Theoretical and Computational Acoustics ICTCA'99: Proceedings of the 4th International Conference Stazione Marittima, Trieste, Italy, 10-14 May 1999

Theoretical and Computational Acoustics'99 Editors

Geza Seriani Ding Lee

World Scientific

Theoretical and Computational +S1 Acoustics'99 , * < % L ! > (with CD-Rom)

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Theoretical and Computational Acoustics'99 ^ ^ v**^

^^

(with CD-Rom)

Proceedings of the 4th ICTCA Conference Stazione Marittima, Trieste, Italy 1 0 - 1 4 May 1999 Hosted by Istituto Nazionale di Oceanografia e di Geofisica Sperimentale, Italy

Editors

Geza Seriani Istituto Nazionale di Oceanografia e di Geofisica Sperimentale, Italy

Ding Lee Yale University, USA

Y | p World Scientific NEWJERSEY

• LONDON • SINGAPORE • SHANGHAI • HONGKONG

• TAIPEI • CHENNAI

Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: Suite 202, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

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THEORETICAL AND COMPUTATIONAL ACOUSTICS (ICTCA'99) Copyright © 2004 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book or parts thereof, may not be reproduced in anyform or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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V

Preface

The Fourth International Conference on Theoretical and Computational Acoustics (ICTCA'99) was held on 10-14 May 1999, at the Stazione Marittima Congress Centre in Trieste, Italy. The conference was hosted by the Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS, Italy) and jointly sponsored by the Charles University of Prague (Czech Republic), the Dept. of Applied Mathematics and Theoretical Physics (DAMTP) of Cambridge University (UK), the IACM-Foundation for Research k. Technology (Crete, Greece), the Roma Tre University (Italy), the Tel Aviv University (Israel), the Technion-Israel Institute of Technology (Israel), the Yale University (USA), the Columbia University (USA), the Boston University (USA), the University of Colorado (USA), the Scripps Institution of Oceanography of the University of California (USA), the U.S. Naval Undersea Warfare Center Division (NUWC), the U.S. Office of Naval Research (ONR), the U.S. Naval Research Laboratory (NRL), the NATO SACLANT Undersea Research Center (Italy), the Society of Exploration Geophysicists (USA), the Acoustical Society of America (USA), and STATOIL (Norway). The objective of the conference was to provide an interdisciplinary forum for active researchers in academia and industry and of varying backgrounds to discuss state-of-the-art developments and results in theoretical and computational acoustics and related topics. About 280 papers have been presented at the meeting, covering acoustical problems of common interest across disciplines and their accurate mathematical and numerical modelling. It was a very successful conference with five parallel morning and afternoon sessions on various topics, from fundamental research to practical applications, among which we want to mention the specific mini-symposia on computational seismology, on finite element for wave problems, on geoacoustics inversion in shallow water, and on ultrasonic field synthesis and modelling. a A large number of the lectures, converted to full papers, have been submitted for publication in the Journal of Computational Acoustics and, after a

BolIettino di Geofisica teorica ed applicata: an International Journal of Earth Sciences, OGS, Trieste (Italy), Vol. 40-1 Supplement: ICTCA'99.

VI

a full revision process that was longer than expected, about 110 of them were printed in various JCA issues from Vol. 8(1) to Vol. 11(1). All the contributions are collected in this book in the hope that a larger number of scientists in the field can take advantage of them for their own studies. This was possible with the help of Prof. Robert Vichnevetsky, from IMACS, whom we wish to thank for granting us the reprint permission. This book and the CD-Rom b are the final result of a cooperative effort of many individuals that contributed to the organization of ICTCA'99 conference: the organizing and scientific committees, the session organizers and all the personnel of the conference office. We gratefully wish to acknowledge and thank all of them for their generous help. Special thanks go to Angela Marchetto, the conference secretary, for her continuous diligent efforts in assisting in all arrangements for the conference. Geza Seriani, Chairman of ICTCA '99 Ding Lee, Co-chairman of ICTCA '99

b

CD-Rom System requirement: files are in PDF format. Acrobat Reader or a similar PDF •file reader is required.

