979). TABLE I VALUES

14TH INDEPENDENT THIRD-ORDER FUNDAMENTAL OF QUARTZ (in 10'' N/m2)." ELASTIC CONSTANTS

OF THE

Coeff.

Value

CIII

-2.10 - 3.45 +0.12 - 1.63 - 2.94 -0.15 -3.12

~

c112 113

CI,, cl23 124 c133

Thurston et al., 1966

Standard error

Coeff.

Value

Standard error

~

~

0.07 0.06 0.06 0.05 0.05 0.04 0.07

c 1 3 4

+0.02

c144

- 1.34

CIS5 C222

- 2.00

c333

- 3.32 -8.15

c344

-1.10

c 4 4 4

-2.76

0.04 0.07 0.08 0.08 0.18 0.07 0.17

RESONATORS, DETECTORS, AND PIEZOELECTRICS

95

The third-order elastic constants of quartz have been measured by Thurston et a/. (1966).There are 31 nonzero third-order constants, and among them, 14 are independent. The values of the 14 independent constants are given in Table I. These values constitute the only complete set available. But confidence in these values is high because of the good agreement generally observed between calculations and measurements of the sensitivities of resonators, for example, to accelerations, forces, pressures, etc. The third-order constants have also been measured for many materials belonging to cubic, trigonal, and tetragonal crystallographic classes. The values can also be found in the Landolt-Bornstein (1979) tables. But the fourth-order elastic constants are almost completely unknown. For quartz, only c6666 (Smythe, 1974),cllll, c3333(Fowles, 1967), and some of the compliance constants (Gagnepain and Besson, 1975) have been measured. B. Piezoelectric, Eiectroelastic, and Eiectrostrictive Constants

The second-order piezoelectric constants are known for most of the piezoelectrics.In the third-order, two different kinds of constants appear in the series expansion of the energy function. The electroelastic constants are denoted by and couple one component of the electric field with two components of the strain tensor, corresponding to the energy term (1/2) wrnqUqk+In the constitutive equation, the strain derivative of this quantity gives the stress tensor q j

OC em.ijklWmqkl.

(46)

Therefore, the electroelastic effect appears as a nonlinear coupling between electric fields and mechanical strains. If, for instance, W, is a static quantity denoted by W,,and qj and qkl are dynamic quantities (Ej and &), then relation (46) becomes

which represents a linearized form of the stress-strain relation. In that case, (em.ijklWm) is equivalent to a correcting term for some of the second-order elastic constants. The electroelastic effect induces therefore a direct change of the elastic constants due to the application of a DC electric field. The electrostrictive constants are denoted by and correspond in the energy function to the coupling of two electric field components with one strain component in the term (1/2) W, Wnqij. After derivation with respect to strain, it follows that Tj

emn.ijWmWn,

(48)

96

JEAN-JACQUES GAGNEPAIN

which is a stress component proportional to a quadratic form of the electric field. This property, called electrostriction, can be observed in all materials, even in materials that are not piezoelectric. The electroelastic effect in quartz has been studied by Hruska (1977, 1978a,b), who evaluated the values of linear combinations of electroelastic constants. Complete sets of the eight independent constants (there are 23 nonzero constants) have been determined by different authors. Kusters (1970) and Brendel(1983a,b; 1984) used frequency measurements of resonators as a function of an applied DC field. Reider et al. (1982).Kittinger et al. (1986),and Kittinger and Tichy (1987)determined the same constants with a pulse-echo method. The values obtained by these authors are given in Table 11. Large discrepancies are observed between the values of these different authors. This was noted by Hruska (1986) and Hruska and Brendel (1987), TABLE 11

ELECTROELASTIC CONSTANTS OF QUARTZ CRYSTAL (INC/m2) IS USED IN THIS TABLE). (THE SINGLE-SUBSCRIPT NOTATION

e1.11 e1.13 e1.14 e1.22 e1.24

e1.34 e1.44

e3.15

E1.24 E1.44

E3.15

Kusters (1970)

Brendel (1984)

Hruska (1977)

Hurska Brendel (1987)

Kittinger et al. (1986)

Reider et a/. (1982)

- 2.91 -49.05 - 28.81 - 114.76 -85.49 2.12 51.71 10.12

- 2.73 - 12 33.4 3.05 34.6 50.5 -0.6 24.9

-- 2.96

- 2.86

-2.18 0.5 -0.28 1.1 -0.78 - 1.63 -0.05 0.9

2.61 0.49 0.39 - 1.47 1.13 1.35 -0.15 - 0.64

- 0.68 - 0.90 -0.88 0.90 1.01

-0.42 - 1.99 -2.41 1.02 0.72

RESONATORS, DETECTORS, AND PIEZOELECTRICS

97

who indicated that only linear combinations of the electroelastic constants can be presently determined (shown in Table 11), and that there is no discrepancy between the authors concerning the values of these combinations. The electrostrictive constants of quartz were also evaluated by Kittinger et al. (1986) using the pulse-echo method. Their values are given in Table 111. Lithium niobate and lithium tantalate crystals have high electromechanical coupling factors and are used in particular for wide-band filters or acoustic convolvers. In the convolver, large nonlinear constants are also needed for increasing the efficiency (Ganguly and Davis, 1980). The electroelastic and electrostrictive constants of LiNbO, were evaluated by Thomson and Quate (1971), Koborov and Lyamov (1975), and for LiNbO,, LiTaO, by Agishev et al. (1979), Chizhikov et al. (1982), and Zelenka (1982). It must be noticed that not all these constants are homogeneous, some are material constants, some others are effective constants. They are also not all defined with respect to the same reference coordinate system. C. Dielectric Constants

Crystal quartz has two independent second-order dielectric constants, one of third order and four of fourth order. All have been measured (Gagnepain and Besson, 1975). The third-order constants of lithium niobate are also available. They have been evaluated by Ganguly and Davis (1980) from electro-optic coefficients measured in the light-frequency range. Electrostrictive and elasto-optic constants are equivalent tensors at low and very high frequencies, respectively (DC and R F for the first, light frequencies for the second). Similarly, the nonlinear dielectric and the electrooptic constants also are equivalent. A rigorous presentation of these different constants must take into account the differences that are due to definitions at constant strains or at constant stresses (Mason, 1966). A similar remark applies to the elasto-optic constants defined at constant electric field or electric displacement. These distinctions will not been made in this short presentation.

TABLE 111 ELECTROSTRICTIVE CONSTANTS OF QUARTZ CRYSTAL (INFlm)." e11.1

e11.2

-4.8

1.1

Kittinger et al., 1986

e11.3

e11.4

10.2

- 2.2

e33.1

e33.3

e13.5

0.8

- 3.9

-4.1

el,,

1.3

98

JEAN-JACQUES GAGNEPAIN

IV. CRYSTAL-LATTICE ANHARMONICITIES (A BRIEF REVIEW) The vibrations of the atoms of a crystal lattice, in the microscopic model, are represented in terms of normal modes, which correspond to collective movements of the atoms. The energy stored in each mode follows the rules of quantum mechanics and is given by a number of phonons, a phonon being an energy quantum. In the harmonic approximation, the different modes are not coupled and do not exchange energy. The concept of specificheat is described by this linear model. But on account of the nonlinear nature of the interatomic forces, interactions and energy exchanges take place between the different modes. This nonlinear behaviour is the origin of a variety of physical phenomena in solids, known in macroscopic models as acoustic attenuation, finite-heat conductivity, and thermal expansion, In addition, the higher-order material constants are also directly related to the lattice anharmonicities. A crystal lattice can be represented by a three-dimensional periodic array of atoms. For a review of the general concepts, it is sufficient to consider just a one-dimensional array (or chain). In the simplest case, only identical atoms are considered, with mass m and distance a between adjacent atoms. Let N be the number of atoms per chain (Fig. 3). The interaction potential between two atoms as a function of their distance a is represented in Fig. 4. The mean distance a, corresponds to an equilibrium position. The corresponding interatomic force is given in Fig. 5. Let u, be the displacement of the nth atom with respect to its equilibrium position. Considering only the interaction between the nearest atoms with force F in the linear approximation, the dynamical equation reads

mi, = F(u,+ - 2u, and the corresponding interaction energy is

+ u,- 1),

(49)

Considering a travelling wave with frequency w and wave number k, the dispersion relation obtained from Eq. (49) is

4F . 2 k a 2'

w; =-sin m n-1

n

- - un-1

un

Un+l

FIG.3. Chain of atoms with mass M, and distance a.

RESONATORS, DETECTORS, AND PIEZOELECTRICS

99

distance between atoms

FIG.4. Interatomicpotential (exact:-;

quadratic approximation:-------).

For a three-dimensional lattice, there are three dispersion relations corresponding to the longitudinal and the two transverse waves (called acoustic branches). In the case of a chain composed of several species of atoms, additional dispersion curves appear at higher frequencies corresponding to the optical branches. Relation (49) represents a set of N coupled equations. This system can be transformed into N uncoupled equations by introducing the normal coordinate Q k e following the transformation

and the interaction energy has the new form

The symbol * represents the complex conjugate, and &(t) = dQk(t)/dt.

8 8 + .-

t

/ /

U

E

s e s.-E FIG.5. Interatomic force (exact:-;linear

distance between atoms

approximation:----------).

100

JEAN-JACQUES GAGNEPAIN

According to quantum mechanics, the creation and annihilation operators

a:

= (2hok)-”2[04Qt - i&],

a,

= (2hok)-”2[okQk

+ @t],

(54) (55)

give the well-known expression for the Hamiltonian H , ,

where h is the Planck constant; hwk represents a quantum of energy (a phonon) in mode k with frequency mk. The total mean energy can then be written k

nk is the mean number of phonons stored in mode k. The summation is performed over all the normal modes of the lattice. A. Specijic Heat

Specific heat is defined as the temperature derivative of the total mean energy per unit volume. The mean number of phonons nk follows the BoseEinstein distribution nk = Cehak/krrT

-

wl,

(58)

where kB is the Boltzmann constant and T the absolute temperature. Therefore, the specific heat is

where I/ is the total volume of the crystal. A more precise approach has to go beyond the harmonic approximation and to consider higher-order terms in the atomic displacements. These anharmonicities lead to interactions between phonons. Details can be found in the works of Klemens (1 95 l), Maradudin (1962), and Maris (197 1). B. Acoustic Wave Attenuation

Two cases must be distinguished, corresponding to low and high temperatures. In the Landau-Rumer theory (1937), the interactions are represented by means of a higher-order Hamiltonian composed of products of the creation and annihilation operators. Thus, for the three-phonon interaction processes,

RESONATORS, DETECTORS, AND PIEZOELECTRICS

101

the interaction energy term is

H, =

1 H(k, k’, k”)uluk,u,,!+ other combinations.

kk’k”

(60)

The interactions must verify the energy conservation law

h a , = ha,.

+ hok.,.

(61)

The quasimomentum is conserved (normal processes) or not (umklapp processes) following the law

k = k’

+ k” + -,2nm U

where m is an integer. If Nk is the number of phonons in mode k when not in equilibrium (nk is the number when in equilibrium), collisions (that is, nonlinear interactions between modes) will force mode k back to equilibrium, with a relaxation time t(k) given by

A sound wave is a beam of low-energy phonons with frequency R, with their number being largely in excess with respect to the equilibrium number. On account of the uncertainty principle, the finite lifetime of a phonon makes its energy uncertain by h/z. Therefore, the Landau- Rumer method should be valid when h / t << hQ, or QT >> 1. This corresponds to a high-frequency sound wave or to thermal phonons with large lifetimes, i.e., when the temperature is low. A semiclassical approach due to Akhieser (1939) is valid in the limit hR << k,T, when the phonon mean free path is smaller than the sound wavelength. This condition is verified at high temperatures. In this theory, the sound wave is treated macroscopically, and the anharmonicities are introduced by stating that the frequency akof a phonon depends upon the state of strains of the crystal. The acoustic wave attenuation is due to the exchange of energy, with the heat reservoir constituted by the cloud of thermal phonons. On average, the exchange corresponds to a loss of energy of the sound wave, with the attenuation factor (Maris, 1971)

where so is the sound-wave mean phase velocity and po the crystal specific mass.

102

JEAN-JACQUES GAGNEPAIN

The Griineisen parameter frequency

Yk

is the strain derivative of the phonon

which refers to a phonon of mode k perturbed by the acoustic wave of polarization e i ( K ) and wave vector K j ; kj is a unit vector of direction K j . In Eq. (641,

(x>= k

Xw:nk(nk

+

/T "k2nk(nk +

(661

has been used. C. Heat Conductivity

Heat diffusion is another phenomenon due to a redistribution of phonons between different modes of the lattice (without interactions, heat would not diffuse but propagate with the velocity of the acoustic wave). The heat flow in a given direction i is

where u,(k)is the phonon group velocity. The difference ANk = Nk - nk

(68)

is calculated with the Boltzmann transport equation, and after some calculation, the thermal conductivity coefficient takes the simpler form Kij

=C(ZU~U~),

(69)

where C is the specific heat, and the averaging ( ) has the form given by Eq. (66). D. Thermal Expansion

Thermal expansion has its origin in the same phenomenon. The free energy A of the crystal is composed of the elastic deformation energy and the thermal phonon energy. The derivative with respect to strain of the free energy, at constant temperature gives the thermodynamic tension, and the thermal expansion coefficient aydis obtained by taking the derivative with respect to temperature at constant tension (Maradudin, 1962).

RESONATORS, DETECTORS, AND PIEZOELECTRICS

103

caPydare the second-order elastic constants, and

is involved in the definition of the Griineisen constant of Eq. (65). These results show that acoustic thermal conductivity, thermal expansion, attenuation, and related velocity (or frequency) shifts all have their origin in the crystal-lattice anharmonicities. The microscopic theory relates these phenomena, which generally are considered as independent in the linearized macroscopic approach. In this way, a connection can be made between microscopic and macroscopic descriptions; and, for instance, the Griineisen constant can be related to the third-order elastic constants (Briigger, 1965).

V. THERESONATOR: SIMPLELINEARMODEL An ultrasonic resonator is a device that stores energy by means of standing waves created by a superposition of incident and reflected waves between two reflectors. A maximum of energy is stored when conditions of synchronism are verified between the waves travelling in the two directions; this corresponds to a condition of resonance. Since their original invention, these devices have found many applications as transducers for emitting and receiving ultrasonic waves. They are also used as narrow- or wide-band filters. In oscillators they control the frequency. Or, when sensitive to a physics quantity, they are used as sensors and detectors. In this section, two kinds of resonators will be described: bulk-acoustic-wave (BAW) and surface-acoustic-wave (SAW) resonators. A. Bulk-Acoustic- Wave Resonator

The simplest model corresponds to an elastic and piezoelectric medium limited by two parallel free surfaces, with a distance 2h between the two free surfaces and with infinite lateral dimension, as shown in Fig. 6. The two planes are electric equipotentials, and a voltage 4 = 4,e'"' is applied between them. Let be the normal to the planes and A$ its director cosines. The variable coordinate along t axis will be s. Combining the equilibrium and constitutive equations reduced to their linear terms gives POEj

= cijkIuk.li

emklUk.lm

+ enij$,.ni,

- Emn4,mn = 0,

(72)

(73)

104

JEAN-JACQUES GAGNEPAIN a3

I

a1

FIG.6. Resonator with thickness 2h and infinite lateral sizes.

with

4 ' at 4 = +AP'

s=

2

+h.

(75)

Let A, and ly) be the three eigenvalues (r = 1,2,3)and the three eigenvector components of the system (CijklNifl

- n 6 j k ) l j = 0.

(76)

After introduction of the curvilinear coordinate s=ya,,

(77)

and the resultant polarization

u, = p1 u I'. the system of Eqs. (72) to (74) is transformed into PO f i r

= ~r U , s s

+ ~rb,ss,

YrKss -4?ss

ArUr,,

+ yr4,,= 0

= 07

at s = fh.

This system has been written in a new coordinate system composed of the three orthogonal eigenvectors, and spatial derivatives are performed with respect to s, with the notation alas = ,s. Now the equations of the three waves (r = 1,2,3) are uncoupled, and the subscript r can be omitted in the following.

RESONATORS, DETECTORS, AND PIEZOELECTRICS

105

The coefficients 2, y, and E read 2 = cijk.&filjlk,

(82)

y = enijNiNnlj,

(83)

= E,,

N, N, .

(84) Integrating Eq. (80) gives the electrical potential, and substitution of the potential into the boundary condition (81) leads to a system that for plane waves can be satisfied only by an antisymmetrical mode solution (this means that a symmetrical mode cannot be piezoelectrically driven). The resonance is given by the determinant of the boundary condition system of equations, which yields the transcendental equation E

uh

- = K’tg-,

V

oh V

where K is the electromechanicalcoupling factor,

and AD is the stiffened eigenvalue

LD = 1 + y 2 / E . The approximate solutions of Eq. (85) are

p is an integer and V, is the wave velocity

v; = P / p , . The normal component on the surfaces of the electric displacement corresponds to the charge density. The electric current through the resonator is obtained by taking the time derivative of the electric charge integrated over the surface area A of the electrodes. This follows

I = -jwq5,-

EA

2h

oh K2Q-

1-

V wh wh K2tg- - -

v

*

v

The first term in Eq. (90) corresponds to the current through the static capacitor Co.The second one corresponds to the motional admittance and contains the resonance ( I = 03) and antiresonance ( I = 0) frequencies. Cal-

106

JEAN-JACQUES GAGNEPAIN

culation of the impedance gives the equivalent electrical circuit represented in Fig. 7. The motional inductance and capacitance are denoted by L1 and C,. The previous model does not take into account the internal acoustic losses of the material. But these acoustic losses are represented in the equivalent circuit by the motional resistor R , . The different motional parameters are given by the relations

poh3 L --, - y2A

'

TZ

R, =

4Ay2 1 h(2p +

2 D

+ q2

n2hq(2p 4yZA

co

(93)

'

&A =z

(94)

+

for a resonator driven on an harmonic mode of odd rank ( 2 p 1); q is the effective attenuation coefficient introduced by the complex elastic constant c ijkl * - Cijkl

+jWijki

(95)

and q = qijkl&Nlljlk*

(96)

The quality factor can be defined from the (3 dB) bandwidth, or from the ratio of the motional inductance impedance on the motional resistance; this yields

co

FIG.7. Resonator-equivalentcircuit for frequencies near the resonance and antiresonance conditions.

RESONATORS, DETECTORS, AND PIEZOELECTRICS

i 07

Energy

4

I

(a)

R

R (b)

FIG. 8. (a) Plano-convex shape for a thickness shear resonator; (b) Energy distribution.

High Qs with narrow bandwidth will be needed, for instance, in stable oscillators; by contrast low Q s with large bandwidth are necessary for ultrasonic emission and detection. In fact, the Q-factor is affected also by the losses due to the coupling of the resonator vibration with the mounting structure. In thickness shear resonators, which are the most widely used for high Q's, coupling with the mounting supports is reduced by means of a plano-convex circular crystal plate, which behaves as an acoustic lens and traps the wave energy near the center, as shown in Fig. 8. The Q-factor can also be improved by means of nonadherent electrodes (Besson, 1976). When the Q-factor limit is only due to the material losses, the product Qofo = AD/2nq is a constant for a given material with a given cyrstallographic orientation. Values are presented in Table IV for some of the piezoelectrics and most common cuts. TABLE IV

.

FOR DIFFERENT PIEZOELECTRIC MEANVALUESOF THE Qo fo PRODUCT FOR DIFFERENT CRYSTALLOGRAPHIC ORIENTATIONS AND CRYSTALS, VIBRATION MODES.

Material

Qo fo product

quartz AT (C mode) quartz BT (B mode) quartz SC (C mode) LiTa03 doubly rotated AIPO,, Y AIPO,, X C mode

1.3. 1013 2.4. 1013 1.4. 1013

Warner, 1960 Ballato, 1977 Kroupa, 1988

1.8 * loL2

Detaint and LanGon, 1976

2 2 * 10'2

Dumas et al., 1987 evaluated from Narayanan et al., 1984

9

~8

- loLz

From

108

JEAN-JACQUES GAGNEPAIN

The previous model corresponds to the thickness modes of a plate with infinite lateral size and driven with an electric field perpendicular to the plate. Many different modes and different driving fields have been studied: thickness modes with lateral driving fields, extensional bars, torsional plates and bars, face-shear plates, flexural plates and bars. A review of these different modes has been given by Meeker (1985). The extension to two- and three-dimensional models has been made for studying the coupling between thickness modes and contour modes in thin plates. An analytical method based on a series expansion in the plate thickness of the elastic equations was developed by Mindlin (1955). Then the method was extended to piezoelectric plates (Tiersten and Mindlin, 1962; Tiersten, 1969). Different kinds of contour (circular, rectangular, etc.) were studied (Lee, 1971). Introduction was made of energy trapping (Shockley et al., 1967; Mindlin, 1967). Most of the latter models included also the mass-loading effect due to the electrodes. A real need of such models comes from the development of high Q-resonators and from monolithic filters. B. Surface-Acoustic-Wave Resonator

Surface acoustic waves, like Rayleigh waves, cannot be reflected at the edge of a plate (they do not satisfy such a boundary condition and are converted into bulk waves). Standing waves are obtained by using multiple reflections in a surface grating as proposed by Ash (1970). The reflection comes from the electrical or mechanical perturbation on each element of the grating: the shorting out of the piezoelectric field by metal strips and, in addition, the massloading effect. For materials with lower electromechanical coupling factor, grooves made by ionic etching are used (Staples, 1974). Ion-implanted strips (Hartemann, 1975) and metal-diffused strips (Schmidt, 1975) have also been studied. The resonator is composed of two identical reflectors realizing a SAW cavity, which is coupled to the external circuit by means of one or two interdigital transducers, as shown in Fig. 9. The surface-grating reflector has the properties of dispersion of a corrugated structure (Fig. 10). If the wave frequency is in the range of the stop band (near kd = n or 274 the corrugated structure behaves as a reflector (Li et al., 1975). A typical admittance curve of a one-port resonator is shown in Fig. 11. This admittance is similar to that of the bulk-wave resonator and exhibits both resonance and antiresonance. Resonance occurs when the phase interference is constructive. This happens when the length of the cavity (the distance between the effective centers of the reflectors) is an integral number of half wavelengths.

109

RESONATORS, DETECTORS, AND PIEZOELECTRICS

P

L

L

6 FIG.9. One-port (a) and two-port (b) SAW resonators.

The one-port resonator can be represented by an equivalent circuit (Fig. 12) composed of a series resonant circuit L , C , , with a capacitance Co in parallel corresponding to the interelectrode capacitance of the transducer. The R,-resistance involves the different losses, and R, represents the acoustic radiation resistance of the transducer (Schoenwald et al., 1975), which can be placed either in series or in parallel with the circuit. The transfer admittance of a two-port configuration, when off resonance, has the (sin x/x)* characteristic of a transmission delay line, since the gratings are transparent in that case. At resonance, the standing wave sets up in the

I

w s

2n kcd

n

0

2n

n

kd FIG.10. Theoretical dispersion curve for an infinite array of grooves of period d ; k , is the unperturbed Rayleigh wave number, and k the wave number on the periodic structure.

110

JEAN-JACQUES GAGNEPAIN 10

h

c Y)

.c

3

499

500

50 1

Frequency (MHz)

FIG. 11. Admittance curve of a one-port SAW resonator.

cavity and enhances the transmission between the transducers. This appears as a sharp resonance on top of the transducer response (Schoenwald et al., 1975). An equivalent circuit (Shreve, 1975), valid for two identical transducers is given in Fig. 13. The two equivalent circuits of Figs. 12 and 13 are simplified circuits valid near the resonance. Other equivalent circuits with a wider frequency range have been also proposed (Joseph and Lakin, 1975). In terms of the reflection coefficient r of the gratings, the motional inductance and resistance are given by the relations (Staples et al., 1974;

P L1

c1

co

b FIG. 12. One-port SAW resonator-equivalentcircuit.

RESONATORS, DETECTORS, AND PIEZOELECTRICS

0-

Q

.L1

co

111

RI

c1

:

3

co

0-0 FIG.13. Two-port SAW resonator-equivalentcircuit.

Schoenwald et al., 1974)

where Leffis the effective cavity length, which equals the distance between the two reflectors plus the penetration length in the reflectors; fo and Izo are the resonance frequency and the mean wavelength. The unloaded Q-factor of a SAW resonator is limited by different sources of losses, as follows 1

1

Q

Qm

- =-

1 +-1 + -1 +--. Qd

Qr

Qb

The term l/Qm is related to the acoustic attenuation in the material and corresponds to the ultimate limitation of the Q-factor. The Q f product can also be used in this case for characterizing a given material with a given crystallographic orientation and in addition for a given propagation direction of the wave. For ST-cut quartz a Q f product close to l.lOI3 was evaluated (Li et al., 1974). If the device is not under vaccum, air loading will be also a limitation of the Q, but generally the device is sealed in an enclosure under vaccum, and air loading is eliminated. The term l/Qd is the loss due to the diffraction of the finite-width beam. During many transits, the beam spreads and a part of its energy is lost beyond the aperture of the reflectors. This can be reduced by optimizing the beam

-

-

112

JEAN-JACQUES GAGNEPAIN TABLE V COMPARISON OF BAW Frequency Q-factor

BAW SAW

AND

SAW-RESONATORS Q-FACTORS.

5 MHz

100 MHz

1 GHZ

3 . lo6

105 8 x 104

0.3-1 x 104

-

1-3 x 104

SC-cut (Y = 0)

width a with respect to the wavelength &. It has been shown that Qd is proportional to (Li et al., 1974).Diffraction can also be generated when the wave propagates on the grating. This will depend on the type of grating, i.e., on the relative speed of the wave on the grating, with respect to the unperturbed Rayleigh wave velocity, and higher transverse modes can be excited (Staples, 1974). Two other important sources of loss due to the gratings arise from the leakage of energy because of imperfect reflections ( l/Qr), and because of mode conversion into bulk waves (l/Qb).The reflecting coefficient can be improved by using deeper grooves in a short grating, or by using a larger number of shallow grooves. The Q-factor is improved by increasing the grooves’ depth, but there is a limit, and beyond that limit the resonance can even vanish. This has been attributed to bulk-wave generation at the front of the grating. A solution consists in gradually tapering the groove depth up to its final value (Li et al., 1975). The second solution consists in using a much larger number ( N 1OOO) of shallow grooves per grating, which minimizes the leakage loss without increasing the bulk generation. The interdigital transducer also contributes to the losses by spurious reflections. It was proposed to use transducers made of aluminum strips recessed in quartz grooves (Dunnrowicz et al., 1976; Haydl et al., 1976) for reducing these reflections. A comparison between achievable Q-factors of BAW and SAW resonators is given in Table V. VI. NONLINEAR PROPERTIES A. Propagation and Resonance of Finite-Amplitude Waves

The nonlinear terms of third and fourth orders change the characteristics of the wave when its amplitude is finite (and not infinitesimal as it was the case in the previous section). The first consequence of these quadratic and cubic

114

JEAN-JACQUES GAGNEPAIN

In this case rrr,r,t = r, when r" = r' = r, and = A, when r"' = 1'' = r' = r, and are neglected for all values of r"', r", r' # r. Several methods are available for solving these nonlinear equations: the perturbation method of PoincarC, the method of multiple scales, the method of characteristics, the method of coupled amplitude equations, etc., (Planat, 1984). Using the PoincarC method, a solution is chosen in the form V, = Vo cos Y

+ A 2 cos 2" + B2 sin 2Y + C2 + A , cos 3"

+ B3cos3Y + C,cosY + D3sinY +-.-,

(110)

with Y = wt - kos. In this expression, Uo is the amplitude of the driving signal, Vo cos ot at s = 0, ko is the wave number ( k , = w/Vo),and Vo is the wave velocity in the linear approximation. Amplitudes of the different harmonics are obtained by substituting the solution (110) in Eq. (109) and by identifying corresponding terms. For the second harmonic,

for the third harmonic,

and for the fundamental,

The terms C, and D, generated at the fundamental frequency correspond to amplitude and phase perturbation of the fundamental. Some discrepancies have been observed between the PoincarC method and the method of

RESONATORS, DETECTORS, AND PIEZOELECTRICS

115

characteristics, in particular for Eqs. (1 13) and (1 17). This was explained by Daher and Maugin (1989), who gave a more accurate solution, in agreement with the method of characteristics, by using a multitonal solution leading to C,

=

i r ---U:k$s, 41

(1 18)

Equations (1 11) to (1 17) show how the second and third harmonic levels increase as a function of the propagation distance and absorb energy at the fundamental frequency. For longer distances, coupling with higher-rank harmonics will induce a reduction of the second and third, with, as a consequence, an increase of the fundamental, and so on. Such effects do not appear in the above relations, since the calculation is limited to the second order of approximation, and the relations are valid only for distances close to the source. The additional terms at the fundamental frequency [Eq. (116)] and [Eq. (1 19)] are equivalent to a perturbation of the amplitude and phase of the wave. Combining with the main fundamental term gives the velocityamplitude effect

and This effect is related to the nonlinear elastic constants, and since (r/A), A/,? are of the same order of magnitude (see Section III.A), both third- and fourth-order elastic constants must be taken into account. A similar relation can be written for the resonance frequency of a resonator. This well-known amplitude-frequencyeffect is shown in Fig. 14. It should be noticed that these results are general. They take into account both the vibration mode and the crystal anisotropy, but are limited to a onedimensional plate. Two-dimensional models have been studied by Tiersten (1975). A second nonlinear phenomenon that arises in resonators used as filters is intermodulation. For a signal with two frequency components wt and 0, (both close to the resonance frequency wo of the resonator, and within its bandwidth), the quadratic nonlinearities generate frequencies 204, 20,, o1+ a,,and o1- 0,. Cubic nonlinearities generate 3w1, 3wz, w1 + 20,, 0,+ 204, 2w, - w 2 , and 201, - wl. All these frequencies are completely out of the resonator bandwidth, except 2 0 , - w, and 20, - ol. If 0 1 N 0,2:

w,,

(121)

116

JEAN-JACQUES GAGNEPAIN

-

-2 x 10-8

10-6

2 x10-6

FRACTIONAL FREQUENCY FIG.14. Amplitude-frequency effect of a 5-MHz AT-cut quartz resonator.

it follows that 20, - 0

2 N

20, - o1N w1 N o2N

0,.

(122)

Therefore, such frequencies will not be eliminated by the filter. This intermodulation can have a serious effect, in particular in front-end filters when high signal levels are received. Intermodulation has been studied by Tiersten (1974), Smythe (1974) in thickness-shear quartz resonators, and by Planat et al. (1980a)in X-cut lithium tantalate resonators. It was shown that both third- and fourth-order elastic constants are again involved. Because the fourth-order constants are unknown, the value of intermodulation cannot be calculated, and, in fact, the models were used for evaluating some values of fourth-order elastic constants from experimental measurements of intermodulation. It should be noticed that these evaluations were based on solutions including Eqs. (113)and (117). The corrected solutions (118) and (119) will yield different values of the corresponding fourth-order elastic constants. But this evaluation has not yet been made. A direct comparison between the elastic nonlinearities of quartz and lithium tantalate resonators is shown in Fig. 15. Lithium tantalate has nonlinearities that are much smaller than those of quartz. The intermodulation ratio PIP, corresponds to the ratio of the power of one of the test tones at frequencies 0,and o2(with Pw, = Po,= P) over the

RESONATORS, DETECTORS, AND PIEZOELECTRICS

117

PI Po (dB)

4

1

*

P (dBrn) -50 -30 -10 FIG.15. Comparison of intermodulation in 456 kHz face-shear mode quartz and lithium tantalate resonators (Planat et al., 1980).

power at the intermodulation frequencies R = 20, - w, or R’ = 20, - o1 (with Pn = Pw). The nonlinear propagation of surface acoustic waves has also been intensively studied. The first approaches were made by Adler et al. (1973) and Alippi et al. (1977). Analytical models were developed by Tiersten and Baumhauer (1974) for isotropic solids and then by Vella et al. (1974,1977),and by Planat et al. (1980b);and by Planat (1984)in the general case of anisotropic crystals. Surface waves are studied using the basic propagation equation [Eq. (lor)] and Eq. (103),with addition of the boundary condition [Eq. (102)]. The solution of a Rayleigh wave propagating on a pure elastic substrate in the s direction on the surface is in the infinitesimal amplitude approximation

where a2 is the direction of penetration normal to the surface, and ny) is the complex penetration coefficient. Applying PoincarC‘s perturbation (Planat et al., 1980b), and a much lengthier calculation than for bulk waves, gives the second harmonic solution

where Ako is a perturbation of the wave number ko calculated by means of the boundary condition. At the next order of approximation, the solution is composed of the third harmonic and of an additional term at the fundamental frequency. Since the propagation distance is a large number of wavelengths, i.e., s >> A0/2a, the

118

JEAN-JACQUES GAGNEPAIN

terms proportional to s2 are predominant, and the terms proportional to s are negligible. This yields the solution at the fundamental frequency 3

uj = - i i k i U : A 2 k o s 2

C C;!)e"r.

(125)

r

The second-order perturbation A2k, is also determined by means of the boundary conditions. Combining the different terms at the fundamental frequency gives the velocity-amplitude effect

v=

(126)

Vo(1 - k : U ; f , s )

This relation shows that the perturbation of velocity depends on the propagation distance s, with fi being evaluated from the previous perturbation terms. The corresponding amplitude-frequency effect has been measured on SAW resonators. A comparison is made between BAW and SAW in Table VI, using the A-F coefficient K defined by w -0 0

= K12,

(127)

WO

where I is the driving current through the resonator. These results show that the amplitude-frequencyeffect for SAW resonators is two orders of magnitude lower that for BAW resonators. This has also been confirmed by intermodulation measurements. The difference is explained by the lower energy density, per , I :unit volume, of surface acoustic waves.

B. Propagation in a Prestrained Medium

A second class of problems corresponds to the propagation of acoustic waves in a nonlinear medium exposed to static or quasistatic deformations, forces, or fields. Due to the nonlinearities of the solid, the wave and the static TABLE VI AMPLITUDE-FREQUENCY COEFFICIENTK SAW AND BAW RESONATORS."

CoMPARISON OF THE

OF

SAW resonators BAW resonators a

Planat et al.. 1980

Frequency

Cut

Q-factor

110 MHz

ST

26 OOO

1.1

100MHz 5 MHz

AT

63 OOO

2.5 x 10-'/AZ 2 x 10-'/A2

2.106

K x 10-3/~~

RESONATORS, DETECTORS, AND PIEZOELECTRICS

119

deformation are coupled. This coupling produces a sensitivity of the wave (velocity, amplitude, etc.), and therefore of the resonator (resonance frequency), to external or internal perturbations resulting from mechanical, thermal, or electrical phenomena. The problem can be simplified by considering that the wave exposed to the static deformation is of small enough amplitude to have no influence on the static bias. Equations for the dynamic deviations from the bias are linearized. New effective elastic, piezoelectric and dielectric constants can then be introduced in the linearized equations. Finally, the change of velocity or frequency is obtained directly by using a regular perturbation method. This problem has been treated by many authors, in particular by Thurston (1964), Baumhauer and Tiersten (1973), and Theobald et al. (1985a, b). The action of the static (perturbation) and the dynamic (wave) deformations of the solid can be described in terms of three states (Fig. 16): the natural state, of coordinates ai, when the solid is at rest; the initial state, of coordinates xi,after the application of the static deformation; and the final state, of coordinates Xi, when the dynamic deformation is superposed to the static one. Let po, p, and p, respectively, be the specific masses of the solid in these different states. Three mechanical displacements are distinguished: static

- = x. - a: u. I

13

(128)

E.1 = x. - X.' I

(129)

1

dynamic 19

total

dynamic u

final (Xi)

natural (a,)

FIG. 16. Reference coordinate systems of a solid submitted to a dynamic deformation superposed on a static bias.

1 20

JEAN-JACQUES GAGNEPAIN

Strains, stresses, and fields are also identified using the same static, dynamic, and total notation. Finally, let N,, 7ii, and n, be the cosine directors of the unit normal at a point of surface in the different states. 1. Mechanical Equilibrium Equations

Following Eq. (21), the mechanical equilibrium equation (in the absence of body forces) is in the final state

where zij is the total stress, composed of a mechanical part part TE, 7.. IJ =

Tjand an electrical

T.. 1J + 7’:.

(132)

The boundary condition corresponding to a free surface is

on the surface.

n.2.. I IJ = 0

(133)

Equations (1 3 1) and (133) can also be written in the initial state

and 7i,Ksj = 0

on the surface,

(135)

with K , representing the stress components with respect to the initial coordinate system. That is

with

J = p/p.

(137)

Finally, in the natural state, d zu j P

O

F

=

aflj -9

aa1

and

N,Sj = 0

on the surface,

(139)

RESONATORS, DETECTORS, AND PIEZOELECTRICS

121

with

and

J=

po/p.

(141)

Similarly, the electrical equilibrium equation is written in the final state as

aD, ~

ax, = 0,

and in the initial state as agj - 0. -

aaj

(143)

In Eq. (143),

g.=J -aa . D,. J

ax,

and J = Po/P.

(145)

If the static problem is assumed to be unaffected by the dynamic deformation and fields (this is true if the amplitude of the wave is small), the static equations can be written

N,qj = 0

on the surface,

(147)

and

Subtracting Eqs. (146), (147),and (148), respectively, from Eqs. (138), (139), and (143), and using Eqs. (128)-( 130), gives the dynamical system

N&, = 0

on the surface.

(150)

122

JEAN-JACQUES GAGNEPAIN

and

2. Constitutive Equations and Effective Constants

ej aj

In these equations, and are obtained by developing the total stress and electric displacement in a power series of the displacement gradients axk/&,and the electric field W,or the potential gradient a4/aar7that is,

aii, 3)+ aar

aar

Therefore,

where Aljkr and

are effective elastic and piezoelectric constants given by

and

Similarly, the dynamic electric displacement is

A,,

where is the effective piezoelectric constant and electric constant.

is the effective di-

RESONATORS, DETECTORS, AND PIEZOELECTRICS

123

The final form of the effective constants is obtained by using the constitutive equations. This yields

and

These quantities depend on the elastic constants of the second and third order, on the second-order piezoelectric constants, on the electroelastic and electrostrictive constants, on the second- and third-order dielectric constants, and on the gradients of the static mechanical displacements and electric potential. The dynamic problem is now represented by a set of linearized equations, which can be solved by the usual manner by replacing the ordinary constants by the effective ones. A perturbation method (Tiersten, 1978) can be used to obtain directly the velocity or frequency variations. For a sinusoidal wave ujeiootin the absence of perturbation, the mechanical equilibrium equation is written

-

(the symbol is now omitted and the notation ,1 is used for alas,). In presence of a perturbation, the solution becomes ujeiw', and the equilibrium equation -pow2uj =

(161)

Multiplying the complex conjugate of Eq. (160) by uj and Eq. (161) by the complex conjugate uj*, integrating over a volume V of the solid limited by a surface S , and taking the difference, yields

where Ao = o - w,,.

124

JEAN-JACQUES GAGNEPAIN

The effective constants of Eqs. (157)' (158), and (159) are written in the form = Cljkr

A,,j = e,ij Ejr

= &jr

+ 21jkr,

(163)

+

( 164)

G j ?

+ Zjr,

(165)

where Cljkr,trlj, and Fjr appear as perturbations of the regular elastic, piezoelectric, and dielectric constants. Using Eqs. (153)' (156), and the electrical equilibrium equation 9j,j = 0,

(166)

9. J.J , = 0

in Eq. (162)and applying the divergence theorem and the boundary conditions gives the final relation P

2p00,Ao

J

GjGT dV V

r

+

ij,Ii?rIjc$:

+ iTIi?rIjc$,r - c$,jE;.rc$f]

dV.

(167)

Therefore, determination of the frequency variation Am requires an independent determination of the unperturbed wave solution tij and the predeformations included in the perturbed effective constants. For a plane wave,

i;i = ajeimo(r

-Niai/Vo) 2

and only an elastic perturbation simple form

Eljkr,

(168)

the perturbation relation takes the

where V, is the unperturbed wave velocity and fjk

=6jkrSNr-

(170)

In the above relation, A o / w , = AV/V, at constant wave number k, was used. For surface acoustic waves, the unperturbed solution is

After integration over a wavelength and a thickness of the substrate much

RESONATORS, DETECTORS, AND PIEZOELECTRICS

125

larger than the penetration depth, this leads to the relation

n(n) = q,

corresponds to the penetration coefficient.

As can be seen from the previous relations, the frequency or velocity

sensitivities to perturbations depend on the crystal anisotropy. Therefore, particular configurations can be expected to minimize the sensitivities when a compensation between the different terms of the effective constants occurs; this is important for the use of resonators in stable devices such as oscillators, filters, and so forth. By contrast, a maximum of sensitivity to a given physical quantity is appropriate for sensors, when this sensitivity can be made selective.

VII. SENSITIVITIES TO EXTERNAL PERTURBATIONS AND THE DESIGN OF DETECTORS A. Temperature

The temperature sensitivity of a resonator is usually described by the thermal expansion coefficients of the crystal and by the temperature coefficients of the fundamental constants, in this case mainly the elastic constants. For quartz crystal, these coefficients were obtained by Bechmann and coauthors (1962) from the frequency-temperature dependence of BAW resonators. Bechmann’s coefficients are therefore phenomenological and can be applied with confidence only to the kind of device used in measuring them. They cannot be considered as fundamental constants. In fact, they implicitly contain the contribution of the nonlinear elastic effects, through the crystal deformation due to thermal expansion. The temperature derivatives of the fundamental second-order elastic constants of quartz were determined by Sinha and Tiersten (1978) by substracting the contributions of the third-order elastic constants from Bechmann’s coefficients. More recently, the same evaluation was made by Lee and Yong (1983)and extended to the second-order temperature derivatives. But the latter must be considered as effective coefficients, since they are a combination of the fundamental second-order temperature derivatives, of the temperature derivatives of the third-order elastic constants (unknown), and of the fourthorder elastic constants (also unknown).

126

JEAN-JACQUES GAGNEPAIN

The temperature derivatives of the fundamental second-order elastic constants combined with the third-order elastic constants, and the thermal expansion coefficients are both necessary for describing nonuniformly heated resonators. When the thermal distribution is not uniform, the temperature gradients induce thermal stresses and strains. These stresses and strains contribute additionally to the frequency variations by nonlinear effects. The so-called dynamic temperature behavior has been studied in detail experimentally and theoretically by Holland (1974a, b), Kusters (1976),Kusters and Leach (1977),Ballato and Vig(1978),Ballato (1979a,b), Thtobald et al. (1979), Sinha and Tiersten (1980), and Hauden and Thtobald (1980) in BAW and SAW resonators. The complete frequency-temperature dependence of a resonator is represented by the relation

’fo

= a,(T

- To)+ b,(T - To)’

+ c,(T

-

J T + a-, dt

(173)

where a,, b,, c, are the first-, second-, and third-order static temperature coefficients of frequency, and a“ the dynamic temperature coefficient. The quantities a,, b, and c, are generally evaluated from the phenomenological Bechmann’s constants, and Zis calculated by using the temperature derivative of the fundamental elastic constants and nonlinear elastic couplings involving the third-order elastic constants. Since temperature gradients induce in-plane thermal stresses (Valentin et al., 1985),compensation is achieved by determining a crystal orientation such that the two in-plane axial stress components cancel out. This was the definition given by Eernisse (1976) of the SC-cut. In quartz crystal resonators, the first- and second-order frequencytemperature coefficients a, and b, can be compensated. The resulting temperature characteristic has a cubic shape, with, for instance, a sensitivity of CZ~O-~/K’ near the upper turnover point for the AT-cut. For SAW resonators, only the first-order coefficient is compensated (ST-cut), and the resulting sensitivity s N -40.10-9/K2. Efforts have been made to find a SAW configuration with a temperature characteristic similar to the BAW AT-cut, but without real success. Configurations with high temperature sensitivity and linear characteristics have also been studied and used as temperature sensors. The BAW LC-cut has a sensitivity of N 30 ppm/K, and similar characteristics were found for SAW (Hauden et al., 1980). The dynamic temperature behavior is characterized by the Zcoefficients of Eq. (173)with values on the order of lo-’ sec/K for the AT-cut and a few lo-’ for the compensated SC-cut. The SAW dynamic coefficient is similar to that of the SC-cut one (Hauden and Thtobald, 1980).

RESONATORS, DETECTORS, AND PIEZOELECTRICS

127

B. Forces and Pressures

The problem of force sensitivity has been extensively studied (Ballato, 1960; Ratajski, 1966; Lee et al., 1975; Ballato et al., 1977; Janiaud et al., 1978; Lee and Tang, 1986). Figure 17 shows an example of the calculated sensitivities of bulk- and surface-wave resonators and delay lines to external diametrically applied forces. This shows the dependence of the sensitivity on the direction of the force application and, in particular, the possibility of a configuration with zero force sensitivity. Conversely, a configuration can be chosen with maximum force sensitivity. A generalizationof the sensitivity,at the center of a circular plate, to the six stress components, following the relation

was presented by Eernisse (1976). This lead to the definition of the stresscompensated SC-cut, which is very similar to the thermal transientcompensated cut previously described. The same generalization was extended to SAW resonators by Bigler et al. (1987, 1989), who showed the possibility of compensation of two or four symmetrically applied forces on circular quartz plates. Bulk w a v e

S u r f a c e wave

I5mm

4O m

I

FIG.

1

1

1

I

30 60 90 120 150 Force aziriiuthal a n g l e 17. Force-sensitivity of BAW and SAW resonators.

128

JEAN-JACQUES GAGNEPAIN

Sensitivity to hydrostatic pressure is an indirect problem in BAW resonators. In principle, the resonator is under vacuum in its enclosure. Therefore, there is no direct effect of the surrounding gas on the vibrating crystal. However, gas pressure acts on the enclosure and deforms it. Forces are then transmitted to the crystal by the mounting supports, and a frequency shift occurs due to the resulting stresses and strains. For regular quartz resonators, sensitivities of the order of lOW9/barare observed. With appropriate mounting, this sensitivity can be reduced by almost a factor 10 (Delaite, 1985). Configurations for pressure sensor applications have also been studied. In most cases the pressure acts indirectly after transduction into a force (Hammond and Benjaminson, 1969; Dias and Karrer, 1974), or by direct application to a thin deformable diaphragm or cantilever (Reeder et al., 1975; Hauden et al., 1980; Hauden et al., 1981; White, 1985). An example of a SAW pressure sensor is shown in Fig. 18. This sensor is made of a thin diaphragm supporting one or two SAW delay lines or resonators located at the maxima of sensitivity on the substrate.