VII

CONTENTS

Preface

v

Wave Propagation Theory Uniformly Asymptotic Solutions for Pseudodifferential Equations with Singular Integral Operators A. Hanyga and M. Seredynska

3

The Kirchhoff-Helmholtz Integral Pair M. Tygel, J. Schleicher, L. T. Santos, and P. Hubral

4

Analysis and Processing of Received Signals in Boreholes J. M. Hovem, H. Dong, and O. Lotsberg

5

Informational Capacity of Acoustic Measurements E. Lichman

6

Resonances of Acoustic Waves Interacting with an Elastic Seabed M. S. Fokina and V. N. Fokin

7

Modeled Velocity and Reflectivity Properties of Anisotropic Hydrated Sediments M. Jakobsen, T. A. Johansen, and B. 0. Ruud

8

Reflection/Transmission Coefficients at a Plane Interface in Dissipative and Nondissipative Isotropic Media: A Comparison J. Brokesovd Analysis of the Reflection and Transmission Coefficients in Three-Phase Sandstone Reservoirs C. L. Ravazzoli Fractional Diffusive Waves F. Mainardi and P. Paradisi

9

10

11

VIII

Acoustic Excitation of Scholte-Stoneley and Lamb Waves on a Reinforced Cylindrical Shell 0. Poncelet, A. Gerard, M. Deschamps, A. Guran, B. Belinskiy, J. Dauer, and H. Uberall

12

On the Adiabaticity of Acoustic Propagation Through Nongradual Ocean Structures E. C. Shang, Y. Y. Wang, and T. F. Gao

13

Ferromagnets and Kelvin's Medium: Basic Equations and Wave Processes E. F. Grekova

14

Propagation of Ultrasonic Waves in Nonlinear Multilayered Media V. Chiroiu, C. Chiroiu, C. Rugina, P. P. Delsanto, and M. Scalerandi Optimal Model for the Diffraction Effect in the Ultrasonic Field of Piston Transducers A. B. Temsamani, S. Vandenplas, and L. Van Biesen Oblique Acoustic Axes in Trigonal Crystals V. G. Mozhaev, F. Bosia, and M. Weihnacht Acoustic Time Series Variability and Time Reversal Mirror Defocusing Due to Cumulative Effects of Water Column Variability K. D. Lepage Numerical and Experimental Time-Reversal of Acoustic Waves in Random Media A. Derode, M. Tanter, A. Tourin, L. Sandrin, and M. Fink

15

16

17

18

19

Fluctuations of Elastic Waves Due to Random Scattering from Inclusions V. A. Korneev and L. R. Johnson

20

Numerical Study of the Wave Instability Problem with the Effect of the Transverse Velocity Component B. S. Attili

21

Sound Propagation, Vibrations and Noise Airborne Acoustics of Explosive Volcanic Eruptions M. J. Buckingham and M. A. Garces

25

Sound Generation of Interacting Perturbed Vortex Rings C. C. K. Tang, N. W. M. Ko, and R. C. K. Leung

26

A Wide-Angle Parabolic Equation for Acoustic Waves in Inhomogeneous Moving Media: Applications to Atmospheric Sound Propagation L. Dallois, P. Blanc-Benon, and D. Juve Acoustics of Kinematically Complex Shear Flows A. Rogava, S. Poedts, and S. Mahajan

27

28

Ultrasound Propagation Through a Rotational Flow: Numerical Methods Compared to Experiments S. Manneville, C. Prada, M. Tanter, M. Fink, and J.-F. Pinton

29

Wave Propagation on an Elastic Beam Traveling in a Tube: Linear Theory of Aerodynamic Loading N. Sugimoto and K. Kugo