I

I

4

1

a-

I

1:xperiiiieiital FIG. 18. SAW pressure sensor.

points

RESONATORS, DETECTORS, AND PIEZOELECTRICS

129

C. Accelerations Under an acceleration field, the crystal is submitted to a system of body forces due to the acceleration field and reaction forces exerted by the supports (Valdois et al., 1974; Lee and Wu, 1977; Janiaud, 1978). Great efforts have been made to reduce this g-sensitivity, because of its implication for spatial and tactical quartz oscillators. Reduction of the sensitivity from a few 10-9/g to a few lO-'O/g and even below has been achieved on BAW resonators (Gagnepain and Walls, 1977; Besson et al., 1979; Ballato, 1979b; Przyjemski, 1978; Emmons, 1978; Debaisieux et al., 1983; Weglein, 1984). With SAW devices, the basic sensitivity is much greater (lO-'/g) (Valdois et al., 1977; Levesque et al., 1979) but improvements have also been obtained, and sensitivities of the order of a few 10-9/g are obtainable today (Montress et al., 1985; Shick and Tiersten, 1986). The solution was mainly by exploiting the symmetry of the resonator structure, as was shown primarily by Janiaud (1978). Accelerometers are being also studied; but here, in general, the acceleration field is transformed into a force by means of an inertial mass in order to obtain higher sensitivities. Different configurations have been used: cantilever (Hauden et al., 1985), diaphragm (Hartemann and Meunier, 1983), and tuning fork (Kass and Snow, 1986). Figure 19 shows an example of a SAW cantilever beam accelerometer, and typical values of the main and transverse sensitivities are given in Table VII. D. Electric Field

The application of an electric field to a resonator induces frequency shifts by a number of different mechanisms. The first consequence is the change in size and specific mass because of the piezoelectric effect, and the correspond-

FIG. 19. Principle of a SAW cantilever beam accelerometer.

130

JEAN-JACQUES GAGNEPAIN TABLE VII MAINAND TRANSVERSE SENSITIVITTES OF THE SAW CANTILEVER BEAMACCELEROMETER.’ SC-cut (Y = 0) at 100 MHz Main g-sensitivity Transverse g-sensitivity Compressiong-sensitivity

Theoretical values (Wg)

Experimental values (Wg)

1387

1318 not measurable 10

3.3

10-3

8

Hauden et al.. 1985

ing modification of the crystal stiffness because of the elastic nonlinearities. However, the electric field also directly modifies the elastic constants by the electroelastic effect. In addition, there is the effect of the electrostrictive constants and nonlinear dielectricconstants. These contributions can be of the same order of magnitude, and therefore all of them must be taken into account (Brendel, 1983). This electric field dependence was shown for the first time in quartz resonators by Kusters (1970) and studied in detail by the authors previously referenced in the section on the electroelastic constants. As shown in Fig. 20, a fast frequency shift due to the previously described effects follows the application of the DC field. The relaxation phenomenon

:02+ -20t. 0

L.

L .

2L 12 18 TIME Ittours) FIG.20. Influence of a DC electric field on a quartz-crystal resonator. 6

RESONATORS, DETECTORS, AND PIEZOELECTRICS

131

that appears after the initial frequency shift is due to ionic impurity migration in the crystal. The presence of interstitial impurities makes the crystal sensitive to irradiation (Kahan et al., 1987). This phenomenon can be reduced by using swept crystals, where the ions have been removed by applying a DC field at high temperature (Martin, 1987). The results also show how necessary it is to insulate the resonator from DC voltages when used in high-stability oscillators. Conversely, this sensitivity could be utilized to use resonators as voltage detectors. But for accurate voltage measurements, the relaxation effect must be cancelled.

E. Miscellaneous Detectors New acoustic resonators and delay lines are being developed for detecting and measuring a large variety of chemical and biological substances (Motamedi and White, 1987). The principle of operation is still based on the detection of frequency, phase, or velocity variations, but these are now due to a change of mass loading on the surface, which is covered with a chemically sensitive coating. One of the first works on the use of SAW delay line as a chemical detector is due to Wohltjen and Dessy (1979),Hou and Van de Vaart (1987). The main difficulty is the selectivity of the coating, which can be improved by different techniques. Porous coating can admit only molecules smaller than a pore in diameter. Molecules can be distinguished by their rate of adsorption (White, 1987). Simultaneous changes of mass loading and of electrical conductivity were used by Venema and coauthors (1987) for detecting NO, gas with a SAW delay line having a ZnO-SO,-Si structure. A similar structure was proposed by Vetelino and coauthors (1987) for the detection of H,S concentrations. Most of the effort today is made on SAW detectors. But studies were also made previously on the possibilities offered by BAW resonators (King, 1971). More recently, they were used as a quartz hygrometer (Ito, 1987), as an enzymes detector (Guilbault, 1983), and others. Various applications were also made of acoustic detectors immersed in a liquid. The difficulty is the high attenuation of the acoustic wave (of the order of several dB/MHz/cm), which is minimized by operating, if possible, at lower frequency and by using acoustic wave with horizontal shear polarization. An interesting procedure was achieved by White and coauthors (1987), who studied the propagation of the lowest-order Lamb waves in very thin Si-ZnO membranes. Velocities of the order of a few 100 mjsec were achieved with membranes 1 pm thick, which make feasible a detector operated in a liquid. Similarly, leaky waves were used for measuring liquid viscosity (Moriizumi and Unno, 1987).

132

JEAN-JACQUES GAGNEPAIN

VIII. CONCLUSION

As has been shown, the basic properties of the crystals are related to the nonlinear nature of the lattice. Consequently, the characteristics of acoustic devices, and in particular of piezoelectric resonators, are strongly influenced by these nonlinearities. Most of the efforts consist in trying to minimize the nonlinearities that are at the origin of the instabilities of resonators, oscillators, filters, etc. As a by-product, nonlinearities are also used for detection and measurement of physical or chemical quantities. In both cases, the control of the nonlinearities in relation to the crystal anisotropy requires knowledge of the values of its fundamental constants. Today, many crystals appear to be well characterised, particularly quartz. In fact, some important gaps still exist. The fourth-order elastic constants are almost completely unknown, and the temperature dependence of the third-order elastic constants must still be measured. Some uncertainties also remain concerning the values of the electroelastic and electrostrictive constants. This is the case for quartz, and a fortiori for the other crystals. In addition to the deterministic mechanisms that were described, problems of random fluctuations must also be considered. For instance, the resonant frequency fluctuations of piezoelectric resonators have not yet been completely explained, in particular the part of the spectrum that exhibits a 1/f dependence.

REFERENCES Adler, E. L., Bridoux, L., Coussot, G., and Dieulesaint, E. (1973).IEEE Trans. Sonics and Ultrason. SU-20, 13. Agishev, B. A., Lemanov V. V., and Yuskin N. K. (1979).Sou. Phys. Solid State 20, 1629. Akhieser A. (1939).J. Phys. U S S R , 1. Alippi, A., Palma, A., Palmieri, L., and Socino, G. (1977). J . Appl. Phs. 48,2182. Ancona, M. G., and Tiersten, H. F. (1980). Phys. Rev. B 22,6104. Ancona, M. G., and Tiersten, H. F. (1983). Phys. Rev. B 27, 7018. Ash, E. A. (1970).IEEE Symp. Microwave Theory and Techniques, Newport Beach, C A . Ballato, A. D. (1960). Proc. 14th Ann. Freq. Cont. Symp., p. 89. Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161. Ballato, A. (1977).Doubly rotated thickness mode plate vibrators. In “Physical Acoustics” (W. P. Mason, R. N. Thurston, eds.), vol. XIII, p. 115. Academic Press, New York. Ballato, A. (1979a). IEEE Trans. Sonics and Ultrasonics SU-26,299. Ballato, A. (1979b).Proc. 33rd Ann. Freq. Cont. Symp., p. 322. Available from EIA, 2001 Eye Street, Washington, DC 20006. Ballato, A., and Vig, J. R. (1978). Proc. 32nd Ann. Freq. Cont. Symp., p. 180. Available from EIA, 2001 Eye Street, Washington, DC 20006. Ballato, A., Eernisse, E. P., and Lukaszek T. (1977). Proc. 31st Ann. Freq. Conr. Symp., p. 8. Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161.

RESONATORS, DETECTORS, AND PIEZOELECTRICS

133

Baumhauer, J. C., and Tiersten, H. F. (1973). J. Acoust. SOC.Am. 54, 1017. Bechman, R., Ballato, A. D., and Lukaszek T. J. (1962).Proc. IRE, 50, 1812. Besson, R. (1976). Proc. 30th Ann. Freq. Cont. Symp., p. 78. Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161. Besson, R., Gagnepain, J. J., Janiaud, D., and Valdois, M. (1979). Proc. 33rd Ann. Freq. Cont. Symp., p. 337. Available from EIA, 2001 Eye Street, Washington, DC 20006. Bigler, E., Theobald, G., and Hauden, D. (1987). El. Lett. 23, 514. Bigler, E., Theobald, G., and Hauden, D. (1989). Ultras. Ferroel. Freq. Cont. Trans. UFFC-36, 1. Brendel, R. (1983a). Effect electroelastique et diffusion des impuretes das le quartz. These de Doctorat d’Etat no. 176. Universiti de Franche-Comte-BesanGon. Available from LPMO, 32 avenue de I’Observatoire, 25000 Besanpon, France. Brendel, R. (1983b).J . Appl. Phys. 54,5339. Brendel, R.(1984).J . Appl. Phys. 55,608. Briigger. R. (1965). Phys. Rev. 137,6A, 1826. Cady, W. G. (1921).Phys. Rev. 17,531. Chizhikov, S. I., Sorokin, N. G., and Petrakov, V. S. (1982). Ferroelectrics 41,9. Curie, J., and Curie P. (1880).Bulletin no. 4 de la Socittt Miniralogique de France, t. 3, p. 90, and C. R. Acad. Sci. Paris 91, 294. Daher, N. (1987). Principe des puissances virtuelles etendu aux discontinuites et interfaces, application a t’acousto-electronique. These de Doctorat d’Etat no. 224, Universiti de Franche-Comte-Besanpon. Available from LPMO, 32 avenue de I’Observatoire, 25000 Besanpon, France. Daher, N., and Maugin, G. A. (1987). Int. f. Engng. Sci. 25, 1093. Daher, N., and Maugin, G. A. (1989).Intermodulation and generation of elastic and piezoelectric waves in anisotropic solids. To appear in Journ. Acoust. SOC. Am. Debaisieux, A., Aubry, J. P., and Groslambert J. (1983). Proc. 15th Ann. PTTI Meeting, p. 635. Goddart Space Flight Center, Greenbelt, Maryland. Delaite, R.(1985). Rev. Phys. Appl. 20, 741. Detaint, J., and Lancon, R.(1976). Proc. 30th Ann. Freq. Cont. Symp., p. 132.Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161. Dias, J. F., and Karrer, E. (1974). Int. Solid-State Conf., p. 166. Dumas, J. C., Goiffon, A., Philippot, E., Toudic, Y., Schwartzel, J., Buisson, X.,Arnaud, R., and Detaint, J. (1987). Proc. Ist European Frequency and Time Forum, p. 205. Available from Observatoire de Besanpon, 25000 Besangon, France. Dunnrowicz, C., Sandy, F., and Parker, T. (1976). Proc. IEEE Ultrasonics Symp., cat. 76 CH 11205SU, p. 386. Dye, D. W.(1926). Proc. Phys. SOC.38,329. Eernisse, E. P. (1976).Proc. 30th Ann. Freq. Cont. Symp., p. 8. Available from IEEE, 445 Hoes Lane, Piscataway, NJ 08854. Emmons, D. A. (1978). Proc. loth PTTI, Nasa Techn. Memo. 80250, p. 55. Fowles, R. (1967). Geophys. Res. 72,5729. Gagnepain, J.-J., and Besson, R. (1975). Nonlinear effects in piezoelectric quartz crystals. In “Physical Acoustics (W. P. Mason and R. N. Thurston, eds.) Vol. XI, p. 245. Academic Press, New York. Gagnepain, J.-J., and Walls, F. L. (1977). Quartz crystal oscillator with low acceleration sensitivity. N B S Techn. Report. NBSIR-77-855. Ganguly A. K., and Davis K. L. (1980).J . Appl. Phys. 51,920. Guilbault, G. (1983).Anal. Chem. 55, 1682. Hammond, D. L., and Benjaminson, A. (1969). IEEE Spectrum 6,53. Hartemann, P. (1975). Proc. IEEE Ultrasonics Symp., cat. 75 CHO 994-4SU, p. 303.

134

JEAN-JACQUES GAGNEPAIN

Hartemann, P., and Meunier, P. L. (1983). Proc. IEEE Ultrasonics Symp., cat. 83 CH 1947-1. p. 291 Hauden, D. and Theobald, G. (1980). Proc. IEEE Ultrasonics Symp., cat. 80 CH 1602-2, p. 264. Hauden, D., Rousseau, S., and Gagnepain, J.-J. (1980). Proc. 34th Ann. Freq. Cont. Symp., p. 312. Available from EIA, 2001 Eye Street, Washington, DC 20006. Hauden D., Planat, M., and Gagnepain, J.-J. (1981). IEEE Trans. Sonics and Ultrasonics SU-28, 342. Hauden, D., Bindler, F., and Coquerel, R. (1985). Proc. I E E E Ultrasonics Symp., cat. 85 CH 2209-5, p. 486. Haydl, W. A., Hiesinger, P., Dischler, A., and Smith, R. (1976). Proc. 30th Ann. Freq. Cont. Symp., p. 346. Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161. Holland, R. (1974a). IEEE Trans. Sonics and Ultrasonics SU-21, 171. Holland, R. (1974b). Proc. IEEE Ultrasonics Symp., cat 74 CHO 896-1SU, p. 592. Hou, J. and Van de Vaart, H. (1987). Proc. IEEE Ultrasonics Symp., cat. 87 CH 2492-7, p. 573. Hruska, C. K. (1977). Proc. 3Ist Ann. Freq. Cont. Symp., p. 159. Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161. Hruska, C. K. (1978a). IEEE Trans. on Sonics and Ultrasonics SU-25,198. Hruska, C . K. (1978b). IEEE Trans. on Sonics and Ultrasonics SU-25,390. Hruska, C. K. (1986). Proc. 40th Ann. Freq. Cont. Symp., p. 54. Available from IEEE, 445 Hoes Lane, Piscataway, NJ 08854. Hruska, C. K., and Brendel, R. (1987). Proc. 1st European Frequency and Time Forum, p. 215. Available from Observatoire de Besanpon, 25000 Besanpon, France. Ito H. (1987). Ultras. Ferroel. Freq. Cont. Trans. UFFC-34, 136. Jaffe, B., Cook, W. R. Jr., and Jaffe, H. (1971). In “Piezoelectric Ceramics.” Academic Press, London and New York. Janiaud, D. (1978). Modelisation de I’influenced’une acdltration sur la frtquence des resonateurs quartz. Thesis report ONERA, ChatiIIonlBagneux, France. Janiaud, D., Nissin, L., and Gagnepain, J . 4 . (1978). Proc. 32nd Ann. Freq. Cont. Symp., p. 169. Available from EIA, 2001 Eye Street, Washington, D C 20006. Joseph, J. R., and Lakin, K. L. (1975). Proc. 29th Ann. Freq. Cont. Symp., p. 158. Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161. Kahan, A., Euler, F. K., and Lipson, H. G. (1987). Proc. 41st Ann. Freq. Cont. Symp., p. 216. Available from IEEE, 445 Hoes Lane, Piscataway, NJ 08854. Kass, M. J., and Snow,G. S. (1986). Proc. 40th Ann. Freq. Cont. Symp., p. 230. Available from IEEE, 445 Hoes Lane, Piscataway, NJ 08854. Kittinger, E., and Tichy, J. (1987). Proc. Ist European Frequency and Time Forum, p. 222. Available from Observatoire de Besancon, 25000 Besancon, France. Kittinger, E., Tichy, J., and Friedel, W. (1986). J . Appl. Phys. 60,1465. Klemens, P. G. (1951). Proc. Roy. SOC.A 203,108. King, W. (1971). Proc. 25th Ann. Freq. Cont. Symp., p. 104. Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161. Koborov, A. I., and Lyamov, V. E. (1975). Sou. Phys. Solid State 17,932. Kroupa, V. F. (1988). IEEE Trans. Ultrasonics, Ferroelectrics and Frequency Control UFFC-35, 406. Kusters, J. (1970).Proc. 24th Ann. Freq. Cont. Symp., p. 46. Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161. Kusters, J. (1976). lEEE Trans. Sonics and Ultrasonics SU-23,273. Kusters, .I. A., and Leach, J. G. (1977). Proc. IEEE, 282. Landau, L., and Rumer, G. (1937). Phys. Z. Sowjet Union 11, 18. Landolt-Biirnstein (1979). “Numerical data and functional relationships in Science and Technology.” Group. 111, vol. 11, Springer-Verlag, Berlin, Heidelberg, New York. Langevin, P. (1918). French Patent, 505,703.

RESONATORS, DETECTORS, AND PIEZOELECTRICS

135

Lee, P. C. Y. (1971). J. Appl. Phys. 42,4139. Lee, P. C. Y., and Kuang-Ming Wu (1977). Proc. 31st Ann. Freq. Cont.Symp., p. 29. Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161. Lee, P. C. Y.,and Yong, Y. K. (1983). Proc. 37rd Ann. Freq. Cont. Symp., p. 200. Available from IEEE, 445 Hoes Lane, Piscataway, NJ 08854. Lee, P. C. Y., and Tang, M. S. H. (1986). Proc. 40th Ann. Freq. Cont. Symp., p. 152. Available from IEEE, 445 Hoes Lane, Piscataway, NJ 08854. Lee, P. C. Y., Wang, Y. S., and Markenscoff (1975). J . Accoust. SOC.Am. 57,95. Levesque, P. Valdois, M., Hauden, D., Gagnepain, J. J., Hartemann, P., and Uebersfeld, J. (1979). Proc. IEEE Ultrasonics Symp., cat. 79 CH 1482-9, p. 896. Li, R. C. M., Alusow, J. A., and Williamson, R. C. (1975). Proc. 29th Ann. Freq. Cont. Symp., p. 167. Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161. Li, R. C. M., Williamson, R. C., Flanders, D. C., and Alusow, J. A. (1974). Proc. IEEE Ultrasonics Symp., cat. 74 CHO 896-1SU, p. 257. Lippman, G . (1881). C. R. Acad. Sc. Paris 12, 1049. Maradudin, A. A. (1962). Phys. Stat. Sol. 2, 1493. Maris, A. J. (1971). In “Physical Acoustics” (W. P. Mason, ed.),vol. VIII, p. 279. Academic Press New York. Martin, J. J. (1987).Proc. 41st Ann. Freq. Cont. Symp., p. 167. Available from IEEE, 445 Hoes Lane, Piscataway, NJ 08854. Mason, W. P. (1943). Bell Syst. Tech. Journ. 22, 178. Mason, W. P. (1966). In “Crystal Physics of Interaction Processes.” Academic Press, New York. Meeker, T. R. (1985).Theory and properties of piezoelectric resonators and waves. In “Precision Frequency Control” (E. G. Gerber and A. Ballato, eds.), vol. I, p. 47. Academic Press, New York. Mindlin, R. D. (1955). “An Introduction to the Mathematical Theory of Vibrations of Elastic Plates.” Monograph, Signal Corps Contract DA-36-039 SC-56772. Fort Monmouth, New Jersey. Mindlin, R. D. (1961). Q. Appl. Math. 19, 51. Mindlin, R. D. (1967). J . Acoust. SOC.Am. 41,969. Montress, G . K., Parker, T. E., and Callerame, J. (1985).Proc. IEEE Ultrasonics Symp., cat 85 CH 2209-5, p. 277. Motamedi, M. E., and White, R. M. (1987). Ultras. Ferroel. Freq. Cont. Trans. UFFC-34, 122. Moriizumi, T., and Unno, Y. (1987). Proc. IEEE Ultrasonics Symp., cat 87 CH 2492-7, p. 579. Narayanan, R. S., Chai, B. H., Vetelino, J. F., Soluch, W. Falconer, R. S., and Chick, B. (1984). Proc. IEEE Ultrasonic Symp., cat. 84 CH 2112-1, p. 262. Nelson, D. E. (1979). “Electric, Optic and Acoustic Interactions in Dielectrics.” John Wiley and Sons, New York. Nicholson, A. (1919).Trans. AIEE 38, 1467. Planat, M. (1984). Propagation non lineaire des ondes acoustiques dans les solides. These de Doctorat d’Etat no. 180, Universitt de Franche-Comtt-Besanwn. Available from LPMOCNRS 32 av. de I’Observatoire 25000, Besancon, France. Planat, M., Theobald, G., and Gagnepain, J. J. (1980). L’Onde Electrique 60, 33. Planat, M., Thtobald, G., Gagnepain, J. J., and Siffert, P. (1980a).Electronics Letters 16, 174. Planat, M., Theobald, G., and Gagnepain, J. J. (1980b). L’Onde Electrique 60,61. Przyjemski, J. M. (1978). Proc. 32nd Ann. Freq. Cont. Symp., p. 426. Available from EIA, 2001 Eye Street, Washington, DC 20006. Ratajski, J. M. (1966). Proc. 20th Ann. Freq. Cont. Symp., p. 22. Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161. Reeder, T. M., Cullen, D. E., and Gilden, M. (1975). Proc. IEEE Ultrasonics Symp., cat. 75 CHO 994-4su, p. 264.

136

JEAN-JACQUES GAGNEPAIN

Reider, G. A., Kittinger, E., and Tichy, J. (1982).J. Appl. Phys. 53,8716. Schmidt, R. V. (1975).Appl. Phys. Lett. 27. Schoenwald, J. S., Rosenfeld, R. C., and Staples, E. J. (1974).Proc. IEEE Ultrasonics Symp., cat. 74 CHO 896-1SU, p. 253. Schoenwald, J. S., Shreve, W. R., and Rosenfeld, R. C. (1975). Proc. 29th Ann. Freq. Cont. Symp., p. 150. Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161. Shick, D. V., and Tiersten, H. F. (1986).Proc. 40th Ann. Freq. Cont. Symp., p. 262. Available from IEEE, 445 Hoes Lane, Piscataway, NJ 08854. Shockley, W., Curran, D. R., and Koneval, D. J. (1967).J. Acoust. Soc. Am. 41,981. Shreve, W. R. (1975).Proc. IEEE Ultrasonics Symp., cat. 75 CHO 994-4SU, p. 262. Sinha, B. K., and Tiersten, H. F., (1978).Proc. 32nd Ann. Freq. Cont. Symp., p. 150. Available from EIA, 2001 Eye Street, Washington, DC 20006. Sinha, B. K., and Tiersten, H. F. (1980).Proc. 34th Ann. Freq. Cont. Symp., p. 393. Slobodnik, A. J. (1972).J . Appl. Phys. 43,2565. Smythe, R. C. (1974).Proc. 28th Ann. Freq. Cont. Symp., p. 5; ADA 01 1 1 13. Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161. Staples, E. J. (1974).Proc. 28th Ann. Freq. Cont. Symp., p. 280. Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161. Staples, E. J., and Smythe, R. C. (1975). Proc. I E E E Ultrasonics Symp., cat. 75 CHO 994-4SU, p. 307. Staples, E. J., Schoenwald, J. S., Rosenfeld, R. C., and Hartmann, C. S. (1974). Proc. IEEE Ultrasonics Symp., cat. 74 CHO 896-1SU, p. 245. Theobald, G., Marianneau, G., PrCtot, R., and Gagnepain, J.-J. (1979).Proc. 33rd Ann. Freq. Cont. Symp., p. 239. Available from EIA, 2001 Eye Street, Washington, DC 20006. Thtobald, G., Hauden, D., and Gagnepain, J.-J. (1985a).L’Onde Electrique 65,5. Thtobald, G., Hauden, D. and Gagnepain, J.-J. (1985b).L’Onde Electrique 65,49. Thompson, R. B., and Quate, C. F. (1971).J. Appl. Phys. 42,907. Thompson, R. B., and Tiersten, H. F. (1977). J. Acoust. Soc. Am. 62,33. Thurston, R. N. (1964).Wave propagation in fluids and normal solids. In “Physical Acoustics”(W. P. Masson, ed.), vol. I, part A, p. 1. Academic Press, New York. Thurston, R. N. (1974). Waves in solids. In “Handbuch der Physik,” vol. VIa/4. Mechanics of Solids IV, p. 109. Springer-Verlag, Berlin, Heidelberg, New York. Thurston, R. N., McSkimin J. J., and Andreatch, P. (1966). J. Appl. Phys. 37,267. Tiersten, H. F. (1969).“Linear Piezoelectric Plate Vibrations.” Plenum Press, New York. Tiersten, H. F. (1971).Int. J. Engng. Sci. 9, 587. Tiersten, H. F. (1974). Proc. 28th Ann. Freq. Cont. Symp., p. 1. Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161. Tiersten, H. F. (1975). Proc. 29th Ann. Freq. Cont. Symp., p. 49. Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161. Tiersten, H. F. (1978). J. Acoust. Soc. Am. 64,832. Tiersten, H. F., and Mindlin, R. D. (1962).Q. Appl. Math. 20, 107. Tiersten, H. F., and Baumhauer (1974).J. Appl. Phys. 45,4272. Valdois, M., Besson, J., and Gagnepain, J.-J. (1974). Proc. 28th Ann. Freq. Cont. Symp., p. 19. Available from NTIS, 5285 Port Royal Road, Springfield, VA 22161. Valdois, M., Levesque P., and Hartemann, P. (1977).Proc. IEEE Ultrasonics Symp., cat. 77 CH 1264-1SU, p. 936. Valentin, J. P., Thtobald, G., and Gagnepain, J.-J. (1985).J. Appl. Phys. 58, 1388. Van Dyke, K. S. (1925). Phys. Rev. 25,895. Vella, P. J., Padmore, T. C., Stegeman, and G. I., Ristic, V. M. (1974). J . Appl. Phys. 45, 1993. Vella, P. J., Stegeman, G. I., and Ristic, V. M. (1977).J. Appl. Phys. 8,82.

RESONATORS, DETECTORS, AND PIEZOELECTRICS

137

Venema, A. Nieuwkoop, E., Vellekoop, M. J., Ghijsen, W. J., Barendsz, A. W., Nieuwenhuizen, M. S. (1987). Ultras. Ferroel. Freq. Coni. Trans. UFFC-34, 148. Vetelino,J. F., Lade, R. K., and Falconer, R. S. (1987). Ultras.Ferroel. Freq. Cont. Trans.UFFC-34, 156.

Warner, A. W. (1960). Bell System Techn. J . 33, 1193. Weglein, R. D. (1984). Proc. 38th Ann. Freq. Cont. Symp., p. 73. Available from IEEE, 445 Hoes Lane, Piscataway, NJ 08854. White, R. M. (1985). Proc. f E E E Ufrrasonics Symp., cat 85 CH 2209-5, p. 490. White, R. M. (1987). Proc. 4 f s t Ann. Freq. Cont. Symp., p. 333. Available from IEEE, 445 Hoes Lane, Piscataway, NJ 08854. White, R. M., Wicher, P. S., Wenzel, S. W., and Zellers, E. T. (1987). Ultras. Ferroel. Freq. Cont. Trans. UFFC-34, 162. Wohltjen, H.,and Dessy, R. (1979). Anal. Chem. 51, 1458. Zelenka, J. (1982). Ferroelectrics 41, 35.

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Scanning Electron Microscopy in the Petroleum Exploration Industry J . M . Huggett Exploration Department BP Petroleum Development Ltd . Moor Lane. London. England*

I . Introduction . . . . . . . . . . . . . I1. Techniques . . . . . . . . . . . . . . . . . . A . Backscattered-Electron Imaging . . . . . . . . . . B. Cathodoluminescence . . . . . . . . C . Color Imaging . . . . . . . . . . . D. Fine-Particle Analysis . . . . . . . . I11. Sample Preparation . . . . . . . . . . . . . . . A . Critical-Point Drying . . . . . . . . . . . . . B. Freeze-Drying . . . . . . . . . . . . . . . . C . Cryogenic Drying . . . . . . . . . . . . . . . D . Conductive Coating . . . . . . . . . . . . . . E . Polymeric-Film Coating . . . . . . . . . . . . F. Enviromenmental Cells . . . . . . . . . . . . . IV . Reservoir Petrography and Diagenesis . . . . . . . . . A. Introduction to Clay Minerals . . . . . . . . . . B . Sandstone Petrography and Diagenesis . . . . . . . C . Carbonate-Rock Petrography and Diagenesis . . . . . D. Shale Petrography and Diagenesis . . . . . . . . . E . Scanning Electron Microscopy in Experimental Diagenesis . V. Paleontology . . . . . . . . . . . . . . . . . . VI. Qualitative Pore Studies . . . . . . . . . . . . . . A. Pore Classification . . . . . . . . . . . . . . B. Direct Observation . . . . . . . . . . . . . . C. Porecasts . . . . . . . . . . . . . . . . . D . Fractures in Mudstone Reservoirs . . . . . . . . . VII . Petrophysics and Reservoir Production . . . . . . . . A Introduction . . . . . . . . . . . . . . . . B. Core Flood Tests . . . . . . . . . . . . . . . C. Scale Evaluation . . . . . . . . . . . . . . . D . Qualitative Porosity Measurement . . . . . . . . . E. Stimulation by Fracturing . . . . . . . . . . . . VIII . Future Developments . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . .

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* Current address: BP Research Centre. Chertsey Road. Sunbury.on.Thames. Middlesex. England 139 Copyright 0 1990 by Academic Press. Inc . All rights of reproduction in any form reserved. ISBN n-12-014677-o

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I. INTRODUCTION

This chapter covers the use of scanning electron microscopy (SEM) in the petroleum exploration industry from the time of the first commercial SEMs to the present day. Brief mention is made of possible and likely future developments. SEM is a versatile and powerful tool for the evaluation of reservoir, cap, and source rocks. Its magnification ( x 10 to x 50,000+) and imaging capabilities, in particular the considerable depth of field, coupled with the ease of sample preparation and instrument operation, have made the SEM a routine tool in the petroleum industry for the analysis of conventional core, sidewall cores, and cuttings samples. Over the past 15 years, the petroleum industry’s understanding and knowledge of reservoir rock mineral, diagenesis, texture, and pore space properties, particularly those affecting log response, fluid flow, and rock-fluid interaction, have been significantly increased through SEM data. In the 1970s, the principal geological use of scanning electron microscopy was to obtain 3D (three-dimensional) images using the secondary electron detector. X-ray analysis was only qualitative, because the surface being examined was in most cases rough and x-rays could therefore not be collected from a single spot without contamination. A few cathodoluminescence studies of polished samples were reported, but it was not until the 1980s, when back scattered electron (BSE) imaging became established as a technique for petrographic and image analysis, that polished samples and quantitative x-ray analysis became routine in geological SEM applications. Sophisticated x-ray analytical techniques developed concurrently with the increasing use of BSE imaging, and even quantitative analysis of rough surfaces is now possible. At the same time when the analytical techniques were being developed and applied, preparation techniques were being improved and methods of examining samples in their natural state were developed. These developments were of particular importance to the petroleum industry because they permitted direct observation of core still wet with its original fluids, or dried in such a way that their original textures were not lost. Techniques are covered in the first section, and sample preparation in the following one. The rest of the chapter is devoted to the discussion of topics that make use of SEM in petroleum geology. 11. TECHNIQUES

This section covers relatively new techniques used by petroleum geologists. A description of secondary-electron imaging is not included, because its use is universal.

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A . Backscattered-Electron Imaging Backscattered electrons can give an image of the surface topography of a sample, or one in which contrast is produced by variations in the mean atomic number of the materials in the sample. The BSE mode of operation is most frequently used with compositional information dominating over topographic data (BSE contrast is lost with increasing topography); this is achieved by using polished specimens. In the image so produced, elements or materials with a high atomic number appear brighter than atomically light elements and materials. Some contrast due to variations in crystal orientation may also occur. This can be recognized easily, because the image intensity varies considerably with changes in specimen tilt or rotation. In a BSE image, resolution is poorer than in an equivalent secondary-electron (SE) image, because the back scattered electrons come from a pear-shaped volume of scattering around the point of contact of the primary beam, whereas the secondary electrons come from a much shallower depth. However, the resolution is better than can be achieved with an optical microscope, and the simple variations in atomic-number contrast (composition) make it especially useful for phase and mineral identification. Details of the theory of atomic number contrast are given in Hall and Lloyd (1981). Several types of detectors have been reported over the past 20 years including: 1) low-loss electron detector (Wells, 1971). 2) solid-state detector (Kuypers et al.; 1973). 3 ) unbiased scintillator-light/guide-photomultiplier detector converted from the SE detector (Kimoto and Hashimoto, 1968). 4) wide-angle scintillator (Takahashi, 1977), 5 ) annular silicon diode (Hall and Lloyd, 1981). The mineralogical study by Robinson and Nickel (1979) introduced the BSE technique to geology. Petrographers were quick to realize the advantages, in particular for the study of rocks too fine grained to be studied in detail with an optical microscope. Robinson and Nickel used a wide-angle scintillator- photomultiplier-type detector in their SEM and were able to obtain BSE images up to x 3000 on uncoated flat samples and almost an order of magnitude greater with goldcoated samples. However, the gold coating partially or completely obscured the atomic-number contrast in the samples. Most subsequent work has therefore been performed either on uncoated or carbon-coated samples. The depth from which information is obtained and the high signal-to-noise ratio may be minimized by lowering the accelerating voltage to below 10 kV with the use of a scintillator-light/guide-photomultiplierdetector and a Yttrium Aluminium Garnet (YAG) single crystal (Bauer and Egg, 1984).

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Most operators now use solid-state detectors, because they routinely operate at TV rather than slow scan rates, which until recently was possible with very few scintillator detectors. Scintillator detectors have the advantage of amplifier stability, which is essential for long automated runs. However, there is now commercially available solid-state detectors with good amplifier stability. 1. Quantitative Analysis of BSE Images

Since images of atomic-number contrast consist of discrete levels of brightness, it is possible, so long as the particles of interest are larger than the probe size being used, to measure the proportions of each mineral in the image. The image signal is simultaneously processed by a multichannel pulseheight analyzer (Hall and Lloyd, 1981; Hall and Skinner, 1981) and recorded photographically. A numerical value (q)for the backscatter coefficient may then be determined (Table I). The spectrum may also be used to determine the proportions of the component phases, provided each brightness level is displayed as a distinct peak, with the area under the peak being proportional to the amount of that brightness level in the image and therefore to the concentration of the mineral responsible for the peak. Alternatively, the image may be quantified by interfacing with an image analyzer (IA). An image is produced by using one or several gray levels and by interfacing with an IA the relative proportions of the minerals, and size and shape data may be recorded. The SEM has been used for quantitative image analysis since the introduction of the Quantimet IA in 1972. Most early use was restricted to pore analysis (Jongerius, 1974; Ismail 1975; Bouma et al., 1977; Bisdom and Thiel, 1981). Geological use of image analysis for mineral quantification took off with the popularization of BSE imaging, because this allowed minerals to be distinguished on the basis of atomic-number contrast. One of the earliest BSE imaging studies was on pore characteristics by Bisdom and Thiel (1981). Their aim was to build up a database of reservoir standstone, mineral, and pore data that could be used to better evaluate reservoirs at the outset of exploration in a hydrocarbon province. By combining BSE imaging with IA data obtained with a Quantimet, they were able to recognize different pore types in a variety of reservoir rocks from the Dutch sector of the North Sea. Porosity patterns, number of pores, shapes, sizes, and diameters of pores were measured on the BSE-image micrographs using the Quantimet. Mineral grains were characterized by using Energy Dispersive Spectra (EDS) x-ray analysis. Bisdom et al. (1983) used BSE imaging with a Quantimet to examine Permian sandstones and limestones. Oil-bearing standstones were examined after hardening with deep-penetrating gamma radiation. By using a mag-

143

SCANNING ELECTRON MICROSCOPY TABLE I"

SiO, TiO, A1203

FeO MnO MgO CaO Na,O KZO Total Mean atomic number

4

CI Chlorite

c2 Chlorite

I Illite

K Kaolinite

27.00 0.12 22.17 16.20 0.55 18.77 0.02

49.36 0.05 37.80 0.89 0.0 1 0.05 0.03 0.80 7.10 96.09

49.9 1

0.03 84.86

26.5 1 0.08 24.36 24.86 0.32 8.87 0.03 0.13 0.15 85.31

0.16 89.15

11.50 0.143

12.38 0.154

10.85 0.135

10.12 0.129

-

-

37.16 1.01 0.07 0.84 -

The above are wavelength-dispersive elemental (WDS) analyses derived using the Ortec ZAF program with full matrix corrections. The mean atomic numbers and BSE coefficients were determined after estimating the H,O content by difference. Accelerating voltage: 15 kV. Probe beam current: 10 nA. Calculated mineral formulae from the above analyses: c1: ~ ~ ~ ~ . ~ ~ ~ ~ ~ . ~ ~ ~ ~ ~ . ~ o ~ ~ o . ~ o ~ ~ a

c2: ~

~ ~ ~ . 8 z ~ ~ ~ . 8 ~ ~ ~ ~ . ~ ~ ~ ~ o , o 6 ~ ~ o . o i ~ ~ ~ ~

I: l.16Na0.20ca0.01~A~4.07Fe0.~OM~0.0~Ti0,01 MnO.OO) Si6.35A11.35020(0H)4.

K:K0.0Z(A13.65M~0.10Fe0.07Mn0.GO)Si4.16010(oH)8

'

nification of x 60, they were able to obtain pore data from a sufficiently large area to obtain realistic porosity measurements. At higher magnifications, the clay morphology could be viewed. In pores partially filled with clay, the image contrast between the clay and the resin-filled pore was insufficient for automatic IA. Quantification of such pores was achieved by subtracting the area occupied by clay from the bulk pore area. The high cost of Quantimet, however, did rule out its widespread geological application. In the early 1980s, simpler and lower-cost IA systems became available. Pye (1984) reports the use of one such system to produce distributional images of phases in a range of rock types, including shales, with far superior resolution to that achieved by x-ray scanning maps produced with a windowless detector. A major limitation of the BSE-imaging method is that it cannot distinguish different minerals with the same backscatter coefficient. In a study that aimed to quantify hydrocarbon reservoirs by mineralogy and pore data,

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J. M. HUGGETT

Dilks and Graham (1985) showed that there is substantial peak overlap between the backscatter coefficient histograms used to identify mineral phases. They found that the sharpest peaks, and therefore the most easily quantified, were those of quartz, K feldspar, and zircon (Fig. 1). Overlap problems can now be overcome by using color X-ray maps to distinguish minerals with similar atomic-number contrast but different chemistry. Cook and Parker (1988) have shown that by using this approach, the mineralogy and porosity of reservoir sandstones may be quantified to a similar if not greater degree of accuracy to the approach that may be obtained through manual pointcounting with an optical microscope, with the additional advantages of speed and automation. This is probably destined to become a routine petrographic tool, though it is as yet in its infancy.

B. Cathodoluminescence Cathodoluminescence (CL) is the phenomenon of light emission from specimens as a result of interaction with an electron beam. The main geological use of CL is for the detection of low levels of impurities, which may indicate cement-grain boundaries and cement stratigraphies. As with x-ray analysis, in the SEM the technique has the advantage of providing both

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GREY LEVEL SCALE, 0 * BLACK. 256 -WHITE, I B.E. INTENSITY I

FIG.1. Pixel-intensity histogram for an image. The arrows are weighted mean backscatter coefficient values.

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spatial and spectral information. For a general review of CL in the SEM, see Muir and Grant (1974). Scanning CL images were first obtained by McMullan and Smith (Smith, 1956), and Smith and Stenstrom (1965) who used a focussed microprobe electron beam to observe CL from crystals in thin section. The microprobe, however, is not an ideal instrument for CL, because the optics are poor and it is expensive to dedicate exclusively for CL work. Subsequent scanning studies have mostly been of metals (e.g., Horl and Mugschl, 1972) and semiconductors (e.g., Holt, 1974; Yacobi and Holt, 1986), with only a few published geological studies (e.g., Grant and White, 1978; Dietrich and Grant, 1985). Optical microscopes have been preferred for geological studies until quite recently, because color images were easily obtained and the SEM light detectors were no more efficient than light microscopes. Two types of optical CL microscopes have been developed. 1) The cold cathode luminoscope, in which air is leaked into a sample chamber, ionized, and used to produce an electron beam (Sippel, 1965). 2) The hot cathode luminoscope, which uses a preheated cathode filament to generate electrons; these are then accelerated towards the sample (Zinkernagel, 1978). The cold cathode luminoscope has proved suitable for examination of luminescence in carbonates, the hot one for quartz. There are, however, problems associated with hot cathode systems (MacQuaker, et al; in press): 1) Although quartz luminescence is brighter, photographic exposure times, even in the most efficient systems are long, typically 2-10 minutes. 2) Considerable specimen damage is produced during electron bombardment, this results in increased luminescence decay time and consequent smearing of the image. 3) Resolution is limited to > 10pm as a consequence of light absorption in the lens system. 4) Limited further analytical capability, i.e., no BSE, SE, or x-ray detectors available. Advantages of using SEM rather than an optical system for examination of quartz luminescence include: 1) Rapid image generation; 2) minimal specimen damage; 3) ability to compare data quickly using other detectors (i.e., BSE, SE, and x-ray) attached to the microscope; 4) better resolution.

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J. M. HUGGETT TABLE I1 MINERALS AND

ROCKS SUCCFSSFULLY IhiACED BY

SEM CL."

Ideal formula Silica Feldspars Zircon Olivine Pyroxene Kyanite Kaolinite Cassiterite Corundum Sphalerite Celestine Anhydrite Apatite Fluorite

SiO, KAISi,O,, NaAISi,O,, CaAI,Si,O, ZrSiO, Mg,SiO, MgSiO, AI,SiO, AI,Si,O d O H )* SnO, A1203 ZnS SrSO, CaSO, CaAPO,),OH CaF,

Adapted from Kearsley and Wright (1988).

In the past, observation of luminescence in the SEM has been hampered by low light intensity and poor collection efficiency. Recently, major improvements in light collection and detector efficiency have made it possible to examine not only quartz but a wide range of other minerals, too (Table 11). The problem of inefficient light collection has been overcome through use of parabolic rather than ellipsoidal mirrors to collect the emitted light. Another useful development ought to be the multifunction detector with signal-mixing facility. This allows BSE and CL signals to be mixed in variable ratios, and either or both these signals may be mixed with the SE signal. Unfortunately, the detector is hampered by inefficient light collection. However, this approach to imaging has successfully been 'applied to petrographic studies of both sandstone and shale (Philips Electron Optics application note 102). 1. Geological Applications

CL of quartz has three major petrological applications: 1) Distinction between grains and cements of the same mineral (usually quartz in the SEM and carbonates in the light microscope); 2) identification of provenance from the style of quartz luminescence; 3) recognition and differentiation of quartzitic rock fragments.

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SEM-CL of diagenetic quartz fabrics makes the distinction between quartz grains and their overgrowths simple. Moreover, authigenic quartzcemented fractures within grains, which cannot be detected either optically or with other electron-beam techniques, are easily recognized. MacQuaker et al. (in press) have used SEM-CL systems with a parabolic mirror to examine both reservoir sandstones and silty mudstones. In all cases, they were able to observe luminescence and complex diagenetic zonation, even in overgrowths < l p m (Fig. 2). Kearsley and Wright (1988) have used the same system to distinguish between sutured grain contacts that are due to pressure solution (i.e., silica loss) and those produced by silica cement growth (i.e., silica gain). With SEM CL, all porosity-reducing mechanisms-cementation, pressure solution, and mechanical compaction-can be quantified. In combination with the chemical data that can be provided by x-ray analysis and BSE imaging, this is a powerful technique that should become routine for quantitative sandstone-reservoir petrography. Spectral analysis of CL emission from quartz grain cores show a variety of colors, with a violet-blue being most common (analysis of the impurity contents of the quartz shows that crystals with high titanium concentrations and low iron concentrations luminesce blue, whereas crystals with low titanium concentrations and high iron concentrations luminesce red (Sprunt and Nur, 1980; Sprunt, 1981). Authigenic quartz cements give a marked blue response, but also show longer wavelengths of low intensity “brown.” Imaging of narrow wavelength bands will undoubtedly distinguish quartz grains of different origins and discrete zones within cement overgrowths. The light wavelength data can be collected and displayed as spectra, but at present there is no software available to correct for absorption effects. Consequently, the spectral data remains qualitative. It should, however, be possible to use the chemical data derived from spectra to find answers to some important unsolved problems: namely, the actual nature of luminescence centres, their distribution, and the cation ordering of luminescent ions. Krinsley and Hyde (1971) and Krinsley and Tovey (1978) demonstrated the value of SEM CL in environmental analysis based on surface textures. They recognized at least seven different CL contrast features in quartz grains. These features are primarily due to properties of the crystal lattice rather than chemical or topographic factors, and are believed to be the result of abrasion or stress that has altered lattice conditions. By using SEM CL, Krinsley and Tovey were able to measure the area and thickness of disrupted lattice quartz on and within quartz grains. They proposed that these parameters may be a function of the degree and conditions under which grinding occured, i.e., they may reflect the energy of the environment in which the grains have been transported. For instance, quartz sand grains from dune, beach, and weathered granite environments show fewer cracks in SEM CL than do those

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(b) FIG.2. (a) BSE micrograph of quartz grains with overgrowths;(b) SEM-CL micrograph of the same area reveals four growth zones in the overgrowth.

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that have at some time passed through a glacial environment (Krinsley and Hyde, 1971). The use of this approach in identification of sedimentary environments is strictly limited to recent sediments, because the disrupted lattice layers heal with time. C. Color Imaging

The application of color to black-and-white BSE images or x-ray maps can greatly enhance clarity of the data. This is a recent development in SEM but is rapidly becoming widely used both in academic institutions and in industry. One of the earliest color imaging facilities is described by Antonovsky (1983). He assigned red, green, and blue to the BSE, SE, and low-collectorvoltage secondary-electron (LCVSE) images, respectively, and then mixed them together. Higher atomic-number features appeared bright red. Sample topography recognizeable in the SE image introduced yellow, brown, and green shades to the red image, with the shade depending upon the intensity of each signal. The LCVSE signal enhanced the sample features facing the detector, which tended to result in a differentiation between subject and background. Antonovsky used this technique to examine metallic ores; however, it has not been taken up generally by either the mining or the petroleum industries. Color imaging facilities are now routinely available with x-ray software for electron microscopes. Color x-ray maps can be produced and mixed, and BSE images can be colored by assigning colors to specific gray-level ranges. By superimposing color x-ray maps on color BSE maps, materials of the same or similar backscatter coefficient but of different composition may be distinguished. Cook and Parker (1988) used this technique to examine a reservoir sandstone, but it is not yet in routine use in the petroleum industry.

D. Fine-Particle Analysis By using a combination of x-ray analysis and IA software, size, shape, and chemical data may be obtained for particles dispersed on a low atomicnumber contrast substrate. The particles should be larger than the volume of the probe being used if meaningful chemical data is to be obtained, and smaller than the area being scanned. From the point of view of IA, fine-particle analysis is easier than making pore measurements, because the particle boundaries are clearly defined. The particles to be analyzed should be mounted on a low-mean atomic-number substrate, such as a polycarbonate filter, and well dispersed to avoid overlap, as overlapping particles of different composition cannot be placed in the mineralogical classification. Particles

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of a particular atomic-number-contrast range can be selected or deselected, for example dust and other organic contaminants may be excluded by cutting out the low end of the range. The technique is not yet in general use in geology, probably because considerable user input, in the form of identification criteria, is required before mineral particles can routinely be identified from their chemistry. There is, however, great potential for use in the petroleum industry for analyzing the fine particles that are released into drilling and production fluids, because not only can particles too small for analysis by other techniques be characterized but size and shape information simultaneously can be obtained for each particle. 111. SAMPLE PREPARATION

Under reservoir conditions, porous rocks contain fluid, with the exception of dry gas reservoirs. It is adequate to examine air-dried rock; however, if delicate, fluid-supported, fibrous or filamentous minerals such as illite or hydrous clays such as smectite are present, air-drying will distort the appearance of the minerals and may cause them to collapse or curl up. This may be very significant in reservoir studies, since collapse of clay particles alters the reservoir properties, in particular the permeability. To avoid this, special drying techniques are required. These include critical-point drying (reviewed by Cohen, 1977), freeze-drying from water and nonaqueous solutions (de Harven et al.; 1970), and cryopreservation (Sargetn, 1982; Read et al.; 1983). Without appropriate core preservation and drying, it is difficult to interpret clay mineral textures and hence their effects upon reservoir properties. This problem is particularly accute in the case of fibrous illite cements. If it is desirable to examine the rock in a wet state, special techniques are again required. Fluid-filled rock samples cannot be placed directly into a conventional SEM, because the water would vaporize and interfere with the electron generation and/or detection system. The effect of hydrocarbons is even worse, because they evaporate and deposit a contaminating organic layer on the inside of the column. To overcome these problems, the samples must either be dried and all traces of hydrocarbons removed, or volatile components must be prevented from escaping up the microscope column, either through freezing or through use of an environmental cell. A. Critical-Point Drying

Critical-point drying (CPD) allows the specimen to be dried with zero surface tension and helps to preserve delicate fabrics. In the petroleum

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exploration industry, it is regularly used for drying core that has been sealed in wax on the rig site. This is done as soon as it is recovered from the core barrel so as to preserve the reservoir fluids as completely as possible. CPD is achieved when a specimen is flooded with a fluid, which is then taken up to its critical temperature and pressure. A slight increase in temperature renders the fluid gaseous, the gas can then be bled off to leave a dry, undamaged sample because at the critical point, the surface temperature is zero. The sample may then be given a conductive coating if desired. Carbon dioxide is used because it has a critical point at a suitably low temperature (32°C)and pressure (1200 psi), is readily available, and is cheap to use. However, direct replacement by carbon dioxide is not possible because it is not miscible with water. An organic transition fluid such as methanol, ethanol, or amyl acetate may be used to progressively replace the water before deplacement by CO, is possible. The formation fluid (the fluid in a preserved reservoir core) is displaced by passing a series of water-solvent mixtures through small core chips, allowing at least a week for complete displacement, more for low-permeability samples. CPD has been used with dramatic results by McHardy et al. (1982) and Heaviside et al. (1983) to examine filamentous illite from sandstones of the Magnus oil field (North Sea). These authors found that the SEM morphology of diagenetic illite occurring in the pores of the Magnus sandstone is very dependent upon the method of drying the specimen. In air-dried specimens, there was little evidence of the ribbon morphology typical of the criticalpoint-dried specimens (Fig. 3). Instead, the illite appeared to have dried to form a continuous thin film adhering to the surfaces of sand grains (Fig. 4).

FIG.3. Critical-point-driedwispy illite.

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FIG.4. Collapsed air-dried illite.

This was an important discovery, because it explained the dramatic difference in measured brine and gas permiabilities recorded for the Magnus sandstone. Subsequent work (e.g., Huggett, 1982; Cocker, 1986)has shown that C P D does not necessarily make a dramatic difference to the SEM morphology of illite. If the filaments are sufficiently thick (the precise thickness has not been determined), they do not collapse, or at least they do not collapse so much that they cannot be observed, if the sample is air dried. This is fortunate, because a great deal of time is involved in preparing CPD specimens. It should however be born in mind that drying is not the only means by which the arrangement of the fibres can be changed. Hydrocarbons entering a reservoir can also modify the fibre distribution, giving rise to various illite textures. In a Brent group reservoir (North Sea), Cocker (1986) reports that, after careful cryopreservation and CPD, filaments are preserved in the water zone and in isolated water-saturated sandstones high in the oil zone. In oilsaturated samples, he found that the illite is matted into flake and honeycomb forms. Many textures in the oil zone are similar to those of conventionally airdried samples that have artificially induced illite morphologies. B. Freeze-Drying

Freeze-drying has the advantage of being a simple technique. The sample is plunged into liquid nitrogen, and the frozen specimen is then transferred

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under liquid nitrogen to a freeze-dryer where it is dried under vacuum at approximately - 50°C. The temperature is slowly raised to ambient temperature over a period of several days. Freeze-drying is not such a satisfactory technique as CPD, because the distortion produced by the formation of ice crystals disrupts the delicate fabric of fluid-bearing or fluid-supported clays. The technique has been very little used by geologists, because CPD was available by the time it was widely realized that careful sample drying was important for the correct interpretation of clay textures. C . Cryogenic Drying

Cryogenic methods of specimen drying probably produce the least shrinkage and distortion of water-bearing or water-supported structures. As a result, the morphologies are believed to most closely resemble those in the undried sample (Sargent, 1982). Cryosystems provide a rapid method of SEM sample preparation. The sample (which should be a few mm in diameter at most) is rapidly frozen by plunging it into nitrogen slush at approximately -210°C. The specimen is transferred under vacuum from the rapid-freezing chamber to a prechamber attached to the SEM, where it can be fractured and coated with a conductive layer. The specimen is then ready for examination on the SEM cold stage, which is kept at a temperature of - 190°C by a flow of liquid nitrogen. Cryopreservation has been used with moderate success to examine cores cut in oil-bearing sands within permafrost (unpublished work by the author). The technique was successful in so far as the oil did not evaporate and the sample remained intact, allowing observation of textures (previous attempts at sample preparation at room temperature had resulted in total disintegration). It was unsuccessful in that equipment problems resulted in ice formation partially obscuring the sample surface and limiting petrographic observation. Once such problems are overcome, the technique should prove of great value to petroleum geologists wishing to examine either oily or unconsolidated reservoir sands. The relative position of various fluids within the pores of reservoir rocks has been a major point of interest for those interested in secondary and tertiary hydrocarbon recovery. The wettability, surface tension, and capillarity of fluids in pores of various sizes and shapes, and with various lining minerals, are factors that directly affect ultimate recovery. Laboratory measurements and observations can provide indirect evidence, but until cold-stage SEM became a reality, the direct observation of fluid-rock and fluid-fluid interfaces within reservoir rock was not possible. This is an application of SEM that has exciting prospects for the petroleum industry but is as yet in its infancy.

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Schwartz (1980) examined frozen, fluid-saturated oolitic grainstone, San Andres Dolomite, and Bromide Sandstone on a cold stage designed specifically for examination of wet rock. Oil was observed in both macropores (intergranular) and micropores (intragranular) in the oolitic grainstone, but brine was not readily observed. In the crystalline San Andres Dolomite, oil was concentrated in the centre of vugs, and in the quartz-cemented lowpermeability Bromide Sandstone, thin films of oil were observed coating quartz overgrowth faces and grains. Brine distribution was mapped as chlorine using EDS. This proved essential to differentiate between brine and oil, because in the frozen state their appearance was similar. A method similar to that described above was used by Pesheck et at. (198 1) to determine the distribution and morphology of liquid phases in porous rock by SEM. Unlike Schwartz (1980), they were successful in distinguishing between oil and brine in reservoir rock. They examined Berea Sandstone that had been artificially injected with both fluids. In the micrographs, the boundaries between both the frozen liquid phases and the rock minerals are quite clear (Fig. 5).

D. Conductive Coating As a matter of principle, totally unknown samples should always be examined uncoated first. If a sample has surface features, these can be

FIG.5. Eldorado crude oil and brine in Berea Sandstone. B = brine, 0 = crude oil. Bar 100 pm.

=

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concealed by coating, or if the sample is unstable at the temperature at which coating is carried out, it may be damaged or dehydrated. Most rock samples can be examined uncoated at low kV, although they are nonconducting, because the small amount of charge that accumulates is insufficient to be detected in the image. If, however, as is often the case, it is desired to carry out x-ray analyses, it is necessary to work at a minimum of 10 kV (20-25 kV is the norm). Consequently, because rocks are poor conductors, they require coating. Poor coating will result if a sample is not properly cleaned of hydrocarbons, or if it has high microporosity that is not adequately degassed before coating. Wispy illite often proves difficultto coat adequately to prevent charging. In the authors experience, this is best overcome by using as small a sample as possible, leaving it pumping overnight before coating, and applying a light coat of carbon or gold. For most geological purposes, applying a conductive coating does not interfere with observation of the sample, because it is not necessary to work at such a high magnification that the coating can be seen. However, a low-temperature coater should always be used if clays are known or thought to be present in a sample to avoid structural or physical damage to the clay. E. Polymeric-Film Coating

Wet objects have successfully been examined in a conventional SEM after coating with a polymeric film (Filipov et al., 1984). The sample is carbon coated and then covered with a polymeric film deposited from solution. This protects the sample from dehydration and degassing in the high vacuum of the microscope. By using two symmetrically positioned BSE detectors, the contrasts due to the structures of the specimen and the film are separated. By using the secondary-electron-imaging mode, it is possible to study the structure of objects covered with films whose thicknesses greatly exceed the escape depth of low-energy secondary electrons. In the SE-imaging mode, the film transforms the high-energy backscattered electrons from the specimen into low-energy secondary electrons that are registered by the secondary electron detector. In contrast to the BSE mode of operation, the microgeometry of the film’s external surface markedly affects image contrast in the SE imaging model. Its use is therefore limited to smooth-surfaced, chemically homogeneous films. N o published work on the use of this technique for the examination of wet core samples is known to this author. This may reflect a reluctance on behalf of petroleum geologists to use complicated and timeconsuming techniques to obtain improvements in qualitative data when petrophysical methods can provide quantitative (though not directly observed) measurements of reservoir characteristics.

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F. Environmental Cells

In an environmental cell, the high-vacuum electron generation and detection systems are partially sealed off from the sample chamber. This is achieved by the use of either a closed window (Swift and Brown, 1970), fast pumping (Lane, 1970), or pressure-limiting apertures (Oatley et al., 1965; Lyon et al., 1976; Robinson, 1975, 1976, 1978). By the addition of a low-vacuum modification to the specimen chamber, Robinson (1976) was able to examine wet, dirty, and porous samples without contamination of the electron column. This technique has the added advantage of reducing sample preparation to the production of a flat surface, thereby allowing rapid examination of uncleaned and wet hydrocarbon reservoir samples, and their subsequent reuse for other purposes, because they have not been given a conductive coating. Environmental cells have received scant attention from petroleum geologists, despite the fact that they permit rapid analysis of core chips because no preparation is necessary. This may therefore be a technique of the future for rapid petrographic analysis.

Iv. RESERVOIR PETROGRAPHY AND DIAGENESIS Most SEM studies in the petroleum industry come under the topic of reservoir petrography and diagenesis. Diagenesis is the physical and chemical modification of sediments after deposition; it is often thought of as the process that makes a sediment into a rock, athough this is not strictly true, since the sediment may still be uncemented after diagenesis. Diagenesis affects the quality of sedimentary hydrocarbon reservoirs from the time of deposition onwards. The final porosity and permeability of a sandstone is greatly affected, even after burial-induced compaction, by the growth of authigenic minerals, particularly quartz overgrowths, clays, and carbonate minerals. SEM is an ideal tool for examining the effects of diagenesis on reservoir properties, if the depth and timing of such diagenetic alteration can be measured and the extent of diagenesis estimated, then prediction of the diagenetic state of undrilled sandstones may become possible and diagenesis related more closely to the timing of hydrocarbon migration and the formation of hydrocarbon traps. A . Introduction to Clay Minerals

Clay minerals are of paramount importance, in terms of the volume of SEM data that exists, both published and unpublished. For the benefit of the

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reader unfamiliar with this diverse group of minerals, a brief summary of the most frequently occuring clay species has been included. Clays are hydrous aluminosilicate minerals, which mostly occur as platy or fibrous crystals. They consist of composite layers built from tetrahedrally and octahedrally coordinated cations. The clay groups are: kandites (kaolinite, dickite, nacrite, and halloysite); illite (illite, hydromicas, and glauconite); smectites (montmorillonite, beidellite, nontronite, etc.); chlorite (ripidolite, clinochlore, chamosite, berthierine, etc.); vermiculites; palygorskite (palygorskite, attapulgite, sepiolite). Interstratified clays can also exist; of these, illite smectite is the most common . Clays may be authigenic (i.e., formed in situ) or detrital. Under the SEM, an authigenic origin is inferred from any or a combination of: 1) radiating grain-coating texture, 2) euhedral crystal morphology, 3) Overgrown upon other mineral cements. Detrital clays that have recrystallized clays are harder to recognise; criteria other than morphology may be used, such as crystallinity data. The more common clay minerals are reviewed briefly in the section on sandstone diagenesis. For an account of the structure and crystallography of clay minerals, the reader is referred to Brindley and Brown (1980), and for an account of clay chemistry to Newman (1987). B. Sandstone Petrography and Diagenesis

The major features of sandstone diagenesis are compaction, dissolution, and cementation by quartz, clays, and carbonates. SEM has been important in the study of all of these, in particular cementation. In the course of the 1970s, many geologists working independently made the important discovery, through use of SEM, that reservoir quality is profoundly influenced by the crystallographic habit and aggregate structure of authigenic clay minerals. Gradually, patterns of authigenic cement distributions emerged, and it became possible to construct broad classes for diagenetic pathways, based on environments of deposition (Hurst and Irwin, 1982), and hence to begin to make predictions as to the nature of authigenic cements in reservoirs. However, the important influence of detrital clays on reservoir quality, whose distribution may be possible to be predicted from knowledge of depositional

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environments, should not be neglected. This section reviews a selection of the more significant studies. 1. Quartz Petrography and Diagenesis Study of surface textures of grains was one of the earliest geological applications of SEM. Previously transmission electron microscopy, (TEM) had been used (e.g., Krinsley and Takahashi, 1964; Wolf, 1967), but despite excellent resolution at high magnifications, shape and surface features are not readily observed and were often damaged during the complicated and timeconsuming sample preparation. In contrast, SEM sample preparation for surface texture studies is straightforward: The sample is simply mounted on a stub and given a conductive coating if required. Interpretation of grain surface textures in terms of provenance and environment of deposition have contributed only marginally to sedimentological understanding of reservoir sandstones. However much attention has been paid to the examination of the surface microtextures of quartz (summarized by Krinsley and Doornkamp, 1973). Stieglitz (1969), Setlow (1971) and Setlow and Karpovich (1972) have attempted to relate heavy-mineral grain surface microtextures to depositional environment. This has subsequently been shown to be unreliable, due to the effects of diagenesis and previous erosion cycles. Morton (1979) demonstrated the importance of depth control on intrastratal solution of heavy minerals using examples from the North Sea. He showed that there is an overall increase in corrosion on susceptible grains with depth of burial, which correlates with a decrease in abundance of these minerals. Features indicative of both mechanical and chemical activity on heavy minerals have been observed using SEM. However the majority of the mechanically produced surface textures were interpreted as resulting from a previous cycle of erosion and sedimentation. Quartz overgrowths were also the subject of many early SEM petrographic studies. Pre-SEM concepts of how quartz overgrowths form and grow were based on optical microscopy of thin sections and on examination of replicas with the TEM (e.g., Waugh, 1965). Recognition of an overgrowth in thin section is dependent on either the presence of a ‘dust’ line between the detrital grain and the overgrowth or the overgrowth’s crystal faces. The first published SEM study of quartz overgrowths was by Waugh (1970) who combined this technique with the more classical petrographic approach. Using the Permian Penrith Sandstone of Northwest England, for his example, Waugh showed that the development of optically continuous quartz overgrowths is governed by the atomic structure and crystallographic orientation of the detrital quartz grains. In a study of over a hundred samples of sandstones ranging in age from Ordovician to Eocene, Pittman (1972) described (for the first time) both

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pressue solution phenomena and overgrowths as seen using the SEM. The following is a summary of his more important findings. The dust line contact between overgrowth and grain is usually surprisingly open, being a combination of voids and impurities such as rutile needles. Overgrowths in sandstones start with numerous small incipient crystals that may grow into a single crystal if physico-chemical conditions, space and time permit (Fig. 6 ) . This results either by overlap and merging of crystallites (Fig. 7) with the same crystallographic orientation (governed by the host grain orientation), or by enveloping of crystallites by one of them growing faster than the rest. The rate of growth of quartz overgrowths varies with crystallographic orientation, being most rapid in the direction of the C axis. Because space in sandstone pores is restricted, overgrowths extend until an adjacent grain or overgrowth is encountered. In many of the examples examined, the points of contact between quartz grains are sites of pressure-solution. These appear on grain surfaces as circular to ellipsoidal depressions marking junctions between visible grains and formerly adjacent grains (Fig. 8). In detail, a pressure-solution surface may have a series of radially arranged ridges and furrows, knobs, and pits. Subsequent to such early descriptive studies, SEM has been used to investigate the origin of quartz overgrowths with the view to understanding and predicting both its distribution in hydrocarbon reservoirs and its influence on overall reservoir quality. Houseknecht (1984) examined the influence of

FIG.6. Well-developed,euhedral quartz overgrowths,surroundingpore-filling kaolinite.

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FIG.7. Epitaxial quartz overgrowths on a quartz grain partially coated by authigenic chlorite.

FIG.8. Pressure-solutionscars are easily identified in SEM images. Scale bar = 100 pm.

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grain size and temperature on pressure solution, quartz cementation, and porosity in the quartzose Hartshorne Sandstone, from the Arkhoma Basin, Ontario. He observed that the diameter of pressure-solution scars relative to the grain diameter in sandstone increases in proportion to thermal maturity (i.e., the maximum burial temperature). The absence of clay diagenesis has been claimed as a reason for lack of quartz cementation in sandstones of the Akata and Agbada Formations, Tertiary of the Niger delta (LambertAikhionbare and Shaw, 1982). They suggested that the lack of alteration of authigenic smectite in the reservoir, which, if it had occured could have released silica into pore solutions, and the presence of thick clay films around the detrital grains are the principal causes for the poor development of quartz overgrowths. Whether or not clay coats on quartz grains inhibit overgrowth precipitation has been widely debated in the literature. Colter and Ebbern (1978) found that coats of tangentially arranged clay platelets (i.e., effectively continuous) did not seem to inhibit overgrowth nucleation. However, it is now generally accepted that whilst thin illite or smectite coats may encourage pressure solution and the formation of silica cements, thick clay coatings, especially if of kaolinite and chlorite, will inhibit quartz overgrowth development (Heald, 1956; Siever, 1959; Pittman and Lumsden, 1968; Heald and Lareses, 1974; Houseknecht and Hathon, 1987). Clay coats that appear not to have inhibited quartz overweight formation are probably discontinuous; this is substantiated by TEM studies (Huggett, 1982). 2. Clay Petrography and Diagenesis The use of SEM in reservoir studies had become routine by the late 1970s, but because it could not be used in a quantitative manner, it was largely limited to identifying authigenic (i.e., formed in situ) and detrital minerals, and unravelling diagenetic sequences. In this latter role, SEM has proved invaluable. An understanding of clay mineral occurrence is important because, firstly, authigenic clays in sandstones have a huge surface area in contact with the pore fluid, secondly, pore-filling and grain-coating clay minerals can drastically reduce reservoir permeability, and thirdly, direct observation of samples with the SEM makes it possible to distinguish the genetic sequence of mineral cements. A combination of SEM and x-ray analysis (XRA) is particularly effective for identifying mineral species. It should be remembered that many of the geological SEM studies before about 1975 were carried out without the benefit of an x-ray analyser and that the identification of minerals was based on morphology and independent x-ray diffraction data. Moreover, even after XRA became a routine aid to identification, analyses remained qualitative due to the problems of x-ray “contamination,” which occur with rough specimens typical of those

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examined by petroleum geologists. There are now software packages available that allow quantitative analysis of rough surfaces, but they are not widely used in the petroleum industry, where it is felt that qualitative analysis is usually adequate. Before describing the role of SEM in reservoir studies in general, a brief description of the distribution and crystal habit may be of benefit to the reader unfamiliar with the subject. The 1970s saw an outburst of publications on sandstone diagenesis and reservoir properties that were illustrated with scanning electron micrographs, mostly of clays, but also quartz and feldspar grains and their overgrowths. Bohor and Hughes (1971) published micrographs showing a wide range of morphologic features of kaolinite (the most common member of the kandite group of clays) from sandstones, clay deposits, geodes, and underclay deposits beneath coals. In the authigenic clays, they observed growth-related phenomena such as layering, crystal habit, topotaxis, twinning, and spiral growth. Detrital kaolinite consists of ragged, disaggregated plates. Authigenic kaolinite morpholog y has also been studied in detail and reported in many papers by Keller and co-workers (e.g., Keller, 1976a, b; Keller and Haenni, 1978; Keller et al., 1986).This is largely a reflection of the commercial value of kaolin deposits. Kaolinite and to a lesser extent dickite (another kaolin mineral) have also been described in many reservoir studies (e.g., Amr, 1971; Stalder, 1973; Sommer, 1975; Pittman and Wilson, 1977; Land and Dutton, 1978; Odom et al., 1979; Huggett, 1982, 1984; Kantorowicz, 1984; Goodchild and Whitaker, 1986; Cowan, 1988). Authigenic kaolinite morphology may be controlled by environment and time, relative to compaction, of deposition, also pore fluid chemistry and possibly the parent minerals that have been replaced by the clay. Platey kaolinite morphology (Fig. 9) is thought to be evidence of compaction or a result of further kaolinite precipitation in an already tightly packed pore; conversely, blocky kaolinite (Fig. 10) may be indicative of formation after compaction and formation of any platey kaolinite present in the same sandstone (Huggett, 1982). Cowan (1988) reports early, poorly crystalline, small particles of kaolinite and late, well-crystallized large particles. Authigenic kaolinite can also occur as an in-situ replacement of detrital mica and chlorite in sandstones and mudstones (Huggett, 1982; White et al., 1984,1985).BSE of polished thin sections is the technique used for examination of these very-fine-scale clay mineral intergrowths. Figure 1 1 shows a typical complex assemblage of clay minerals replacing chlorite. By using BSE imaging and XRA, it was a simple procedure to unravel the sequence of events. Huggett (1982) and White et al. (1984) showed authigenic clays in mica and chlorite “stacks” to be interlayered on a scale not previously recognized (Figs. 12 and 13), with clear deformation of the detrital phyllosilicate structure caused by the authigenic clay. In Fig. 13 the fine-scale intergrowths

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FIG.9. Platey authigenic kaolinite. Bar = 1 pm.

FIG. 10. Blocky authigenic kaolinite. Bar = 1 pm.

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FIG.11. BSE micrograph of detrital chlorite partially replaced by kaolinite.

FIG. 12. BSE micrograph of detrital chlorite partially replaced by apparently cohesive kaolinite.

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FIG.13. BSE micrograph of mineralogically complex assemblage of phyllosilicates. Mg-rich chlorite, K = kaolinite.

= illite, C1 = Fe-rich chlorite, C2 =

appear to be coherent, suggesting layer-by-layer replacement of the chlorite by kaolinite; however, where the kaolinite has grown to a measurable thickness, it can clearly be seen that it is noncoherent and that the kaolinite growth appears to have deformed the chlorite (Fig. 12). Further study by BSE microscopy (White et al., 1985) demonstrated that phyllosilicate intergrowths thicken and become more coherent with metamorphic grade. Work in progress by this author suggests that this form of authigenic kaolinite is more common than is generally thought, because SE SEM images d o not reveal the presence of the kaolinite. Illite is the most abundant detrital clay and is also a widespread authigenic clay. Authigenic illite occurs as platelets and laths (also described as whiskers, needles, ribbons, or wisps). Authigenic, wispy illite, observed using SEM (Fig. 3), has been described from many hydrocarbon reservoirs (Stalder, 1973; Hancock, 1978a + b; Colter and Ebbern, 1978; Sommer, 1978; Blanch and Whitaker, 1978; Guven et al., 1980; McHardy et al., 1982; Seeman, 1982; and others). It usually occurs as radial coatings on grains. Tangentially or radially arranged grain coating, “cornflake”-shaped particles (e.g., Taylor,

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1978; Huggett, 1982) are also common. It is less easy to determine whether these are authigenic but ragged, detrital, or recrystallized detrital illite. Chlorite (Fig. 14) also occurs as platelets. In authigenic form, these are usually pseudo-hexagonal, often arranged on grain surfaces with a radial boxwork texture. More rarely, chlorite has a blocky pseudo-hexagonal morphology, which is visually indistinguishable from blocky kaolinite. Detrital chlorite is usually indistinguishable (on the basis of morphology alone) from mica, when coarse grained, or detrital illite, when fine grained. Authigenic chlorite in reservoirs is less widespread than authigenic illite or kaolinite, however it has been well described (Land and Dutton, 1978; Alford, 1983; Kantorowicz, 1984; Huggett, 1984; Imam and Shaw, 1985; Hurst and Archer, 1986). This is largely because early grain-coating chlorite is found preserving porosity through prevention of quartz overgrowth nucleation (e.g., Imam and Shaw, 1985) and therefore can have an important influence on reservoir quality (Fig. 14). However, more pervasive, late pore-filling chlorite reduces porosity and permeability (e.g., Janks et al., 1985). Authigenic smectite in sandstones consists of irregular, undulose platelets, which form radial honeycomb grain coatings in samples (Fig. 15). Detrital smectite is not generally observed due to its similarity to the more common detrital illite. Authigenic smectite in hydrocarbon reservoirs is relatively rare and hence infrequently described (Stanley and Benson, 1979; LambertAikhionbare and Shaw, 1982). It is tentatively recognized on the basis of x-ray analysis and its honeycomb morphology.

FIG.14. Grain-coating authigenic chlorite. Bar = 5 pm.

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FIG.15. Illite smectite containing 90% smectite layers.

Even less SEM data is available on interstratified clays. SEM data alone is insufficient to identify these clays with certainty, because neither their morphology nor their chemistry is sufficiently distinct to distinguish them from their pure end-member constituents. X-ray diffraction data is required to identify the interlayering. Tompkins (1981) describes corrensite (mixed-layer chlorite smectite) from a reservoir sandstone in the Guadaloupe Formation (Permian), West Texas. He concluded that this clay may be distinguished from chlorite by its undulose honeycomb morphology. Consequently, it is usually indistinguishable from smectite. Illite smectite is similar to illite in appearance when it contains mostly illite layers, and similar to smectite when most of the layers consist of smectite (e.g., Hurst and Irwin, 1982; Burley, 1984; Pollastro, 1985; Keller et a/., 1986). Keller et al. (1986) used SEM to examine the morphology of illite smectite from deeply buried bentonites and hydrothermally altered Tertiary volcanic rocks from Japan. They found that the clay morphology changed from the honeycomb appearance of smectite (Fig. 15) to the platy appearance of illite (Fig. 16) at a composition of roughly 60-70% illite layers. Pollastro (1985) records honeycomb illite smectite (also identified by x-ray diffraction) with rigid laths and plates of ordered, highly illitic, illite smectite growing out from the surface of less illitic illite smectite. From this,

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FIG.16. Illite smectite containing 30%smectite layers.

Pollastro concluded that the ordered illite smectite formed by cannibalization of the smectite layers in the substrate, as has been suggested by Boles and Franks (1979).This, however, is not undisputed. The foregoing illustrates, that whilst SEM usually requires no special skills to identify the most common clays in reservoirs, those less-frequently observed, including mixed-layer clays, should not be identified by SEM observation alone, nor even by SEM and XRA, but by a combination of SEM, XRA, and x-ray diffraction. 3. Diagenetic Controls of Sandstone Reservoir Quality

One of the earliest applications of SEM to reservoir-rock evaluation was carried out by Sarkisyan (1971). By means of mineralogical and petrological studies, zones of kaolinite, kaolinite plus chlorite, and chlorite clay cement were distinguished in reservoir sandstone from the Volgograd region (Shilin, 1969). Good reservoir quality was characterized by grain-coating detrital kaolinite or when authigenic grain-coating chlorite was observed. Poor reservoir quality occurred where there was a mixture of authigenic pore-filling kaolinite and grain-coating detrital kaolinite.

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Until SEM generated serious interest in clay mineral cements, their importance was not appreciated. It was known that the permeability of sandstones depends, for a given fluid viscosity, on the rock pore sizes and pore connectivity. The latter being determined principally by: 1) Median grain size and sorting, and 2) diagenetic features such as degree of cementation and compaction.

These factors, excluding median grain size, also directly determine the porosity of a sandstone for a given median grain size. Hence, there should be a constant relationship between permeability and porosity. For quartz or carbonate cemented sandstones, this is generally the case. What was not known before the use of SEM was widespread, was the influence that authigenic clays can have on these relationships. One of the first to demonstrate this was Stalder (1973) in a significant study of an important North Sea gas reservoir, the Rotliegend Sandstone. He demonstrated that shifts in permeability/porosity trends in the Rotliegend Sandstone may be explained in terms of clay particle morphology and distribution. He showed that there are two distinct trends, one for kaolinite-cemented sandstone and one for illite-cemented sandstone. For a given porosity, he found the permeability to be lower, sometimes by several orders of magnitude, in the illite-cemented sandstone (Fig. 17). From SEM observations, Stalder was able to conclude that this was because the kaolinite, which has a blocky pore-filling texture (as in Fig. 6), is less damaging to the permeability of a reservoir than the illite, which has a wispy, pore-bridging morphology with an extremely high surface-to-volume ratio (as in Fig. 3). Wispy illite, therefore, can drastically reduce the effective pore-throat radii (which are more significant to permeability than are pore sizes) by massive subdivision of one pore throat into thousands, without significantly reducing the porosity. A similar relationship between illite, kaolinite, and poroperm was noted by Pittman and Thomas (1978) for the upper Cretaceous Almond and Ericson Formation sandstones from Southwestern Wyoming, and by Colter and Ebbern (1978) for Triassic sandstones from the northern Irish Sea basin. They found that at porosities of < lo%, small reductions in porosity by cementation produced considerable reductions in permeability, probably due to the blocking of pore throats by clay with a limited size range of some critical pore throat sizes. Through these and other SEM studies (e.g., Seeman, 1982; Heaviside et al., 1983), it has now been established that the most frequent cause of low-permeability, highporosity sandstones is authigenic, pore rimming platy, or wispy illite. Colter and Ebbern (1979) found that adequate SEM data may be collected from drill cuttings to establish the distribution of permeability-reducing illite. This was important, because the ability to predict likely poroperm relationships from observations on drill cuttings made it possible to reduce coring programs and

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2000

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hence cut well costs. However, most oil company work still uses core material rather than cuttings, because core is required for many other geological and petrophysical measurements. SEM has proved a particularly useful means of studying sandstones that, either because they are fine grained or argillaceous, have low permeability. This is because it is usually straightforward to distinguish between authigenic and detrital clay. Thomas (1978) found that early authigenic illite formation had reduced permeability and effective porosity in shaley sands from Wyoming and Alberta. As a result of early pore space reduction by authigenic clays, fine-grained sandstones, such as these, are poor liquid-hydrocarbon reservoirs but are still potential targets for gas. Pollastro and Bader (1983) used detailed SEM and x-ray diffraction studies to obtain detailed mineralogical characterizations of low-permeability gas and oil-bearing sandstone and shale sequences in the Green River Basin, Wyoming. They found discrete detrital illite to be abundant in the shales and authigenic chlorite in the

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sandstones. In the cleaner sandstones, they also found authigenic illite smectite. The authors point out that, because of these differences in clay mineral assemblages between the sandstones and the shales, log interpretations of these and similar low-permeability sandstones should not be extrapolated from adjacent shales.

4. Diagenesis and Hydrocarbon Migration In studies of the Middle Jurassic Brent Formation, Sommer (1975, 1978), and Hancock and Taylor (1978) used SEM in conjunction with thin-section petrography and x-ray diffraction to examine and interpret clay mineral authigenesis and its relationship to hydrocarbon migration. Near the top of the reservoir interval, they observed books of well-crystallized authigenic kaolinite. A little lower down in the section were rare illite flakes surrounding the kaolinite, and in the middle reservoir section, ragged books of illite pseudomorphs after kaolinite were observed. Near the base of the Brent Sand Formation, recrystallization is complete, with typical illite morphologies, rather than pseudomorphs. The authors suggested that oil migration into the reservoir inhibited and was concurrent with the illite diagenesis. The earliest oil migration into the top of the reservoir protected kaolinite from the K+-rich waters, which subsequently reacted with kaolinite deeper in the reservoir to form illite. The transition from kaolinite to illite with depth represents the gradual filling of the reservoir. However, the work described above does not explain why there are reservoirs where illite is absent from the water leg. In a SEM/opticalmicroscope study of the Leman Sandstone (Permian), Arthur et al. (1986) demonstrated that the formation of permeability-reducing illite increases with the extent of pre-Cretaceous burial, and that late kaolinite in the gas-bearing structures is precipitated from pore waters accompanying gas migration. Inhibition of diagenesis through partial filling of a reservoir by hydrocarbons has now been observed in a wide range of diagenetic settings (LambertAikhionbare and Shaw, 1982; Rottenfuser, 1982). In the Bluesky and Gething Formations (lower Cretaceous) of Northwestern Alberta, extensive deposits of heavy oil occur. In-situ extraction technologies require a detailed knowledge of porosity, permeability, and mineralogy within the reservoir and the effect of diagenesis on these porosities. The following is a summary of the work by Rottenfuser (1982). In the Gething Formation, migration of heavy oil effectively stopped, or slowed down, diagenesis. Thin-section petrography and SEM were used to establish the diagenetic sequence and the timing of oil migration. Authigenic kaolinite and illite are most abundant in the water-bearing sandstones. Secondary porosity was formed after feldspar overgrowths but before

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kaolinite formation. Oil migration occurred during kaolinite formation and halted diagenesis in the oil zone. Clay authigenesis continued in the water zone, consequently porosity is better in the oil zone; however, the effective permeability has been reduced in the oil zone by the heavy oil. Subsequent to oil migration into a reservoir, it can become biodegraded, resulting in (usually) undesirable heavy oil or tar. Biodegradation is principally caused by aerobic bacteria, which also produce large amounts of CO, and H,S as waste products. Understanding the nature of biodegradation is important, because these difficult-to-recover hydrocarbons will be increasingly important as reserves of the light crude oils become depleted. SEM has been used to investigate biodegradation of crude oil in samples from the Heterrostegina Limestone of the Damon Mound Salt Dome, Texas (Sassen, 1980). Calcite, pyrite, and some elemental sulfur were found in association with microbes, biodegraded crude oil, and gypsum. The surface of the degraded crude oil represents the present oil-water contact and is a likely site of microbial activity and mineral deposition. SEM revealed unexpected variation in surface texture. A botryoidal form was frequently observed, whilst the surfaces of other oil samples were characterized by hemisperical pits that are possibly the result of gas evolution during biodegradation. In addition, the crude oil was commonly found to occur as isolated globular masses, 10-100 pm across. The sessile microbes are intimately associated with crude oil and gypsum crystals. Moreover, surface textures of some of the samples suggested that sessile microbes have been entrapped by successive depositions of migrating hydrocarbons. SEM has also helped to elucidate what becomes of the CO, and H2S that are generated by the microbes. Secondary minerals characteristic of shallow Gulf Coast salt domes (Feely and Kulp, 1957) occur both on the surfaces of and enclosed within the crude oil. Euhedral to subhedral rhombic crystals of calcite less than 100 pm across and small crystals of pyrite are often intimately associated with the biodegraded crude oil. This is good evidence that the minerals were deposited during biodegradation.

5. Carbonate Cementation Carbonate cement in sandstones that is present as tiny crystals (micrite) is readily observed. However, sandstones that have large crystals of pore-filling carbonate are not usually suitable for fracture surface SEM examination because the samples tend to fracture across the cement crystals, and the infilling of interparticle porosity by the carbonate limits observation of any earlier clay or overgrowth cements. Consequently, this SEM technique has not been widely applied to the study of carbonate cements in sandstones.

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BSE of polished thin sections has proved more informative. Coupled with quantitative x-ray analysis it is possible to obtain data on the chemistry and zoning of the cement. From this, the pore-fluid history may be deduced.

C . Carbonate-Rock Petrography and Diagenesis

SEM has proved invaluable in petrographic and diagenetic studies of carbonate reservoirs (e.g., Sellwood et al., 1985; Aissaoui, et al., 1986; M’Rabet, et al., 1986; Purser and Schroeder, 1986). This is particularly true of finegrained carbonate cement (micrite) and chalk. In fine-grained sediments, it can be extremely difficult to distinguish between detrital and authigenic micrite, but in the SEM, the equant form of authigenic micrite crystals is easily recognized. Chalk is a very pure limestone composed almost entirely of coccolith shells (e.g., Gillott, 1969; Scholle, 1974, 1977; Mapstone, 1975; Patsoules and Cripps, 1982; Jorgensen, 1983, 1986), because their fine grain size (generally 50- 500 pm) limits the amount of petrographic information that can be gleaned using a petrographic microscope. Consequently, the emphasis of this section has been placed on chalk. No attempt has been made to cover the entire range of carbonates that has been examined by SEM, but the most significant progress is illustrated by a selection of examples. The transformation of carbonate ooze to chalk has been studied in Deep Sea Drilling Project (DSDP) cores of Eocene sediments bordering the Baltimore Canyon Trough by Wilkins et al. (1987). They found that compaction in the purely mechanical sense, which crushes and rearranges grains into a more compact microstructure, is dominant up to 100 m burial depths. Many of the radiolarian, diatom, and foraminifera tests remain intact through the ooze-to-chalk transition, though most of the coccoliths disintegrate into their constituent plates. The open tests contribute as much as 1520% of the sediment porosity. At around 300 m, there is an abrupt zone of dissolution of biogenic silica (opal A), which reprecipitates as opaline lepisperes (opal CT), and a more gradual change in the morphology of the calcite resulting from progressive dissolution and reprecipitation of CaCO, . Qualitative and quantitative SEM examination of Cretaceous Chalk petrography has led to the recognition of three nannofacies in the North Sea chalk sequence on the basis of the percentage relationship of three grain categories, i.e., microspar, carbonate mud, and nannofossils (Jorgensen, 1986). The chalk nannofacies primarily reflect increasing diagenesis with depth of burial. Pressure dissolution and reprecipitation of skeletal calcite are the most important mechanisms of chalk burial diagenesis down to burial depths of approximately 3000 m. The formation of microspar is quantitatively the most

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important diagenetic process observed, and it is believed to be responsible for a significant reduction in porosity with depth under normal burial conditions. Using SEM, Scholle (1977) observed a similar trend in progressive loss of porosity due to dissolution and cementation and from this was able to deduce approximate maximum burial depths. SEM has shown that most of the pore space in the North Sea chalks is preserved primary porosity (Harper and Shaw, 1974; Scholle, 1974; Mapstone, 1975).There is some small-scale dissolution (as in most chalks), and cementation at grain contacts (“spot welding”) is common (Rickards, 1974; Mapstone, 1975), but most of the pore space remains uncemented. These chalks, despite over 3000 m of burial, closely resemble onshore-chalks that have been buried to less than 1OOOm. The factor that best correlates with highly porous chalk is overpressuring. This has been clearly demonstrated for the Ekofisk field in the Central graben by Harper and Shaw (1974) and Rickards (1974). Ramsden (1983) used SEM to show that the Cretaceous oil shales in northwestern Queensland are in fact chalks, but that they differ from the Cretaceous chalks found elsewhere in the world in that they formed under anoxic conditions; and consequently, large quantities of organic matter have been preserved. SEM was used to examine the organic matter in detail. From this information, it was possible to identify the organic sources. Nondescript lamellae comprise the bulk of the organic matter and probably represent the algal biomass (plankton), which secreted the coccoliths forming the inorganic portion of ;he rock. Minor filamentous organic matter and rare sporelike bodies were also observed. A carbonate reservoir that is not a chalk and that has been extensively studied using SEM is the Midale Beds (Mississippian) in southeastern Saskatchewan. The reservoir is in limestones, dolomites, and evaporites. Kaldi (1982) showed that many of the characterisitc pore types in the lower zone of the Midale Beds can be related to both original depositional environment and to diagenesis. A lack of pore connectivity precludes this lithology from being an effective reservoir. In the middle zone, dissolution of calcite or arragonite from between dolomite rhombs after incomplete dolomitization has resulted in good intercrystalline secondary porosity. The upper zone consists of fractured calcareous microcrystalline dolomite. Porosity and permeability have been reduced by stylolitization and anhydrite cementation, but this has been offset by vertical microfractures, which enable hydrocarbon production to occur. SEM studies can beneficially be combined with stable isotope studies of limestones. Baltuck (1987) examined Cretaceous cyclic pelagic sediments from the North Atlantic. The pelagic cycles consist of dark, laminated marl,

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containing 75-80% CaCO, and about 0.5% organic carbon, alternating with lighter, bioturbated limestone with about 90% CaCO, and 0.1% organic carbon. SEM observations indicate significant dissolution and diagenetic precipitation of carbonate in the limestone but only minor precipitation of carbonate in the dark marl. Isotopic analysis showed that the dark marl contains heavier 18 0 and 13 C than the limestone. Precipitation of calcite under elevated burial temperatures during diagenesis would result in the light oxygen recorded in the limestone. The shift to the heavier carbon in the marl may reflect changing paleoceanographic conditions. 1. Source-Rock Studies Little is known of carbonates as source rocks compared with clastic source rocks, and until recently there has been a reluctance by petroleum geologists to accept that it is probable that some oils are sourced from limestones. Ferguson (1987) showed that modern ooids can be artificially matured, using enhanced temperature and pressure, in the presence of natural sea water, so that an evolutionary series of kerogen and soluble hydrocarbons is produced that is comparable with material isolated from British Jurassic ooliths. He confirmed by SEM that the concentric voids between layers or aragonite needles and the smaller voids between intermeshing needles in modern ooids are normally filled with algal material. This, however, is probably only a minor source of hydrocarbons. D. Shale Petrography and Diagenesis

Most SEM petrographic studies of shales have been concerned with the fabric. Until recently, this is probably because they were too fine grained for indepth petrographic analysis using SEM. Now, high-resolution SEMs are available, and thorough studies of shale petrography are possible. So far, very little at all has been published. Shale fabric is of special interest to petroleum geologists in connection with hydrocarbon migration, identification of depositional environment, and the ability of shales to act as seals to hydrocarbon reservoirs. Shales are also a common source of problems during drilling (most frequently, caving in, to give an abnormally large hole that upsets downhole log measurements, and swelling, which can cause the drill bit to stick). Such problems can often but not always be ascribed to the presence of unstable minerals. When this is not the case, the cause is likely to be physical rather than chemical, and examination of the shale fabric and textures in the SEM could prove informative. So far, this use of SEM has not been taken particular advantage of.

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Because of the difficulties involved in making detailed textural and petrographic studies of fine-grained sedimentary rocks, most theories regarding such rocks were based on gross generalizations or indirect evidence from xray diffraction until SEM and TEM techniques became available. However, very little petroleum-related SEM work on shales has been published, reflecting the continuing general paucity of shale studies. 1. Fabric Measurement

Gipson (1965) demonstrated that SEM can be used to measure particle orientation and fissility in shales by means of the “gap” test and the “chisquare test” to determine particle orientation. Combined optical and electron microscope studies revealed that particles in a fissile shale that overall exhibit a strong preferred orientation locally have a random distribution. It was inferred from these studies that fissile planes occur: 1) in zones of preferentially oriented particles; 2) at interfaces between zones of preferentially oriented particles and organic matter; 3) at interfaces between zones of randomly oriented particles and organic material. In a study of Ordovician shales from Ontario, Gillott (1969) showed that although a shale may display well-developed fissility in hand specimen and even when examined at low magnification with a SEM, high-magnification SEM images show a surprising degree of random arrangement of platey particles. These findings were confirmed by Huggett (1989), who also showed that the numerical x-ray diffraction method for fabric measurement described by Gipson (1966) can be correlated with SEM fabric studies. This enabled a numerical classification of fabric types observed with the SEM, which could be incorporated into a statistical analysis of the correlations between fabric, mineralogy, and textures. Fabric studies may improve our understanding of shale behavior during drilling. 2. Environmental Significance of Fabric It is important for petroleum geologists to be able to recognize indications of depositional environment in sedimentary rocks. With this information, it is possible to predict the extent and quality of reservoir rocks, caprocks (often shales), and source rocks (organic-rich shales). Consequently, studies of shale fabric and mineralogy ought to be a routine part of oil-company petrographic studies. However, because shales are usually cored by accident rather than design, this is not the case.

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SEM studies of clay fabric in shales have proved successful in distinguishing various depositional environments (OBrien et al., 1980; OBrien, 1987; and others). O’Brien et al. (1980) used SEM of mudstones fractured perpendicular to bedding and TEM of platinum replicas of fissile plane mudstone surfaces to establish close correlation between clay-flake-preferred orientation and fissility. He found randomness of clay flakes to prevail in nonfissile claystones. OBrien et al. (1980)demonstrated, using SEM, that clay fabric may be used in combination with other sedimentary features to distinguish hemipelagic (deep-, quiet-water) sediments from turbidites (deepwater sediments deposited by intermittent turbidity currents). By using xradiography and SEM, O’Brien (1987) investigated the effects of bioturbation on the fabric of 50 different shales. He distinguished bioturbated fabrics from those formed from lithified, flocculated clay by the absence of the stepped clay domains or stepped cardhouse fabric characteristic of the latter. In this author’s experience, however, this is not at all straightforward, since there are many factors, especially compaction and formation of authigenic cements during diagenesis, which may influence shale fabric. Only bioturbated and nonbioturbated fabrics are readily distinguished (Byers, 1974; Cluff, 1980; Rhoads and Boyer, 1982). Torresan and Schab (1987) and Huggett (1989) concluded that the dominant fabric of undisturbed shale is not controlled by the different depositional settings but rather by the dominant clay mineralogy, which may be influenced by the environment of deposition.