30

On the Vibration of Membrane Partially Protruding Above the Surface of Liquid G. V. Filippenko and D. P. Kouzov

31

Vibrational Analysis of Ships with Coupled Finite and Boundary Elements C. Cabos and F. Ihlenburg

32

Transverse Resonant Oscillations in Acoustic Ducts P. Vainshtein Noise Shielding by Simple Barriers: Comparison Between the Performance of Spherical and Line Sound Sources D. Ouis Wave Propagation Through Hollow Bodies and Noise Reduction S. Germes, C. Stawicki, and D. Aubry

33

34

35

X

Generation of Ground Elastic Waves by Road Vehicles V. V. Krylov

36

Underwater Acoustics Broadband Matched-Field Localization Performance in Uncertain Environments Using a Short Array B. F. Harrison A Frequency Domain Inversion Method Applied to Oblique Reflected Signals from a Water-Sediment Interface S. Vandenplas, A. B. Temsamani, Z. Cisneros, and L. Van Biesen Application of a Three-Dimensional Two-Way Parabolic Equation Model for Reconstructing Images of Underwater Targets D. Zhu

39

40

41

Determination of a Buried Object in a Two-Layered Shallow Ocean R. P. Gilbert, M. Werby, and Y. Xu

42

New Schemes of Ocean Acoustic Tomography E. C. Shang, A. G. Voronovich, Y. Y. Wang, K. Naugolnykh, and L. Ostrovsky

43

Numerical Simulation of Transverse Current Monitoring in the Pram Strait K. A. Naugolnykh, Y.-Y. Wang, and E. C. Shang Prospects for Medium-Scale Diffraction Tomography on the Shelf I. P. Smirnov, A. I. Khilko, and J. W. Caruthers

44

45

Engineering Seismology Applications of the Modal Summation Technique to the Theoretical Site Response Estimation F. Romanelli, F. Vaccari, and G. F. Panza

49

Earthquake Ground Motion Simulation Through the 2-D Spectral Element Method E. Priolo

50

XI

The Variational Indirect Boundary Element Method: A Strategy Toward the Solution of Very Large Problems of Site Response F. J. Sdnchez-Sesma, R. Vai, and E. Dretta Efficiency and Optimization of the 3-D Finite-Difference Modeling of Seismic Ground Motion P. Moczo, J. Kristek, and E. Bystricky Three-Dimensional Ground Motion Simulations for Large Earthquakes on the San Andreas Fault with Dynamic and Observational Constraints K. B. Olsen Modifications of the Ground Motion in Dense Urban Areas D. Clouteau and D. Aubry Numerical Simulations of Strong Ground Motion During Destructive Earthquakes in Hokkaido, Japan M. Furumura and T. Furumura Application of the Integral Laguerre Transforms for Forward Seismic Modeling G. V. Konyukh, B. G. Mikhailenko, and A. A. Mikhailov Parallel 3D Fourier Spectral Simulation of Strong Ground Motion in Osaka Basin During the 1995 Kobe Earthquake T. Furumura

51

52

53

54

55

56

57

Ultrasonic Field Synthesis and Modelling Guest Editor: M. Pappalardo Speed-Accuracy Trade-Offs in Computing Spatial Impulse Responses for Simulating Medical Ultrasound Imaging J. A. Jensen

61

Mechanism of Acoustic Wave Propagation: A Real Role of Virtual Sources H. Lasota

62

XII

Synthesis of Unequally Spaced Arrays with Asymmetric Beam Patterns A. Trucco and V. Murino

63

Real-Time Deconvolution in Ultrasonic Imaging Systems G. Cincotti, R. Carotenuto, G. Cardone, P. Gori, and M. Pappalardo

64

Time Reversal in Acoustics M. Fink

65

Computation of the Ultrasonic Field Radiated by Segmented-Annular Arrays O. Martinez, L. G. Ullate, and F. Montero