3. Shale Diagenesis Because most theories of diagenesis rely to some extent upon exchange of fluids containing reactive ions, between shales and sandstones, an understanding of shale petrology and diagenesis is needed if sandstone diagenesis is ever to be fully understood. This topic is covered in the section on BSE microscopy, because this is the SEM technique generally used to investigate shale petrography and diagenesis. Most published geological BSE studies have been of shales (Krinsley et al., 1983; Pye and Krinsley, 1983; White et al., 1984; Shaw and Primmer, 1987; Primmer and Shaw, 1989; Huggett, 1989). This is undoubtedly because electron-microscope resolution is almost essential for detailed petrographic analysis of shales, with the optical microscope being inadequate for most petrographic studies of fine-grained rocks. Indeed BSE imaging has probably been partially responsible for the increasing interest shown in shales by geologists. The burial diagenesis of shales is slowly becoming of major research interest in petroleum geology. The nature of the pore fluids expelled from shales and their role in sandstone diagenesis, organic maturation, the importance of fabric to seal capacity and hydrocarbon expulsion, the relative

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importance of time, temperature, pressure, and changes in pore-water chemistry to shale diagenesis are all incompletely, or poorly understood. Surprisingly few authors (White et al., 1985; Huggett, 1986) compare the diagenesis of sandstones with that of shales. Pye and Krinsley (1983) found clay stacks similar to those seen in sandstones by Huggett (1982) in lower Jurassic shales from the North Sea but interpreted them as being completely authigenic, having formed at shallow burial depths during early diagenesis. They argued that these structures are too delicate to have been transported. However, their interpretation seems improbable because micas are not known to form at the low temperatures and pressures associated with diagenesis. It is most probable that they are detrital micas partially replaced by authigenic clay. The progressive diagenesis with depth of the Gulf Coast Shales has been the focus of much attention over the years, however, the interpretation of diagenetic reactions from bulk shale X R D and chemical analyses remains speculative. Perry and Hower (1972), Hower et al., (1976), Yeh and Savin (1977), and others have proposed that the observed depth trends in clay mineralogy are the result of progressive illitization of smectite and replacement of kaolinite by chlorite. They suggest that decomposition of detrital feldspar and mica provides the extra K t and A13+ required for illitization, with S O 2 , Fe2+ and Mg2+ being released and reprecipitated as chlorite. Using BSE imaging, direct observations of shales have been made (Pye et al., 1986; Burton et al., 1987; Shaw and Primmer, 1989) that previously had only been studied in depth by x-ray diffraction. BSE observations by Pye et al. (1986)confirmed the mineralogical trends with depth reported by Hower et al. (1976) for the Frio formation in the Gulf Coast Shales and produced new evidence concerning the causes and timing of the changes. EDS analyses of clay aggregates confirmed the increase in K and A1 and the decrease in Si and Fe. From textural and chemical data provided by BSE and EDS, they concluded that the sequence of diagenetic changes was: 1) reduction of pH due to excess decarboxylation of organic matter during simultaneous iron reduction; 2) dissolution of carbonate; 3) dissolution of feldspars and micas; 4) buildup of negative octahedral layer charge due to reduction of Fe3+ in mixed layer clays; 5 ) fixation of interlayer K + and substitution of A13+ for Si4+; 6) precipitation of neoformed illite and chlorite in pores, and partial replacement of kaolinite by chlorite. More recent BSE and microprobe data from overpressured shales also in the Gulf Coast Frio formation (Shaw and Primmer, 1989 suggest that the

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illitization of smectite is accompanied by loss of A13+ and the incorporation of Mg2+/Fe2+into the structure to produce the increased layer charge required for illite fixation of K'. However, other recent work by Pearson and Small (1988) supports the reaction proposed by Hower et al. (1976): smectite

+ K + + AI3+ = illite + Si4+;

clearly this is a mechanism that will continue to be argued over for a while yet. Shaw and Primmer also found that the K + content of illite smectite in foraminifera tests and other cavities, as opposed to the rock matrix, increases with depth, becoming indistinguishable from illite. It is possible that this reaction may have contributed to the overpressuring through the release of water from the smectite layers. In an overpressured system, the fluid flow is insignificant, which usually results in diagenesis being halted or restricted to very localized diffusion-controlled reactions. However, Shaw and Primmer did not find that overpressuring has inhibited diagenesis in the Frio formation. Whereas the system may have been effectively closed in terms of long-distance fluid migration, there was apparently sufficient fluid-rock interaction and fluid migration laterally and over short vertical distances to allow diagenetic reactions to proceed. In addition to illite and illite smectite, Shaw and Primmer found authigenic chlorite (Fig. 18), kaolinite, pyrite, and calcite in

FIG. 18. BSE micrograph of fossil shell containing authigenic chlorite and illite smectite.

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shells and foraminifera tests. Pye et al. (1986) also noted infilling and replacement of foraminifera tests by illite; but perhaps because they did not observe the illitization of illite smectite with increasing depth observed by Shaw and Primmer, they concluded that this mineral is at least partially neoformed and not entirely produced through the transformation of smectite. However, it is important to remember that the pattern of shale diagenesis found in the Gulf Coast differs from that in many other sedimentary basins such as the North Sea, the Niger Delta, and the Po basin. The vast number of publications on the Gulf Coast can give an unbalanced view of the global variation in shale-diagenetic pathways. In contrast to the Gulf Coast, many North Sea Jurassic shales initially contained little smectite or mixed-layer illite smectite relative to degraded micas, and experienced low burial rates (Irwin et al., 1977; Huggett, 1986; Pye and Krinsley, 1986; White et al., 1984). White et al. (1984) also examined an argillaceous oil shale of Carboniferous age from Lothian, Scotland. The microstructure of the clay and pyrite framboids, and the angular quartz grains and calcite are clearly seen in the BSE micrographs (Figs. 19 and 20). The compaction of the

FIG. 19. BSE micrograph of an oil shale showing a vein or fossil fragment of calcite.

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FIG.20. BSE micrograph of an oil shale showing the presence of pyrite framboids.

phyllosilicates around the large quartz fragments and the pyrite framboids are clearly visible. Optical microscopy revealed neither the compaction, nor the blocky nature of the calcite. BSE imaging also revealed fine-scale intergrowths in the clays of illite and chlorite (identified by x-ray analysis). Xray mapping was used to map out areas rich in elements characteristic of specific minerals; Fig. 21 shows how this was used to map carbon. The ability to image-map for carbon, in addition to oxygen and nitrogen, allows the distribution and diagenesis of individual grains of organic matter to be monitored in terms of these elements. This could prove important in improving understanding of organic maturation and migration processes in oil source rocks, because current source-rock studies are, with few exceptions (e.g., unpublished work by Kearsley), concerned with the bulk organic matter rather than individual in-situ particles.

4. Shale Source Rocks Most hydrocarbon source rocks are organic-rich shales. Studies of source rocks have mostly concentrated on geochemical aspects rather than physical properties such as fabric and texture. Consequently, there are few published

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FIG.21. (a)BSE micrograph of an oil shale with the discrete organic matter appearing very dark; (b) secondary electron image of the same specimen in 6(a). The internal structure of the organic matter is now visible. (c) Map showing distributionof elemental carbon seen in the same specimen as 6(a),confirming the high carbon content to be expected in the organic particles. The higher the carbon concentration,the more intense is the signal (same scale as (a) and (b)).

SEM studies of source rocks, although with increasing interest in the Kimmeridge Clay (an important North Sea source rock) and greater use of BSE detectors (see above), this is beginning to change. The SEM work of McAullife (1979), Barrows (1980), and Nuhfer et al. (1981) demonstrated that the most continuous fabric element of laminated shales is the organic network. McAullife (1979) was able to examine the organic network, together with associated pyrite, in three dimensions by removing the mineral matter and bitumins with acid and carbon disulfide from shales of moderate organic content. Using SEM to study the fabric, porosity, and fractures in organic-rich Devonian mudstones from West Virginia, Nuhfer et al. (1981) were able to explain gas production in terms of fabric properties. Surprisingly, the most porous rock constituent is aggregates of pyrite, with 30-50% of the total porosity being associated with this mineral. The remainder appears to be micropores of less than 5-A diameter in the associated clay matrix. However, SEM reveals that the pyrite-associated pores in source rocks are poorly interconnected (Fig. 22), except perhaps in the organic matter, where it is possible that permeability is sufficient for primary hydrocarbon migration, because the anastomosing organic network is sufficiently well interconnected (Huggett, 1988). Numerous thin laminae appear to favour lateral migration of fluids. Most of the gas production in the West Virginia Devonian mudstones is from thinly laminated and lenticularly laminated intervals (Nuhfer and Vinopal, 1978), rather than homogenous (this frequently means bioturbated) fabrics. However, whether this could be because the laminated intervals contain more organic matter is not apparent. Total porosity in the source rocks is insufficient to account for hydrocarbon production.

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FIG.22. BSE micrograph of unusually large clusters of pyrite framboids.

E. Scanning Electron Microscopy in Experimental Diagenesis Huang et al. (1986) showed through experiments on the conversion of feldspar to illite that variation of the fluid-rock ratio (flow rate) has a significant effect on the kinetics of feldspar dissolution and illite precipitation. The results were visually monitored by SEM. Dissolution of albite in nearneutral KCI solution at 200°C and 500 bars showed that Si and Na rates of release per unit surface area of albite is faster with a higher fluid-rock ratio, and the precipitation rate of secondary minerals is lower. This has the important implication that under similar reservoir conditions, porosity and permeability may be enhanced where flow rates are high. Their experiments also showed that there can be mass nucleation and growth of illite platelets on albite surfaces in an initially acidic solution with low fluid-rock ratio (Fig. 23). In similar experiments with higher fluid-rock ratio, kaolinite formed instead of illite (Fig. 24), due to there being insufficient reactive solid to titrate the large volume of acid solution passing through the system. This work marks an important improvement in our understanding of the controls on diagenesis and has particular implications for the Rotliegend Sandstones referred to above. Kaolinite and illite are the most frequently encountered authigenic clay cements in these reservoirs, with kaolinite dominating in those with a better permeability. However, it would be unwise to assume from a single account of experimental results that this is the only control of kaolinite and illite distribution in sandstone.

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FIG.23. Illite platelets experimentally grown on a feldspar grain in a 1 M KCI solution at 200°C. Bar = 2 pm.(From Huang et al., 1986.)

FIG.24. Kaolinite platelets experimentally grown on feldspar grain in acidic solution with high fluid-rock ratio at 200°C and 500 bar. (From Huang et al.,1986.)

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V. PALEONTOLOGY The study of surface features of microfauna and microflora was one of the earliest geological applications of SEM (e.g., Hay and Sandberg, 1967; Wise and Hay, 1968a,b; Muir, 1970).With SEM, highly detailed observations could be made of the surface features of microfauna and flora (particularly pollen grains). This resulted in major improvements in classification and hence in biostratigraphy. This in turn had important consequences for the petroleum industry: better well correlation and better climatic and environmental interpretations. Today SEM continues to be widely used in paleontological studies.

VI. QUALITATIVE PORESTUDIES The purpose of most pore studies is to relate observed pore character to reservoir quality and measured petrophysical parameters, and eventually, to improve production efficiency. This section deals mainly with the qualitative study of pores in 3D: quantitative 2D (two-dimensional)pore studies are dealt with in the section on BSE imaging and image analysis.

A. Pore ClassiJication

Pores in sandstones may be either simple, as in a clean quartz sand, or they may be partially filled with clay. According to Neasham (1977),common pore types, in order of decreasing reservoir quality and pore aperture size, are: 1) discrete, loosely packed clay particles partially filling pores (Figs. 9 and 10); 2) clay lining pores (Fig. 14); 3) clay bridging from one sand grain to an adjacent sand grain (Fig. 25).

Soeder and Randolph (1984) used the SE imaging mode of polished plug ends to identify pore types and relate them to core-analysis poroperm measurements. Observations of the Mesa Verde Sandstone (a tight gas reservoir) revealed three types of pores: 1) grain-supported pores; 2) solution pores connected by narrow intergranular slot pores; 3) matrix porosity.

Type 2) was the most frequently observed in the Mesa Verde Sandstone.

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FIG.25. Pore-bridgingauthigenic illite. Bar = 1 pm.

Carbonates contain the following pore types: 1) interparticle (primary or secondary due to removal of cement); 2) intraparticle (primary, e.g., within a fossil fragment, or secondary due to partial dissolution of a particle); 3) vuggy (very large, often due to dissolution); 4) moldic (due to complete dissolution of a fossil or fossil fragment).

B. Direct Observation Porosity may be directly observed in the SEM using either fracture surface samples or polished thin sections. BSE of polished thin sections is particularly valuable for observing pore-filling cement and porosity distributions in 2D. Cowan (1988) used BSE imaging in this manner to complement SE fracture surface imaging and other standard petrographic techniques in a study of the diagenetic textures in Carboniferous reservoir sandstones from the East Midlands, United Kingdom. Most oil companies use SEM to make simple visual assessment of porosity. But it is permeability that determines whether a reservoir with good porosity will flow, and this is hard to estimate using SEM. In one of the earliest SEM pore studies, Weinbrandt and Fatt (1969) attempted simple permeability measurements using SEM. This was probably the first study to produce

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semiquantitative measurements from SEM images of porosity, pore sizes, and the tube interconnection parameter, B,which is defined as the number of flow channels connected to each flow channel. Stereo pairs were found particularly useful for B-parameter measurement, because the additional depth perception enabled the viewer to recognize pores partially obscured by overhang. The connectivity has also been expressed as the number of throats connecting each pore by Wardlaw and Cassan (1978),who called it the “coordination number.” Timur et a/.(1971) used SEM to investigate the pore systems in a diverse group of lithologies at magnifications, which for the time, were very high (over x 10,000).The main purpose of this study was to investigate the extremely small pores in shales and granites, which had not previously been imaged; they did, however, also examine sandstone, limestone, and dolomite. In a study of the Spirit River Sandstone (a tight gas sandstone), Walls (1981) used qualitative SEM observations to interpret the measured permeability data. He concluded that pore structure was the major factor in determining permeability behavior, with clay content being of secondary importance in the Spirit River Sandstone. Pore types identified were flat cracks between quartz grains and a few open pores partially filled by illite. He concluded that the flat cracks provide most of the permeability at low effective pressures, however they would easily be closed by increasing overburden pressure and may not be significant at reservoir depths. SEM has been widely used to determine porosity types in fine-grained carbonate reservoirs. In North Sea Cretaceous Chalk SE (Harper and Shaw, 1974; Rickards, 1974; Mapstone, 1975; Kaldi, 1982; and others), Matiisen and Shehata (1987) showed that the two main porosity types in the Midale Beds of the Tatagwa oil field, Southern Saskatchewan, could be related to reservoir properties measured from core plugs and downhole logs. The Midale Beds consist of a marly dolomite with good to excellent intercrystalline porosity and a vuggy unit with intergranular, moldic, and vuggy porosity. Because of the varying types of porosity and its varying areal distribution, these two limestone units show a significant difference in reservoir characteristics. Consequently, each one requires a separate approach with regard to completion, production, and enhanced recovery. C . Pore Casts

Pore casts are epoxy-resin replicas of pore space. Prior to the widespread use of SEM in petroleum geology, pore casts had not been much used, because light microscopes are inadequate for examining all but the largest pores and pore throats and have a severely limited depth of focus. Pore casts are undoubtedly the best technique available for evaluation of pore shapes and their connectivity, but they have the disadvantage of not

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being quantitative (except in the case of a complex technique described below). This is best resolved through integrated studies such as that by Pittman (1979), who showed how SEM examination of pore casts and their corresponding rocks can be integrated with mercury porosimetry data and optical microscopy to evaluate the pore geometry and its influence on reservoir productivity. Pore casts are made by dissolving the rock in HCl and then HF after resin impregnation of the pore space. Pittman and Dushatko (1970) showed, using pore casts, that a continuous network of pores surrounds every grain in quartz sandstones with a few percent or greater porosity. These interconnected pores are commonly invisible in thin sections. Pittman and Dushatko observed that the original pore network in a quartz sandstone shrinks without disruption of continuity as a result of quartz overgrowth, but that this still leads to drastic reductions in permeability. This important observation has subsequently been supported by the observations of tight gas sandstone reservoirs by Walls (1981) and Soeder and Randolph (1984). In contrast, they noted that the same volume of intergranular cement (e.g., calcite) concentrated in fewer pores would have less effect on permeability. The distribution and flow of a nonwetting phase such as oil within a reservoir is of interest to petroleum engineers. Through examination of Wood’s metal pore casts obtained over a range of impregnation pressures, Swanson (1977) was able to observe the extent to which a nonwetting fluid was able to penetrate the pore network of the Permian San Andres Limestone. At low impregnation pressures, only the largest, most accessible pores will be impregnated, and as the pressure is increased, the width of the pore throats that are penetrated decreases. From this information, the pores from which hydrocarbons will most readily be expelled during a water flood, and those that are likely to be bypassed may be identified. Moreover, estimates of the relative proportions of various grades of pore allows rough calculation of the amount of hydrocarbon that is recoverable. This is now a routine petroleum engineering procedure. In the San Andres, Swanson found pores 3 mm long and with diameters of up to 80 pm (created by natural leaching of carbonate skeletal fragments), which contributed greatly to the permeability (Fig. 26), whereas the dominant dolomite matrix pore system with very small pores was bypassed by Wood’s metal pore casts, except at the highest impregnation pressures (Fig. 27). The implication is that the tubular pores offer pathways that, depending upon wetting states, could bypass the smaller pores during a water flood, leaving much oil behind. Chalk has been the subject of numerous resin-impregnation pore studies. This is because in some areas it is both an important hydrocarbon reservoir and has a wide range of porosities and permeabilities. Even with the high

FIG.26. Wood's metal pore cast at low impregnation pressure.

FIG. 27. Wood's metal pore cast at high impregnation pressure.

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magnification offered by the SEM, direct visual examination of the pore space provides little information about chalk microstructure. But SEM examination of pore space casts in chalk can be very informative, particularly if stereo-pair micrographs are used, because these make it possible to undertake quantitative analyses of pore geometry. Walker (1978) impregnated chalk samples from southern England using an epoxy resin. Patsoules and Cripps (1982)were successful in producing resin casts of chalk, which replicated every detail of the microstructure. Their SEM observations of complete pore networks and internal microstructures in chalk showed that the accessible pores are connected by tubes and sheetlike throats. Various pore shapes were observed, including tabular, spherical ellipsoidal, polyhedral, discoid, and ring-shaped (in section). Quantitative analysis of pore-size distribution of the Upper Chalk from East Yorkshire (England) showed that the bulk of the pores have a range between 0.3 pm and 10 pm, with a median size of 1.5 pm for throats and 5.9 pm for pores. These results are rather different from those obtained by Price et al. (1976), who, by using a mecury-injection method, found pore diameters between 100 and 0.012 pm with a median size of 0.39 pm. However, this could well reflect lithological variation, since the data of Price et al. was obtained from the Middle rather than the Upper Chalk. Quantitative measurements by Patsoules and Cripps of pore connectivity give values of between 13 and 18 for the Upper Chalk (no units given). As should be expected, they found a strong inverse correlation of pore connectivity with permeability, rather than pore or pore-throat diameter. Walker (1978) records different pore diameters for mercury injection and SEM measurements from the same samples. In this case, the difference is probably due to the fact that the mercury-injection measurements are calculated as spherical diameters, whereas SEM observations indicate that the pores are lamellar. Yadav et al. (1984)developed a technique for examining the distribution of wetting and nonwetting phases in reservoir rock. They injected Berea Sandstone with wetting (resin) and nonwetting (Wood’s metal) phases, which could then be solidified. Serially cut, polished thin sections allowed them to build up a picture of the 3D distribution of the phases. The nonwetting phase engulfed some clay particles, but in most instances the clay did not allow the metal to penetrate the entire pore space, because the capillary pressure was low. The wetting phase penetrated into the kaolinite booklets, but only partially into clays that were very fine-grained and in-situ replacement of grains. A rather more complicated method for examining the 3D structure of pores was evolved by Straley and Minnis (1982).A resin-impregnated sample was etched out completely by using acid and replaced with a second resin of contrasting backscatter coefficient. Replicas produced by this means were sliced with a microtome to give sections just a few microns thick. Serial

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sectioning revealed the 3D structure. Although a much more complicated procedure to follow than pore casting, this technique has the advantage that the data is readily digitized and hence may be used quantitatively. However, due to the complex and time-consuming sample preparation, this technique has not been widely adopted by the petroleum industry.

D. Fractures in Mudstone Reservoirs Many economic gas reservoirs exist in shales in the United States, though not worldwide. In these reservoirs, fractures are the crucial conduits. SEM observations of shales suggest that microfracturing does not make a significant contribution to mudrock porosity (Nuhfer et al., 198 1; Huggett, 1988). Natural macrofractures enhance production flow rates, but appear to provide a minor contribution to total reservoir storage volume (Nuhfer and Vinopal, 1978; Vinopal et al., 1979; Vinopal, 1981). Most gas encountered in macrofractures is depleted during the first few hours of production (Schettler, 1979). Nonetheless, the presence of natural fractures in gas wells can improve production, and the completion of such wells by hydraulic fracturing is a proven method for increasing production. SEM study of the surfaces of natural fractures has helped to explain why some fractures are associated with increased open flow to wells, whereas others are not (Vinopal et al., 1979). Fractures with high open flow invariably have surfaces whose original fabric is undamaged (Fig. 28). In contrast, those

FIG.28. Natural fracture in mudstone, the original fabric is undamaged.

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FIG.29. Slickensliding on natural fault in mudstone.

natural fractures that appear to have no association with enhanced gas production reveal surfaces whose fabric has been destroyed (Fig. 29). In the former type of fracture, a tension stress appears to create failure of the individual particles, so that the fabric remains open and undamaged. In the latter type, the fracture surface is glazed, which in organic-rich shales appears to be an effective seal (Nuhfer et al., 1981). The sealing properties of such fractures have not been tested for a wide variety of shales, so their overall importance is unclear. Nuhfer et al. (1981) showed that laboratory preparation damage to shales is analogous to that induced by drilling wells and by slickensiding on faults in thinly laminated shales as shown in Fig. 29. The rock permeability is damaged by smearing of clay across the cut surface. Conversely, artificial tensile fractures have pores open to the fracture. More petrophysical studies of samples with induced damage are required to measure the extent of the permeability damage.

VII. PETROPHYSICS AND RESERVOIR PRODUCTION A . Introduction

The 3D relationships between grains, clays, and pores as determined by SEM aid the interpretation of porosity and permeability and other petrophysical measurements, and may aid in predicting core flood efficiency. The

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potential for problems involving clay swelling or migration of loosely attached fine particles may be qualitatively assessed from SEM images. SEM of fracture surfaces is particularly useful for these types of studies because it clearly shows the pore surfaces exposed to fluids, rather than a section through the grains and their coatings as is seen in thin sections. The technique also provides an insight into fracture mechanisms and the rock-fluid interactions resulting from real or experimental hydrocarbon production operations. Experimental studies have the advantage that the rock sample may be examined before and after fluid flow tests.

B. Core Flood Tests Acid stimulation of the reservoir is undertaken to enhance permeability. In the near wellbore region, acidization is often undertaken to remove drilling mud that has invaded the rock and reduced the permeability. A number of approaches have been tried using SEM in conjunction with core flow tests, to evaluate the effects of acidization and other treatments used in drilling and production. If only the effluent is of interest, then the filter on which it is deposited can be coated and directly observed in the SEM. The examples below summarize the range of procedures that have been adopted. Hancock (1978a) examined the effluent from North Sea sandstone plugs that had been injected with seawater. The purpose of this study was to determine whether their were any deleterious effects of injecting unfiltered seawater into the reservoir. He found that pores became plugged with fines, which by SEM observations of the filters were revealed to be planktonic particles from the seawater. Hancock showed that whether the particles form a filter cake or penetrate into the reservoir and block the pore depends on the relative size of the particles and the pore-throat diameters. The most important plugging constituents proved to be coccoliths of 3-5 pm diameter, which unfortunately are difficult to filter out from seawater, though this can now be achieved. The simplest method for examination of the rock both before and after flooding involves cutting pairs of plugs, using one of each pair for the treatment and the other as a control. Both samples are then examined in the SEM. This approach was employed by Pittman and Thomas (1978) to examine the effects of flooding sandstone core with a surfactant-water mixture. The original mineralogy as indicated by the control plug included partial grain coats of smectite. In the treated sample, the smectite had become detached and had migrated into pore throats and partially blocked them, thereby reducing permeability. A similar method involves the removal of a slice from either end of a core plug before the plug is subjected to flow (Boyer

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and Wu, 1983).This has the advantage over the first method that there are less likely to be differences between the two ends of one plug than there are between two plugs. The slices are examined in the SEM to determine the grain and pore structure prior to treatment. After the flow test, the treated core plug is examined using the untreated ends as a reference for evaluating changes. The plugging of pores and dissolution effects may be observed, but because the same pores and grains are not examined before and after the test, minor changes, such as small-scale calcite dissolution, may not be detected. Nor is it possible to be sure whether an open pore was previously filled with loose particles or not. Kantorowicz et al. (1986) used SEM to examine sandstones, partially cemented by thin quartz overgrowth and siderite, before and after acidization. They found that acidization removed siderite and chlorite, with a consequent slight rise in porosity. However, the dissolution released fine clays and siltsized quartz grains into the pore space. This countered any improvement in permeability resulting from the siderite and chlorite dissolution. In addition, the thin quartz overgrowths were etched, resulting in an increase in the proportion of loose grains. These results indicate that acidization could result in either production of sand and other fines with the hydrocarbons, or the fines could cause minor blockage of the pore throats around the wellbore. Which of these happens will depend upon whether the fines are predominantly smaller or larger than the pore throats. Neasham (1980)showed that whilst kaolinite is stable in the presence of acid, because it is frequently loosely attached to grain surfaces, it has the potential to be mobilized when fluid flow occurs during production. Kantorowicz et al. (1986) also examined sandstone core plugs before and after water injection. Permeabilities measured on the same plugs were lower after injection, but some of the loss was reversible. The authors concluded that the reversible permeability loss was due to fines migration, and the irreversible loss was due to expansion of swelling clay. The effect of brines saturated with CO, on limestone reservoirs was investigated and observed by Sayegh et al. (1987) and Krause et al. (1987) using SEM. The core floods were conducted in both “circulating” and “oncethrough” modes. The measured permeability changes during flooding ranged from large increases to decreases. All postflood cores showed dissolution textures. Large crystal faces display rhombic corner- and staircase-etching features, whilst etching in micrites gives the rock a chalky appearance, which close up was seen to be due to micron-sized needles and abundant crystalshaped pits. SEM observations also showed that the brines etched and followed preferred paths, forming a braided network of variably sized tubules. Insoluble minerals such as quartz and illite bound to the matrix and mixed with drilling fines were released during the etching process. These migrated and, in some cases, became lodged in constrictions. Hence, as with acidization,

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the result of using carbonated brines, from the point of view of enhanced oil recovery, may or may not be beneficial. McLane and Scott (1983)also used SEM to study the effects of acidization on reservoir rocks, but in an indirect manner. They were concerned with evaluating the maximum HCl strength that may be used in acid stimulation of a highly fractured, slightly dolomitic sandy limestone from the Mission Canyon formation, North Dakota. The rock was characterized through detailed SEM/x-ray analysis and optical microscopy. One-gram samples were tested for acid solubility by placing them in 5 % , 15%, and 20% HCI at room temperature and allowing them to react for three hours. The fines remaining after dissolution were examined by SEM and analyzed by using an EDS attachment. They were found to consist of quartz, illite, illite-smectite, albite, and incompletely dissolved dolomite and anhydrite. The proportion of sample remaining after acid treatment (i.e., the fines) decreased with acid strength, thereby confirming that low-strength acid is most suitable for acid stimulation because it releases fewer fines than does high-strength acid. A system whereby the same point in a sample was examined before and after treatment was used by Thomas et al. (1976). The samples were reference marked before examination so that clay particles could be relocated. After preliminary examination in the SEM, the samples were stripped of their conductive coating (aluminium rather than gold or carbon was used for the coating because it is easily removed by acid), treated, recoated, and reexamined with the SEM. Thomas et al. (1976) used this technique to evaluate the effects of commonly used stimulation (HCI and mud acid) and clay stabilization treatments (hydroxy aluminium and zirconium oxychloride) on Berea Sandstone. Results showed that on prolonged exposure, hydroxy aluminium forms extensive deposits on clay surfaces and produces fusion of platelets. Zirconium oxychloride, however, was found to stabilize clays without buildup of reaction products on the clay surface. Mud acid was found to rapidly dissolve clays within the matrix of the rock, with negligible attack upon the sand grains. The technique described above has two disadvantages. The samples examined are not those used in the flow tests, instead they are saturated with the solutions, whilst the core flow test samples are simultaneously flushed with the same solutions. The effect of flow (as opposed to saturation) on particle movement and filtrate straining can therefore not be evaluated. The other disadvantage is that the aluminium coating is stripped with a 28% HCI solution. Thomas et al. demonstrated that this caused no morphological damage to kaolinite or illite, but this would not be the case for chlorite or carbonate minerals. Also it was not known whether the surface chemical properties were changed. Coulter et al. (1983) and Rothbard et al. (1987)overcame these problems by

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clearly marking each end of the core plug with locating marks and by examining the sample uncoated before treatment. To prevent charging, this was done at 5-kV accelerating potential. Coulter et al. (1983) used this technique to examine the effect of fracturing fluid on permeability. The permeability of each sample was measured before and after treatment with 2% KCI solution in the pH range 4.7 to 11.5. They found only very slight permeability changes and negligible change in the surfaces observed with the SEM (minimal in the range pH 7 to 9). Rothbard et al. (1987) examined uncoated reservoir core plugs before and after formation of a siderite mudcake, a 6% HCI preflush and a 2% H F acid wash. The mudcake occluded many pores at the point of contact, indicating mud invasion (Fig. 30). The 6% HCI was not found to be effective at removing the mud (Fig. 31); the subsequent 2% H F flood was, although it also caused pitting of the framework grains, especially feldsparts. SEM is also an ideal tool for the examination of effluent from core flood tests, or for “real” fines produced with water or hydrocarbons. The particles are readily mounted on a stub; or if they have been collected on a filter, this may be attached directly to a stub. This technique may be used to examine the size, shape, and mineralogy of fines (Muecke, 1978; Ward et al., 1981; Udell and Lofy, 1985). Software is now available for both physical and chemical quantification of fine particles. By adding in chemical criteria for mineral identification, it is possible to obtain output that combines mineralogy and

FIG.30. Berea Sandstone with drilling mud coating grain surfaces and bridging pores.

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FIG.31. Berea Sandstone after mud treatment and subsequent 6% HC1 treatment.

size data, either plotted as area/volume or as the number of particles in each category. Now that fines can be quantified, their study is likely to become an important SEM application. Crocker et al. (1983) used SEM to obtain rapid analyses of pore size, pore geometry, pore size distribution, and diagenesis of sandstones used in ionexchange capacity experiments. Understanding ion-exchange processes in reservoir rock is an important part of understanding the adhesion of oil to rock on a molecular scale, which could assist selection of chemicals for oil displacement in tertiary hydrocarbon recovery. They found: 1) ion-exchange capacities of rocks are directly related to the type of clay and its distribution among the sand grains in the rock; 2) ion-exchange capacity and surface area are related to the distribution of the clays in the rock matrix. C . Scale Evaluation A minor, but important, use of SEM in petroleum production has been the examination of pipe scales (Figs. 32 and 33). The surface textures of these can give valuable indications as to the type of fluid that deposited the scale and the flow conditions under which deposition occurred. SEM also provides a rapid means of obtaining an x-ray analysis from which the nature of the constituent minerals can often be identified, as scales rarely have a complex mineralogy.

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FIG.32. Barytes scale. Bar = 10 pm.

FIG.33. Iron oxide pipe scale from an oil terminal. Bar = 10 pm,

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Scale formation is a problem in injection and production wells and in the associated process equipment. It is frequently the unwanted byproduct of seawater injection into a reservoir to maintain well pressure; either the pH and temperature change may precipitate insoluble salts from the seawater, or the mixing of seawater and the formation water may cause precipitation of solids. Both mechanisms can result in damage to the near-well-bore formation in injection wells. In production wells, the associated pipes may also be affected, particularly by sulfur-bearing hydrocarbons. Read and Ringen (1982) used SEM coupled with x-ray diffraction (XRD) to observe laboratory tests designed to evaluate the extent of formation damage that could result from scales formed within a North Sea reservoir scheduled for major seawater injection. As a result of this study, they were able to prepare remedial and preventative (scale inhibitors) strategies for the real operation. Porous alumina cores (used because they are temperature and pressure stable) were first injected with reservoir formation water. They were then injected with formation water and seawater, from separate ports to prevent scaling of the outside of the core before the waters entered into the pores. SEM examination revealed pores blocked by large euhedral crystals of strontian barite [(BaSr)SO,]. These are mainly large planar crystals, sometimes twinned (in cores where a high proportion of seawater was injected, or stacked (Fig. 32). Where the injection fluid is dominated by formation water, well-developed rosettes of crystals are more frequent. The worst permeability loss occurred for blends of 90% formation water and 10% sea water; the loss increased with decrease in the percentage of seawater injected. SEM has also been successfully used to determine the composition, textures, and growth history of pipe scales. These commonly consist of carbonates, sulphates, or iron oxides/hydroxides. Morphologies include feathery gypsum, baryte (Fig. 32), or (BaSr)SO, crystals, blocky porous baryte or calcite, arld many other crystal morphologies that can be used as indicators of the chemical environment of deposition. Iron oxide/hydroxide scales often include siderite or sulfur crystals and have a globular (Fig. 33), vuggy, or vesicular form, with abundant gas/fluid escape holes visible with the SEM. BSE microscopy has proved particularly useful in this respect for distinguishing zones of CaCO, scale from BaSO, or (BaSR)SO, and for unravelling the sequence of chemical events that led to the scale formation. D. Qualitative Porosity Measurement

SEM has found widespread use in the petroleum industry as a means of making rapid and simple qualitative measurements of reservoir porosity. Such data is now routinely used to improve interpretation of log and core analysis data, and thin-section measurement of visible porosity. In particular,

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potentially productive zones in carbonate reservoirs may easily be missed because log suites fail to indicate the extent and nature of effective porosity. In an example from the Silurian Interlake Formation, Vida field, northeastern Montana, Powell and Stevenson (1981) showed that large moldic pores isolated by a tight dolomite matrix, and abundant microporosity developed in pellets and carbonate muds may yield anomalously high log porosities, which taken in isolation would be misleading. Similarly, in oomoldic limestones (i.e., limestones that contain molds of ooids) such as the Jurassic Smackover Formation, Texas, can exhibit high resistivity, high porosity values and low calculated water saturation (which is frequently taken to indicate high oil saturation), yet have low permeability and produce water with little or no oil. The ooids in the Smackover were cemented by a fine-grained calcite cement; the ooids were then dissolved leaving large, poorly interconnected pores, hence the low permeability despite the high porosity. Mitchell-Tapping (1983) demonstrated by using SEM that the Smackover high porosity and low water saturation was due to the relatively low surface areas of the oomoldic pores. There have also been instances of over-estimation of the irreducible water saturation for specific zones of the Smackover (Turner, 1983), which again has been interpreted with the aid of SEM. In these zones, the recrystallized ooids have rough irregular surfaces as well as intercrystalline porosity within the particles. Water adheres to these grain surfaces and occupies some of the intercrystalline porosity in hydrocarbon-productive zones. This results in high water saturation values despite the presence of hydrocarbons in the pores. Using log values to pick diagenetically altered zones (confirmed by SEM data), Almon and Schultz (1979) also determined that anomalous water saturation values are related to large pore-surface areas, for the Cretaceous Muddy Formation (Powder River Basin). Clay-rimmed pores have particularly high surface areas, and hence may give rise to especially high water saturation measurements. Similary in carbonate reservoir rocks, it is important to determine the relative amounts of micro- and macroporosity. When the reservoir has approximately equal amounts of each and the macropores are interconnected, bound water in micropores can yield high water saturations based on log calculations. This in turn may lead to underestimation of hydrocarbon production potential. Kieke and Hartmann (1973) used SEM to assess the effects of microporosity (defined as pores < .5 mm; Pittman, 1971) on water saturation. By using pore geometry in formation evaluation and by relating their findings to log responses, they determined that micropores may account for many anomalous results, in particular high values for log-derived porosities for reservoirs that have low measured permeabilities or low hydrocarbon flow rates. A rather different, but equally important clay mineral effect on measurements of reservoir properties was reported by Heaviside et al. (1983). They

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found puzzling differences between reservoir permeability derived from well testing data and laboratory-measured core permeabilities. In the oil zone, well test data indicated reservoir permeability to be about 1.2 times greater than that from routine core data, rising to 20-30 times greater in the water zone, yet initial SEM core studies showed no significant petrographic differences between the oil and water zone. Subsequent permeability tests on preserved core samples that were prepared by critical-point drying (see section on sample preparation) gave values comparable with the well test data. This suggested that it was the drying process that was responsible for the high permeability to gas. This was confirmed by SEM examination of critical-point-dried core chips. These show large amounts of filamentous illite clay, spread throughout the pore space (similar to that shown in Fig. 3). This clay had not been observed in the air-dried samples because it had collapsed onto the grains, and being very thin particles (a few nm at most), they had no relief detectable within the resolution limits of the SEM (as in Fig. 4). The much greater discrepancy between the well test and laboratory permeability data for the water zone, compared with the oil zone, was found to be due to the presence of greater amounts of filamentous illite in the water zone. The actual amount of clay is not great in either zone, but its effect on permeability is considerable because this clay has an extremely high surface area to volume ratio, combined with morphology that results in a tortuous pore system. E. Stimulation by Fracturing

The SEM has seen increasing use as a means of studying fracture mechanisms in rock since the pioneering work by Brace et al. (1972). Most subsequent work has concentrated on fracture mechanisms. More recently, SEM has been used to examine explosively induced damage in sandstones, in order to test such fracturing processes as a means of assessing their suitability for reservoir stimulation. Results have not been promising. The absence of long fractures from the gas-bearing sandstones observed by Durham (1981) after experimental explosive loading suggests that reservoir stimulation by this means is unlikely to be profitable.

DEVELOPMENTS VIII. FUTURE SEM began as a tool for making qualitative observations and has evolved into one capable of sophisticated analytical measurements, which are increasingly automated. This is reflected in the increasing use of SEM to obtain analyses of individual particles, quantification by point counting, and

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pore measurements. Manual point counting of thin sections could become a thing of the past. The accuracy will be increased once robust means are devised for identification of minerals, and the precision will be improved because many more particles may be measured in less user time. The development and improvement of BSE and CL detectors have meant that chemical variations can be observed, and improved resolution has recently enabled the detailed examination of fine-grained rocks. The detailed study of fine-grained rocks is an SEM application that will undoubtedly become more frequently used in the petroleum industry, both by those interested in the diagenesis of shales and its influence on the diagenesis of surrounding rocks and by engineers investigating the effects of drilling and drilling fluids upon shales. The study of quartz grains and cements is beginning to benefit from recent improvements in CL detectors, and no doubt other minerals will too. A disadvantage of SEM has been that three-dimensional observations have always been limited to qualitative measurements of pores and particles exposed on fractured surfaces. Now a software package is available for measurement of depth in stereo pairs. If this can be combined with automated image analysis of rocks and pore casts, it will be a significant advance in accurate pore and pore throat measurements. Petroleum geology is continually becoming a more numerical subject. So long as the development of techniques, such as those outlined, continues to meet the demand for new types of measurement and improved accuracy, SEM will remain an important tool in the industry. REFERENCES Aissaoui, D. M., Coniglio, M., James, N. P., and Purser, B. H. (1986).In “Reef Diagenesis” (J. H. Schroeder and B. H. Purser, eds.), p. 112. Springer-Verlag, Berlin, Heidelberg. Alford, E. V. (1983).Unpublished M. Sc. thesis, University of New Orleans. Alrnon, W. R.,and Davies, D. K. (1979). In “Aspects of Diagenesis” (P. A. Scholle and P. R. Schluger, eds.), SEPM Special Publ. No. 26, p. 379. SEPM, Tulsa. Almon, W. R., and Schultz, A. L. (1979). G.C.A.G.S. Trans. 29, 1-10, Amr, A. R. A. (1971). Neues Jahrbuch Geol. Paleontol. Ahhandl. 138,259-268. Antonovsky, A. (1983). Micron and Microscopica Acta 15,77-84. Arthur, T. J., Pilling, D., Bush, D., and Macchi L. (1986).In “Habitat of Palaeozoic Gas in N. W. Europe”(J.Brooks, J. C. Go& and B. van Hoorn,eds.), Geol SOC.Special Publ. No. 23, p. 251. Baltuck. M. (1987). Initial reports of the Deep Sea Drilling Project V 93, pt. 2, 989-995, US Govt. printing office, Washington. Barrows, M. H. (1980). In “Scanning Electron Microscopy”, 1980/1(0. Johari, ed.), p. 579. SEM Inc., AMF OHare (Chicago), Illinois. Bauer, B., and Egg, B. (1984). Pract. Met. 21,460-471. Bisdom, E. B. A,, and Thiel, F. (1981). I n “Submicroscopy of soils and weathered rocks. 1st workshop of the international working-group submicroscopy of undisturbed soil materials

SCANNING ELECTRON MICROSCOPY

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(IWGSUSM) 1980” (E. B. A. Bisdom, ed.), p. 117-162. Centre for Agricultural Publishing and Documentation, Wagenheim, the Netherlands. Bisdom, E. B. A., Thiel, F., Volbert, B., and Jackman, J. (1983). Geoderma 30,93-116. Blanche, J. B., and Whitaker, J. H. M. (1978). J . Geol. Sac. Lond. 135, 73-82. Bohor, B. F., and Hughes, R. E. (1971). Clays Clay Miner. 19,49-54. Boles, J. R., and Franks, S. G. (1979).J . Sed. Pet. 49, 55-70. Bouma, J., Jongerius, A., Boersma, 0.. Jager, A., and Schoonderbeek (1977). Soil Sci. Sac. Am. J . 41,945-950. Boyer, R. C., and Wu, C.-H. (1983).SPE Paper 11722,519-523. Brace, W. F., Silver, E., Hadley, K., and Goetze, C. (1972).Science 178, 162-164. Brindley, G. W., and Brown, G. (1980). “Crystal structures of clay minerals and their X-ray identification,” Miner. SOC.London monograph no. 5, London. Burley, S. (1984). Clay Miner. 19,403-440. Burton, J. H., Krinsley, D. H., and Pye, K. (1987).Clays Clay Miner. 35,291-296. Byers, C. W. (1974). Sedim. 21,479-484. Cluff, R. M. (1980).J . Sed. Pet. 50, 767-780. Cocker, J. D. (1986). Amer. Assoc. Petrol. Geol. 70, 575. Cohen, A. L. (1977). In “Scanning Electron Microscopy,” 1977/I, (0. Johari, ed.), p. 525-536, SEM Inc., AMF O’Hare (Chicago), Illinois. Colter, V. S., and Ebbern, J. (1978). J. Geol. SOC.Lond. 135, 57-62. Colter, V. S., and Ebbern, J. (1979). In “Scanning Electron Microscopy,” 1979/I (0.Johari, ed.), p. 531-538, SEM Inc., AMF OHare (Chicago), Illinois. Cook, S., and Parker, A. (1988). Microsc. & Analysis 6,24-25. Coulter, A. W., Jr., Frick, E. K., and Samuelson M. L. (1983).SPE Paper 12150. Cowan, G . (1988).Geol. SOC.Spec. Publ., in press. Crocker, M. E., Donaldson, E C., and Marchin, L. M. (1983).SPE Paper 11973. de Harven, E., Lampen, N., and Pla, D. (1970). In “Scanning Electron Microscopy,” 1970/1 (0. Johari, ed.), p. 519-524. SEM Inc., Amf O’Hare (Chicago), Illinois. Dietrich, D., and Grant, P. R. (1985). J . Structural Geol. 7, 541-553. Dilks, A., and Graham, S. C. (1985). J. Sed. Pet. 55,347-355. Durham, W. B. (1981). In “Scanning Electron Microscopy,” 1981/I (0.Johari, ed.), p. 585-594, SEM Inc., Amf OHare (Chicago), Illinois. Feely, H. W., and Kulp, J. L. (1957). Bull. Am. Assoc. Pet. Geol. 41, 1802-1853. Ferguson, J. (1987). “Marine Petroleum Source Rocks,” Geol. SOC.Spec. Publ. 26,207-215. Filippov, M. N., Spivak, G. V., and Rau, E. I. (1984). Phys. Chem. Mech. Surface. I , 3612-3629. Gillott, J. E. (1969). J. Sed. Pet. 39,90-105. Gipson, M. (1965). J . Sed. Pet. 35,408-414. Gipson, M. (1966). J. Sed. Pet. 36,888-903. Goodchild, M. W., and Whitaker, J. H. M. (1986). Clay Miner. 21,459-478. Grant, P. R., and White, S. H. (1978).In “Scanning Electron Microscopy,” 1978/I (0.Johari, ed.), p. 789-794. SEM Inc., AMF OHare (Chicago), Illinois. Guven, N., Hower, W. F., and Davies, D. K. (1980).J. Sed. Pet. 50,761-766. Hall, M. G., and Lloyd, G. E. (1981).Am. Miner. 66,362-368. Hall, M. G., and Skinner, G . K. (1981).J. Microsc. 124,69-75. Hancock, N. J. (1978a).J. Geol. Sac. Lond. 135, 35-40. Hancock, N. J. (1978b). Scanning electron microscopy in the study of sediments, a symposium, Swansea (Geo. Abstracts, Norwich), 61-70. Hancock, N. J., and Taylor, A. M. (1978). J. Geol. Sac. 135,69-72. Harper, M. L., and Shaw, B. B. (1974).Offshore North Sea Technology Con$, Stavanger, Norway, paper G IV/4. Hay, W. W., and Sandberg, P. A. (1967). MicroplaeontoL 13,417-418.

204

J. M. HUGGETT

Heald, M. T. (1956). J . Geol. 64, 16-30. Heald, M. T., and Lareses, R. E. (1974). J . Sed. Petr. 44, 1269-1274. Heaviside, J., Langley, G. O., and Pallatt, N. (1983). 8th European Formation Evaluation Symp. London A. Holt, D. B. (1974). In “Quantitative scanning electron microscopy” (D. B. Holt, M. D. Muir, P. R. Grant, and 1. M. Boswarva, eds.), p. 213-286. Academic Press, London. Horl, E. M., and Mugschl, E. (1972). Proc. 5th European Congress Electron Microscopy, Manchester, UK, 502-503. Houseknecht, D. W. (1984). J. Sed. Pet. 54,348-361. Houseknecht, D. W. (1988). J . Sed. Pet. 58,228-246. Houseknecht, D. W., and Hathon, L. A. (1987). Appl. Geochem. 2,507-521. Hower, J., Eslinger, E., Hower, M. E., and Perry, E. A. (1976). Geol. SOC.Amer. Bull. 87,725-737. Huang, W. L., Bishop, A. M., and Brown, R. W. (1986). Clay Miner. 21,585-602. Huggett, J. M. (1982).The growth and origin of authigenic clay minerals in sandstones. Unpubl. Ph.D. thesis, Univ. London, p. 21 1. Huggett, J. M. (1984). Clay Miner. 19, 343-358. Huggett, J. M. (1986). Clay Miner. 21, 603-616. Huggett, J. M. (1989).Scanning Microsc. 3, 99-109. Hurst,A., and Archer, J. S. (1986). Clay Miner. 19,811-826. Hurst, A,, and Irwin, H. (1982). Clay Miner. 17, 5-22. Imam, M. B., and Shaw, H. F. (1985). J . Sed. Pet. 55,665-671. Irwin, H., Curtis, C. D., and Coleman, M. L. (1977). Nature 269,209-213. Ismail, S . N. A. (1975). Soil Surwy Papers 9, p. 104. Netherlands Soil Survey Institute, Wageningen, the Netherlands. Janks, J. S., Sanness, T., and Rasmussen, B. A. (1985). Trans. Gulf Coast Assoc. Geol. SOCS.35, 415-423. Jongerius, A. (1974). In “Soil microscopy. Proceedings of the 4th international working-meeting on soil micromorphology, Kingston, 1973.” (G. K. Rutherford, ed.), pp. 67-83. The Limestone Press, Kingston, Ontario. Jorgensen, N. 0.(1983). J . Sed. Pet. 53,557-564. Jorgensen, N. 0.(1986). Sed. Geol. 48,267-294. Kaldi, J. (1982). Bull. Am. Assoc. Pet. Geol. 66, p. 587. Kantorowicz, J. D. (1984). Clay Miner. 19,359-376. Kantorowicz, J. D., Lievaart, L., Eylander, J. G. R.,and Eigner, M. R. P. (1986). Clay Miner. 21, 769-780. Kearsley, A. T., and Wright, P. (1988). Microscopy & Analysis 7,49-51. Keller, W . D. (1976a). Clays Clay Miner. 24, 107-1 13. Keller, W. D. (1976b). Clays Clay Miner. 24, 114-117. Keller, W. D., and Haenni, R. P. (1978). Clays Clay Miner. 26,384-396. Keller, W. D., Reynolds, R. C., and Inoue, A. (1986). Clays Clay Miner. 34, 187-197. Kieke, E. M., and Hartmann, D. J. (1973). G.C. A. G. S . Trans. 23,60-67. Kimoto, S., and Hashimoto, H. (1968). SEMI11 TRI 1968,63-78. Krause, F. F., Sayegh, S . G., Girard, M., and DeBree, C. (1987).Petrol. SOC.C I M , Paper 87-38-79. Krinsley, D. H., and Doornkamp, J. C. (1973). “Atlas of Quartz Sand Surface Textures.” Cambridge University Press, Cambridge. Krinsley, D. H., and Hyde, P. W. (1971). In “Scanning Electron Microscopy,” 1971/IV (0.Johari, ed.), p. 409-416. SEM Inc., AMF OHare (Chicago), Illinois. Krinsley, D. H., Pye, K., and Kearsley, A. T. (1983). Geol. Mag. 120,109-115. Krinsley, D. H., and Takahashi, T. (1964). J . Sed. Pet. 34, 423-426. Krinsley, D. H., and Tovey, N. K. (1978). In “Scanning Electron Microscopy,” 1978/I (0.Johari, ed.), p. 887-894. SEM Inc., AMF OHare (Chicago), Illinois.

SCANNING ELECTRON MICROSCOPY

205

Kuypers, W., Thompson, M. N., and Anderson, W. H. J. (1973). In “Scanning Electron Microscopy,” 1973/1 (0.Johari, ed.), pp. 9-16. SEM Inc., AMF OHare (Chicago), Illinois. Lambert-Aikhionbare, D. O., and Shaw, H. F. (1982). Clay Miner. 17,91-104. Land, L. S., and Dutton, S. P. (1978). J. Sed. Pet. 48, 1167-1 176. Lane, W. C. (1970). In “Scanning Electron Microscopy,” 1970/I (0.Johari, ed.), pp. 41-48. SEM Inc., AMF OHare (Chicago), Illinois. Lyon, N. C., Gasiecki, E., and Parsons, D. F. (1976). In “Scanning Electron Microscopy,” 197611 (0.Johari, ed.), p. 101-106. SEM Inc., AMF O’Hare (Chicago), Illinois. McAullife, C. D. (1979). Am. Assoc. Petrol. Geol. Bull. 63,761-781. McHardy, W. J., Wilson, M. J., and Tait, J. M. (1982). Clay Miner. 17,23-40. McLane, J. E., and Scott, M. A. (1983). SPE Paper 11839. MacQuaker, J. H. S., Burley, S., Kearsley, A. T., Bishop, A. N., Wright, P., and Curtis, C. D., in preparation. Mapstone, N. B. (1975). Sedim. 22,601-613. Matiisen, A., and Shehata, M. (1987). Bull. Can. Petrol. Geol. 35,443-453. Mitchell-Tapping, H. J. (1983). The Log Analyst 24, 3-13. Morton, A. C. (1979). Scott. J. Geol. 15,293-300. M’Rabet, A., Negra, M. H., Purser, B. H., Sassi, S., and Ben Ayed, N. (1986). In “Reef Diagenesis” (J. H. Schroeder and B. H. Purser, eds.), p. 210. Springer-Verlag, Rerlin, Heidelberg. Muecke, T. W. (1978). J . Petrol. Tech. 31, 144-150. Muir, M. D. (1970). Rev. Palaeobotan. Palynol. 10,85-97. Muir, M. D., and Grant, P. R. (1974). In “Quantitative Scanning Microscopy” (D. B. Holt, M. D. Muir, P. R. Grant, and I. M. Berwana, eds.), p. 287-333. Academic Press, London. Neasham, J. W. (1977).In “Scanning Electron Microscopy,” 1971/I (0.Johari, ed.), p. 101-108. SEM Inc., AMF OHare (Chicago), Illinois. Neasham, J. W. (1980). 27th Southwestern Petrol. Short Course Ass. Mtg. 1980, p. 185. Newman, A. C. D. (1 987). “Chemistry of Clays and Clay Minerals,” Mineralogical Society, London. Nuhfer, E. B., Vinopal, R. J., Hohn, M. E., and Klanderman, D. S. (1981). In “Scanning ElecJohari, ed.), pp. 625-632. SEM Inc., AMF O’Hare (Chicago), tron Microscopy,” 1981/I (0. Illinois. Nuhfer, E. B., and Vinopal, R. J. (1978). US.Dept. Energy Preprintsfor Second Eastern Gas Shales Sym., V. I . Springjield, Va., N T I S , METC, Sp-7816, pp. 39-43. Oatley, C. W. (1972). “The Scanning Electron Microscope.” Cambridge University Press, Cambridge. Oatley, C. W., Nixon, W. C., and Pease, R. F. W. (1965). Advances in Electronics and Electron Physics 21, 181-247. Odom, I. E., Willand, T. N., and Lassin, R. J. (1979). In “Aspects of Diagenesis” (P. A. Scholle and P. R. Schluger, eds.), SEPM Special Publ. No. 26, p. 425. SEPM, Tulsa. OBrien, N. R.,Nakazawa, K., and Tokuhashi, S. (1980). Sedim. 27,47-61. OBrien, N. R. (1987). J . Sed. Petrol. 57,449-455. Patsoules, M. G., and Cripps, J. C. (1982). Eng. Geol. 19, 15-27. Pearson, M. J., and Small, J. S. (1988). CIay Miner. 23, 109-132. Perry, E. A., and Hower, J. (1972). Am. Ass. Petrol. Geol. Bull. 56,2013. Pesheck, P. S., Scriven, L. E., and Davis, H. T. (1981). In “Scanning Electron Microscopy” (0. Johari, ed.), p. 515-524. SEM Inc, AMF OHare (Chicago), Illinois. Philips Electron Optics application note 102. Pittman, E. D. (1972). J. Sed. Pet. 42, 507-519. Pittman, E. D. (1971). Bull. Am. Assoc. Petrol. Geol. 55, 1873-1878. Pittman, E. D. (1979). In “Aspects of Diagenesis” (P. A. Scholle and P. R. Schluger, eds.), SEPM Special Publ. No. 26, p. 159. SEPM, Tulsa.

206

J. M. HUGGETT

Pittman, E. D.,and Dushatko, R. W.(1970). J . Sed. Pet.40,1153-1157. Pittman, E. D., and Lumsden, D. N. (1968). J. Sed. Pet. 38,668-670. Pittman, E. D., and Thomas, J. B. (1978). S P E Paper 7550. Pittman, E. D., and Wilson, M. D. (1977). J . Sed. Pet. 47,3-31. Pollastro, R. M. (1985). Clayst Clay Miner. 33,265-274. Pollastro, R. M., and Bader, J. W. (1983). Bull. Am. Assoc. Petrol. Geol. 67, 536. Powell, T. G., and Stevenson, G. M. (1981). SPE Paper 10139. Price, m., Bird, J. M., and Foster, S. S. D. (1976). Bull. Am. Assoc. Petrol. Geol. 21,259-267. Primmer, T. J., and Shaw, H. F. (1987). In “Proceedings of the International Clay Conf. Denver, 1985” (L. G. Schultz, H. van Olphen and F. A. Mumpton, eds.), pp. 135-143. Clay Minerals Press Bloomington, Indiana. Purser, B. H., and Schroeder, J. H. (1986). In “Reef Diagenesis” (J. H. Schroeder and B. H. Purser, eds.), p. 210. Springer-Verlag, Berlin, Heidelberg. Pye, K. (1984). Geol. Mag. 121, 81-84. Pye, K., and Krinsley, D. H. (1983). Nature 304,618-620. Pye, K., and Krinsley, D. H. (1986). Geof.Mag. 120, 191-203. Pye, K. Krinsley, D. H.,and Burton, J. H. (1986). Nature 324,557-559. Ramsden, A. R. (1983). J . Geol. SOC.Australia 30, 17-23. Read, N. D., Porter, R., and Beckett, A. (1983). Can. J . Bot. 61, 2059-2087. Read, P. A., and Ringen, J. N. (1982). SPE Paper 10593. Rhoads, D. C., and Boyer, L. F. (1982).In “Animal-Sediment Relations, the Biogenic Alteration of Sediments” (P. L. McCall and M. J. S. Tevesz, ed.), p. 3. Plenum Press, New York, London. Rickards, L. M. (1974). OfJshore North Sea Development Conf.,Stavanger, Norway, Paper G-IVJ3. Rhoads, D. C., and Boyer, L. F. (1982). In “Animal-Sediment Relations, the Biogenic Alteration of Sediments” (P. L. McCall and M. J. S. Tevesz, ed.), p. 3. Plenum Press, New York, London. Rickards, L. M. (1974). Offshore North Sea Development Conf., Stavanger, Norway, Paper G-IV/3. Robinson, B. W. (1976). In “Scanning Electron Microscopy,” 1976/I (0.Johari, ed.), p. 91-100. SEM Inc., AMF OHare (Chicago), Illinois. Robinson, B. W., and Nickel, E. H. (1979). Amer. Miner. 64,1322-1328. Robinson, V. N. E. (1975). J. Microsc. 103, 71-77. Robinson, V. N. E. (1976). Proc. 6th Eur. Cong. 2, p. 85. Robinson, V. N. E. (1978). Scanning 1, 149-156. Rothbard, D. R., Skopec, R. A., Bajsarowicz, C. J., and Fate, T. H. (1987). Scanning Microscopy I , 489-494. Rottenfuser, B. A. (1982). Bull. Am. Assoc. Petrol. Geol. 66, p. 626. Sargent, J. A. (1982). J. Microsc. 129, 103-1 10. Sarkisyan, S. G. (1971).J . Sed. Pet. 41,289-292. Sassen, R. (1 980). Organic Geochem. 2, 153- 166. Sayegh, S. G., Krause, F. F., Girard, M., and DeBree, C. (1987). Petrol. SOC.C I M paper 87-38-78. Scholle, P. A. (1974). Internat. Assoc. Spec. Pub. 1, pp. 177-210. Scholle, P. A. (1977). Bull. Am. Assoc. Petrol. Geol. 61,982-1009. Schettler, P. D., Jr. (1979). U.S. Dept. Energy Proc. Third Eastern Gas Shales Sym., Sprindeld, Virginia, NTIS, METC/79/6,27-34. Schwartz, D. E. (1980). SPE Paper 9248. Seeman, U . (1982). Clay Miner. 17,55-68. Sellwood, B. W., Scott, J., Mikkelsen, P., and Akroyd, P. (1985). Mar. Petrol. Geol. 2,44-55. Setlow, L. W. (1971). Coast Res. Notes 3,2. Setlow, L. W., and Karpovich, R. P. (1972). J . Sed. Pet. 42,864-875. Shilin, A. V. (1969). Moscow SOC.Nature Bull., Investigations No. 3, 147-148. Shaw, H. F., and Primmer, T. J. (1989). Mar. Petrol. Geol. 6, 121-128. Siever, R. (1959). In “Silica in Sediments” (H. A. Ireland, ed.), SEPM Special Publ. 7, p. 55.

SCANNING ELECTRON MICROSCOPY

207

Sippel, R. F. (1965).Reviews of Scientific Instruments 36, 1556- 1558. Smith. K. C. A. (1956). Ph.D. Dissertation, University of Cambridge, Cambridge, England. Smith J. V., and Stenstrom, R. C. (1965). J . Geol. 73, 627-635. Soeder, D. J., and Randolph, P. L. (1984). S P E Paper 13134. Sommer, F. (1975). Reuue Inst. Fr. Petrole 30, 729-741. Sommer, F. (1978).J . Geol. Soc. Lond. 135, 63-68. Sprunt, E. S. (1981). In “Scanning Electron Microscopy,” 1973/1 (0.Johari, ed.), pp. 525-535. SEM Inc., A M F O H a r e (Chicago), Illinois. Sprunt, E. S., and Nur, A. (1980). SPWLA Logging Symp. Trans. 21, B1-B16. Stalder, P. J. (1973). Geologie Mijnb 52,217-220. Stanley, K. O., and Benson, L. V. (1979). In “Aspects of Diagenesis” (P. A. Scholle and P. R. Schluger, eds.), SEPM Special Publ. No. 26, p. 401. SEPM, Tulsa. Stieglitz, R. D. (1969).Proc. 12th Con$ Great Lakes Res. 1969, p. 351. Straley, C., and Minnis, M. M. (1982).J . Sed. Pet. 53, 667-669. Swanson, B. F. (1977). SPE Paper 6857. Swift, J. A,, and Brown, A. C. (1970). J . Phys. E 3,924-926. Takahashi, R. (1977).I n “Scanning Electron Microscopy” 1977/I (0.Johari, ed.), pp. 71-77, SEM Inc., A M F O’Hare (Chicago), Illinois. Taylor, J. C. M. (1978).J . Geol. SOC. 135, 83-92. Thomas, J. B. (1978).J . Geol. Soc. 135,93-100. Thomas, R. L., Crowe, C. W., and Simpson, B. E. (1976). S P E Paper 6007. Timur, A., Hempkins, W. B., and Weinbrandt, R. M. (197 I). J . Geophys. Research 76,4932-4948. Tompkins, R. E. (1981).Clays Clay Miner. 29, 233-235. Torresan, M. E., and Schwab, W. C. (1987). J . Sed. Petrol. 57,408-418. Turner, J. R. (1983).33rd Annual Gulf Coast Ass. Geol. Soc. Mtg., Jackson, Miss., 26-28/10/83, Trans., 22 1 - 230. Udell, K. S., and Lofy, J. D. (1985). SPE Paper 13655. Vinopal, R. J. (1981). Ph.D. thesis, West Virginia University, Morgantown. Vinopal, R. J., Nuhfer, E. B., and Klanderman, D. S. (1979).U.S. Dept. Energy Proc. Third Eastern Gas Shale Sym., Springjeld, Virginia, NTIS, MTEC/SP/6, p. 63. Walker, M. B. (1978). Scanning Electron Microscopy in the Study of Sediments. Proc. Symp. Swansea. Geo-Abstr. Ltd., Norwich, pp. 17-27. Walks, J. D. (1981).SPE Paper 9871. Ward, B. M., Kupperman, G. S., and Blanks, G. L. (1981).SPE Paper 10302. Wardlaw, C. N., and Cassan, J. P. (1978).Bull. Can. Petrol. Geol. 26, 572-585. Waugh, B. (1965). Proc. Yorkshire Geol. SOC.35,59-69. Waugh, B. (1970).Sedim. 14,309-320. Weinbrandt, R. M., and Fatt, 1. (1969).J . Petrol. Tech. 21, 543-548. Wells, 0. C. (1971). Appl. Phys. Lett. 19, 232-235. White, S. H., Shaw, H. F., and Huggett, J. M. (1984).J . Sed. Pet. 54,487-494. White, S. H., Huggett, J. M., and Shaw, H. F. (1985). Miner. Mag. 49,413-423. Wilkins, R. H., Caruso, L., Simmons, G., and Schreiber, B. C. (1987). Initial Reports of the DeepSea Drilling Project V 95, 527-547, U.S. Govt. Printing Office, Washington. Wise, S. W., and Hay, W. W. (1968a). Trans. Amer. Microsc. Soc. 87,411-418. Wise, S . W., and Hay, W. W. (1968b). Trans. Amer. Microsc. SOC.87,419-430. Wolf, M. J. (1967). Sedim. 8,239-247. Yacobi, B. G., and Holt, D. B. (1986). J . Applied Physics 59, Rl-R24. Yadav, G . D., Dullien, F. A. L., Chatzis, I., and MacDonald, I. F. (1984). SPE Paper 13212. Yeh, H.-W., and Savin, S. M.(1977). Bull. Geol. SOC. A m . 8 8 , 1321-1330. Zinkernagel, U. (1978). “Contributions to Sedimentology “8. Schweizerbart’sche Verlagsbuchhandlung, Stuttgart.

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Signal Analysis in Seismic Studies J . F. BOYCE L . R . MURRAY Wheatstone Laboratory King’s College. London United Kingdom

I . Introduction . . . . . . . . . . . . . . . . . . . . . I1. The Wave Equation . . . . . . . . . . . . . . . . . . A . The Force Law . . . . . . . . . . . . . . . . . . . B. Dilatational Stress . . . . . . . . . . . . . . . . . . C. Shearstress . . . . . . . . . . . . . . . . . . . . D. Derivation of the Wave Equation . . . . . . . . . . . E. Solution of the Wave Equation for Uniform Density . . . . . F. An Ideal Seismic Pressure Impulse . . . . . . . . . . . G . Absorption . . . . . . . . . . . . . . . . . . . . 111. Wave Propagation across Plane Interfaces . . . . . . . . . . A . Propagation across a Liquid-Solid Interface . . . . . . . . B. The Generation of Evanescent Waves at a Liquid-Solid Interface C. Wave Propagation across a Solid-Solid Interface . . . . D . Numerical Examples at a Solid-Solid Interface . . . . . . . IV. Preprocessing and Prestack Deconvolution . . . . . . . . . A . Dix’sEquation . . . . . . . . . . . . . . . . . . . B. Noise Characterisation . . . . . . . . . . . . . . . . C. F-K Filtering . . . . . . . . . . . . . . . . . . . D. Multiple Suppression and Primary Reflection Enhancement . . E. Predictive Deconvolution . . . . . . . . . . . . . . V. Velocity- Field Determination and Stacking . . . . . . . . . A. Stacking Velocity . . . . . . . . . . . . . . . . . . B. Normal Moveout and Stacking . . . . . . . . . . . . VI. Migration . . . . . . . . . . . . . . . . . . . . . . A . Geometrical Migration . . . . . . . . . . . . . . . . B. DipMoveout . . . . . . . . . . . . . . . . . . . C. The Common Midpoint Frame . . . . . . . . . . . . D . Fourier Space Migration . . . . . . . . . . . . . . . . E. Finite-Difference Migration . . . . . . . . . . . . . VII . Amplitude Variation with Offset . . . . . . . . . . . . . A . Approximations to the Zoeppritz Equations . . . . . . . . B. Subsurface Parameter Estimation . . . . . . . . . . . . 209

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Appendices . . . . . . . . . . . . . . . . . . . . . . . A. The Wiener Filter for Common Midpoint SeismicGathers . . . . B. Ray-Acoustic Geometry . . . . . . . . . . . . . . . . . C. Stacking by Maximisation of the Posterior Probability Distribution . Acknowledgement . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . .

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I. INTRODUCTION Seismic exploration geophysics is concerned with the location and identification of economically useful deposits. This objective requires the determination of the geometrical structure of the earth’s subsurface. Petroleum deposits originate from carbonaceous source rocks, from which, due to their mobility and relatively lesser density, they rise, until trapped by an impervious cap rock. The aim of petroleum exploration is to locate such traps, where the deposit forms a gas, oil and water sequence. Significant deposits mostly occur in sedimentary basins, where the original strata occur in layers. Traps may be caused by subsequent deformation of the layers, occuring, for example, as an anticlinal cap rock formation, or as a closed high point of a dipping layer that is truncated by a fault. In favourable circumstances the gasoil or oil-water interface may be directly observable as a “bright-spot’’ in a seismic section. In any event, complete three-dimensional information is necessary. Although other methods of exploration such as gravimetric, magnetic and electrical play important roles, the primary technique, especially for hydrocarbon exploration, is that of acoustic seismic reflection surveying. From an imaging viewpoint, the main characteristics of seismic surveying are as follows. An amplitude is observed rather than an intensity; in this it resembles radar imaging. There is a well established, and approximately linear, theory underyling the physical phenomena. Although the initial signal-tonoise ratio is poor, this is compensated by the ability to gather multifold data, both multisignal and multireceiver, thereby permitting the application of statistical techniques without the necessity for ergodicity assumptions. The problem is three-dimensional, with the large overhead of data storage and processing that it entails. As in astronomical imaging, exact comparison with a defined experimental configuration is not practicable. Comparison is, of course, made with the results of borings; but these occur only at a few separated points. The inferences must be consistent with deductions from other survey techniques and, most importantly, be geologically acceptable. This latter condition imposes stringent conditions upon the results and is the point where the experience of the interpreter becomes predominant. In fact,

SIGNAL ANALYSIS IN SEISMIC STUDIES

21 1

the task of a seismic processor is to present the information to the interpreter in as useful a manner as possible. This may, for example, mean accepting a lower signal-to-noise ratio than would otherwise be possible, if, by so doing, the “character,” i.e., the fine structure, of a particular reflection horizon is preserved. Similarities between this and diagnostic medical image processing are apparent. A typical seismic experiment, or “shot” (Dobrin, 1976; Aki and Richards; 1980; Claerbout, 1985), consists of the generation of an impulse of sound energy (either an actual impulse or one synthesised via time convolution of an extended signal) at a point at or near to the earth’s surface. The acoustic response to such an impulse is recorded on a linear array of geophones. The geophones record either the vertical component of velocity, if land based, or the variation of pressure, if sea based. The received signal lasts for about 5 seconds and is sampled at 2-millisecond intervals with a digital word length of 15 bits. A geophone array typically contains 96 geophones with an interphone spacing of 30 meters. The trend is to larger arrays and smaller spacings. Each geophone record, or “trace,” contains 38 Kbits. Each shot therefore generates some 3.6 Mbits of data, known collectively as a “shot gather.” The seismic survey proceeds by shifting the source and geophone array along the array direction (or seismic line) and by repeating the experiment. Each kilometer of survey generates approximately 100 Mbits of data. When account is taken of the necessity to repeat the complete sequence along parallel seismic lines in order to cover the two dimensions of the earth‘s surface, the magnitude of the data handling problem becomes apparent. Sound energy propagates within the earth according to the wave equation for elastic solids (Kennet, 1983) where both longitudinal and transverse modes of excitation are supported, in a manner determined by the elastic moduli and density of the subsurface material. The waves are thus subject to the usual phenomena of reflection, refraction, diffraction, and attenuation, but with the additional complication of mode conversion at impedance discontinuities. Their velocities lie in a range from 1500 ms-’ to 6000 ms-’ with wavelengths from 30 m to 200 m, hence the corresponding frequencies are typically from 5 Hz to 200 Hz. Aliasing effectsdue to the finite sampling lengths in space and time are an ever-present problem. Since the 5 seconds of geophone record represents a two-way travel time, information is being obtained from depths down to 5 or 6 kilometers. Transversely polarised waves generally attenuate more rapidly than longitudinal excitations (Ricker, 1977; Ben-Menachem and Singh, 1979). As a result, except for certain specific phenomena, they may, as a first approximation, be ignored, though their possible presence must be born in mind during any detailed interpretation. The space-time variation of the (pressure) wavefield, p ( x , y, z, t), at position r and time t is then determined by the bulk

212 modulus

J. F. BOYCE A N D L. R. MURRAY K(r)

and density p(r), via the equation

In sedimentary basins, the regions where petroleum deposits are normally encountered, the subsurface is stratified, with large variations of density occurring only at the stratum interfaces. These are, in general, dipping. However, even where faulting has occurred the structure remains locally stratified. For the region within a stratum, the above equation becomes approximately

W r , M r , t ) = 0,

(2)

with (3)

where

is the acoustic velocity. The exploration problem then becomes that of determining the intrastratum velocities together with the interface positions and fault boundaries. Acoustic energy is reflected only from points where there is a sharp change of acoustic impedance, this being the product of density times acoustic velocity, and in significant amounts only when the interface is locally continuous. The standard approach (Claerbout, 1976) is to first determine the velocity field and then the stratigraphic structure. The two problems are not truly separable in any realistic situation; however, the amount of processing that would be necessary to solve the complete problem is at present economically infeasable, though this may change in the not so distant future. Two general principles of the processing system are, firstly, to reduce the volume of data to no more than that which is necessary for exploration purposes, secondly, to apply only computationally simple algorithms to the full data set, with the algorithm complexity increasing as the volume of data is reduced during the processing sequence (Berkhout, 1982,1984). The objective of seismic processing is a three-dimensional map of the earth’s acoustic reflectivity as a function of position, together with the corresponding acoustic velocity field, and any additional lithographic characteristics that may be accessible, for example from the variation of reflectivity with angle of reflection. As will be discussed in the sequel, this requires that the

SIGNAL ANALYSIS IN SEISMIC STUDIES

213

seismic field be migrated, i.e., continued in space and time. The complete processing sequence may be conveniently considered as three successive subsequences: (1) Preprocessing and prestack deconvoiution. (2) Velocity determination and signal-to-noise ratio enhancement via stacking. (3) Migration.

We shall give only an overview of each topic, referring the reader, at appropriate points, to the more exhaustive reviews that exist within the seismic literature. There have, however, been some recent developments, firstly in the area of velocity determination and stacking, known as “prestack partial migration,” “offset continuation,” or “dip moveout,” and secondly in the direct detection of oil and gas deposits via “bright-spot’’ identification, and characterisation, known as “amplitude variation with offset,” which we shall cover in more detail. In the interest of consistency and completeness, we begin in Section I1 by deriving the equation for acoustic waves in a homogeneous isotropic medium for the domain of linear elastic theory. The assumption of homogeneity permits an explicit formal solution as a Fourier integral expansion of progressive plane waves, both forwards and backwards, and having both dilatational and shear degrees of freedom, together with corresponding phase velocities. The analysis of shear wave data, with the objective of determining lithological characteristics, is likely to be a field of development. The propagation of seismic energy is then considered by describing the form of an idealised pressure impulse, or Ricker wavelet, together with the effect upon it of attenuation, both due to spherical divergence and absorption due to frictional effects. Since we shall later be concerned with the variation of reflectivity with angle as an indicator of the presence of hydrocarbon deposits, Section 111 discusses the incidence of dilatational waves on a liquid-solid and a solidsolid planar interface, respectively, derives expressions for the corresponding transmission and reflection coefficients,and exhibits their angular dependence for representative interfaces. Preprocessing and prestack deconvolution is discussed in Section IV. A standard reflection experiment in the ray approximation (geometrical acoustics) is introduced, leading to the formation of “shot,” “geophone,” and “common midpoint” gathers. Examination of such gathers reveals the potential of utilising signal coherence across a gather as an analytical tool. The various sources of coherent noise are described together with the techniques of deconvolutional filtering that have been developed for their discrimination.

214

J. F. BOYCE AND L. R. MURRAY

The assumption of a horizontally layered model of the earth in Section V permits the introduction of the concept of a stacking velocity via Dix’s equation relating time delay to source-receiver offset distance. The resulting normal moveout transformation serves both to define the stacking velocity field and to establish the stacking procedure whereby a common midpoint gather of traces is reduced to a single optimal trace that most closely resembles the ideal signal that would be recorded by a source-receiver pair normally above the reflection location. The process of migration, which relaxes the preceding assumption of horizontal layering, is described in Section VI. After demonstrating the necessity for migration, the method of prestack partial migration is presented. The wave equation is expressed in the common midpoint coordinate frame and then utilised to continue the observed amplitude, which is obtained at zero depth for all significant time delays, to the required amplitude, which is needed at zero time for all significant depths, using either Fourier-based or direct methods. Section VII then contains a discussion of how “amplitude variation with offset,” i.e., the variation of the reflectivity with the angle of incidence of the wave, may be utilised to characterise and hence locate “bright-spots” which are indicative of gas-oil interfaces. 11. THEWAVEEQUATION A. The Force Law

The wave equation is an expression of Newton’s second law, relating the transient deformation induced by a stress, together with the constituent relations between stress and strain within an elastic material. Consider an isotropic material of density p and within it an elemental cuboid with centroid (x,y,z) and having sides Sx, Sy, 6z parallel to the coordinate axes (see Fig. 1).Let a, be the traction, i.e., the force per unit area on a surface with normal in the x direction, with similar definitions for ay and a=, and let u(x, y, z ) be the deformation of the material induced by the stress. The increase across the elemental volume of the component of the force in the x direction due to a, is

[ ( + ”2” - ( -,? )] -, y , 2

axx x

a,

y, z

x-

6 y S z = -a%, 6x6y6z. ax

(5)

Similarly, the component in the x direction due to a,, is [ay,(x,

y

+

2,

z) - ayx(x, y

-

2,

z)] 6 x 6 = ~ da nyySx x 6 y S z ,

(6)

SIGNAL ANALYSIS IN SEISMIC STUDIES

215

X

FIG. 1. Traction across a cuboid.

while that due to a, is

[ (

a,, x, y, z

F)

+-

-a ,,

(

F)]

x, y, z - -

6 x 6 y = -a%, 6xdy6z. ax

(7)

Hence the total net force in the x direction acting upon the elemental volume of the material is

{%

+% ay + %aZ) d x 6 y 6 r .

By Newton's second law, the increase in the force acting on the two faces, i.e., the net force, equals the rate of change of momentum in the x direction, therefore

and hence

Due to isotropy analogous equations apply for u, and u,,

and

216

J. F. BOYCE AND L. R. MURRAY

B. Dilatational Stress

If we consider the stress induced within the material by a deformation that is represented by the coordinate transformation x --f x’ u, then the associated change of elemental volume is

+

6x 6y 6z --+ 6x’ 6y‘ 6z’

where the Jacobian of the transformation is

-

to first order in the derivatives. Hence the fractional increase in volume is V u, and assuming that the material responds elastically, this will induce a corresponding outwards pressure on each face of the cuboid. Therefore, a ,

= ayy= cTzz = AV ’ u,

(15)

where 1 is the dilatational elastic constant of the material. This is the constitutive equation of dilatational stress. C. Shear Stress

Suppose that a shear stress acts as shown in Fig. 2. Under the action of the above deformation, the point A(x, y, z) transforms to A’(x’, y’,z’), with

similarly B(x

+ dx, y, z) transforms to B’(x’,y’, z’), where

( +2)

x’ = x‘(x

+ Gx,y,z) = x + u, +

y’ = y’(x

+ Gx,y,z) = y + uy + 2auax6

z’ = z‘(x

8% + 6x,y,z) = 2 + u, + -6x ax

1

6x

x

(17)

217

SIGNAL ANALYSIS IN SEISMIC STUDIES

B

A

X

FIG.2. Shear stress.

while C(x, y

+ 6y, z) transforms to C’(x‘,y’, z’) with au, XI = x’(x, y + 6y, z) = x + u, + -6y aY

y’ = y’(x, y

+ 6y,

=z

y

(18)

au + u, + -2

6y aY One effect of the deformation is to introduce a shear s t r e s s t h e y s c t i o n which is proportional to the scalar product of the vectors A’C’ and A‘B’. The corresponding stress is 2’ = z’(x,

y

+ 6y, z ) = y + uy + (1 + ?)6 2)

.A’B’

d -

oxy6x 6y = pA‘C’

where p is the shear stress constant of the material. It follows that, to first order in the derivatives, oxy=

+ $),

and due to the isotropy of the medium, the corresponding relations that are obtained by cyclic permutations of x, y, and z apply also.

218

J. F. BOYCE AND L. R. MURRAY

Now the deformation of BD relative to AC, viz., the change in length of AB, is accompanied by the stress d

A

d

+

axx(Sx)2= p{A’B’ * A’B’ - AB * A B )

(22)

and therefore, to first order,

together with its cyclic permutations.

3% a,, = 21.1-.

aYy= 2 p - ;

(24)

aZ

aY

Equations (20), (21), and (23) are the constitutive equations of shear stress. The total stress is the sum of the dilatational Eq. 15 and shear contributions. Notice that, if the stress is due to a pressure field p , then, considering the component in the x direction and combining Eq. (15) and (23), -p

= AV

*

u

+ 2p-.8% ax

(25)

Upon averaging over the three directions, - p = K V . u,

where K

+

= (1

(27)

$,U)

is the bulk elastic modulus of the material. There is therefore a direct correspondence between a dilatational distortion V u of an elastic material and an accompanying pressure field p .

-

D. Derivation of the Wave Equation Upon utilising the constitutive equations of dilatational and shear stress in the force equation for the x-component of deformation, we obtain

”i

ax 1 ( V * u)

+ 2PdU.j ax +;

{ P ( Z

+ f{ P ( Z + $)] =

;

+

{P%)

$)}

219

SIGNAL ANALYSIS IN SEISMIC STUDIES

If we assume that the material is homogeneous, then the elastic constants are independent of position. This assumption will not be valid in general, since the elastic constants may be depth dependent. It should be noted, however, that the density occurs in terms to which time derivatives are applied, not space derivatives. From homogeneity, it follows that

+ i.e.,

a

(A + p)-(V ax

*

u)

+ pvzu, = :t{

2}.

p-

By cyclic symmetry in x, y and z, it follows that

(A + p)V(V - u) + pv2u = at a { p-

}:

,

or by making use of the vector identity,

v x v x u = V(V * u) - v2u,

(32)

an alternative expression is

(A + 2p)V(V - u) - pv

x

}:

v x u =at a { p-

.

(33)

The above equation is the wave equation for homogeneous isotropic elastic materials. It relates the dilatational (or fractional volumetric) distortion V u, together with the components of the shear distortion V x u, to the instantaneous rate of change of momentum. The two components may be separated by taking the divergence and curl of Eq. (33), when the following independent equations are obtained,

-

(A + 2p)V2v =

;iP$}

(34)

and pvw=2

where v

=V

:t

{

p-

u and w = V x u, it therefore follows that

v.w=o also.

(35)

7}:

(36)

220

J. F. BOYCE AND L. R. MURRAY

For media of constant density, the above equations may be recognised as wave equations, having corresponding phase velocities c p and cs, where c: = p-l(12 + 2p) and c: = p -- ' p , respectively. We may identify the dilatational wave, v(x, t), with that of the accompanying pressure wave via Eq. (26), and hence with the wave equation given in Section I and the solenoidal vector field w(x, t )with that of shear waves. Since physical values of the elastic constants L and p are always positive, the phase velocity of the pressure wave is always greater than that of the shear waves. (As a result, pressure waves arrive before shear waves, and for this reason the two are known as P, or primary, and S , or secondary, waves, respectively.) E. Solution of the Wave Equation for Uniform Density

In a material of constant density, the wave equation of the dilatational field corresponding to Eq. (34) is

where cz = p - l ( L + 2p). Any square-integrable solution of the equation may be expanded as a Fourier integral of wave-vector and frequency components as

s I

.

v(x, t) = (d3k) (dw)v(k,W ) exp{ - i(k x - at)},

(38)

where solution of the wave equation requires that

s s

-

(d3k) (dw)(02 - c:k2)v(k, w)exp{ - i(k x

- cot)} = 0.

(39)

Since this must hold for arbitrary x and t, thus, v(k, W ) = v(k) S(o2- c:k2)

(40)

and hence the general solution may be expanded as

j

u(x, t ) = -[v'+'(k) exp{ -i(k : ; (

.x - w p t ) }

+ v'-)(k)exp{ -i(k - x + ~ ~ t ) } ] ,

'

(41)

We use the notation (d3k)o d3k/(2n)3and (dw) 0dwl(2n)together with &w) o 2n6(w), with 6 being a Dirac delta function.

SIGNAL ANALYSIS IN SEISMIC STUDIES

22 1

where up= cplkl,with c p being the P-wave velocity; d+)(k)is the amplitude of the dilatation having wave vector k, which is travelling in the positive kdirection; d-)(k) is the corresponding amplitude in the negative k-direction. Since the dilatational field is real, is follows that U(+)(k)*= v ( - ) ( -k).

(42)

An analogous analysis may be applied to the wave equation satisfied by the shear vector field w, resulting in w(x, t) =

s (;2

-[w‘+)(k)exp{ - i(k x

- cost)}

+ w(-)(k)exp{-i(k. x + cost)}],

(43)

where 0,= cslk(, with cs being the S-wave velocity, with c3 = p - l p . The solenoidal character of the shear field

v-w=o

(44)

requires the conditions k * w(*)(k)= 0.

(45) For each wave vector k, we may define transverse unit vectors e,(k), orthogonal to k,

-

k e,(k) = 0

u = 1,2,

(46)

in terms of which the shear field amplitude may be expanded as 2

w(*’(k) =

1 w!*’(k)e,(k), a= 1

(471

it following that w(x,t) =

{(;2.fl1 -

[w!+)(k)exp{ -i(k. x - cost)}

+ wb-)(k)exp{ - i(k - x + w,t))]e,(k),

(48)

where wF’(k) is the shear wave amplitude of wave vector k travelling in the positive k-direction and polarised transversely to k in the e,(k)-direction; wb-)(k) is the corresponding amplitude in the negative k-direction. Since the shear wave field is real, Wb+’(k)*= wb-’( -k)

(49)

The general displacement amplitude u(x, t) resulting from the combined dilatational and shear waves (Eqs. (41)and (48),respectively),may be obtained

222

J. F. BOYCE AND L. R. MURRAY

from Eq. (33), viz., p-

a2u = (A + 2p)Vv - p v x w, at2

(50)

i.e., upon Fourier expanding,

s s

-

u(x, t) = (d3k) (do)u(k, o)exp{ - i(k x - at)>, it follows that p

5 3kS

(d ) (do)w2u(k,o)exp{-i(k = i(A

+ 2p)

j(2

(51)

- x - at))

-k[u(+)(k)exp{

-i(k. x - qd)}

+ u(-)(k)exp{-i(k.x + opt)}] + wh-)(k)exp{ -i(k

x

+ wst)}].

(52)

1

(53)

Upon multiplying by exp( - i o t ) and then integrating over t,

and hence the total displacement field may be expanded as [d+)(k)exp{-i(k

-x

+ u(-)(k)exp{-i(k --

ip

2pw:

1 k x e,(k)[wh+)(k)exp(-i(k a= 1

+ w!-)(k)

-x

- opt)}

- x + opt)}] - cost)}

- + wst)}3 ,

exp{ - i(k x

)

where d*)(k) are the dilatational (P) wave amplitudes corresponding to wave vector k in the fk directions and w;*)(k) are the analogous shear (S) wave amplitudes polarised in the direction defined by the unit vector E,(k). (In the case of a liquid, p = 0 and the displacement field reduces to the dilatational

223

SIGNAL ANALYSIS IN SEISMIC STUDIES

component.) Now cs/osk, e,(k), e,(k) form a right-handed orthonormal set of vectors, hence

It follows that

If el(k) is chosen in the vertical and e,(k) in the horizontal plane, then wH(k) represents horizontally and w,(k) vertically polarised shear waves, respectively. Upon choosing e,(k) and el(k) within and normal to the surface plane, i.e.,

then, explicitly,

Since the P and S wave velocities are given by (A + 2p) = pc: and p = peg, it follows that the total displacement field may be expressed as u(x, t ) = i

j

-

k[u(+)(k)exp{ - i(k x - opt)}

(d3k) (;:p

+ u(-)(k)exp{ -i(k

- x + opt)}]

CS

-7 [{q(k)wr)(k) - e2(k)wv)(k)}exp{ -i(k

2%

+ {el(k)wk-)(k) - e2(k)wL-)(k)}exp{ -i(k

x

.x - cost)}

+ ost)}] (60)

224

J. F. BOYCE AND L. R. MURRAY

where wH(k)is the amplitude of horizontally and w,(k) of vertically polarised shear waves, viz., SH and SV amplitudes, respectively. Now v(x, t) = v u(x, t ) = ](d3k)M 20:k 2 [ u ( + ) ( k ) e x p {-i(k. x - apt)}

-i(k

+ u(-)(k) exp{

-

-x

- apt)}

-

i(k x

+ shear terms.

+ w,t)}] (62)

Hence, if u(+)(k)is nonzero only for k in a vertical direction upwards, i.e., kw, = (0, 0, c,k2), then the vertical component of velocity is 8%

-(x, t ) N at

-cpu(x, t),

and therefore, the velocity and pressure pulse profiles will be similar. As a result, the signals recorded by marine geophones, which respond to overpressure, and land geophones, which react to the vertical component of ground velocity, will be approximately equivalent. Notice that u can be written in the form U(X,t ) = V ~ ( Xt ,)

+ V x A(x,t),

(64)

where 4 is determined by v, and A by w, being a scalar and a vector potential, respectively, which leads to an equivalent formulation in terms of potentials rather than fields.

F. An Ideal Seismic Pressure Impulse

We shall consider a marine seismic survey where the initiating seismic signal is produced by a submerged impulse generator. We shall approximate the impulse by an instantaneous increase of pressure of p o within a sphere of radius a about the origin of the coordinate system. From Eq. (26), the corresponding dilatational increase is u(x,O) = -u,B(a - Ixl),

(65)

225

SIGNAL ANALYSIS IN SEISMIC STUDIES

with uo = p 0 / x while, since the increase is instantaneous, a0

-(x,O) = 0. at Being a liquid, the sea does not support shear wave propagation, hence only P waves are radiated. Equation (41) is the general expression for a P-wave amplitude. Upon requiring it to satisfy Eqs. (65) and (66) at time zero and utilising the Fourier expansion of a theta function

J

O(a - 1x1) = (d3k)7

ns[i):(

-

1 1

-

cos ka exp{ - ik x},

1

(67)

we may identify the solution at any positive time to be a!;s[)i cos ka u ( x , ~=) U O ( d 3 k ) 7 -x exp{ -i(k

-x

- wt)}

+ exp{ -i(k. x + w t ) } ]

(68)

by choosing the k-axes such that k, is in the x-direction, and integrating over the angles, the expression becomes

Irn (T

avo u(x, t ) = 7

dki1 sin(ka) - cos ka

(69)

This represents a superposition of outgoing spherical waves. The maximum wave number amplitude occurs when

-[

d 1 (--coska)]=O, sin(ka) ka dk k

namely, tanka

=

2ka k2a2 - 2'

for which the dominant solution occurs when ka I 1.5. Since the velocity of sound in water is 1500ms-', an initial impulse generated by a volume of radius a = 1 m yields frequencies I350 Hz. As r increases, the wave amplitude decreases as r-', due to the geometrical spreading of the spherical wave front. The amplitude at subsequent times may be expressed as a Fourier integral expansion of the wave-number amplitude.

G. Absorption It has been shown by Ricker (1953) that absorption may be taken into account by including within the dilatational wave equation a frictional term

226

J. F. BOYCE AND L. R. MURRAY

that is proportional to the first time derivative of the dilatation, the equation then becoming VZU(X,

t)

1 a20 t ) = - -(x,

1 av +-(x, at

c2

woc2

at2

t),

where wo, having dimensions of frequency, is a measure of friction. He further showed that the solution corresponding to a unit impulse at time zero is given by

+ p2)-1/4c0s For large values of r, due to the negative exponential, only those values of /? that are close to zero will yield any significant contribution to the integral. We may therefore replace the exponent and trigonometric argument by their lowest-order approximations in p, thereby obtaining v(x,t) x -

:1

p2 exp{ - Wp2} C cos{%(r C - ct)b

001

2c

a2

C

= 2q”)5’2[(2)(r

C

- ct)2 -

l]exp{ -%(r 2cr

- ct)2

with the form shown in Fig. 3. Equation (74)may be expressed as a wave-number expansion of the pulse by defining k=-,0 0 s

(75)

C

when we obtain az

u(x, t ) = --

exp{ik(r - ct)} dk exp{ik(r - ct))dk,

(76)

SIGNAL ANALYSIS IN SEISMIC STUDIES

227

[z

E (D

.

Tina Id FIG.3. Ricker wavelet.

which may be identified as an outgoing spherical wave having wave-number spectrum

2nc 3 v(k) = -Tk2exp

(77)

UOT

with the form shown in Fig. 4. The maximum at wave number k,,, = ( 2 0 ~ / r c ) ' / is ~ equivalent to a frequency of v, = (2w0c/r)'/*.Hence the dominant frequency decreases as r-1/2, i.e., the higher frequencies of the initial pulse are attenuated by propagation through the earth. Seismic energy can be absorbed either by viscous fluid flow and internal or solid friction (White, 1965). In the viscous fluid flow model, the instantaneous pressure varies across the accumulation as the wave propagates, giving rise to pressure gradients and the movement of fluids within the pore spaces. Energy is taken from the wave as work is done against the fluid viscosity. A pore containing compressible gas should, therefore, have a different attenuating action from one containing incompressible fluids such as oil or brine. Thus absorption gives some information about the type of interstitial fluid present, but there is no method yet available that allows this information to be elicited directly from surface seismic data.

228

J. F. BOYCE AND L. R. MURRAY

16.00

-

14.00

-

1e.w

I

1

P)

-0

3

Y

2

a E Q

r

0

2

P,

> Q

3

0.W

0.02

0.04

0.04

0.00

0.10

0.12

0.16

Yavenunber ( 1 /n)

0.16

0.111

0.20

0.22

.

FIG.4. The wave-number spectrum of a Ricker wavelet.

The internal friction model (Biot, 1956; Volarovich et al., 1969), however, is regarded as representative of the most important loss mechanism in low-permeability rocks (Gregory, 1977). The internal friction of a volume of material when it is cycled under stress at a given angular frequency o is given by

where E is the peak strain energy stored in the volume, - 6E is that energy lost in each cycle due to imperfections in the elasticity of the material, and Q(w) is the quality factor. A high Q-factor = 200 indicates that a material has a very small attenuating effect. In seismology, the attenuation of a signal comprised of a range of frequencies is involved, and it has been experimentally verified that this attenuation is linear with frequency (McDonal et al., 1958; Attewell and Ramana, 1966; Tullos and Reid, 1969).This is referred to as the constant Q-model of attenuation (Kjartansson, 1979). For a linear stress-strain relation, the wave amplitude A is proportional to E 'Iz, and applying the constraint that successive peaks have almost identical

SIGNAL ANALYSIS IN SEISMIC STUDIES

229

strain energies, Q >> 1,

Setting A ( t ) = A . at t = 0, as A decreases by n/Q at successive intervals t = 2nzn/w, n = 0, l , . . .,

As n + co,that is, for long times,

{

3

A(t) = Aoexp --

.

Since the angular frequency is related to the wave number by w = cI kl, and the wave front of a spherical wave is given by r = ct, the decay factor of the amplitude due to absorption is A(r) = exp{

-%},

and hence the amplitude of an outgoing spherical wave becomes u(x,t)

a!jm r.