66

Numerical Techniques for Modeling Doppler Ultrasound Spectra Systems M. G. Ruano

67

Influence of the Inter-Element Coupling on Ultrasound Array Radiation Patterns P. Gori, A. Iula, M. Pappalardo, N. Lamberti, and F. M. De Espinosa

68

Computational Methods A Direct Discrete Formulation for the Wave Equation E. Tonti

71

An Hexahedral Face Element Method for the Displacement Formulation of Structural Acoustics Problems A. Bermudez, P. Gamallo, and R. Rodriguez

72

A Comparison of Numerical Methods for Active Sonar Array Performance S. Morgan, D. J. W. Hardie, and P. C. Macey

73

On the Efficient Implementation of the Integral Equation Method in Elastodynamics E. V. Glushkov and N. V. Glushkova

74

XIII

A Generalized Mode Matching Method for Scattering Problems with Unbounded Obstacles A.-S. Bonnet-Bendhia and A. Tillequin

75

AILU for Helmholtz Problems: A New Preconditioner Based on the Analytic Parabolic Factorization M. J. Gander and F. Nataf

76

Application of a Domain Decomposition Method with Lagrange Multipliers to Acoustic Problems Arising from the Automotive Industry F. Magoules, K. Meerbergenm and J.-P. Coyette Visualization of the Energy Flow in and Around a Fluid Loaded Elastic Sphere C. E. Dean and J. P. Braselton Noise Prediction Based on the Spectral Method for Solving a Dissipative Boundary Value Problem in Acoustics and Its Numerical Realization E. Sviageninov Sine Solution of the Shallow Water Equations K. Al-Khaled

77

78

79

80

Finite Elements for Wave Problems Guest Editors: R. J. Astley, K. Gerdes, D. Givoli, and I. Harari Numerical Studies of Conjugated Infinite Elements for Acoustical Radiation R. J. Astley and J. A. Hamilton

83

A Reflection Free Boundary Condition for Propagation in Uniform Flow Using Mapped Infinite Wave Envelope Elements W. Eversman

84

A Review of Infinite Element Methods for Exterior Helmholtz Problems K. Gerdes

85

XIV

On Fundamental Aspects of Exterior Approximations with Infinite Elements F. Ihlenburg Finite Element Solution of Two-Dimensional Acoustic Scattering Problems Using Arbitrarily Shaped Convex Artificial Boundaries R. Djellouli, C. Farhat, A. Macedo, and R. Tezaur

86

87

Third-Order Doubly Asymptotic Approximations for Computational Acoustics T. L. Geers and B. J. Toothaker

88

Analytical and Numerical Studies of a Finite Element PML for the Helmholtz Equation /. Harari, M. Slavutin, and E. Turkel

89

Continued-Fraction Absorbing Boundary Conditions for the Wave Equation M. N. Guddati and J. L. Tassoulas

90

Optimal Local Nonreflecting Boundary Conditions for Time-Dependent Waves I. Patlashenko and D. Givoli

91

Mixed Finite Elements with Mass-Lumping for the Transient Wave Equation G. Cohen and S. Fauqueux

92

Short Wave Modelling Using Special Finite Elements 0. Laghrouche and P. Bettess

93

A Numerical Comparison of Finite Element Methods for the Helmholtz Equation A. A. Oberai and P. M. Pinsky

94

Efficient Computation of Multi-Frequency Far-Field Solutions of the Helmholtz Equation Using Pade Approximation M. Malhotra and P. M. Pinsky

95

An Iterative Time-Stepping Method for Solving First-Order Time Dependent Problems and Its Application to the Wave Equation G. Seriani

96

Wave Propagation Modeling Fictitious Domains, Mixed Finite Elements and Perfectly Matched Layers for 2-D Elastic Wave Propagation E. Becache, P. Joly, and C. Tsogka

99

Higher-Order Mass-Lumped Finite Elements for the Wave Equation W. A. Mulder

100

Numerical Study of Elastic Wave Scattering by Cracks or Inclusions Using the Boundary Integral Equation Method E. Liu and Z. Zhang