-w

k’exp{ - g ] e x p { i k ( r

- ct)}dk

when it may be compared with that derived from the Ricker model in Eq. (76). For the limited range of wave numbers that occur in seismic wavelets, the difference between a linear and a quadratic k-dependence in the exponent is unlikely to be of significance. 111. WAVEPROPAGATION ACROSS PLANE INTERFACES A . Propagation across a Liquid-Solid Interface

Although in marine surveying the initial displacement field is purely dilatational, ( P waves), shear displacements, (S waves) are generated at the first interface, and thereafter mode conversion takes place between P and S waves at each subsequent interface. The equations of continuity at any interface are conveniently expressed in terms of the wave-vector amplitudes u( *)(k)and wb*)(k), respectively. The conditions of continuity at an interface remove (as stated by Hadamard) are that the displacement field u(x,t) be continuous across the

230

J. F. BOYCE AND L. R. MURRAY

FIG.5. Incident, reflected, and refracted wave amplitudes

interface and that the normal component of the traction = Ox&

+ a y v y + a,%,

(84)

where ii = nxi + n,,j + n&, be continuous also. If we consider a plane interface normal to the z direction, as shown in Fig. 5, then a, = a,, with components, from Eqs. (15) and (23),

azy= p($

+ %),

Is,, = I V . u

+ 2 pauaZL .

We shall consider a dilatational (P)wave incident on the interface. Physical parameters of the upper (lower) half spaces will be distinguished by being unprimed (primed), respectively. Incident (refracted/reflected) wave functions and angles will be unprimed (primed/doubleprimed). Dilatational (shear) wave-vector angles will be denoted by 0(4),as shown in Fig. 5. Initially, we shall consider a liquid-solid interface (e.g., the sea bed) so that no progressive shear waves are generated by reflection. From Eq. (60), the incident, reflected, and refracted wave amplitudes may be expanded as

Ik

-

u(k) exp{ - i(k x - opt)},

s

23 1

SIGNAL ANALYSIS I N SEISMIC STUDIES

Ik” u”(k)exp{ - i(k” x - w;t)}, 2p0 ; 3

.

u”(x, t ) = i (d3k”)-

- wkt)}

u’(x,t) = i ~ ( d 3 k ’2P ) [ ’~OuP ’ ( k ‘ ) e x p ( - i ( k ’x 2

y’ 1 k’ x e,(k’)wb(k’)exp{-i(k’.x 2 ~ 0 ,

--

,3

- wkt)}].

a=l

(88)

Due to the orthonormality of c$/w‘k‘, E2(k’),and q(k’), it follows that 2

w’ 1 k’ x &,(k’)wb(k’)= 7 {El(k‘)W;l(k’)- ~z(k’)w;(k’)). a=l

CS

(89)

If el(k’) is chosen in the vertical and e2(k’) in the horizontal plane, then wk(k’) represents horizontally and w;(k‘) vertically polarised shear waves, respectively. Continuity of the normal component of displacement at the interface requires UZ(X,t )

+ U:l(X, t ) = Ui(X, t )

= 0,

(90) whereas continuity of the z-component of the traction acting on a surface normal to the x-direction requires a~x(x, t)

+ all,(x, t ) = a:,(x,

t)

2

z = 0,

(91)

together with the analogous expressions for a,, and a,,, %y(x,t )

+ all,(% t ) = a:&, 0,

azz(x,t )

+ &(x,

t ) = ai,(x, t )

2

192)

= 0.

Since the medium occupying the upper half space is a liquid, p = 0, and, from Eq. (85), the three conditions of continuity of traction across the interface become

(93)

-

IV u(x, t ) + IV u”(x, t ) = A’V ’ u‘(x, t ) + 2p‘-.

aU:(x, t )

aZ

Equations (90) and (93) represent the conditions that the displacement fields given by Eqs. (86)and (88) must satisfy on the interface z = 0.

232

J. F. BOYCE A N D L. R. MURRAY

Upon Fourier-transforming Eq. (90) with respect to x, y, and t, we obtain

where, due to the translation invariance in x and y,

k,

=

kY

k: = k:;

= k”Y = k’Y ’

while the delta functions in w arise from time-translation invariance. Now wP = cp(kZ k,’ + k:)’I2 and thus

+

the continuity of the normal component of displacement hence becomes

with

(951

(96)

233

SIGNAL ANALYSIS IN SEISMIC STUDIES

where cpkp = (w’ - c:(k: ClpkZ = (W 2 - c;?(kZ

+ k;))”’, + k,2))”2, + k;))”’.

(102)

c$k$ = (0’- ck’(k2 The equations that represent continuity of traction are also invariant under space translations in x and y, and time translations, hence they too give rise to linear relations between the wave-vector amplitudes at wave-vector values given by Eqs. (101)and (102). From the first equation of conservation of traction, we obtain 0 = ur(klp)

w + -(k,Z + ky) c$k$

2 -112

whereas from the second follows

x

[

-k,k$w;(k$)

C’

- $k$’k,w;(k$)

C‘ + ”ky(k: + k;)w;(k$) W

1

. (104)

Upon subtracting the product of k, times Eq. (103) from the product of k, times Eq. (104), we obtain wh(k$) = 0, (105) hence no horizontally polarised shear waves are created at the interface. The third condition of conservation of traction yields Ik’

-o(k)

kP

Rk’ +U”(k”) kP

1‘”’

= ___ o’(klp)

kZ

p’kp + -u’(klp) k,

+ 2p‘(k; + k;)”’W;(k$).

(106)

Equations (loo), (103), (104), and (106) reduce to three independent equations, namely,

k2 1-(u(k) kP

+ U”(k”))= (I’kp + 2p’k;?)u’(klp) + 2p’(k3 + kt)”2w;(k;). klp

234

J. F. BOYCE A N D L. R. MURRAY

Since kcp = k‘ck = w

in terms of the reflection and refraction angles,

(k:

0 + kyZ)1/2= -sin

8,

CP

when the continuity equations become

At normal incidence,

(u(k) - d’(kl’))= u’(k;), w;(k$) = 0,

(v(k)

+ v”(k”)) = -u’(klp), P’Ck PCP

from which it follows that, at normal incidence,

235

SIGNAL ANALYSIS IN SEISMIC STUDIES

Therefore, the transmission and reflection coefficients may be identified as

u’(k‘) T(k)==2 u(k) pc,

+ p’cl, ’

u”(k”) = - p ~ -p p’cl, R(k) = u(k) pcp p‘cl, ’

+

with T(k)

+ R(k) = 1.

(115)

B. The Generation of Evanescent Waves at a Liquid-Solid Interface

The z components of the wave number at a liquid-solid interface are given by Eq. (102), where, since the elastic moduli are positive, clp > c $ . Assuming that cl, > c p ,the condition that kl, be real is c:(k:

+ k,’ + k t ) - c;?(k: + k,’) 2 0;

(116)

however, as

(k:

o2

+ k,’) = C P sin’ 8,

the above is the condition that the angle of incidence be less than the critical angle of dilatational (P) waves, i.e.,

Naturally there is a similar, though less stringent, condition for dilatationalto-radiative shear wave conversion, namely,

Equation (116) may be equivalently expressed as

~gk2 g (c?

- cg)(k:

+ k;),

( 120)

therefore such a condition should be included in the solution for z 5 0 , i.e., Eq. (86), in order for Eq. (88) to be applicable. For ranges of k p where the critical angle of the dilatational (P) wave has been exceeded, but that of the shear wave has not, we may look for solutions of the wave equation having the form of Eqs. (86) and (87) for z I 0, whereas

236

J. F. BOYCE A N D L. R. MURRAY

instead of Eq. (88),

+ u’(-)(k’)exp{-i(k’

- x’ +

wkt) - k,z})

-12

- x - wit)}],

x exp{ -i(k‘

where o;(k) = clp(kI + k,’ - k ; ) l ” Equation (122) may be obtained from Eq. (88) by making the replacement k, -+ - i k , in the dilatational component of the integrand. As a result, the analysis leading to Eq. (110) proceeds formally as before, subject to the replacements klp” -+ -kip";

klp” = k:

+- k,’ - klp”,

(123) The solutions now describe refraction of an incident dilatational wave at a liquid-solid interface for incident angles that are greater than the dilatational critical angle but less than the shear-wave critical angle. For z > 0, the solution is an evanescent wave that is localised on the interface, viz., the amplitude decays exponentially with the distance from the interface. Each of its amplitude components u’(*)(k’) propagates transversely along the interface in the direction determined by k = kxil + kyi2, with corresponding phase velocity clp. This wave can become radiative at a scattering centre within the surface, caused by morphological distortion or material inhomogeneity, when it generates dilatational waves upwards, as shown in Fig. 6. C. Waue Propagation across a Solid -Solid Interface From Equation (60)the general displacement for z < 0 takes the form ik

-i(k-x

-

w,t)},

( 124)

237

SIGNAL ANALYSIS IN SEISMIC STUDIES

I\

I

L

FIG.6. Evanescent and refracted wave generation.

and

s

( ;:,

ic;

--

20s

.

u”(k) exp{ - i(k x - wpt)}

u”(x, t ) = (d3k)

1 k x e,(k)[wb+)(k)exp{-i(k.

x - w,t)}

a=t

+ w!-)(k) exp( -i(k

x

+ w,t)}]

),

(125)

whereas for z 2 0, U’(X,

t) =

s

ik’

.

(d3k’)clpz[u’(+)(k’)exp{ - i(k’ x 202

- w,t)}

+ u’(-)(k‘)exp{ - i(k’ - x + mpt)}] ic;’ 1 2 -k’ x e,(k’)[wl+)(k’)exp{-i(k’ 2 ~ a =s l

-x

+ wb(-)(k’)exp( - i(k’ - x + wst)}]),

- wst))

(126)

Continuity of displacement at the interface requires that u(x, t )

+ U”(X, t ) = u’(x, t).

(127)

Now the time invariance of the constraint implies 0 ,

= w; = a; =

= w ; l = w,

( 128)

whereas space invariance in x and y requires similar identities between the xand y-components of the wave vector k. The relations between the amplitudes may be obtained by inverse Fourier transforming and utilising Eq. (98),

238

J. F. BOYCE AND L. R. MURRAY

We adopt the definitions given by Eqs. (101) and (102), with, in addition, ki

= (kx, ky,-

and utilise

M Y

+ (n, + 2p’) =

(1 2p) = pc:;

1 k,

+ u”(k”)} + (kf +c sk:)-ll2 ki

(131)

p’ = p’ck2.

PIC:;

Continuity of the x component yields -{u(k)

p = pcs”,

2

+ cskswk(kB))

-co:wp(k”)

+ csksw’;(k”)

{

o- wk(k:)

while from continuity in y, 1 -{u(k) kP

+ V”(k”)) + (kf +csk:k:)-llz

= -u’(k‘) 1

{

+ (kf + k;)-li2

kk

c$kk

wh(k’) - c;k;w;(kf)},

(133)

and from continuity in z,

where wy represents vertically polarised and wHhorizontally polarised shear waves, respectively. By subtraction of the equations that express the continuity of the x- and y-components, we obtain w&(ki) - W;(ki)

= 0,

(135)

the equations then reducing to

and {U(k) - v”(k;)}

sin I$’’

sin fp’

+w’;(ki) = d(kk) + -w;(k$), cos cos fp‘

(137)

where they have been expressed in terms of the angles defined by Eq. (109).

SIGNAL ANALYSIS IN SEISMIC STUDIES

239

The conditions for continuity of the normal, i.e., z components, of traction are aza(X,

t ) + a:b(x,t ) = a:a(x, t),

a = X, Y , Z,

(138)

with ozagiven by Eq. (85). Written fully, the equations are

and

Upon inverse Fourier transforming the corresponding relations among the amplitudes become 2pk,{~(k)- u”(kg)} - 2p’k,~’(kk)+ p,(kf csks 0

k;k,w;(k;) x

{

CSkX

- -(ki2

w

C$kX -k$k,wL(k$) - -(ki2

w

+ k;)-’/2 0

- k; - k;)w;l.(k:) - k,2 -

(141)

with

+

0

+

2pkY{u(k)- u”(kg)} - 2p’kYu’(kk) p F ( k f k:)-”2 csks csky x -k;k,w;(k;) - -(k;2 - kf - k;)w’;(k;)

{

0

0

ckk, +k$k,wh(k$) - -(kk2 w

- kf - k;)w;(k$)

and

I

= 0,

(142)

k2 &-{U(k) k,

+ v”(kg)} + 2ppkp{~(k)+ u”(kg)} - 2pp(k; + k;)1/2W;l.(k;) - 2p1p’(ki+ k;)’/2w;(k$) - 2p’p’kk~’(k;) - 2A’p’-

k k2

klp

~’(klp)= 0.

(143)

240

J. F. BOYCE A N D L. R. MURRAY

Upon multiplying Eq. (141) by k, and Eq. (142)by k , and then subtracting, we obtain Wk(kg)

+ wh(k$)= 0.

( 144)

Taken in conjunction with Eq. (135), we may infer wk(kg) = wh(k$) = 0,

(145)

and hence that no horizontally polarised shear waves are created at a planar interface. In terms of the angles defined by Eq. (109) and by utilising the identity

A + 2p cos2 e = pc; cos 24,

(146)

the pair of independent equations becomes 2/l{~(k)- d’(kg)} - 2/i’~’(klp)

and cos 24 cos 24’ pep- {u(k) - u”(kg)} - p’c’pcos 4 cos Wlp) el

- 2pc,

sin @’w’;(ki) - 2p’c$ sin 4’w;(k$)

= 0.

( 148)

At normal incidence, the equations become = w’;(kg) = 0,

(149)

{v(k) - u”(kg)} - o’(kb) = 0,

(150)

+ u”(kg)} - p’ClpU’(klp)= 0,

(151)

w;(k$) pcp{u(k)

Equations (149), (150), and (151) are identical with the corresponding equations, Eq. (11l), of the liquid-solid interface propagation, hence the reflection coefficientsat normal incidence are, similar to Eqs. (1 13) and (1 14),

with T(k) + R(k) = 1.

(1 54)

SIGNAL ANALYSIS IN SEISMIC STUDIES

24 1

We may identify Eqs. (136), (137), (147), and (148) with the more usual statement of the Zoeppritz equations, as given, for example, in Appendix 2A of Waters (1981), by making the identifications

where

is the Snell parameter. The transmission and reflection coefficients at nonzero angles of incidence are hence defined by

T(k) =

cose u’(k(p) __ cos8’ u(k) ’

~

(157)

D. Numerical Examples at a Solid-Solid Interface Two horizontally layered models having typical values of density and velocity are shown in Figs. 7 and 8. The parameter values of Fig. 7 illustrate a normal interface, having a density and P-wave velocity that increase with depth; those of Fig. 8 are representative of values to be expected at a “brightspot” arising from a shale-gas sand interface, exemplified by decreasing density and P-wave velocity.

cp = 2400 m/s

chalk

c. = 1475 m/s p = 2.0 g/cc

c,‘ = 3600 m/s

shale

c.’ = 1470 m/s p’ =

2.4 g/cc

FIG.7. Densities and velocities typical of a normal interface.

242

J. F. BOYCE A N D L. R. MURRAY cp

= 3600

m/s

c. = 1470 m / s

shale

p = 2.4 g/cc

c,' = 2900 m/s c.'

gas-sand

= 1925 m/s

p ' = 2.1 g/cc

FIG. 8. Densities and velocities typical of a shale-gas sand interface.

1.00

.

e

0.60

-_ _ _ _ _ _ y---=-

0.40

-

0.20

-

C

!!

-0 u* 0 u0

0.00

7m

-0.20

c, -

a

-0.40

E

-z

-0.60 -0.80 -1.00

RP

O.W

10.00

3.00 30.00

40.w

s0.w

60.00

Angle o f Incidence Ideg)

70.00

moo

90.00

.

FIG.9. P-wave reflection and transmissioncoefficientsat a normal interface.RP = reflected P-wave, TP = transmitted P-wave.

The reflection and transmission coefficients corresponding to the normal interface are shown in Figs. 9 and 10. For the normal interface, a critical angle for P-wave reflection occurs a t an angle of incidence of 42", leading to zero P-wave transmission together with accompanying evanescent and hence refracted waves at larger angles. The Pwave reflectivity is approximately constant for angles of incidence less than

243

0.06

r

0.w

I\ I \

-

I I I I

I

C

-a, -0 uu-

a, 0 0

0.00

-

,

I

-_ _ _ - - - -

0

\ \ \ \

/

TS,

\

\

/

0.07

\

\

'

\ \ \

\

P)

-0

3

r d

n E <

0

A n g l m o f Incldoncm (dog).

FIG. 10. S-wave reflection and transmission coefficients at a normal interface. RS = reflected S-wave, TS = transmitted S-wave.

1.00 0.0 0.60

0.40

0.20

-

-

--- - - - ---_ ' Tp

----_- -

I

. .. \

\ \ \

\ \ \

\ \ \

\

\ \

0.00

Anglm o f ~ncidoncm Id091

.

FIG.11. P-wave reflection and transmission coefficients at a shale-gas sand interface. RP = reflected P-wave, TP = transmitted P-wave.

244

J. F. BOYCE A N D L. R. MURRAY

Anglo o f incidmcm I&$.

FIG. 12. S-wave reflection and transmission coefficients at a shale-gas sand interface. SP = reflected S-wave,TS = transmitted S-wave.

30", but increases rapidly as the critical angle is approached. The energy is mostly concentrated in the P-wave mode, there being little P-to-S-wave conversion. The form of the coefficients for the shale-gas sand interface is shown in Figs. 11 and 12. No critical angle exists for P-wave reflection. The P-wave reflection coefficient becomes more negative as the angle of incidence increases, with the ,corresponding transmission coefficient gradually reducing to zero at glancing incidence. As in the previous example, there is relatively little P-to-S-wave conversion. IV. PREPROCESSING AND PRESTACK DECONVOLUTION A. Dix's Equation

The standard exploration reflection experiment consists of the excitation of a source of acoustic energy (the shot), which is localised in both space and time and the subsequent recording of acoustic signals over a period of time at an array of receivers (geophones), as shown in Fig. 13. For definiteness, we shall consider mainly marine seismic data, the basic principles of the analysis

245

SIGNAL ANALYSIS IN SEISMIC STUDIES

SI

GI Ga Ga G

Ga

Ga

FIG.13. Shot gather source-receiver configuration.

are common both to it and land data. The major differences between the two cases are that marine data suffers from reverberant effects caused by the seasurface/sea-bed forming an effective waveguide, whereas land data is affected by static corrections due to local variation of the earth’s surface and by difficulty of geophone placement and acoustic coupling caused by terrain irregularity. A typical marine shot gather is shown in Fig. 14. It may be regarded as being composed of a plethora of approximate Ricker wavelets at varying time delays and magnitudes. There is a clear coherence between events as represented by similar wavelets across the gather. The strong early arrivals that form a steeply dipping collection are a combination of direct (waterbourne) arrivals and refracted waves. As we shall now show, their hyperbolically correlated successors are a combination of primary and multiple reflections. As a first approximation the earth’s subsurface may be represented by a set of distinct horizontal layers (strata) of homogeneous isotropic material having arbitrary thicknesses but constant physical properties. This assumption, the horizontally layered earth approximation, together with that of ray optics for wave-front propagation, is sufficient to establish the basic experimental parameters such as shot interval and number of geophones. The assumptions within the approximation may then be progressively relaxed. Consider the earth model shown in Fig. 15, with a single shot and geophone, and where refraction of the rays and multiple reflections have been

n

5 w

*u ri i

8 d

8 d

8 ni

8 ni

0

u

4

U

f G

Lr,

SIGNAL ANALYSIS IN SEISMIC STUDIES

247

ignored. Even in this simplest of models, it is necessary to determine both the times of delay of the reflections from each of the interfaces and the wave velocities of the separate strata in order to predict the depths of the interfaces. It is therefore necessary to consider a collection of shot-geophone responses at different separations. Practically this means a number of geophones for each shot at a set of increasing separations with, for simplicity, a fixed intergeophone distance. If we assume a constant velocity c, then, for a reflection from an interface at a depth z, a geophone at distance 2h from the shot will receive a reflection signal at time 2t, where

h = ctsine;

z

= ctcose.

(158)

At a source-receiver separation of zero, i.e., if both shot and geophone were located at M of Fig. 15, then the reflection time is 2t0, where ( 159)

z = cto.

Hence to = t COS

e,

( 160)

and therefore, from Eqs. (158) to (160), t 2 = t;

hZ +7

(known as Dix’s equation (Dix, 1955)). It follows from the above that reception times vary with source-receiver separation in a velocity-dependent manner and that if a set of corresponding reflections can be identified and their arrival times be determined with sufficient accuracy, then the corresponding velocity can be deduced. Since Eq. (161) may be rewritten as

the (t, h) dependence is hyperbolic (the moveout hyperbola), symmetric about separation zero, and with a curvature that decreases as the velocity increases, and thus usually decreases with depth. A collection of geophone traces corresponding to a single shot upon which such reflection time variation may be observed is a shot gather. The intergeophone separation determines the sampling rate of the acoustic field in the horizontal direction, and thus, via the sampling theorem, the limit of the horizontal resolution that is possible. The rays do not all reflect from the same reflector point; therefore, any change in reflection properties will affect the reflected pulse. For the horizontally layered earth approximation and ignoring refraction, this effect may be removed by considering common midpoint gathers, these being collections of traces

248

J. F. BOYCE A N D L. R. MURRAY

corresponding to shot-geophone pairs having increasing separations while remaining symmetrically disposed about a common midpoint. Such data sets are obtained by combining appropriate traces from successive shot gathers. The shot and geophone linear array are displaced between successive shots in the array direction by a distance equal to the geophone separation. A sequence of such operations results in a “line” of data. It is illuminating to display the shot and geophone positions as a twodimensional grid, see Fig. 16, a stacking chart, relative to the shot and geophone positions along a shooting line, each point of the grid representing a single geophone trace. A collection of traces from a grid line that is parallel to the geophone axis is a common shot gather, with all of the traces originating from the same shot. A collection of traces that is parallel to the shot axis is a common geophone gather, with all of the traces arising from geophones at the same location. For a spread of geophones that is asymmetrical relative to the shot, as shown in Fig. 13, only a portion of the stacking chart is accessible. Collections of traces at angles of n/4 to the axes are common midpoint and common offset gathers, respectively. Common shot and common offset gathers become significant when noise characterisation and removal is considered. Three-dimensional coverage is provided by shifting the entire shotgeophone array complex laterally relative to its axis and repeating the procedure, thereby generating a succession of seismic lines of data. As may be observed from Fig. 13, only half of the traces of a shot gather yield reflection points that lie vertically beneath geophone locations, the remainder being at positions that are midway between such locations; therefore the number of traces (or “fold”) of a common midpoint gather is half that of the shot gather from which it derives.

4 42

C -

0

a

m

common

common shot

m Idpo Int

common 0ffm.t

0 L

a

0

cmmon pophonm

m

U

0

O

O

D

0

0

0

O

Shot potnt

FIG. 16. The stacking chart.

SIGNAL ANALYSIS IN SEISMIC STUDIES

249

B. Noise Characterisation

An ideal recorded data set consists of a collection of geophone time traces recorded at a sequence of grid points on the earth's surface; these being the responses to a series of seismic shots at points on the same grid. The purpose of the inital stage of processing is to reorganise the data into a form convenient for the subsequent processing; to filter it such that any individual shot dependence is removed, with all shots becoming equivalent to a unit impulse at time zero; to reduce the effective shot and geophone vertical heights to a common datum plane; and to eliminate, as far as possible, surface waves and short-period multiple reflections, which otherwise obscure the primary reflections present in the data. The types of coherent energy may be classified according to the corresponding ray path geometries as: 1. direct arrivals, which on land includes both an air wave having a velocity of 350ms-', and ground roll, the latter being a surface wave for which the earth's surface acts as a free interface; for marine surveys, this corresponds to a water wave with a velocity of 1500ms-', for which the water layer acts as a waveguide; 2. refractions, caused by the evanescent waves formed at an interface when the angle of incidence is greater than the critical angle, and which can then reradiate from interface discontinuities. The velocity of propagation of the evanescent waves along the interface is that of the lower stratum; such waves occur at the sea bottom. Since the wave velocity is greater in the sea bed than in water, energy refracted from the sea bed precedes that transmitted directly in spite of the longer path length, except when the source receiver offset is so short that the direct path is faster; 3. reflections, of which the significant information are the true reflections, but which must be distinguished from multiple reflections, long period arising from reflections of which one reflector is the surface, and short period from interbed reflections; together with ghost reflections, both of the shot and receiver in the water surface; 4. diffractions, arising from discontinuities that are usually associated with reflecting interfaces, yield hyperbolic correlations across the gather, but with vertices that lie vertically above the discontinuity. The raw data is demultiplexed, i.e., reorganised from a time-sequential to a trace-sequential order. Each trace is scaled using an exponential gain factor in order to compress the dynamic range of the data, thereby approximately compensating for the geometrical dispersion and attenuation of the seismic waves. Approximate shot independence is achieved by deconvolving each shot

250

J. F. BOYCE AND L. R. MURRAY

gather, as will be described in Section E.I. Obviously “dead” or highly noise corrupted traces are removed. For land-based data, the traces are the simultaneous responses of localised clusters of geophones with the cluster being designed to attenuate incoherent and surface-associated noise. The vertical height of each cluster is reduced to a common datum level by time-translating the corresponding trace. Similarly, each shot point, which may also be formed by a cluster of individual shots triggered simultaneously, is reduced to the datum level by shifting entire shot gathers. An equivalent, though simpler, static correction is applied to sea-based data. The shot gathers are reorganised into common midpoint gathers, viz., a set of traces each having the same midpoint between the shot and geophone locations. The reason for this rearrangement is to prepare for the determination of the velocity field together with signal-to-noise enhancement and its accompanying reduction of data volume. The effect of surface-wave propagation, i.e., ground roll, is reduced by the use of arrays of both shot generators and geophones rather than the single elements we have considered. By taking account of their known wavelength range, surface waves may be attenuated relative to upcoming longtitudinally polarised waves. They may also be reduced by muting the early portions of the traces. Sea based data, in particular, is characterised by short-period multiple reflections caused by the reverberation of the seismic energy between the seabed and the sea surface, which acts effectively as an acoustic wave guide. The result is for each primary reflection to be accompanied by an oscillatory tail having a period equal to the acoustic two-way travel time between the seabed and sea surface. It may be readily identified on the trace autocovariance function. The modelling of this system and its removal via predictive deconvolution is a major success of the application of digital signal processing techniques to seismic processing (Kulhanek, 1976; Robinson and Treitel, 1978; Silva and Robinson, 1978). The underlying theory is statistical and is based upon the two assumptions: (i) that the seismic event sequence is random in arrival time, and (ii) that the seismic wavelet associated with each reflection is minimum delay, i.e., its energy is concentrated towards the first point of nonzero amplitude, i.e., the “break-point,’’ as much as is permitted by the constraint of causality (Robinson and Silva, 1981; Arya and Aggarwal, 1982). High-velocity noise, principally due to incoherent backscattering, may be removed by filtering within the frequency- wave-number space, known as “f-k” filtering. The filter acceptance extends over a wedge about k = 0 in f k space, with an angle set by the acoustic velocity. As a final preprocessing operation, the traces within a common midpoint gather are noise equalised, with possible schemes being via their average or root mean square values either for the entire trace or in a time dependent manner along the trace.

SIGNAL ANALYSIS IN SEISMIC STUDIES

25 1

C. F - K Filtering

On a common shot gather, the refracted wave energy precedes the earliest reflected waves and hence may be removed by muting the traces with a time delay that increases with offset distance, with the rate of increase being determined by the observed diffracted wave velocity. Direct arrivals may be removed both by receiver array design and by f - k filtering. The acoustic amplitude u(h, t), where h is the offset distance and t the twoway travel time, is expanded as an inverse Fourier transform in angular frequency -w and wave number k. -u(o,k)exp(-i(kh

- ot)}.

(163)

Since the amplitude is real, u*(-w,k) = u(--w, - k ) , whereas, since it is a solution of the wave equation corresponding to velocity c, u(w, k) = 6(w - ck)u'+'(k)

+ 6(w + ck)u'-'(k);

(165)

therefore, in the o - k plane, the amplitude is localised along the lines W =

kck,

(166)

with a strength that is k-dependent. Now we may interpret w > 0, k > 0 as a wave travelling in the direction of increasing offset h, and w < 0, k < 0 as a wave travelling in the direction of decreasing offset, hence the amplitude spectrum in the w-k plane may be conveniently represented as shown in Fig. 17.

FIG. 17. The dispersion relation of a forward propagating wave.

252

J. F. BOYCE AND L. R. MURRAY

Any physical seismic amplitude is sampled at a set of discrete values both in space h = nAh, n = -N, -N + 1,..., N, and in time t = mAt, m = O , l , ...,2M. Therefore, the expansion equivalent to Eq. (163) is that of a double discrete Fourier transform.' The acoustic amplitude is zero for negative time, hence the appropriate Fourier expansion is u(h,t) = (2N

+ 1)-'(2M + 1)-'

c c u"(k,w)exp{-i(kh N

2M

n = - N I=O

wt)}, (167)

where

h=nAh; k=

(2N

t=lAt

2zn * 1)Ah'

-N
+

(3M

01212M

2x1 1)At

(168)

+

with N

u"(k,w)=

2M

C C u(h, t)exp{i(kh - wt)} n=-N m=O

If we require that v(h, t) be a solution of a discretised wave equation, viz.,

1 {u(h, t (c At)'

--

+ At) - 2 + u(h, t - At)},

then N

2M

(0' - c2k2)u"(k,w)exp{-i(kh- at)} n=-N m=O

+ O(Ah4,At4) = 0,

(171)

and therefore, the discrete Fourier amplitude u"(k,w), will be approximately zero unless (172)

w(1) = +ck(n),

+

+

where the equality is modulo (2N 1)in n and modulo (2M 1)in 1due to the periodicity of the discrete exponent. Solutions for k and w that correspond to Algorithmic implementations of Fourier transforms are most efficient when implemented over numbers of points that are powers of 2. In the subsequent development, the ranges of n and / may be modified to - N 1 5 n I N and 0 5 I < 2M - 1, with (2N + 1) + 2N and (2M 1) + 2M, which may then be chosen to be powers of 2. We have chosen and maintained the ranges - N I n 5 N and 0 I l I 2M, since these arise naturally from an analogy with the continuous Fourier transform.

+

+

253

SIGNAL ANALYSIS IN SEISMIC STUDIES

-n/Ah

+n/Ah -c

I

“1 FIG. 18. Aliasing of the dispersion relation due to discrete spatial and temporal sampling.

values outside the ranges - N 5 n IN , 0 II 5 2M are permitted. As a result, the dispersion relation between angular frequency and wave number may consist of disjoint segments, and hence aliasing may arise, as illustrated in Fig. 18. Now the velocity which enters the above wave equation is the effective wave velocity across the common midpoint gather, viz., as given by the gradients on Fig. 18. Therefore, by defining a triangularly (wedge) shaped muting filter in (w,k ) space that is symmetric about the average velocity of the water waveguide mode energy of Fig. 18, the corresponding energy may be removed from the gather in (h, t) space. If the acoustic medium is dispersive, viz., the velocity c is dependent on the frequency, then a linear dispersion relation passing through the origin of (w, k) space may not suffice. The explicit form may be determined from a preliminary analysis of the gather prior to coherent noise attenuation. The limits of the wedge are determined by the range of velocities across the gather which it is required to remove. The upper limit, in particular, needs to be chosen with care in order that primary reflection energy is not muted inadvertently. A major problem may arise, however, due to the aliasing of the dispersion relation. Since the energy from primary reflections, this being the signal we wish to preserve, has a very high velocity across the gather, the moveout hyperbolae have small curvatures, and hence the corresponding dispersion curves in (w,k) space are nearly vertical. Therefore they may intersect the

254

J. F. BOYCE AND L. R. MURRAY

aliased components of the water waveguide mode, and as a result, any filter that mutes that portion of the waveguide noise contained within the aliased component would then mute the primary reflection signal. In addition, Gibb’s oscillation effects may occur, caused either by discrete filter edges or discrete data cutoff at the edges of the gather. An example of just such an effect is shown in Fig. 19, which is a frequency-wavenumber plot of a shot gather in the marine data set shown in Fig. 15, where both aliasing and Gibbs effectsare evident. The response of the filter with regard to Gibb’s oscillations may be improved by smoothing the theta function cutoff at the edges and by progressively reducing its effect along the dispersion relation. An improvement with respect to aliasing is obtained by padding the midpoint gather with zero values in the range N < (nl < 2 N , thereby preventing noise. Gibb’s oscillationsdue to sudden termination of coherent signals at the gather edges may be reduced by muting the contributions from the long offset traces consistently with the rate of decrease of the wedge-shaped filter response k) function. The general principles governing the design of filters in the (0, plane are that a minimal region should be muted, that the filters should be smooth with tapered edges, and that the data of the common midpoint gather should be padded with zeroes to obviate aliasing.

D. Multiple Suppression and Primary Reflection Enhancement We wish to exhibit the reflection coefficients of the primary reflectionswith as accurate a location as possible and in such a way that their character, viz., local structure, is retained. This latter condition is highly necessary, since a large part of the geological interpretation, for which seismic processing is merely an aid, depends upon such information, whose significance is not diminished by the fact that it is difficult to describe in quantitative terms. The analysis is applied to a sequence of successive common midpoint gathers. It will be assumed that the individual traces of which the gathers are comprised have been muted at short arrival times to remove refracted wave energy, while the gathers have been f-k filtered in the frequency-wave number plane in order to suppress directly propagated water-bourne (waveguidemode) energy. The standard sequence of processing operations is firstly to remove shortperiod multiples by predictive convolution applied to each separate trace; then to normal moveout correct the common midpoint gather using the velocity field available from earlier analyses and to sum the traces into a stack; finally, to apply a spiking deconvolution filter to the stacked trace. Each component step will be considered in turn.

SIGNAL ANALYSIS IN SEISMIC STUDIES

255

256

J. F. BOYCE AND L. R. MURRAY

E. Predictive Deconvolution The observed amplitude g(t), after removal of refracted wave energy and direct water-bourne (waveguide) noise, is assumed to be linearly related to the reflection coefficient field r(t) by g(t) =

jy

H ( t , t’)r(t’)dt’

+ n(t).

(173)

The kernel H(t,t’) represents the effects of the source wavelet, multiple reflections, absorption, receiver (geophone) response, and recording instrumentation, together with source and receiver ghosts. Uncorrelated noise is represented by the additive term n(t).The problem is to recover r from g, given a knowledge of H. As a first approximation, the effects are assumed to be separable and to be invariant under time translations. Hence, each individual effect may be expressed as a convolution

where h(t) depends on the underlying physics, and may be compensated for by an appropriate inversion. The overall system may be represented by a succession of such convolutions, and hence the required reflection coefficient field may be recovered by a sequence of inversions. The basic techniques employed are those of crosscorrelation and Wiener filtering. 1. Source- Wavelet Compensation

Suppose that the subsurface consists of discrete reflecting interfaces of varying reflectivities, ra,a = 1,. . . . The reflection coefficient field is hence a set of impulses r(t) = Crah(t a

(175)

where ta is the reflection time from interface a. Given a source wavelet s(t) and ignoring amplitude decrease due to geometrical spreading, absorption and multiple reflection,the reflected amplitude from such an idealised subsurfaceis

where s ( t ) represents the source wavelet. Now the correlation of s ( t ) with g ( t ) is,

SIGNAL ANALYSIS IN SEISMIC STUDIES

as defined by geophysicists, Rsg(t)=

jym

s(t’)g(t

+ t’)dt’.

For the case considered it, becomes

where

R,,(t) =

+ t)s(t‘) dt’

s(t‘

(179)

is the autocorrelation of the source wavelet. Therefore the crosscorrelation of s with g is a sum of autocorrelations of s localised about the reflection times of the reflecting interfaces. By the Schwartz inequality, given square integrable functions u(t) and u(t),

Irw

u(t‘)u(t’)dt’l 5

[

U 2 ( t t ) dt’

;jmu’odt.]1’2,

(180)

and hence, upon identifying, u(t’) = s(t‘

+ t - ta);

u(t’) = s(t‘)

m

R,,(t

- la) I

s2(t’)dt’, J -m

with equality being achieved for t = t,. Therefore the crosscorrelation R,,(t) of a set of maxima at t = to,a = 1,2,. . .,whose local structure is approximately that of an autocorrelation of the source wavelet with itself.

s with g consists of

Ghost Deconuolution The effect of the sea surface on the source wavelet s(t) is to subtract from it a delayed replica, i.e., s(t) + s(t) - s(t

- t, sec a),

(183)

where the subtraction occurs since the water-air reflection coefficient is - 1, and t s is the two-way travel time from the source to the water surface along the normal to the surface. The combination may hence be expressed as a convolution s(t) -+

jo@

h S ( t - t’)s(t’)dt’,

258

J. F. BOYCE A N D L. R. MURRAY

where the surface ghost is represented by hs(t) = d(t) - 6(t - t s sec a).

(185)

By a similar argument, the effect of the sea surface on the received wavelet is represented by convolution with the kernel hR(t)= 6(t)- d(t - tRsec a),

(186)

with t , being the two-way travel time from the receiver to the water surface along the normal. The overall effect of ghosts is provided by convolution with the convolution of both kernels, explicitly,

1;

h,(t - t’)h,(t‘)dt’ = d(t)

- d(t - t s sec a) - 6(t - t, sec a) + d(t - ts sec a - t , sec a) (187)

3. Multiple Deconoolution In general the autocorrelation of a random function is localised about the origin; that of a periodic function is itself periodic with the same wavelength. The periodicities contained within a reverberant seismic trace appear as prominent secondary peaks, either positive or negative, in the autocorrelation function. This characteristic permits their identification and hence removal. Consider a single plane reflector with reflection coefficient ro at a two-way travel time to. The reflection coefficient field at zero offset is then r(t) = ro d(t - to).

(188)

The effect of a water layer (the sea) upon an upcoming seismic signal f ( t )is to add a regular sequence of reflections at time delays that are multiples of the two-way travel time tw in the water, i.e.,

f (t) s(t) +

= f(t) - r f ( t

- t w ) + r2f(t - 2t,)

- . .* ,

(189)

where r is the sea bottom reflection coefficient. This expression may be written as a convolution g(t) =

[:‘

m(t - t’)f(t’)dt’,

(190)

where m(t) = d(t) - rd(t - tw)

+ rZd(t - 2,) - ....

(191)

SIGNAL ANALYSIS IN SEISMIC STUDIES

259

In terms of a Z operator formalism, where 2 denotes time translation through a time interval tw, viz.,

Zf(t) = f(t - tw), ( 192) the convolution kernel of the reflection sequence may be represented as

rn = (1 = (1

- rZ

+

+ r 2 Z 2 - . ..) ( 193)

Kq-1.

Each seismic signal is doubly affected by the reverberant water layer, once for the downgoing and once for the upcoming amplitudes, hence the overall convolution kernel is

m2 = (1 + r Z ) - 2 =1

-

2rZ + 3r2Z2 -

-.a,

(194)

with the corresponding convolution being g(t) =

Jym

rn(2)(t-

t‘)f(t’)dt’,

(195)

where d 2 ) ( t )= d(t) - 2rd(t - tw)

+ 3r2 d(t - 2tw)- ..-.

(196)

It follows that if the time period t w may be determined, for example from the autocorrelation of the trace, then application of the inverse operator will deconvolve the reverberant effects of the water layer, viz., remove the corresponding short-period multiples. This assumes, however, that the time period tw and the sea-bottom reflection coefficient r are known accurately. The above problem, the removal of the reverberant wave train, may be regarded as a particular case of a more general problem, namely that of designing a stable linear filter that deconvolves a known signal from a noisy realisation of it. Such an identification then permits the application to the problem of general methods of solution, in particular the Wiener filter. Specifically,Eq. (195)may be regarded as a particular case of Eq. (1 73), and we may seek a filter function h(t), such that f(t) =

J-:

h(t - t’)g(t’)dt’

(197)

best approximates a known form of seismic wavelet f(t) in an average sense across a common midpoint gather. This enables us to use the statistical properties relative to the gather as a means of optimising the deconvolution for each individual trace.

260

J. F. BOYCE A N D L. R. MURRAY

Formally, we wish to minimise

f(t)12),

(198) e = ( C f ( t )where ( ) denotes the average relative to the common midpoint gather. As shown in Appendix A, the optimum h is a solution of the Wiener-Hopf equation rw ( f ( t ) g ( t ’ ) ) = J (g(t’)g(t - t”))h(t’’)dt”. 0

If the seismic trace may be modelled as a stationary stochastic process, then the equation becomes

Rrg(t)=

1;

R,,(t

- t’)h(t’)dt’,

(2W

where R f g , and R,, are the crosscorrelations and autocorrelations, respectively, of f and g, relative to the comon midpoint gather. In order to remove short-period multiples at any value of time, h(t) is defined to be that filter that predicts the amplitude at time t , ahead, given the values of the amplitude at all times less than t. f(t) = j)(t

- t’)f(t’)dt‘

with

t 2 0,

(201)

m2>

e = ( C f ( t + tw) (202) being a minimum. The required filter is then a solution of the Wiener-Hopf equation (Eq. 199), with g(t) = f ( t + tw).

(203)

As a result of this definition, f(t) then contains any of the reverberant characteristics of the seismic amplitudes that occur with period t , or greater, and therefore (204) f ( t >- At - t w ) W - tw) yields the deconvolved trace. In terms of discretised variables, Eq. (199) is f

(.LA+,,>

=

1 <S,f,-t~>h,*,

t’=O

which, assuming stationarity, becomes

(205)

SIGNAL ANALYSIS IN SEISMIC STUDIES

26 1

The correlation functions R, are obtained by averaging across the gather. Solving the above equations is equivalent to inverting a symmetric Toeplitz matrix, for which a fast algorithm due to Levinson exists. The forward predicted amplitude is then given by the discretised analogue of Eq. (201)

A=

i

t’=O

ht-t!fk

(207)

with the reverberant free amplitude following from Eq. (204). If a prediction length of one time interval is chosen, then a spiking deconvolution filter is obtained, viz., one which replaces each primary reflection by a single impulse. Such an operation is usually applied after stacking, however, because interpreters prefer to retain some of the character of the wavelet by extending the prediction distance to the order of the wavelet duration. The validity of the entire approach of predictive deconvolution depends upon the absence of periodic structure within the reflection coefficient sequence, at least over the length of the filter. Practical experience has shown that the filter can still yield adequate results even when this condition is not rigorously valid. The four parameters required for the application of a predictive operator are prediction time delay, operator length, design window, and application window. Their validity for a given section is established by a set of preliminary trial deconvolutions. The major constraint on the above algorithm for short-period multiple removal is imposed by the assumption of stationarity, which limits both the prediction time delay and the length of the convolution operator that may be employed with confidence. The prediction length, i.e., the minimum period of any multiple energy that is to be removed, may be obtained from the autocorrelation function of the unfiltered traces of the section, a sectional autocorrelogram. For long reverberant periods, the traces are no longer stationary due to the effect of dip and moveout; such multiples are removed more effectivelyby normal moveout stacking. The same effects limit the length of the deconvolution operator to less than 0.5 s, whereas, in addition, long operators may inadvertently attenuate primaries as a result of chance correlations. The duration of the design window should be at least ten times that of the operator length in order to achieve statistical significance. Since the travel time is not, in general, a multiple of the recording sample length, the prediction filter will also act as an interpolator. The effect of a noise impulse is to generate a signal in the filtered trace that is proportional to the strength of the impulse. It follows that a noise transient, which will be without an accompanying echo, will have a set of associated reverberants that have been erroneously predicted and removed from the deconvolved trace. Figure 20 shows the effect of predictive deconvolution on the marine gather of Fig. 14. The deconvolution operator had a variable window length

262

J. F. BOYCE AND L. R. MURRAY

ooo

1. OOO

1.

2. OOO

2.

FIG.20. A predictively deconvolved marine shot gather.

from [SOO, 40001 ms for a near trace to [2000,4000] ms for a far trace. The predictive gap was 28 ms. The effect of muting the data within one operator length of the first breaks is demonstrated in Fig. 21. Later sections of this paper deal with amplitude versus offset analysis, for which this data is examined. Therefore, a front-end mute was used, instead of applying an ‘fk’filter to remove the first breaks and refraction arrivals, because, by considering Fig. 19, the result of employing such a filter would be to affect the region of the ‘fk’spectrum that also contains primary energy. The sensitivity of the geophones may be determined by averaging each of their individual responses along a seismic line, viz., determining the average energy of a receiver gather. The effect of thereby equalising the geophone sensitivities upon the processed shot gather is displayed in Fig. 22. It may be observed that the systematic trace variability that was previously present in Fig. 21 has been removed.

263

SIGNAL ANALYSIS IN SEISMIC STUDIES

am

1. Ooo

1. OOO

m

2. Ooo

2.

FIG.21. A front-end muted, deconvolved marine shot gather.

V. VELOCITY-FIELD DETERMINATION AND STACKING A. Stacking Velocity

A basic assumption common to all processing systems that do not employ prestack migration is that determination of the velocity field may be separated, at least approximately, from that of the reflectance field. Recall that both are required for depth recovery. The analysis described in Section IV was designed for reflectance-field analysis with the component techniques being optimised for its accurate recovery. Assuming that such an analysis has been performed, we may now reanalyse the data with regard to the second objective of velocity analysis, subject however, to consistency with the reflectance field. The processing applied so far has been directed towards the suppression of

264

J. F. BOYCE A N D L. R. MURRAY CAOOO

1. OOO

1. OOO

ooo

2. OOO

2.

FIG.22. A geophone sensitivity-equalised processed marine shot gather.

coherent noise, removal of refracted energy by muting the early arrivals, attenuation of direct waterbourne energy by f-k filtering, source and receiver ghost compensation by inverse filtering, and short-period multiple removal by predictive deconvolution. The result of the preprocessing sequence is a data set of filtered geophone responses, in the form of individual geophone traces that are grouped into sets of common midpoint gathers. Each such gather consists of traces where the shot point and geophone location are symmetrically disposed about a common midpoint at progressively increasingseparations on the same seismic line. Geometrical dispersion has been approximately compensated by a timedependent gain factor. The shot and geophone are effectively on the same horizontal datum level. Each shot is effectively identical. Surface waves and short-period reverberations have been eliminated. The traces have been compensated so as to be of equal statistical weight.

265

SIGNAL ANALYSIS IN SEISMIC STUDIES S \

hi

hi

G

M

I

:/

I

I

I

I I I I I I I

I I I 1

ZI

FIG.23. Refraction in a two-layer system.

Apart from f - k filtering and noise equalisation, the processing up to this point has been one-dimensional and, to that extent, may be regarded as signal processing. The further processing becomes increasingly two- and threedimensional, and hence becomes progressively more akin to image processing. Algorithms for estimating the velocity field are based on a more detailed analysis of the ray acoustic approximation. It is shown in Appendix B that if the reflector of Fig. 13, rather than being horizontal, has an angle of dip 8, then Dix’s equation, Eq. (161), becomes

2hcos8

($-(lo) = The effect of refraction on Dix’s equation is demonstrated by the two-layer system of strata having velocities c1 and c2 with interfaces at depths z1 and z 2 shown in Fig. 23. The total half-separation between source and receiver may be expressed as

h = cltl sin 8,

+ c 2 t 2sin

82,

(209)

where the total half-reflection time is t = t,

+

t2,

(210)

with the time to at zero offset being given by to = tl

cos el

Snell’s law at the interface requires that

+ t2 COS 8,.

(21 1)

266

J. F. BOYCE AND L. R. MURRAY

hence

c2

h =-tsinO,, C1

where

+ cit2)

= t-'(c:t,

E2

is a mean square velocity. A further application of Snell's law to Eq. (213) yields

h F2

-=

cl't,sine,

+ c;'t2sine2,

and therefore, upon multiplying Eqs. (209) and (219,

h2 _ c2- t(tl sin2el + t2 sin2 02).

(216)

But, from Eqs. (210)and (21 l), t 2 - t g = t(tl sin2 8,

+ t2 sin20,) + t,t2(cos O1 - cos 82)2,

(217)

with it following that t2 = ti

h2 + -z + t , t , ( ~ ~ ~-e , C

this being the generalisation of Dix's equation (Eq. (161)),that is, the normal moveout equation for a two-layer system of horizontal strata. The above equation is again hyperbolic to the extent that the final term is negligible. Snell's law permits its reformulation as

8, - cos 82)2 = C O S ~el (COS

[(

1 - -tan2 8, c:

- 11'.

(219)

where Ac2 = C: - c:. The square root may be expanded by the binomial theorem, subject to the condition tan2e, < when the first-order approximation is

Ic: - c y

SIGNAL ANALYSIS IN SEISMIC STUDIES

267

and yields a negligible contribution to Eq. (218). However, for cz > c l , again by Snell's law, Eq. (221)is equivalent to (sin8,I < 1.

(223)

It is therefore violated at the critical angle of incidence, when 8, = 5, while the first-order approximation will become increasingly invalid as the critical angle is approached. We may therefore expect the normal moveout equation to deviate from the hyperbolic form near the critical angle. For a sequence of ( A 1) horizontal strata separated by A interfaces, indexed by Q = 1,. ..,A, the source receiver half-separation distance h may be expressed as

+

A

1 catasinOa,

h=

a= 1

while the half-reflection time t is

with the half-reflection time to at zero separation being A

1 t, cos 6,.

to =

a= 1

Snell's law of refraction at each interface requires that

-=--...=sin6, sine,

-

c2

C1

sin eA CA

Analogously to Eq. (213), we may express h as

c2

h =-csinO,, C1

where A

c2

= t-'

1 c;ta a= 1

by again applying Snell's law

and hence, by multiplying with Eq. (224),

h2

-= t

z2

A

1 tasin20a.

a=l

268

J. F. BOYCE A N D L. R. MURRAY

The analogue of Eq. (218) is t 2 - tg = t

A

A

a= 1

a
1 ta sin’ en + 1

t,tb(cos en - cos 8b)2;

(232)

and hence the normal moveout equation is

As in the two-layer case, since the correction term to the hyperbolic form is a sum of differences of cosines,it may be neglected in comparison with the h2/C2 term unless one of the incident angles approaches the critical angle of the corresponding interface. For a sequence of A strata, having velocities c,, a = 1,. ..,A and angles a, to the horizontal, the offset dependence of reflection time remains approximately hyperbolic (Shah, 1973),

where the squared stacking velocity is given by

in which 0, and 0; are the incident and refracted angles of the zero-offset ray path at the ath interface, with cos20, = cos2 Ob, i.e., t2

= tg

h2 + -2 + o(h4). C

(236)

The velocity field, viz, the acoustic velocity within a given stratum, may be obtained from the change in stacking velocity on entering a statum if the angle of dip of the interface is known. Determination of the dip, however, requires that the imaging problem be solved, hence the two problems of geometric structure and velocity field determination are at best only approximately separable. Given a midpoint gather of amplitudes g(t, h) composed of recorded amplitudes at reflection time t and source receiver separation h, the method for determining the stacking velocity field F(t) is to apply the normal moveout transformation

SIGNAL ANALYSIS IN SEISMIC STUDIES

269

for a representative set of velocity fields and then to select or “pick” from the set a function c(t),usually piecewise linear, that provides a best estimate, as measured by maximum signal coherence across the transformed gather. Initially, this may be performed by transforming the midpoint gather using a set of constant velocity fields, with the resulting set being known as a constant velocity gather, and by visually estimating the reflection-time interval during which each is applicable. Operational consistency and the occurrence of large data sets require standardisation and automation of the procedure. A suitable measure of coherence, though by no means the only one, is provided by the semblance (Al-Chalabi, 1979)

where 0 S s ( t ) I1, with s ( t ) = 1 when an identical pulse appears at the same time delay for each trace of the gather. Uncertainties of the stacking velocity field arise, however, due to the combined effects of the distortion of a reflected pulse, known as NMO stretch, introduced by the normal moveout transformation, and the occurrence of multiple reflections. The effect of the distortion may be demonstrated by considering the reflection of a Ricker wavelet (Eq. (74)) from a planehorizontal interface at a depth z in a medium of velocity c. Since the ray path r in a common midpoint gather for a source receiver separation of 2h is given by r(h) = ( c 2 t i + 4h2)1/2, (239) where to

= 2c/z

(240)

is the zero-offset travel time, it follows that the amplitude recorded by the receiver at offset 2h is

The wavelet is a maximum for t = (ti+ 4h2/c2)’/’; hence we may define a relative time variable

270

J. F. BOYCE AND L. R. MURRAY

when the amplitude becomes g(t, h) = 21’2 ( w ~ h ) ) 5 ” [-

~

r

] { --Gf2}

-2 1 exp

Now the normal moveout transformed amplitude g’(th,h) at offset2h is defined by

where

Hence

0

exp[

-2cr(h)

1

(r(h) - ( c 2 t ; + 4h2)1/2)2.

The exponent of the transformed wavelet is zero when th = to

and the corresponding relative time variable is th

= th - to,

in terms of which the squared term of the exponent becomes

where the higher-order terms may be neglected, since the wavelet is of significant magnitude only for zh << t,. It follows that to O(T:),the normal moveout transformed wavelet is

SIGNAL ANALYSIS IN SEISMIC STUDIES

27 1

Upon comparing Eqs. (243) and (250), it may be observed that the approximate NMO corrected wavelet may be obtained from the original by the transformation

and that the wave-number expansion of the corrected wavelet is consequently

The width of the Gaussian distribution has altered by the factor - 112

h=(l+%)

,

(253)

with the wave number distribution progressively narrowing as the offset increases. Therefore, the effect of the NMO transformation is to increase the longer wavelength content of the wavelet. In fact, the wavelet has been simply “stretched” by the factor (1 + 4h2/~2t6)1/2. An alternative method of exhibiting this effect is to notice from Eq. (243) that the first zero of the original Ricker wavelet occurs at (254)

whereas, from Eq. (250), that of the NMO corrected wavelet is at

(255) The effect of the NMO transformation has thus been to broaden the wavelet by the same factor, (1 + 4h2/~2tg)1/2, which occurred in the narrowing of the wave-number distribution. A consequence of the wavelet distortion is that, even when the correct normal moveout is applied to the gather, any measure of coherence, including the semblance as defined by Eq. (238),no longer yields a uniform maximum within the time interval occupied by the wavelet. This situation is exacerbated by the not infrequent occurrence of multiple reflections that are received contemporaneously with the primary reflection pulse. Multiple reflections arise either from surface or interbed reflections at shallower depths. Although the amplitudes of such events are substantially reduced by the multiple nature of the reflections in comparison with the

272

J. F. BOYCE AND L. R. MURRAY

corresponding direct reflection amplitudes, since their transmission time intervals are longer, the geometrical and absorptive gain factors that are applied to the traces means that their amplitudes may be comparable in magnitude with the direct reflection data that is received simultaneously.Since the multiply reflected wavelets spend a greater time interval in the upper strata, their velocities are, usually, significantlydifferent, most commonly lower, than the contemporaneously received direct data. Hence their moveout hyperbolae have relatively larger curvatures and thus intersect those of the direct events. As a result, interference effects are introduced between the direct and multiple wavelets, thereby further reducing the effectiveness of coherency criteria, such as the semblance of Eq. (238), for determining a correct stacking velocity field F(t). A further complication arises from the discontinuous nature of the velocity field. If we consider the reflections from three closely spaced interfaces, with a decrease in velocity from the first to the second layer, and an increase in velocity from the second to the third, the resulting midpoint gather is shown in Fig. 24. Since the moveout hyperbola of the second reflector is less curved than that of the first, the event wavelets have begun to interfere at the larger moveouts. The figure demonstrates the general principle that the velocity field is being determined by the behaviour of the far offset traces, whilst the arrival times of the wavelets, and thus the horizon locations, are most reliably represented by the short offset traces. This principle has implications for any technique of signal-to-noise improvement, a topic that will be considered in

Synthetic Reflection Sectlon

-

. .... ..

FIG.24. Wavelet interference.

SIGNAL ANALYSIS IN SEISMIC STUDIES

273

the sequel. In particular, any attempt to simply sum the normal moveoutcorrected traces corresponding to the gather of Fig. 24 will have difficulties, since the discontinuous change of stacking velocity will introduce a distinct gap in the data between the first and second wavelets in the corrected traces at large offsets: a gap that must somehow be interpolated. Given a picked velocity field F ( t ) obtained by optimising coherence across a gather, it is then possible to estimate the corresponding interval velocities. For a horizontally layered model, Eq. (233) yields successive estimates of the c, whilst for planar, though nonhorizontal, layers, the more general equation [Eq. (235)l yields successive estimates of the vertical components c, cos 8,. Both models assume an absence of anomalies, such as sand lenses, which may affect only one of the downgoing or upcoming raypaths. Noise, i.e., amplitude distributions that do not follow a hyperbolic distribution across a common midpoint gather, may be classified as source generated, such as scattering from near surface discontinuities; or ambient noise, arising from extraneous sources such as far off ocean storms, earthquakes, deeply sited seismic activity; or noise emanating from the recording activity itself, such as tow noise from the streamer cable at sea. The transformation of the data from shot gathers to common midpoint gathers decorrelates source-generated noise, thereby lessening its effect. An exception, however, is provided by energy that has been diffracted from discontinuities on the seabed, due to the waveguide effect of the water layer, since it appears to resemble a dipping reflector whose angle of dip changes for different common midpoint gathers. This distinguishing characteristic permits the identification of diffractions and their explicit nullification in the velocity-field analysis. The general effect of noise is to cause a deterioration in the localisability of the true maxima and an increase in the number of spurious maxima. In those circumstances where reflection from an interface having angle of dip 8 is being considered, then, as follows from Eq. (235), (ccos 8)’ is obtained from a coherent common midpoint stack. In addition, however, the reflection point of the rays is displaced in the up-dip direction as the source-receiver offset increases. Any variation in the reflection coefficient of the interface will exhibit an effect on the amplitude across the gather and hence affect the coherence. The initial estimate of the velocity field of an exploration prospect requires considerable intervention from an experienced interpreter, who is able to take account of the possible existence of diffractions with higher stacking velocities than primary events, and multiples with, usually, lower stacking velocities. Such an interpretation should take into account any information from previous surveys, and the resulting interval velocities should exhibit geological consistency, at least qualitatively. In consequence, the accuracy of the results depends heavily on the skill of the interpreter.

274

J. F. BOYCE A N D L. R. MURRAY

B. Normal Moveout and Stacking

Following the sequence of preprocessing operations, the seismic data set is a common midpoint gather {g}, which consists of M seismic traces g(a), a = 1,..., M, at increasing offsets. Each trace is a vector g t , t = A t , 2 A t , . . .,N At, whose elements are time-sampled amplitudes. A typical marine gather may consist of 72 traces, each with a sample interval of 4 ms over a 4 5 s duration, thus N 1000. From Eq. (173), the traces take the form

-

where Htt, is a symmetric Toeplitz matrix and n, is the additive noise distribution. The Htr,convolution matrix represents the combined effect of all of the inherent physical processes and approximations, such as dip, velocity variations, nonplanar geometry, angular dependence of reflection coefficients, and ray-geometrical acoustics, which have not been taken into account by the preceding processing; f,(a) is the reflection coefficient for two-way travel time t at an offset indexed by a. Assuming horizontal plane interfaces, this takes the form

where r, is the reflection coefficient from the ath interface, having two-way time t,. Due to the assumed geometry, the two-way travel time takes the approximate form given by a normal moveout hyperbola

where Cis the stacking velocity obtained from the velocity field analysis, and t o is the travel time at zero separation between source and receiver. Upon making the normal moveout transformation gt(a)

8’ = g(t2+ h2(a)/E2)1/2(a),

(259) the reflection from a given interface will occur at approximately the same travel time for every trace of the gather. If the set of such corrected traces are now summed, or “stacked,” +

then the contributions from an interface will tend to reinforce each other while any additive noise will be distributed randomly and hence, by the central limit theorem, be attenuated by a factor (M)-’/’. An example of a normal moveoutcorrected gather (with amplitude clipping) is shown in Fig, 25.

275

SIGNAL ANALYSIS IN SEISMIC STUDIES

ao00

234:

1 1 I 1 I 1 12222222222333333332 345678901234567890 1234567E

144444444: 123456789i

1. OOO

2. OOO

a O O O

1. aK)

mt

2. OOO

FIG.25. A normal moveout-corrected gather.

A further benefit accrues from the effect of stacking upon energy arising from multiple reflections. These are due to reflections between widely spaced interfaces, frequently, though not invariably, involving a surface reflection. As a result, the curvature of the moveout hyperbola differs significantly from that of any primary reflections with which it may be temporally coincident, since the summation appearing in the stacking velocity of the multiple [Eq. (229)] is over a different set of strata than those corresponding to nearby primary reflections. As velocity generally increases with depth, and the summation yielding the multiple's stacking velocity will be confined to shallower layers, its C is smaller than those of nearby primaries; in consequence its moveout hyperbola is more curved. It follows that a normal moveout transformation that is performed with the stacking velocity of the primaries will leave any reflection wavelet due to a multiple unaligned across the gather, so that, upon stacking, its energy becomes dispersed into a smooth background.

276

J. F. BOYCE AND L. R. MURRAY

The effect of stacking has been to reduce the set of common midpoint gather traces {g} to a single average trace g via Eq. (260).This achieves a data reduction by a factor of M , the fold of the gather, at the expense, however, both of a loss of resolution, due to the inevitable fluctuations of position and structure of the normal moveout traces, and of the discarding of any wavelet variation, and hence reflection-coefficient variation, across the gather. Were it not for the poor signal-to-noise ratio of individual traces, then the trace having minimum offset would be the most reliable, since it is the geometry of this trace that corresponds most closely to a normal incidence ray path upon which the validity of the subsequent migration will depend. (This argument is subject to the caveat that the trace should not be corrupted by propellor noise from the survey ship.) From this point of view, we may regard the purpose of the remainder of the gather as that of providing a statistical sample set that may be employed to improve the signal-to-noise ratio of the minimum offset trace. A development of the above approach is given in Appendix C, where the use of Bayesian statistics to, maximise the posterior probability of the traces leads to a weighted estimate f(a)for each trace, having

where the weighting factor v, is given in terms of the trace and noise variances 0,2 and a:, respectively, by

The mean trace Q of Eq. (261) is now replaced by the estimate T(1) of the minimum offset trace. The traces of the weighted gather { T ) preserve the resolution and wavelet localisation of the original traces, whilst attaining a signal-to-noise ratio comparable to that of the stacked trace. In addition, they retain any amplitude variation across the gather, thus permitting the characterisation of intrinsic reflection coefficient dependence on angle of incidence. The effect of maximum a posteriori (MAP) processing on the gather of Fig. 25 is displayed in Fig. 26. The final signal processing operation before display or migration is that of band-limiting filtering, with time variant band limits. Reflected wavelets received at early arrival times have larger signal-to-noise ratios and broader bandwidths compared to those received at later times. The objective of the band-limiting filters is to obtain the broadest signal bandwidth permitted by the prevailing signal-to-noise conditions. Structural interpretation of an exploration prospect is based on the filtered and deconvolved common midpoint stacked section.

277

SIGNAL ANALYSIS IN SEISMIC STUDIES

am 0.100

a000 a 100

0.200

0.200

0.300

0. 300

0.400

0.400

0.500

0.m

0.600

0. My)

0.700

0.700

am

0.En0

0.900

0.900

1. 1.

m

1. OOO

im

1. 100

1.200

1.200

I. a0

1.300

1.400

1.400

1. 500

1.500

1.600

1.600

m

1.700

1.

1.800

1. BM

1.900

1.900

2. OOO

2. OOO FIG.26. A MAP-processed gather.

VI. MIGRATION A . Geometrical Migration

The result of the velocity determination and stacking is, firstly, a stacking velocity field as a function of position and, secondly, a set of seismic traces approximating to the seismic response that would have been observed at a grid point of the datum plane if the shot and geophone had been coincident at that point and only the response due to primary reflections had been recorded. This latter property, however, is contingent upon the ability of the normal moveout transformation, using the stacking velocity field, to compensate for the effect of the offset dependence of the trace of a common midpoint gather. This

278

J. F. BOYCE AND L. R. MURRAY

supposition becomes invalid for steeply dipping interfaces due to reflectionpoint dispersion,in the neighbourhood of faults or unconformities,when, due to migration, primaries may intersect across the common midpoint gather, thereby yielding an ambiguous stacking velocity (Rocca, 1984), and in regions having complex overburdens, when the incident and reflected rays may traverse significantly different geologies (Chambers et al., 1984). A partial alleviation of these difficulties is provided by the technique of dip moveout. It has been shown (Hale, 1984; Fowler, 1984) that, for a constant velocity earth, dip moveout, followed by stacking and poststack migration, is equivalent to the ideal of prestack migration of every trace followed by stacking. This development will be considered in the next section. The remaining, highly nontrivial, problem is to convert the information from a surface-geophone response as a function of time to a map of the seismic-reflectioncoefficient at a true location in depth. The necessity for a redistribution of energy becomes apparent from rayacoustic considerations, since for a coincident source-receiver pair, a pulse received at time t may have originated from a reflector at any point of a hemisphere of radius $ct and center the source-receiver position. The process of migration may be regarded as a redistribution of the energy of each pulse over the surface of such a hemisphere. If we apply ray acoustics to the reflections observed from a dipping 6 in (x, ct) reflector (Robinson, 1983)as shown in Fig. 27, then the angle of dip , space, as measured by the difference of half-reflection times between successive traces with an offset interval of Ah, satisfies At

tan8, =c-. Ah

Ah x

(a1

hh x

(bl

FIG.27. Dipping reflectors.

SIGNAL ANALYSIS IN SEISMIC STUDIES

279

In the true earth coordinate system, the rays are reflected normally from the interface, thus the true angle of dip 6, satisfies A1 sin 9, = -. Ah The spaces are related by A1 = c At, and hence sin 0, = tan 6, ;

(266) therefore the true dip is always larger than the observed dip unless the reflector is horizontal. From a consideration of Fig. 27, it follows that the reflected energy at (x,ct) must be migrated through a distance of 2ctsin()6,) in the direction at an angle $9, to the horizontal, in order to coincide with its correct physical location. Arguments such as this, based upon ray acoustics, were utilised to formulate geometrical migration algorithms, but have been superseded by methods founded on the acoustic-wave equation. B. D i p Moveout

As just noted, reflection-point dispersion occurs when dipping reflectors are present (Deregowski, 1982).The ideal method for its removal would be to take the wave equation in offset h, which follows from Eq. 37, and use that to continue the trace to offset zero. Since this would entail continuation of every trace of each midpoint gather, the computational load would be considerable. A number of approximations to the above, termed variously “prestack partial migration” (Yilmaz and Claerbout, 1980), “offset continuation” (Bolondi et al., 1982; Salvador and Savelli, 1982), “dip moveout” (Deregowski and Rocca, 1981) may be arrived at from a consideration of ray acoustics. In the analysis that follows we shall, for simplicity, consider a homogeneous earth of constant seismic velocity c in only two spatial dimensions, x and z. Let the shot-geophone offset be 2h and let the geophone detect a single pulse at time t after the emission of an impulsive shot.3 Since the geophone responds omnidirectionally,the direction of the reflected ray is unknown. As shown in Fig. 28, since the sum of the lengths of the incident and reflected rays is determined, the point of reflection lies on the surface of the ellipse in (x, ct)

Notice that we now consider the two-way reflection time rather than the one-way time variable that was utilised in Sections IV and V.

280

J. F. BOYCE AND L. R. MURRAY

5

B M

G

I

ct

FIG.28. The fixed offset ellipse.

space having the shot and geophone positions as foci and a semimajor axis of 1

ZCt,

The reflection point may lie anywhere on the ellipse, and hence, to achieve a partial migration, the recorded pulse should be smeared along it. If we now consider how such a notional reflector would be observed at zero offset, characterised by coincident incident and reflected rays if t , is the observed reflection time, then, since the rays are normal to the reflecting surface,

whereas in terms of the lateral position x of the observation point B,

(;y + (;y

=1

for values of x such that 1x1

x,,

where

2h2

xm =-

cth

and

for

’

28 1

SIGNAL ANALYSIS IN SEISMIC STUDIES

Thus, upon transforming to a zero-offset section, the ellipse of Eq. (267) is converted into the partial ellipse, or “smile,” defined by Eqs. (269) and (272). The transformation from the observed amplitude u(x, t; h) at midpoint x and offset h to the zero-offset amplitude u,(x, t ; O ) may be achieved via the convolution Vo(X,

where

ss

t;0) = dth dx‘s(x - x’, t, th)U(th,X’, h),

s(x, t, t h ) = L(x)h[t - t,(l - x2h-2)”2] L(x) defines the amplitude distribution along the smile. If we define t ( x ) = (2xJ’

=o

1x1 < x,

1x1 > x,,

i.e., if we assume constant reflectivity but neglect the horizontal ray contributions of Eq. (267), then, upon Fourier-expanding the convolution kernel

we find that S(k, w, th) = (2x,)-’

”:s

[

dx exp i kx

+ ot,

(

;:)”’I

1 --

.

(278)

The integral may be approximated by using the method of stationary phase when it yields

where

and

282

J. F. BOYCE A N D L. R. M U R R A Y

whereas @(x) is the probability integral (Gradshteyn and Ryzhik, 1965). A necessary condition for the validity of the stationary phase approximation is that the point of stationarity xo should not approach the end points of the integration range, i.e., xo < x,. A sufficient condition to ensure this is (kl < 20/c, viz, that the angle of dip be small. From the properties of the probability integral, lim S(k,w,th) = lim exp[i(h’k’ h-0

h-0

+ 0’t,2)”’], (282)

= exp(iot,)

leading to an identity for Eq. (274) in the h -+ 0 limit. Alternatively, for large values of h, S(k,0, t h ) = (2X,)-’

exp[i(h2k2

+ o’t,2)’/’], (283)

consistent with the result of Deregowski and Rocca (1981). Now, from Eqs. (268) and (269), the time t on the zero-offset section is related to the observed time t h at offset h by t

= (t,” - 4h2C-2)’/2(1 - x2h-2)1/2,

(284) whereas, since zero-offset reflection is along the normal to the ellipse, for a given angle of dip 8, cos’ 6 = h-’[h4 - ( + C t h X ) ’ ] ( h ’

-

x2)-’,

(2851

with it following that (1 - x2h-2)-1

= (t: - 4 ~ ~ - 2 ) - 1 ( t-; 4~

cos2 8);

(286)

and hence, from Eq. (284), t = t,”(tl

+ 4h2c-’ sin’ 8 p 2 ,

(287)

where we may identify (tf + 4h2c-’ sin’ 8)’/’ as the zero moveout time that would be observed at M if the reflector consisted of a straight line passing through P with angle of dip 8. This identification suggests an alternative formulation of the dip moveout correction in terms of the normal moveout amplitude un(x,t; h), defined by the normal moveout transformation [Eq. (237)], to be V n ( x , t h ; h) =

u(x, (t’

+ 4h2C-’)’/’;

h).

(288)

Upon Fourier expanding the observed amplitude at offset h,

o(k, t h ; h) eXp(- k X ) ,

(289)

283

SIGNAL ANALYSIS IN SEISMIC STUDIES

together with the amplitude at zero offset

where, from Eqs. (288) and (289),the integral may be expressed in terms of the normal moveout amplitude as

s

vo(k,o;O) = dt,t,(ti

+ 4h2c-2)-”2S(k,w; th)V,(k,t,; h).

(292)

Using the approximation to S(k, o;t h )given by Eq. (282), the above relation becomes

s

uo(k,w;0) = dt,t,(t;

+ 4h2~-2)-1’2exp[i(h2k2 + ~ ~ t i ) ~ ~ ~ ]t,;u h), , , ( k(293) ,

when it may be identified with the expression obtained by Hale (1984) by assuming that the wave number k conjugate to the midpoint coordinate x, is related to the angle of dip by

k = 2oc-’ sin 6,

(294)

i.e., that the wave vector of the reflecting wave front is at an angle 6 to the vertical. As may be observed from Fig. 42 of Appendix B, for small angles of dip, a ray along M P will have an emergence angle that closely approximates to 6. The significant feature of either expression, [Eq. (283) or Eq. (293)], is that, acting upon a normal moveout corrected plane wave exp[i(wt, - kx)],

(295)

they introduce a time shift At = ( t i

+ h2k2m-2)1’2 - t ,

= 2h2(c2t,)-’

sin2 6,

which exactly compensates for the dip moveout of the sloping reflector. C. The Common Midpoint Frame

The seismic traces of the common midpoint gather may be regarded as samples of the seismic amplitude. Assuming only dilatational waves, and that

284

J. F. BOYCE A N D L. R. MURRAY

first-order density variations may be neglected, the amplitude u ( x ~t ,G ;xs, ts) observed at position xG and time tG in response to a seismic shot at position xs and time ts satisfies the acoustic wave equation

By the principle of reciprocity (that sources and receivers may be interchanged), the amplitude similarly satisfies

These equations are invariant under the transformation fs + ts

+T

tG + t G

+ T,

(299)

hence u is a function of t = t , - t s . Upon defining midpoint and offset coordinate systems x and h by

then, following Stolt (1978), if the second-order derivatives of mixed midpoint and offset coordinates are neglected, both equations transform to the form, c2 atz

V(X,

1

t;h) = - S 3 ( h ) b(t). 2

If it is assumed, in addition, that the offset dependence is small compared with that due to the midpoint, then the V,Z derivatives may be neglected. The common midpoint traces relate to coincident source and receiver, viz, to lim,,-o u(x, t ; h) [(which will be denoted simply by u(x, t)]. The section of common midpoint gathers is u(x,y,z = 0, t), with x and y being at grid points of the datum plane. The seismic reflectivity is the ratio of the reflected to the incident amplitudes. As shown by Claerbout, the wave equation [Eq. (30111 may be utilised to downwardly continue the surface amplitudes, both the wave field that propagates from the shot and that which is observed at the detector. Their values in the neighbourhood of a given point permit the determination of the required reflectivity. In order to relate the dip moveout and offset continuation expressions (Eqs. (278) and (293), respectively) to that of prestack partial migration, we shall assume a constant velocity in Eq. (301), when, except for h = 0, it has the solution

285

SIGNAL ANALYSIS IN SEISMIC STUDIES

where 1 2

0 = -C(k2

+ K2)”2.

(303)

We wish to continue the amplitude at known frequency w, lateral midpoint wavenumber K,, and depth z from finite moveout h to zero moveout (Berg, 1984).Considering, for simplicity, only two space dimensions and a horizontal moveout component h, from Eq. (302), u(K,,z,w; h) =

jK

(24

s d K , a ( K x , K , , w ;k)exp[i(K,z (24

-

kh)].

(304)

In a ray acoustic approximation

K = kG

+ ks

k

= kG - ks,

(305)

with ks and kG being in the directions of the shot and geophone rays, respectively, and having angles of emergence (a 8) and (a - 0) as shown in Appendix B. Hence

+

K,

= wc-1[cos(a

+ 8) + cos(a - ,911.

(306)

This is known as the “double square root” equation. If the k dependence of the integrand is weak, then the integral may be approximated by using the method of stationary phase. As shown by Deregowski and Rocca (1984),the stationary point is determined by the requirement

2h = ([tan(B

+ a) - tan(8 - a)],

(307)

where ( is the depth of the reflection point. But Theorem 3 of Appendix B shows that this condition is satisfied by the shot and geophone rays. Hence, as pointed out by Deregowski and Rocca, the condition of stationarity, as is usual, implies the condition of ray acoustics. If the amplitude is simply approximated by its value at the stationary point, then the expression becomes u(K,,z,w; h) = ~(K,,w)exp{iwc-’[cos(8 - ioc-’[sin(8

+ a) + cos(8 - a)]z

+ a) + sin(8 - a)]h}.

(308)

But from Appendix B, 22 cos 8 = ct,;

ct, tan a

= 2h cos 8;

(309)

hence, in terms of the time th at offset h related to the normal moveout time t, by Eq. (2681, u(K,,z,w; h) = u(K,,w)exp{i[wth

+ O(h4)]},

(3 10) representing a time shift from zero offset to finite offset consistent with that of Eq. (296).

286

J. F. BOYCE A N D L. R. MURRAY

D. Fourier Space Migration The major problem inherent in migration is that of taking proper account of complex interfaces and the corresponding spatial dependence of the velocity field. The techniques of migration may be classified as either direct or Fourier-space techniques (Hood, 1981; Gazdag and Sguazzero, 1984). For a homogeneous earth of constant velocity c, if we consider only the upcoming wave amplitudes, u(x,t) =

s$$

s$u(k,w)exp[-i(k-x

- w t)],

(31 1)

with

k,

= - [ ~ W ~ C - ’ - (k:

+ k;)]1’2.

(3 12)

Since u(k,w) may be recovered from the surface amplitude via the inverse Fourier transform,

ss

-

u(k,w) = d2x dtu(x,y,z = O,t)exp[i(k x - at)];

(313)

hence u(x, y, z = 0) may be recovered from the surface data. These relations, since they depend upon Fourier transforms, may be readily discretised and implemented using “fast” numerical algorithms. They form the basis of most migrations presently performed. Alternatively, the k,, k,, and w dependence of Eq. (311) may be integrated out, yielding a Kirchoff integral relation between u(x, t = 0) and its time derivative at the surface. Of course, the basic premise, that the earth is homogeneous, is invalid, so the above approach must be progressively modified to take account of increasing geological complexity.

E . Finite-Diflerence Migration At the opposite extreme, the wave equation may be used directly to continue the amplitude. As the equation is second-order in the space and time derivatives, two classes of plane wave solutions, downgoing and upcoming, occur. The only boundary data available, however, is the amplitude at the surface. It follows that only one set of solutions, either downgoing from the shot, or upcoming to the receiver, may be c o n t i n ~ e d The . ~ two sets are separately continued downwards in space and either forwards or backwards in The situation may change, at least for marine data, if vertically double streamers of geophones are utilised, since the amplitude and an estimate of its first derivative would then become available.

287

SIGNAL ANALYSIS IN SEISMIC STUDIES

time until the same space-time point is reached by each continuation, when their ratio yields the reflectivity at that location. A one-way wave equation for upward propagating waves is given by

where the square root operator is defined by expanding the amplitude as a frequency space Fourier integral. u(x, t ) =

SI:

(dw)u(x,o)exp(iwt)

(3 15)

when it becomes

au aZ

-(x,

0) =

D(x,W)U(X, w),

(316)

where

This equation is not in a suitable form for finite-differenceimplementation due to the large magnitudes that the square root factor on the right-hand side may assume. It may be reformulated by transforming to a time-retarded frame of constant velocity u by the depth-variant time translation, t +7 = t

+ z/u.

(318)

The actual phase velocity c may be position dependent, in particular a function of depth; the frame velocity is chosen close to the mean value of the range of phase velocities corresponding to the range of depths for which migration is being performed. The square-root operator in the retarded frame becomes D(x,o)= i

[("' + a2 + --r -:] a2)lI2

c

ax

dy

,

(319)

enabling the equation to be separated (with slight error) by Marchuk splitting and refraction, Dr(x,w), components as into diffraction, Da(x,o),

and D,.(x,w)= i(:

-

:).

288

J. F.BOYCE AND L. R. MURRAY

The above two components are the diffraction and refraction components of the operator. The wave equation may now be solved in finite intervals of z by the alternate application of the two parts. In the sequel, we shall consider only two space dimensions, suppressing any y dependence. The techniques of analysis extend directly to three dimensions, although implying a significant increase in computational load. Moreover, in order to develop the technique, only the diffraction term will be considered explicitly,since the refraction term may be included in any migration scheme without approximation. Now expansion of the square root as a continued fraction

Y = (1

+ X2)”2

=1+-

X2 l + Y

yields various orders of approximation. In particular, from the third-order approximation, Y=l+

X2 2 + X2/2’

(323)

the 45-degree equation results. {4d

+ C Z pa 2

I

a20

z(x,z,w) = 2ioc+x,z,w), au dX

(324)

with expression in (z,T ) space as

We may exhibit the error inherent in this approximation by considering plane waves of frequency w with angle of propagation 6, i.e., v,,(x,z,T) = exp(ik,x

+i

(

k,

3+ I

-- z

iwz

,

with w

0

k, =-cosO.

k,=-sin8 C

C

(327)

The phase shift experienced by such a wave due to migration through a distance Az is w

~ ( 6W,) = -( 1 - cos 6 )Az. C

(328)

289

SIGNAL ANALYSIS IN SEISMIC STUDIES

0 x

c

0

10

20

30

40 50 Ang Le (degrees)

60

70

80

90

FIG.29. Phase errors of the continuous 45-degree equation. The contours are of phase errors lo, lo", loo", respectively.

The corresponding phase shift that arises from a solution of the 45-degree equation is

A plot of the resulting phase error (Whitlesley and Quay, 1977), is shown in Fig. 29 for a phase-velocity of 2400 ms-' and a migration length Az of 24 m. In order to formulate a migration algorithm in the (x, z, z) domain, the derivatives in Eq. (325) are approximated by finite differences for the secondorder derivatives in x and 7,together with Crank-Nicholson averaging for the z derivative. The phase shift corresponding to a finite-difference approximation to the 45-degree equation is

where i,x

=2sin(F)/Ax

(331)

GI = sin(GAClz)/A.z,

(332)

and

290

J. F. BOYCE AND L. R. MURRAY

120 100

-.. 80 I x

60

m 03

m

&

40 \

20

\

-

\ \

.. - - - _ _ \

0 0

10

20

40

30

so

60

70

80

90

hng l e (degrees)

FIG.30. Phase errors of the discrete 45-degree equation.

with Lj = 2 sinr+)/Az,

(333)

while A x and AT are the increments in x and T,respectively. The corresponding phase errors for a migration step of 24 m at a phase velocity of 2400 ms-' when A x = 15 m and AT = 4 ms are shown in Fig. 30. The errors exhibited in this figure are much greater than those of the continuous 45-degree equation. They arise both from the third-order approximation to the square root and from the finite-difference approximations to the derivatives. Koehler (1983) noted that the finite-difference migration equation could be formulated as U(X, z

+ Az, T) = - U ( X , N

Z,

+ n =1- N

T

+ AT)

An[u(x + n A x , z, z)

+ u(x + n A x , z + A z , z + AT)], (334)

where the A , are defined by requiring that the plane wave

I (+ : )

u,(x, z, z) = exp ik,x

i k, - - z

+ iwz

I

(335)

at a fixed angle be a solution of the equation. The phase errors resulting from such an approximation for an angle t9 = 30" and N = 12 are shown in Fig. 31. The region of small errors is more extensive than that of Fig. 30.

291

SIGNAL ANALYSIS IN SEISMIC STUDIES 120

100

- 80 z x 2

60

& k

40

m

20

0 0

10

50

40

30

20

60

70

80

90

Angle (degrees)

FIG.31. Phase errors of the discrete equation, optimised to a 30-degree propagation angle.

An alternative approach may be made in the space-frequency domain. By approximating the z-derivative using a Crank-Nicholson scheme, we obtain the finite-differenceequation U ( X ,z

+ Az,W ) = H ( x , W ) U ( X ,Z,w),

(336)

where

I-" :

[:

H ( x , w ) = 1 --D(X,W)

1 +-D(x,w)

],

(337)

with D ( x , w ) being given by Eq. (317), without the y-dependence. We wish to construct a linear finite-difference approximation to the above, i.e., to approximate H by

2 N

Q(X,W)

=

Hn(0)Z",

n=-N

(338)

where 2 is the linear translation through A x in x . Z U ( X ,Z, W ) = U ( X

+ AX,

Z,

a),

(339)

since the migration then becomes N

v(x, z

+ 6 2 , W ) = n =C- N

H,(o)u(x

+ n A x , z, a).

(340)

292

J. F. BOYCE AND L. R. MURRAY

Following Stolt (1978)and Berkhout (1984), we consider the effect of thefinitedifference approximation upon the plane wave uo(x) [Eq. (326)]. The migration equation yields N

exp( - ir(8,w))= n = - N Hn(w)exp(inK,),

(341)

where K,

= k,

AX.

(342) Hence, by defining the expansion coefficients H,,(o) to be the discrete Fourier transforms of the exact transfer function, the approximation H ( x , w)= E?(x,w )

(343)

will yield the correct phase shifts for plane waves at the values K,

=n

2n (2N 1)

-NlnlN.

+

(344)

Since w

K, = -sin 8 Ax, c

(345)

this is equivalent to plane waves propagating at angles with sin 8 =

2nn (2N + l ) K ’

(346)

where K=-

C

WAX‘

(347)

In terms of K,, we have

and hence the expansion coefficients H n ( o ) may be obtained directly. The range over which the transform is applied is

However, the physical range is determined by Isin81 I 1.

(350)

SIGNAL ANALYSIS IN SEISMIC STUDIES

293

Therefore, if w is such that

Ax

w-

I sc,

C

(351)

then the range of application of the transform extends beyond the physical range. For values of K , beyond the physical range, (1 - x2K;}'/' becomes complex, the transfer function is no longer of unit modulus, and the approximation of H(x,w) by A(x,w) breaks down. This effect occurs at the lower frequencies. In terms of wavelength, it corresponds to the condition

A x I4. (352) Physically it means that we are attempting to fit data having a sampling length of A x by waves whose wavelength is too long to accommodate the possible variation. The problem may be overcome by increasing A x to 2 A x or 3 A x at the lower frequencies, i.e., by Fourier expanding in terms of 2K, or 3K, whilst maintaining the order of the expansion. The input data to the migration algorithm at lower frequencies for a given x value will be the wave field at displacements 2 A x or 3 A x from it; however, since the number of such contributions is maintained, the range in x is correspondingly increased. If this principle of adapting the effective A x to w is accepted, then it becomes possible to envisage migration utilising 3 Ax12 or 5 Ax12 for certain frequency ranges, with the wave field at half-integer values of A x being obtained by interpolation. The phase shift that arises from the finite-difference approximation is (353) The corresponding phase errors are shown in Fig. 32. The frequency at which Eq. (352) applies is 40 Hz. For lower frequencies, the discrete Fourier expansions were made in terms of 3KX/2,2K,, 5KX/2,.. ., as appropriate. The region of phase errors of less than 1' extends much further than that of the optimised 45" equation. The spatial Nyquist frequency inherent in our approximation is K, = X,

(354)

i.e., c V =

2 A x sin 8'

(355)

For frequencies of 40 Hz and below, the limit is set both by the order of the discrete Fourier transform and by the effective A x corresponding to the frequency. For example, since 3KX/2was utilised at 30 Hz, the maximum angle

N

c. 0

OI

0

0)

Frequency (HA 0 0

N 0

p

N \o

SIGNAL ANALYSIS IN SEISMIC STUDIES 00

295 -00

01

01

oa

02

03

03

04

04

06

p

06

00

i::

g 6

0s

O7

j

O8

B

09

I 0

LO

11

11

12

12

1s

15 14

14

FIG.34. Migrated section, interpolated in steps of Ax/2.

permitted at the frequency is 63". A synthetic seismic section is shown in Fig. 33. It consists of a single curved discontinuous horizon with a maximum angle of 50" in a medium of constant velocity, 2400 ms-'. Figure 34 shows the effect of migration using the migration algorithm corresponding to Fig. 32, together with an eight-point interpolation operator for the wave field at half-integer values of A x . The limiting angle at which spatial aliasing occurs due to discrete sampling in x follows from equation 354. For low frequencies, this extended beyond the physical range - 4 2 5 0 In/2, hence causing the migration operator, equation 338, to become undefined. Increasing the effective A x to 3 Ax12 or greater alleviates the problem, but at the expense of introducing an aliasing angle that is less than n / 2 for that frequency. Ideally it should be possible to utilise an effective sampling interval that may be increased continuously from the lower limit A x set by the physical sampling length. This, in turn, implies the requirement of interpolating the field at any position between the sample points, not just at the Ax12 values. We shall now show how such an interpolation filter may be based upon the forward and inverse discrete Fourier transform. Let the wave field u(x, z, w) be defined at the sample points x = n A x , - N I n IN . The forward and inverse discrete Fourier transform is

-

u(x, z, 0 )=

1 ~

2N

N

+1 1

m = -

2inmn W, 2, a)exp ( ( 2 N + 1 ) A x ) ' ~

(354)

296

J. F. BOYCE AND L. R. MURRAY

where N

1 u(x,z,w)exp

ij(rn,z,o) =

(357)

n= -N

Since, by the discrete Fourier transform, F(x, 2, 0) = u(x, 2, 0)

(358)

for x = n A x , - N In I N , ?(x, z, w), which is defined for all x, will provide an approximation to u(x, z, w) at any intermediate value. In particular, we shall be interested in values of x in the range 0 s x I A x . The accuracy of the approximation may be exhibited by considering the transfer function of the interpolation filter defined by eqs. (356) and (357). Before doing so, however, notice that, by interchanging the order of the summations, for the range O S E I 1 ,

c A(a,n)u(nA x , z , w ) , N

?(aAx,z,w) =

(359)

n= -N

where A(a,n) =

sin[n(a - n)]

1 (2N

+ 1) sin(rr(u - n)/(2N + 1))’

with the corresponding transfer function being N

F(w)=

1 A(a,n)exp(ino). n=-N

Further, the asymmetry that exists between the data range n Ax( - N I n S N ) and the interpolation range a A x ( 0 I us 1) may be removed by averaging the interpolated field over the value obtained from Eq. (359), and that obtained from the equivalent operator defined over the range - N 1I n I N 1 and interpolated within the same range, a A x ( 0 I a I 1). The interpolation equation then becomes

+

F(CIA X ,Z, W) =

[:

- A(u, - N)u(- N

A X ,Z , W)

+ j1A ( a , N + l)U((N + 1 ) A x ,

+

c N

n= - N + I

+

Z, W)

1

A(a,n)u(nAx,z,co)

.

(362)

The modulus of the resulting transfer function is shown as a function of frequency f in Fig. 35, when N = 7, for various values of u. When compared

297

SIGNAL ANALYSIS IN SEISMIC STUDIES

' " r l T r a n s f e r f u n c t I on

m

H

0.0 i

N = 7

modulus.

(I

H If) 0.5

(I

-

= 1/8

n/2

f

"12

f

= 218

I

i

r

n/2

6

Y

"

3/8

FIG.35. Interpolation operator transfer function.

with that which results from an eight-point polynomial interpolation filter (Hamming, 1977)for tl = 0.5, the discrete Fourier transform filter is superior at frequencies approaching the Nyquist. Figure 36 shows the effect of migration utilising the corresponding migration algorithm. 00

-

-00

01

01

02

02

03

03

04

04

06

05

Boa

08

io7

07

P O 8

08

09

09

10

ia

11

11

12

10

13

13

14

I4

FIG.36. Migrated section, interpolatedin steps of Ax/16.

g 6

I

1

298

J. F. BOYCE AND L. R. MURRAY

The slight amount of dispersion exhibited in Fig. 34, due to spatial aliasing in the frequency range 30 to 40 Hz, has now been eliminated as a result of the improvement in the design of the interpolation operator. By interpolating to Ax/16, the limiting angle of dip has been extended to 70”. We may expect that increasing the order of the interpolation operator in Eq. (362) will enable reflections arising from arbitrarily large angles of dip to be migrated successfully. The method may be extended to three space dimensions by replacing the single-dimensional Fourier transform by one of two dimensions.

VII. AMPLITUDE VARIATION WITH OFFSET A. Approximations to the Zoeppritz Equations

The variation of reflection coefficient of the dilatational (P-wave) amplitude with angle of incidence may be utilised to obtain information about subsurface parameters, specifically to identify and locate “bright spots” caused by shale-gas sand interfaces. This possibility arises since the P-wave velocity is lower in a gas-filled porosity than in a water-filled one, whilst the S-wave velocities are almost equal. This in turn means that the Poisson ratio 1/2(A + p ) (Hamilton, 1976; Gregory, 1976; Domenico, 1976, 1977), decreases from ~ 0 . to 4 ~0.1. In the case where the two strata that border the interface have properties that differ only slightly, since the acoustic impedance is small, the transmission coefficient will be large for waves of the same type as the incident wave, but all other coefficients will be small. The ratios of the changes of the parameters across the interface to their means will be much less than unity, viz.,

6 p / p << 1;

6cp/Fp<< 1;

6c&

<< 1,

(363)

6c, = c$ - cs,

(364)

where 6 p = p’ - p ;

6cp = c(p - c p ;

and

+ p);

+

Cs = *(c; + cS). (365) It is possible to develop an approximation to the expression for the P-wave reflection coefficient of Eq. (157) assuming that none of the angles approaches ~ / 2 Snell’s . law then gives, to first order in the changes of the velocities,

p = )(p’

Cp = Q(cl, cP);

)::(

6e=tan - ;

d $ = tan(%),

SIGNAL ANALYSIS IN SEISMIC STUDIES

299

where

6%= and

$1

-

e=

$(el

- e;

64

+ e);

6 = $(4’ + 4).

= 41 -

4,

(367) (368)

Expanding the terms of Eq. (157) to first order in the changes of the parameters yields the approximate form of P-wave ~oefficient.~

This equation, known as the Aki and Richards equation (1980) is a rewritten version of an expression given by Bortfeld (1961) as part of a more general approximation to the Zoeppritz equations. Various alternative expressions have been derived by other authors (Richards and Frazier, 1976; Shuey, 1985). An estimate of the parameter ratios in Eq. (369) may be obtained by a leastsquares fitting to the reflection events of a common midpoint gather (Mayne, 1962), having first determined the angle of incidence of the P-wave on the interface at each offset. Such an analysis is known as “amplitude versus offset.” Its efficacy relies on the approximation that a common midpoint gather provides multiple realisations of the reflection response from the same reflection point at different angles of incidence. An approach of this kind was developed by Smith and Gidlow (1985)from earlier work by Stolt and Weglein (1985) to perform a weighted averaging process (“geostack”) to display information concerning rock properties in the form of P- and S-wave reflectivities. Smith and Gidlow rearrange Eq. (369) to the form +--tan2e

(370)

and then used the “mudrock line” assumption for water-saturated silicate rocks (Castagna et al., 1985)

cp N 1360

+1.66~~

(371) to express cs in terms of c p and hence to utilise in Eq. (370). Unfortunately the constants in Eq. (371) are survey dependent, so well control data, i.e., compressional and shear wave velocities obtained by drilling, is required. This is not always available, and, although estimates may be made from the seismic data (Carrion and Hassanzadeh, 1985), the values so obtained may not be For notational simplicity, the bars indicating the means across the interface will be omitted.