101

Finite-Difference Modeling in Media with Many Small-Scale Cracks G. B. Van Baren, G. C. Herman, and W. A. Mulder

102

Scale and Angle Dependent Reflection Properties of Self-Similar Interfaces J. Goudswaard and K. Wapenaar

103

Elastic Waves Generated by High-Speed Trains A. Ditzel, G. Herman, and P. Holscher Adaptive Finite Element Techniques for the Acoustic Wave Equation W. Bangerth and R. Rannacher Wave Propagation in 2-D Elastic Media Using a Spectral Element Method with Triangles and Quadrangles D. Komatitsch, R. Martin, J. Tromp, M. A. Taylor, and B. A. Wingate A Comparative Study of Explicit Differential Operators on Arbitrary Grids M. Kdser, H. Igel, M. Sambridge, and J. Braun

104

105

106

107

XVI

A High-Order Fast Marching Scheme for the Linearized Eikonal Equation J. B. Franklin and J. M. Harris

108

Frequency Domain Wave Propagation Modeling in Exploration Seismology P. M. Gauzellino, J. E. Santos, and D. Sheen

109

Three-Dimensional Time Domain Modeling of Ultrasonic Wave Propagation in Concrete in Explicit Consideration of Aggregates and Porosity F. Schubert and B. Koehler Time Domain Modeling of Axisymmetric Wave Propagation in Isotropic Elastic Media with Cent — Cylindrical Elastodynamic Finite Integration Technique F. Schubert, B. Koehler, and A. Peiffer

110

111

On the Propagation of Acoustic Pulses in Porous Rigid Media: A Time-Domain Approach Z. E. A. Fellah and C. Depollier

112

Triangle-Quadrangle Grid Method for Poroelastic, Elastic, and Acoustic Wave Equations J. Zhang

113

Absorbing Layer via Wave-Equation Splitting J. M. Carcione and F. Cavallini

114

Optimised Absorbing Boundary Conditions for Elastic-Wave Propagation A. Lange, J. Zhou, and N. Saffari

115

Conjugated Infinite Elements for Two-Dimensional Time-Harmonic Elastodynamics T. Pinto and J.-P. Coyette

116

Inverse Problems and Tomography Reconstruction of Layered Elastic Bottom Characteristics by the Frequency Dependence of Sound Reflectivity V. N. Fokin and M. S. Fokina

119

Joint 3D Traveltime Inversion of P, S and Converted Waves G. Rossi and A. Vesnaver

120

Complete Families and Rayleigh Obstacles G. F. Crosta

121

A Simple Regularization Method for Solving Acoustical Inverse Scattering Problems M. Piana

122

The Use of the Herglotz Function Method to Reconstruct Obstacles from Real and from Synthetic Scattering Data P. Maponi and F. Zirilli

123

Nonlinear Inversion of Piezoelectrical Transducer Impedance Data L. Carcione, J. Mould, V. Pereyra, D. Powell, and G. Wojcik

124

An Algorithm for the Fully Nonlinear Inverse Scattering Problem at Fixed Frequency F. Natterer

125

Maximum Likelihood Inversion of Active Reverberation for Boundary Localization on a Moving Sonar Platform R. B. Macleod

126

Mathematical Simulation in Diffraction Acoustical Tomography with Multielement Transceiver A. V. Osetrov and A. P. Khrenov

127

Radial Ultrasonic Tomography Technique as a New Method of Flaw Imaging A. V. Osetrov

128

Multiresolution in 3D Seismic Tomography Within Physical Limits G. Bohm, P. Galuppo, and A. Vesnaver

129

Geoacoustic Inversion in Shallow Water Guest Editors: R. Chapman and M. Taroudakis Objective Functions for Ocean Acoustic Inversion Derived by Likelihood Methods C. F. Mecklenbrduker and P. Gerstoft