300

J. F. BOYCE A N D L. R. MURRAY

reliable. In addition, Eq. (371) is incorrect for regions where carbonates are present, such as the North Sea. A further problem arises from the terms sin’ 0 and tan’ 0 in Eq. (370).These have similar magnitudes at small angles; thus small errors in the data may produce an incorrect distribution between the two terms. To combat this effect, Smith and Gidlow assumed a relationship between density and P-wave velocity that holds for water-saturated rocks, excluding evaporites (Gardner et. al., 1974),namely, p

N

0.23cy4,

(372)

where c p is in feet/sec. It follows that 6p P

-

1 6cp

4

(373)

CP’

yielding the final form of the equation to be fitted to the common midpoint data

When this equation is fitted to the seismicdata, the ratios 6cp/cpand 6c,/c, can be obtained, where the latter relies upon the validity of Eq. (373). Notice that the former is the P-wave reflectivity at zero offset, and should, in principle, be a more accurate estimate than that obtained by stacking. By assuming a constant density model, Smith and Gidlow showed that the 6 p l p term in Eq. (370) could be removed without significantly affecting the results, indicating that the parameters that determine the characteristics of the reflection are primarily the phase velocities of the dilatation and shear waves. The problem of reliably estimating the shear wave velocity was clearly demonstrated when, even with well control allowing cross-plots of the two velocity fields cpand cs and thus the constants of Eq. (370)to be determined for the gas prospect being investigated, the results did not give a satisfactory indication of the gas-bearing sediments. A form of Eq. (369) that is more suitable for amplitude variation with offset analysis may be obtained by rewriting it as a parabola in terms of the three parameters of intercept, gradient, and curvature at zero offset. Upon defining the P- and S-wave moduli of the two strata by

SIGNAL ANALYSIS IN SEISMIC STUDIES

30 1

Then

to first order, where

SM = ( M ’ - M ) ;

6 p = (p’- p),

(377)

+ M);

ji = f(p’ + p).

(378)

and

M

= +(M’

Upon utilising Eq. (376) in Eq. (369), sin2~+2& -sin40. M

(379)

This is the Pan and Gardner (1985, 1987) approximation to the Zoeppritz equations. It is of the form y = a,

+ a,x +

u3x2,

(380)

where y = R cos2 8;

x = sin2 8.

Fitting the above equation to common midpoint data provides estimates for the parameter ratios 6p/p, 6 M / M , and d p / M . Model calculations (Murray, 1989) have shown that even with significant changes in the values of the parameters (16c,l < 20%, 16c,l < 29%, 16pJ< 12%), good agreement is obtained between the fit to a common midpoint gather yielded by Eq. (380) and that of a calculation using the exact Zoeppritz equations. Hence it may be inferred that the approximation should be adequate to account for any parameter variations likely to be encountered when fitting real seismic data. Due to preprocessing, however, real data are scaled in a manner that precludes the determination of the true values of the ratios in Eq. (380); nevertheless, the relative values that can be obtained are sufficient for the characterisation of the horizons of interest.

302

J. F. BOYCE A N D L. R. MURRAY -DO 01

02

03 04 OL 00 07

FIG.37. Stacked section of real data.

B. Subsurface Parameter Estimation

Given an amplitude anomaly such as that between 1.1 s and 1.2 s on the stacked section of Fig. 37, amplitude versus offset analysis may be used to determine whether the anomaly is hydrocarbon related. Although methods for analysing the amplitude of a seismic event have existed for a couple of decades (Grant and West, 1965; Anstey, 1980), only in the last few years have quantitative methods been proposed, due to the improvement in acquisition techniques and a better appreciation of the effects of the processing operations on the true amplitude of the seismic wavelet (Gassaway and Richgels, 1983; Gelfand and Larner, 1984). The problem may be approached from a knowledge-based, forwardmodelling point of view, the elements of which may be summarized as: (i) identifying a possible hydrocarbon prospect from bright-spot or related anomalies on a section, usually by visual inspection; (ii) proposing the lithologic constituents of the suspected reservoir by using knowledge of the regional geology;

SIGNAL ANALYSIS IN SEISMIC STUDIES

303

(iii) calculating synthetic seismograms or reflection coefficient plots to give an indication of the amplitude variation with offset that may be anticipated from this lithology; (iv) designing a filter based on this expected amplitude variation that characterises the horizon and applying it to the data, such that post filtering, only those sections of the gather that possess this amplitude variation remain. The last step may be regarded as a form of automatic pattern recognition. Pursuant to the above scheme, the amplitude variation with offset observed for a synthetic top gas-sand reflection was characterised and used to construct a pattern-recognition filter. This filter was then applied to the real data of Fig. 37. A stacked section data set is shown in Fig. 38, on which a gas sand can be seen from 1.10 s to 1.18 s. The fault in the base of the gas sand can be clearly seen around trace 375 at 1.14 s, as can the faults in the Base Tertiary at traces 303 to 345 and 0.48 s to 0.53 s. It should be noted that the data of Fig. 38 has been scaled in such a way as to preserve relative amplitude. All the data in the gather has been scaled such that the maximum amplitude in the gather has a set number of trace deflections, in this case 1.5 trace deflections. The values of the parabolic coefficients a , , . . u3 of Eq. (380) were obtained for each sample of the MAP-processed section. In order to obtain a confident estimate of these coefficients, no sample time was fitted that did not have nine live traces. This resulted in no output for the data at times less than w0.4 seconds, however this region of the section is of little interest. The physical

am

a O O 0

a la,

a LOO

am

am

a m

a m

am

aw

am

am

am

am

a m

a m

am

amo

asm

asm 1.

ooo

1.

ooo loo

1. la,

1.

1.200

1.m

FIG.38. Stacked section showing gas sand.

304

J. F. BOYCE A N D L. R. MURRAY

parameters that can be derived from the parabolic coefficients, namely 6 p / p , 6 M / M , and 6 p / M , were then derived. It was immediately apparent from the corresponding sections that the main area of signal is not in the region of the gas sand, but at around 0.85 s to 0.95 s. This region is in fact a Karst sequence of beds, an area where leaching of limestone or dolomitic rocks by percolating ground water or underground streams has occurred, producing a deposit of terra rossa, a red soil similar to clay. The leaching process itself may have been initiated by the erosion and gradual downcutting of a stream through a layer of other sediments until it reached the limestone,by the uplift of the limestone on which there has already been normal surface water runoff, or most probably due to the presence of the Late Cimmerian Unconformity, which may have allowed water to penetrate the rock and eventually completely transform the limestone. Whatever the method, the result is to create a sequence of variable velocity layers, some of relatively high velocity, some of relatively low velocity, which generates the large reflections evident on the section. The gradual conversion of some carbonates in this manner is the reason why their presence in a sedimentarysequence creates problems in amplitude variation with offset. It is possible to overcome these, however, by applying a filter to the data that rejects any events that are not hydrocarbon related. What is required is some form of selection criterion whereby the gas-sand interface can be recognised in the data and displayed, whilst at the same time all other horizons are rejected. The Bacton layer above the gas sand is known to be a conglomeritic mixture of shales and sandstones, thus some form of shale-gas sand horizon amplitude variation with offset pattern-recognition filter is required. By making reasonable assumptions about the Poisson ratios of the adjacent strata, or alternatively the S-wave velocity, and the densities of the shale and gas sand Koefoed (1955) showed that if there is a significant change in the Poisson ratio across the reflecting interface, the P-wave reflection coefficient can vary greatly with angle of incidence for values well within the critical angle. For a decrease in Poisson ratio across the interface, positive reflection coefficients decrease with angle of incidence whilst negative reflection coefficients increase. If the Poisson ratio increases across the interface, the reverse situation occurs. Poisson ratios, therefore, play a significant role in describing any amplitude variation with offset behavior. There have been several detailed studies of the Poisson ratio for various sedimentary rocks made in recent years. These indicate several points that allow an estimate of Poisson ratios for the shale-gas sand interface to be made with some confidence, namely,

SIGNAL ANALYSIS I N SEISMIC STUDIES

305

(i) exceptionally high Poisson ratios, of 0.45-0.5, the maximum value they can have, are found for shallow, relatively unconsolidated brinesaturated sediments such as shales; (ii) the value of the Poisson ratio decreases with depth of burial, usually due to the sediments becoming more consolidated, resulting in a reduced porosity; (iii) brine-saturated sandstones of high porosity have Poisson ratios of the order of 0.3-0.4, but when they are gas saturated, the Poisson ratio is reduced to approximately 0.1. These points can be explained by the observation that the shear modulus of a formation p is independent of the type of formation fluid present, but the incompressibility or bulk modulus K, where, by Eq. (27),

2 3

K=A+-p

(382)

may alter greatly because, for example, a liquid is incompressible but a gas is easily compressed. Now

II;

(383)

so the c p of a brine-saturated sediment is significantly greater than that of a gas-saturated sediment, whilst the cs of a gas-saturated sediment is greater than that of a brine-saturated sediment, owing to its lower density. This explains why the significance of the factor 6 p / p in the fit Eq. (379)is negligible when compared to changes due to SM/M and 6 p / M . Ostrander (1984), using results obtained by Gassmann (1951), demonstrated that when the interstitial fluid of an initially brine-saturated formation is gradually changed to complete gas saturation, the main reduction in Poisson ratio observed occurs within 10% replacement for a high-porosity sandstone. This means that the porosity of the reservoir, and hence the actual amount of gas physically present, does not need to be accurately determined, and the Poisson ratio of both the shale and gas sand can be estimated with some confidence without knowing it. The a, coefficient is a measure of the amplitude at zero offset, not the physical reflection coefficient, so this was not used to characterise the amplitude variation with offset behavior observed, except for the fact that it

306

J. F. BOYCE AND L. R. MURRAY

was noted to be negative for the shale-gas sand interface. What are more important, however, are the relative values of the coefficients a, and a 3 , because these are derived from the amplitude variation across the gather. From the calculated amplitude variation with offset coefficient, a2 is negative whilst a3 is positive in both cases; and this fact, together with their ratio and the negative a, observation was used to characterise the shale-gas reflection. From these considerations, the conditions characterising a shale-gas sand interface can be stated as

Note that

Therefore, if la,l < a 3 ,

giving 6P

- < 0,

P

that is, 6p must be negative. As p' < p, this is physically consistent with the model Also, if a3 < 21a21,

8P SP 2-<-+ M

P

4-SP M

or 6P P

-

+ 2-6 P > 0. M

Using Eq. (386), this results in the condition

2-6P > 0, M

(387)

which in turn states that 6 p must be positive. As c;, > c& by an amount proportionally greater than p' < p, Eq. (387) is valid and the constraints of Eq. (384) are physically acceptable.

SIGNAL ANALYSIS IN SEISMIC STUDIES

307

FIG.39. The a p / p stack after filtering.

FIG.40. The 6 M / M stack after filtering.

When the constraints of Eq. (384) are applied to the coefficient stacks and the conversion to 6p/p, 6 M / M , and Bp/M is made, the results obtained are shown in Figs. 39 to 41. The cumulative action of the constraints of Eq. (384) is to produce a filter that passes only that region of the data consistent with the shale-gas sand horizon characterisation. Comparing the three “subsurface

308

J. F. BOYCE AND L. R. MURRAY

FIG. 41.

The 6 p / M stack after filtering.

parameter sections” with the stacked section of Fig. 38, the only area where there is a significant amount of coherent signal is where the shale-gas sand horizon is in fact situated. The success of the filter is qualified, however, firstly by the fact that the signal at the shale-gas sand horizon is only evident on one side of the reservoir. This is most likely due to the incorrect estimation of angles of incidence, arising from an erroneous velocity model, across that half of the section containing the dipping Base Tertiary horizon, and the deleterious effect the faulted portion of this same interface has on the true amplitude of the wave front. Secondly, the lack of response from the edges of the gas sand is probably due to tuning effects between the top and bottom gas-sand reflections.

APPENDICES A. The Wiener Filter for Common Midpoint Seismic Gathers

The traces { g(t)j of a common midpoint gather are assumed to be of the form [Eq. (173)]

:1

g(t) =

+

h(t,t ‘ ) f ( t ’ ) d t ’ n(t),

(388)

SIGNAL ANALYSIS IN SEISMIC STUDIES

309

where f ( t )is an “ideal” trace and n(t) represents the effect of additive random noise. We wish to find a filter function h(t) such that is a minimum, where

h(t - t’)g(t‘)dt‘,

f(t) =

(390)

and the average, ( ), is taken with respect to the common midpoint gather. Now

therefore, a necessary condition for e to be a minimum is ( f M t - 1)) =

Y j m(g(t

t ’ )s (t - z)>h(.r’)dz’,

(392)

which, if we require h(z) = Ofor t < 0, is known as the Wiener-Hopf equation [and upon making the replacements t - z + t’ and t’ -,t“, yields Eq. (199)l. But

RJ, = ( f ( t ) s ( t- 7)) is the crosscorrelation of f with g relative to the gather, whereas R,, = ( g ( t

- t’)s(t - 7))

(393)

(394)

is the autocorrelation of g. If we assume that the seismic traces of a common midpoint gather are stochastic processes (Parzen, 1962) that are jointly stationary, viz., of constant mean, with auto and crosscorrelations that are invariant under time translations, then RJgdepends only on z and R,, only on z - t’.Hence the (Wiener-Hopf) equation becomes

Upon taking the Fourier transform, this becomes

R f , ( 4 = R,,(4h(o). (396) Therefore h(w)is the ratio of the crosspower spectrum of the true signal with the observed signal to the power spectrum of the observed signal. Instabilities due to random zeroes of R,,(w) may be eliminated by adding a small constant background to it. This is equivalent to adding a small component of Gaussian noise to the signal and is known as “pre-whitening.”

310

J. F. BOYCE AND L. R. MURRAY

For discretely sampled functions, Eq. (173) becomes the matrix equation

where, since it is derived from a convolution, h,. is a Toeplitz matrix, viz., the elements on any diagonal are all equal. The discrete analogue of the Wiener-Hopf equation is

c a,

1” = -m

h,t,*(gt,,gt,>= ( f t S t * > ,

(398)

viz., in matrix formalism

h = RfgRij,

(399)

where R,, and R,, are the cross- and autocorrelation matrices, respectively. If the signal and noise are uncorrelated, i.e., if

= 0, then, from Eq. (397),

(f,s,,>= C(f,f,->&,, 1”

or R,, = R,,HT,

where HTis the transpose of H, and similarly,

and consequently, from Eq. (447),

h = R,,HTpR,,HT

+ R,,]-’,

(405)

Although Eq. (405) is a formal solution to the problem of deconvolution, the absence of knowledge of the detailed structure of H, coupled to its lack of stationarity along a trace, together with the computational overhead implied by the matrix inversion inherent within it, means that the direct application of the equation is infeasible and necessitates the sequence of approximate deconvolutions described in Section 1V.E.

SIGNAL ANALYSIS IN SEISMIC STUDIES

311

B. Ray-Acoustic Geometry

Consider seismic reflections in a subsurface of constant velocity c from a plane reflector having an angle of dip 8. Theorem 1. The points formed by the shot, geophone, reflection point, and the intersection of the shot-receiver perpendicular bisector, with the perpendicular to the line of reflection at the reflection point, all lie on a circle.

Proof. As shown in Fig. 42, S and G are the shot and geophone positions, respectively; M is their midpoint. AD is the reflection line, with D being vertically below M. S, G, and D define a circle whose centre lies on M D ; P is its intersection with AD. Since ED is a diameter of the circle, E P is perpendicular to the reflection line AD. The proof consists of showing that the angles a and a’ are equal and therefore that P is the reflection point for a ray that emanates from S and is reflected from AD to be received at G . Now it follows from the property that the angle subtended by the chord of a circle at any point of the circumference is a constant and that ct and a’, subtended at P by SE and EG, respectively, are equal to the corresponding angles subtended at D, with the latter being coequal, by the property of congruent triangles, since M is the midpoint of SG. Corollary 1. It follows directly from the above that

SM tana = -. MD

E

FIG.42. The ray-acoustic circle.

312

J. F. BOYCE AND L. R. MURRAY

Lemma 1. The angles of emergence of the incident and reflected rays are (a - 8) and (a + 8), respectively. Proof. The angle of emergence of the incident ray SP is 4 2 - A i P . But, from the triangle ASP, ASP = (n/2 - 0 + a); hence the result for the incident ray follows, while, by considering the triangle SPG, the angle of emergence of the reflected ray is obtained.

Theorem 2. In a subsurface of acoustic velocity $c, the travel-time t at a shot-geophone offset distance of 2h is related to the travel time t o at zero offset by

Proof. If SG is of length 2h and D is a distance z below M, then both SD and G D are of length (h2 + z ~ ) ~By ’ ~considering . the triangles SPD and GDP and utilising Lemma 1, we find that

Their sum yields the ray path length

SP

+ PG = (h2 + z2)lI2 cos 8

(409)

with consequent travel time

Similarly t o , the zero-offset travel time, is given by

22 cos 8

to=----,

and hence

C

(411 )

(

t = t ; + ( 2 h y 0”””

Theorem 3. The shot-geophone offset 2h and reflection point depth [ are related to the angles of emergence, (a - 0) and (a + 0) of the incident and

SIGNAL ANALYSIS IN SEISMIC STUDIES

reflected rays, respectively, by 2h = ([tan(cr

Proof.

+ 0) - tan(a - O)]

From Fig. 42, ( = APsin 8,

where, from the triangle APG,

But AG=AM+h and AM=-

CtO

2 sin 8 ’

hence

r = (&

COqe

+ h)

+ a) sin 0.

cos a

Upon utilising Corollary 1,

5

+ a) sin 6 + 1)cos(e cos a - 2h cos(8 - a)cos(8 + a) = h cot 8 cot(&

sin 2a

3

and since we may write 2u = (e + a) - (e - a), the theorem follows by trigonometric identity.

C. Stacking by Maximisation of the Posterior Probability Distribution The objective of stacking is to coalesce the gather into a single trace that displays the signal characteristic of primary seismic reflections while suppressing noise and spurious signals caused by long-period multiples or diffractions. Realisation of this intention requires a model to determine the statistical behaviour of a trace element across the gather. The model may be expressed in

314

J. F. BOYCE AND L. R. MURRAY

terms of an ideal trace, it being the trace that would be observed if the system were noise free, the instrumentation were perfect, and the static and normal moveout corrections exactly compensated for seismic propagation path differences. Since the recorded amplitude is regarded as being derived from an ideal signal that has been transformed by propagation and instrument response effects, and corrupted by noise, from Eq. (173), an individual trace of the normal moveout corrected gather takes the form g(a) = (H* f)(a) + n(a),

(42 1)

where the action of dispersion and instrumentation effects on the signal f (a) is represented by convolution with H,whilst n(a) represents noise, assumed to be additive and independent for different traces. If the static corrections, stacking velocity analysis, and corresponding normal moveout corrections were to compensate exactly for the seismic propagation path differences, then f (a) would be the ideal signal. If secondorder effects, such as normal moveout stretch, may be neglected, then for primary reflections,f (a)would be the same for each trace of the gather. In fact, due to errors arising both inherently from the approximations underlying the preliminary processing and from observational effects, f (a) varies around some mean trace f, assuming that, since the errors are due to many residual effects, the probability distribution p(f(a)) of observing a trace f(a) may be approximated by a Gaussian distribution p(f(a)) = [ ( ~ X ) ~ I R ~ I ] exp{ - " ~ -(f(a) - ?)T(2Rf)-'(f(a) - i)}, (422) where Rf is the autocovariance matrix. Systematic errors do arise when there is signal due to a long-period multiple reflection. The ideal trace then contains a wavelet whose location' varies across the gather along the residual moveout hyperbola arising from the difference between the primary and multiple stacking velocities at the same time. This effect, however, may be removed by introducing a semblance threshold consistent with the velocity field analysis. The noise is similarly assumed to be Gaussian distributed about zero mean, with the probability of observing a trace containing noise component n(a)being p(n(a)) = [ ( ~ x ) ~ I R , ~ ] -exp{ ' / ~ - n(a)T(2R,)-'n(a)},

(423)

where R, is the autocorrelation matrix of the distribution of noise traces. Now the conditional probabilities for observing either f (a) or (H * f (a)), given that g(a) has been observed, are related by p(f(a)lg(a)) = ldet Hlp(H * f(a)/g(a))*

(424)

SIGNAL ANALYSIS IN SEISMIC STUDIES

315

The optimum trace for each offset distance is that f(a) that maximises the above quantity, the posterior probability distribution of the ideal trace f, given the observed trace g. It depends both on the observed trace g(a) and the overall statistics of the complete gather, with the latter dependence being expressed via the autocovariance matrices RHf and R, of signal and noise, respectively. The maximum occurs for

a

---In[p(f(a)/g(a))] afi (a)

=0

i = 1, ..., N ,

(425)

which leads to the specific estimate where g is the mean trace of the observed gather. This equation expresses the optimum trace?@)for each offset distance in terms of the mean observed trace g and the observed trace g(a) at that offset,weighted by the inverse correlation matrices R,' and R;? of the noise and noise-free signal, respectively. When the signal-to-noise ratio is small, the optimum trace is weighted towards the usual stacked trace g, and when the ratio is large, the optimum is weighted towards the observed trace g(a). The common midpoint gather of observed traces f (a), a = 1,. . . ,M has been transformed into a common midpoint gather of optimal traces H * T(a), a = 1,. . .,M . The arithmetic means of both sets are equal, being the usual stacked trace. The signal-to-noise ratio of an optimal trace is significantly increased relative to that of the corresponding observed trace, being of the same order as that of the stacked trace, whereas its resolution is comparable to that of the observed trace. Moreover, since the minimum offset trace g(1) is least affected by errors due_to stacking, velocity determination, and normal moveout corrections, H * f(1) will be chosen as the overall optimum trace. Effectively, the minimum offset trace g(1) has been regarded as the most reliable, and the remainder of the gather has been employed to constru_ct a statistical filter to convert from g(1) to the corresponding MAP trace H * f(1). The continued appearance of the dispersion and instrumentation convolution H is not surprising since the poststack processing is designed to remove it. Although Eq. (426) defines the optimal trace, its application requires a knowledge of the autocovariance matrices. Fortunately these may, to a sufficient approximation, be assumed to be diagonal. In addition, the noise variance may be identified with a background upon which signal peaks are superimposed, with this structure enabling the signal component c& to be separated from that of the noise 0,' and permitting the MAP equation to be simplified to

j i ~ a= ) (1 + Vi)-l(gi

+ vigi(a)),

(427)

316

J. F. BOYCE AND L. R. MURRAY

where &c V =

+ 0;

0; ‘

The effect of systematic variations in the noise due to long-period multiple reflections may be taken into account by introducing a filter on the components of v, which is based on the coherence of the signal across the gather. If the semblance, as defined by Eq. (238), is less than a threshold, then the signal is presumed to be noise, i.e., aHris set equal to zero. As a result, the corresponding optimal trace element is equal to that of the usual stacked trace, thus reducing the significance of the multiple.

ACKNOWLEDGEMENT

The authors wish to thank Seismographic Services (United Kingdom) Ltd. for permission to utilise the seismic data contained within the figures showing real data. They also wish to thank Mr. D. W. March and Dr. R. Silva of Seismographic Services for their generosity both of time and patience during many discussions. Any shortcomings within the above work are the responsibility of the authors alone.

REFERENCES Aki, K., and Richards, P. G. (1980). “Quantitative Seismology.” Freeman, San Francisco. Al-Chalabi, M. (1979). “Developments in Geophysical Exploration Methods” (A. A. Fitch, ed.). Applied Science, London. Anstey, N. A. (1980). “Seismic Exploration for Sandstone Reservoirs.” International Human Resources Development Corporation, Boston. Arya, V. K., and Aggarwal, J. K. (1982). “Deconvolution of Seismic Data.” Hutchinson Ross, Stroudsburg, Pennsylvania. Attewell, P. B., and Ramana, Y. V. (1966). Geophysics 31, 1049. Ben-Menachem, A., and Singh, S. J. (1979). “Seismic Waves and Sources.” Springer, Heidelberg. Berg, L. G. (1984). Society of Exploration Geophysicists 54th Annual Meeting, Atlanta, Georgia, p. 796. Berkhout, A. J. (1982). “Seismic Migration A. Theoretical Aspects.” Elsevier, Amsterdam. Berkhout, A. J. (1984). “Seismic Migration B. Practical Aspects.” Elsevier, Amsterdam. Biot, M. A. (1956). Journal of the Acoustic Society of America 28, 168. Bolondi, G., Loinger, E., and Rocca, F. (1982). Geophysical Prospecting 30,813. Bortfeld, R. (1961). Geophysical Prospecting 9,485. Castagna, J. P., Batzle, M. L., and Eastwood, R. L. (1985). Geophysics 50, 571. Carrion, P. M., and Hassanzadeh, S. (1985). Geophysics 50,530.

SIGNAL ANALYSIS IN SEISMIC STUDIES

317

Chambers, R., Jakubowicz, H., Lamer, K. L., and Mai Yang (1984). Society of Exploration Geophysicists 54th Annual Meeting, Atlanta. Georgia, p. 45 1. Claerbout, J. F. (1976). “Fundamentals of Geophysical Data Processing.” McGraw-Hill, New York. Claerbout, J. F. (1985). “Imaging the Earth’s Interior.’’ Blackwell Scientific Publications, Oxford. Deregowski, S. M., and Rocca, F. (1981). Geophysical Prospecting 29, 374. Deregowski, S. M. (1982). Geophysical Prospecting 30,318. Dix, C. H. (1955). Geophysics 20, 68. Dobrin, M. B. (1976). “Introduction to Geophysical Prospecting.” McGraw-Hill, New York. Domenico, S. N. (1976). Geophysics 41,882. Domenico, S . N. (1977). Geophysics 42, 1339. Fowler, P. (1984). Society of Exploration Geophysicists 54th Annual Meeting, Atlanta. Georgia, p. 383. Gardner, G. H. F., Gardner, L. W., and Gregory, A. R. (1974). Geophysics 39,770. Gassaway, G. S., and Richgels, H. J. (1983). Society of Exploration Geophysicists 53rd Annual Meeting. Las Vegas. Gassmann, F. (1951). Vier. der Natur. Gesellschaft in Zurich, Heft I. Gazdag, J., and Sguazzero, P. (1984) Proc. ZEEE 72 1302. Gradshteyn, I. S., and Ryzhik, I. M. (1965). “Tables of Integrals, Series and Products.” Academic Press, New York. Gelfand, V., and Lamer, K. (1984). “SeismicLithologic Modeling.” The Leading Edge, Nov., p. 30. Grant, F. S., and West, G. F. (1965). “Interpretation Theory in Applied Geophysics.” McGrawHill, New York. Gregory, A. R. (1976). Geophysics 41,895. Gregory, A. R. (1977). “Seismic Stratigraphy- Applications to Hydrocarbon Exploration” (C. E. Payton, ed.). The American Association of Petroleum Geologists, Memoir 26, p. 15. Hale, D. (1984). Geophysics 49, 741. Hamilton, E. L. (1976). Geophysics 41,985. Hamming, R. W. (1977). “Digital Filters.” Prentice-Hall, Englewood Cliffs, N.J. Hood, P. (1981). “Developments in Geophysical Exploration Methods, Vol2” (A. A. Fitch, ed.). Applied Science, London. Kenneth, B. L. N. (1983). “Seismic Wave Propagation in Stratified Media.” Cambridge University Press, Cambridge. Kjartansson, E. (1979). Journal of Geophysical Research 84,4737. Koefoed, 0.(1955). Geophysical Prospecting 10,304. Kulhanek, 0.(1976). “Introduction to Digital Filtering in Geophysics.” Elsevier, Amsterdam. Mayne, W. H. (1962). Geophysics 27,927. McDonal, F. J., Angona, F. A., Mills, R. L., Sengbush R. L., Van Nostrand R. G., and White J. E. (1958). Geophysics 23,421. Murray, L. R. (1989). “Amplitude Versus Offset Analysis of Seismic Data.” Ph.D. Thesis, Univ. of London. Ostrander, W. J. (1984). Geophysics 49, 1637. Pan, N. D., and Gardner, G. H. F. (1985). Seismic Acoustic Laboratory Semi-Annual Progress Review, Uniu. of Houston 16,349. Pan, N. D., and Gardner, G. H. F. (1987). Seismic Acoustic Laboratory Annual Progress Review. Uniu. of Houston 19, 123.

318

J. F. BOYCE AND L. R. MURRAY

Parzen, E. (1962). “Stochastic Processes.“ Holden Day Inc., San Francisco. Richards, P. G., and Frazier, C. W. (1976). Geophysics 41,441. Ricker, N. H. (1953). Geophysics 18, 10. Ricker, N. H. (1977). “Transient Waves in Visco-Elastic Media.” Elsevier, Amsterdam. Robinson, E. A. (1983). “Migration of Geophysical Data.” International Human Resources Development Corporation, Boston. Robinson, E. A,, and Silvia, M. T. (1981). “Digital Foundations of Time Series Analysis.” Holden Day, San Francisco, California. Robinson, E. A., and Treitel, S. (1978). “Digital Signal Processing in Geophysics: Applications of Digital Signal Processing” (A. V. Oppenheim, ed.). Prentice-Hall, New Jersey. Rocca, F. (1984). Society of Exploration Geophysicists 54th Annual Meeting, Atlanta, Georgia, p. 61 1. Salvador, L., and Savelli, S. (1982). Geophysical Prospecting 30,829. Sengbush, R. L. (1983). “Seismic Exploration Methods.” International Human Resources Development Corp., Boston. Shah, P. M. (1973). Geophysics 38, 812. Shuey, R. T. (1985). Geophysics 50,609. Silvia, M. T., and Robinson, E. A. (1978). “Deconvolution of Geophysical Time Series in the Exploration for Oil and Natural Gas.” Elsevier, Amsterdam. Smith, G. C., and Gidlow, P. M. (1985). Geophysical Prospecting 35,993. Stolt, R. H. (1978). Geophysics 43,23. Stolt, R. H., and Weglein, A. B. (1985). Geophysics 50,2458. Tullos, F. N., and Reid, C. (1969). Geophysics 34, 516. Waters, W. H. (1981). “Reflection Seismology. A Tool for Energy Resource Exploration.” WileyInterscience, New York. White, J. E. (1965). “Seismic Waves: Radiation, Transmission and Attenuation.” McGraw-Hill, New York. Whitlesley, R. B., and Quay, R. G. (1977). Society of Exploration Geophysics 47th Annual Meeting, Calgary. Volarovich, M. P. (1969). Physics Solid Earth, English edition, No. 12, p. 741. Yilmaz, O., and Claerbout, J. F. (1980) Geophysics 45, 1753.

A

Chemical detectors, 131 Chromaticity diagram, full-color TFT LCD, 60-61 Clay minerals, 156-172 Coating, 154, 155 Coherent energy, types, 249 Color filter, TFT LCD, 61-63 Color imaging, 149 Common midpoint frame, 283-285 Common midpoint seismic gathers, Wiener filter, 308-310 Computers, LCD applications, 73-74 Conservation laws, 89 Conservation of traction, 233 Constant Q-model of attenuation, 228 Convolution kernel Fourier-expansion, 281 reflection sequence, 259 Coordinates (normal), 99 Cove flood, 193 Critical point drying, 150-152 Cryogenic drying, 153 Crystals, 84

a, coefficient, 305-306 Absorption, wave equation, 225-229 Acceleration sensitivity, 129 Acoustic amplitude, 251-252 Acoustic wave equation, 284 Active-matrix LCDs, see Liquid-crystal displays, active-matrix Aki and Richards equation, 299 Amorphous Si field-effect transistor, 33-35 Amorphous Si TFT characteristics, 33-37 gate electrode, 32 gate insulator film, 32 metal contact, 32 mobility, 33 multigap liquid-crystal cell spacing method, 37-38 performance, 37-39 photoconductivity effects, 35-36 stability, 37 structure and fabrication processes, 31-33 threshold voltage, 33 uniformity, 37 very-thin-film transistor, 36 Amplitude-frequency effect, 116, 118 Attenuation, 100, 106

D Deconvolution, 256-263 filter function, 259 marine shot gather, 261-263 multiple, 258-263 predictive, validity, 261 source-wavelet compensation, 256-257 Weiner-Hopf equation, 260 Defects, elimination, TFT, 25-27 Diagenesis, 157, 173, 175 Dilational field, wave equation, 220-221 Dilational stress, 216 Diode LCDs compared with TFTs, 66-67 configuration, 10-11 Dip moveout, 278-283 amplitude distribution along smile, 281 fixed offset ellipse, 280 Fourier-expansion of convolution kernel, 281

B Backlighting, LCDs, 27 color-image TFT, 63-64 Back scattered electron imaging, 141 Band-limiting filtering, 276 Bulk acoustic waves, 103 Bulk modulus, 305

C Cathodoluminescence, 144-149 CdSe TFT, 13, 29-31 characteristics, 30-31 performance, 31 structure and fabrication processes, 29-30 319

320

INDEX

method of stationary phase, 281-282 Dipping reflectors, 278 Dispersion, 98 Dispersion relation aliasing due to discrete spatial and temporal sampling, 253-254 forward propagating wave, 251 Displacement, 86 Dix’s equation, 244-248 refraction effect, 265 Double square root equation, 285 Driving schemes color LCD panels, 64-65 TFT LCDs, see Thin-film transistor liquidcrystal displays Dye-type color filter, fabrication method, 62

Fourier space migration, 286 Freeze drying, 152 Frequency-wave number dispersion, marine gather, 254-255

G Gas sand interface, 304 stacked section, 303 Gaussian distribution, 271 Geophone array, 211 Ghost deconvolution, 257-258 Grey-scale operation input-signal modification, 53-54 line-at-a-time driving scheme, 52 Gruneisen parameter, 102

E Effective constants, 123 ELDs, 74 Electrical circuit, 84, 106, 110-111 Electric field sensitivity, 130 Electromechanical coupling factor, 105 Environmental cell, 156

F Field-effect transistor, amorphous silicon, 33-35 Filter function, 259 Finite-difference migration, 286-298 Crank-Nicholson scheme, 291 discrete Fourier transform, 295-296 one-way wave equation, 287 phase errors, 289-291, 294 spatial Nyquist frequency, 293 square-root operator, retarded frame, 287 synthetic section, 294-295 transfer function, 296-297 Finite-difference migration equation, 291-292 f-k-filtering, 251-255 Fluorescent tube, peak-enhanced, 64 Force law, 214-215 Forces (electrical), 88 Force sensitivity, 127 Forces (surface), 88 Forward propagating wave, dispersion relation, 251

H Harmonics, 114 Heat conductivity, 102

I Impurities, 131 Integrated TFT drivers, 55-57 Interaction energy, 101 Intermodulation, 115 Internal friction model, seismic energy, 228

L Large-scale integration drivers, LCDs, 54-55 Limestone, 173 Line-at-a-time data transfer method, 50-53 Liquid-crystal displays active-matrix advantages, 9-11 compared with directly multiplexed, 67-68 based on alternative technologies, performance, 65-68 comparison between TFT and diodecontrolled, 66-67 diode, 10-11 directly multiplexed. 67-68 dot-matrix-type, 55 full-color, 38-39, 46-47 historical background, 2-4

INDEX portable personal computer, 3-4 status relative to other technologies, 74-75 supertwisted-nematic, 67-68 temperature effects, 27 TFT addressed, 9-10, 12-17 CdSe, 13 history, 12-13 silicon-on-sapphire, 14 silicon TFTs and diodes, 15-17 single-crystal silicon and diode arrays, 14-15 Liquid-solid interface evanescent waves, 235-237 wave propagation across, 229-235

M MAP-processing gather, 276-277 Material constants, 93 Migration, 277-298 algorithm, 289 common midpoint frame, 283-285 dip moveout, 278-283 double square root equation, 285 finite-difference, see Finite-difference migration Fourier space, 286 geometrical, 277-279 redistribution of energy, 278 Mobility, amorphous Si TFT, 33 MOS transistors, 14 Motional parameters, 106 Multiple suppression, 254 Muting filter, wedge, 253

N Natural, initial, final states, 119 Nematic-phase liquid crystal, 3 NMO stretch, 269-271 Noise additive distribution, 274 characterisation, 249-250 classification, 273 f-k-filtering, 251-255 high-velocity, 250 trace distribution, 314 Nonlinearities, 85, 86 Normal moveout hyperbola, 274-275 stacking and, 269-271, 274-277

32 1 P

Paleontology, 185 Particle analysis, 149 PDPs, 74 Petrography, 157, 173, 175 Phonons, 100 Photoconductivity, a-Si TFT effects, 35-36 Photolithography methods, 26 Photomask, poly-Si TFT, 40-41 Piezoceramics, 84 Piezoelectricity, 84 Pixel color, arrangements, 59-60 equivalent circuit, 19-20 LCDs, 9 Pocket TV, 69-70 Point-at-a-time data transfer method, 48-50 Poly-Si film, 16-17 Poly-Si TFTs, 39-47 characteristics, 22, 42-46 dual-gate structure, 44 film thickness effects, 44-45 gap-state density, 42 high-temperature-processed, 40-41 characteristics, 43-44 integrated drivers frequency range of shift registers, 56 microphotograph, 57 photograph, 58 leakage current, 44 low-temperature-processed, 41-42 characteristics, 43-44 ON/OFF current ratio, 44 performance, 46-47 stability, 45-46 structural and fabrication processes, 39-42 types, 40 Pores, 185-187 Porosity, 199 Portable personal computer, LCDs, 3-4 Posterior probability distribution, maximisation, stacking by, 313-316 Pressure sensitivity, 128 Pressure wavefield, space-time variation, 211-212 Primary reflection enhancement, 254 Projection TV, 71-73 P wave incident on interface, 230 transmission, 242-243

322

INDEX

P-wave reflection, 242-243 coefficient. 298-299

Q Quality factor, 106, 111

R Ray-acoustic geometry, 311-313 Reflection coefficient, 235 field, 256, 258 at nonzero angles of incidence, 241 at normal incidence, 240 P-wave, 298-299 S-wave, 243-244 variation with angle of incidence, 298 Refraction, two-layer system, 265 Reliability CdSe TFTs, 30 LCDs, 28 Resonator, 84, 103 Ricker wavelet, 226-228 reflection, 269-270

S Sandstone, 157 Scale, 197-199 Seismic energy internal friction model, 228 viscous fluid flow model, 227 Seismic pressure impulse, ideal, wave equation, 224-225 Seismic signal, water layer effect, 258 Seismic studies, 209-214; see also Wave equation amplitude variation with offset, 298-308 Aki and Richards equation, 299 shear wave velocity, 300 stacked section, 303 subsurface parameter estimation, 302-308 Zoeppritz equation approximation, 299-301 band-limiting filtering, 276 frequency-wave number dispersion, marine gather, 254-255 imaging characteristics, 210-211 MAP-processing gather, 276-277 marine shot gather, 245-246 migration, see Migration

preprocessing and prestack deconvolution, 244-263 Dix’s equation, 244-248 earth model, 245-247 f-k filtering, 251-255 ghost deconvolution, 257-258 multiple deconvolution, 258-263 multiple suppression and primary reflection enhancement, 254 noise characterisation, 249-250 normal moveout geometry, 245-246 predictive deconvolution, 256-263 source-wavelet compensation, 256-257 stacking chart, 248 subsurface representation, 245 preprocessing sequence, data set of filtered geophone responses, 264 pressure wavefield, space-time variation, 211-212 processing sequence, 213 ray-acoustic geometry, 311-313 sea based data, short-period multiple reflections, 250 shot gather source-receiver configuration, 244-245 stacking, posterior probability distribution maximisation, 313-316 stacking velocity, 263-273 traces of weighted gather, 276 typical shot, 211 wave propagation, see Wave propagation Wiener filter, 308-310 Shale, 175 Shale-gas sand interface, 306 densities and velocities, 242 P-wave reflection and transmission coefficients, 243 S-wave reflection and transmission coefficients, 244 Shear stress, 216-218 Shear vector field, 221 Shear wave velocity, estimation, 300 Silicon film, deposition, 15-16 Silicon TFTs and diodes, 15-17 LSI and VLSI, 17 N-channel, 16 Snell parameter, 241 Snell’s law, 265-266 Solid-solid interface numerical examples, 241-244

INDEX wave propagation across, 236-241 Sound energy, propagation in earth, 211 Source-wavelet compensation, 256-257 Specific heat, 100 Stacking chart, 248 normal moveout and, 269-271, 274-277 posterior probability distribution maximisation, 313-316 velocity, 263-273 acoustic velocity, 268 determination of field, 268-269 discontinuity of field, 272 Dix’s equation, 265 Gaussian distribution, 271 horizontal strata, 267-268 refraction effect, 265-267 uncertainties of field, 269 wavelet interference, 272 Strains, 87 Substrate material, TFT, 25 Subsurface parameter estimation, 302-308 a , coefficient, 305-306 bulk modulus, 305 coefficient stacks, 307-308 gas-sand interface, 304 parabolic coefficients, 303-304 Poisson ratios, 304-305 shale-gas sand interface, 306 Supertwisted birefringence effect liquid-crystal, 4 Supertwisted-nematic LCDs, 67-68 Surface acoustic waves, 108 S-wave reflection and transmission coefficients, 243-244

T Television, LCD applications, 69-73, 75 future, 76 pocket TV, 69-70 projection TV, 71-73 wall-type flat TV, 70-71 Temperature sensitivity, 125 Thermal expansion, 102 Thin-film transistor liquid-crystal displays, 4, 17-28 amorphous silicon, performance, 37-39 applications computers, 73-74 pocket TV, 69-70

323

projection TV, 71-73 wall-type flat TV, 70-71 backlighting, 27 CdSe, performance, 31 circuit arrangement, 19 color-image, 57-65 backlighting, 63-64 chromaticity, 60-61 color filter fabrication, 61-63 driving scheme, 64-65 light transmission, 60 pixel arrangements, 59-60 structure, 58-61 compared with diode-controlled LCDs, 66-67 configuration, 9-10 cross-sectional view, 18 defect elimination, 25-27 device structure, 24-25 driving schemes, 47-57 input-signal modification for grey-scale operation, 53-54 integrated TFT drivers, 55-57 line-at-a-time data transfer method, 50-53 LSI drivers, 54-55 point-at-a-time data transfer method, 48-50 driving waveforms, 20-21 electrical requirements, 21-23 environmental problems, 27-28 future expectations, 76-77 leakage current, 27 OFF and ON resistances, 21 photolithography methods, 26 physical arrangement and operation, 18-21 pixel equivalent circuit, 19-20 poly-Si, see Poly-Si TFT problem areas, 75-76 reliability problems, 28 required voltage, 23 structural requirements and fabrication processes, 23-28 substrate material, 25 switching ratio, 22 Thin-film transistors amorphous, see Amorphous Si TFT CdSe, 13, 29-31 semiconductors, 11 silicon-on-sapphire, 14 Threshold voltage, amorphous Si TFT, 33 Transmission coefficient, 235

324

INDEX

at nonzero angles of incidence, 241 Twisted-nematic field-effect mode, 3 Twisted-nematic LCD cell, 4-6 multiplexed, 3, 6-8 operating principle, 4-5 optical response, 5-6 transmission as function of applied voltage, 53-54

V Velocity-amplitude effect, 115 Viscous fluid flow model, seismic energy, 227

W Wall-type flat TV, 70-71 Wave amplitudes, incident, reflected, and refracted, 230-231 Wave equation, 214-220 absorption, 225-229 across solid-solid interface, numerical examples, 241-244 derivation, 218-220 dilational stress, 216 force law, 214-215 ideal seismic pressure impulse, 224-225 one-way, 287 Ricker wavelet, 226-228

shear stress, 216-218 solution, uniform density, 220-224 Wavelet interference, 272 Ricker, 226-228, 269-270 Wave propagation, 229-244 across liquid-solid interface, 229-235 conditions of continuity, 229-231 conservation of traction, 233-234 normal component continuity, 231-232 transmission and reflection coefficients, 235 wave amplitudes, 230-231 across solid-solid interface, 236-241 conditions of continuity, 239 reflection coefficient, 240-241 relations among amplitudes, 239 transmission coefficient, 241 Zoeppritz equations, 241 evanescent waves at liquid-solid interface, 235-237 Weiner-Hopf equation, 260, 309 discrete analog, 310 Wiener filter, common midpoint seismic gathers, 308-310

Z ZnO diodes, 14 Zoeppritz equations, 241 approximations, 298-301

Advances ln Electronics and Electron Physics Volume 77 Pew w.H a w h , Editor-in-Chief Benjamin Kazan, Associate Editor Errata In the chapter "Scanning Elecmn Microscopy in the Petroleum Exploration Industry" by J. M.Huggeu: Figure 1 is reprinted fm Dilks. A., and Graham, S. C. (1985). J . Sed. Per. 55. 350. Figure 5 is reprinted from Peschek, P.S.,Scriven, L. E.,and Davis, H. T. (1981). In "Scanning Electron Microscopy" (0.Johari, ed.) p. 514-524. SEM Inc., AMF OHare (Chicago), Illinois.

Figure 8 is reprinted from Houseknecht, D. W.(1988). J. Sed. Per. 58,228246.

Figures 11,12,13,19,20,21 and Table 1 are reprinted from White, S. H., Shaw, H. F., and Huggett, J. M.(1984). J. Sed. Per. 54,487-494.

Figure 15 and 16 are reprinted from Keller, W. D.,Reynolds, R.C., and Inoue, A. (1986). Clays and Clay Minerals 34, 187-197.

Figure 17 is reprinted from Stalder, P.J. (1973). Geologic Mijnb 52,217-220. Copyright 0 1973 by Martinus Nijhoff Publishers. Reprinted by permission of Kluwer Academic Publishers. Figures 23 and 24 are reprinted from Huang, W.L.,Bishop, A. M..and Brown, R. W.(1986). Clay Mimr 21.585-602.

Figures 26 and 27 are reprinted from Swanson, B. F. (1977). SPE Paper 6857. Copyright Q 1977, Society of Petroleum Engineers. Figures 28 and 29 are reprinted from Nuhfer, E.B.,Vinopal, R. J., Hohn, M. E.,and Klandefman, D. S. (1981). In "Scanning Electron Microscopy," 1981/I (0.Johari, ed.), p. 625-632. SEM Inc., AMF OHare (Chicago), Illinois. Figures 30 and 31 arc reprinted from Rothbard, D. R., and Skopec, R. A., Bajsarowicz, C. J.. and Fa& T. H. (1987). Scanning Microscopy 1,489-494.

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