133

XVIII

Deductive Multi-Tone Inversion of Seabed Parameters M. A. Ainslie, R. M. Hamson, G. D. Horsley, A. R. James, R. A. Laker, M. A. Lee, D. A. Miles, and S. D. Richards

134

Tomographic Inversion for Geoacoustic Parameters in Shallow Water A. Tolstoy

135

Matched Field Tomographic Inversion to Determine Range Dependent Geoacoustic Properties V. Corre, N. R. Chapman, and M. J. Wilmut

136

Identifying Modal Arrivals in Shallow Water for Bottom Geoacoustic Inversions M. I. Taroudakis

137

Geoacoustic Tomography: Range Dependent Inversions on a Single Slice G. R. Potty and J. H. Miller

138

Nonlinear Soliton Interaction with Acoustic Signals: Focusing Effects O. C. Rodriguez, S. Jesus, Y. Stephan, X. Demoulin, M. Porter, and E. Coelho Seafloor Properties Determination from Acoustic Backscattering at Normal Incidence with a Parametric Source A. Caiti

139

140

Wave Propagation Theory

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3 International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

UNIFORMLY ASYMPTOTIC SOLUTIONS FOR PSEUDODIFFERENTIAL EQUATIONS WITH SINGULAR INTEGRAL OPERATORS*

A. HANYGA Institute

of Solid Earth Physics, University of Bergen, Allegaten 4U N-5007 Bergen, Norway andrzej@ifjf. uib. no

M. SEREDYNSKA Institute

of Fundamental Technological Research, Polish Academy of Sciences, 00 049 Warszawa, ul. Swi§tokrzyska 21, Poland [email protected] Received 18 June 1999 Revised 28 May 2000

Uniformly asymptotic frequency-domain solutions for a class of hyperbolic equations with singular convolution operators are derived. Asymptotic solutions for this class of equations involve additional parameters — called attenuation parameters — which control the smoothing of the wavefield at the wavefront. At caustics the ray amplitudes have a singularity associated with vanishing of ray spreading and with divergence of an integral controlling the rate of exponential amplitude decay. Both problems are resolved by applying a generalized Kravtsov-Ludwig formula derived in this paper. A different asymptotic solution is constructed in the case of separation of dispersion and focusing effects.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

4 International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS

,dife\ | | g INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

THE KIRCHHOFF-HELMHOLTZ INTEGRAL PAIR*

MARTIN TYGEL, JORG SCHLEICHER, and LUCIO T. SANTOS Department

Applied Mathematics, IMECC, State University of P.O. Box 6065, 13081-970 Campinas, SP, Brazil

Campinas,

P E T E R HUBRAL Geophysical Institute,

Karlsruhe

University, Hertzstr.

16, 76187 Karlsruhe,

Germany

Received 11 June 1999 Revised 6 July 2000 The Kirchhoff-Helmholtz integral models the reflected acoustic wavefield by an integration along the reflector over the incident field multiplied by the specular plane-wave reflection coefficient. Based on the structural relationships between the reflector and the reflection-traveltime surface, we design an asymptotic inverse Kirchhoff-Helmholtz integral. Analogously to the forward integral, the proposed inverse consists of an integration along the reflection-traveltime surface over the recorded reflected field. We show that the new inverse integral asymptotically recovers the input to the standard KirchhoffHelmholtz integral, that is, the reflector position and the reflection coefficients along it. A simple numerical example demonstrates the inverse relationship between the proposed and the standard Kirchhoff-Helmholtz integrals. In this way, a new technique for kinematic (positioning) and dynamic (amplitude) wavefield inversion becomes available. This is realized by means of an integral operation that is most naturally related to its counterpart Kirchhoff-Helmholtz integral.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

5 International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

ANALYSIS AND PROCESSING OF RECEIVED SIGNALS IN BOREHOLES*

JENS M. HOVEM, HEFENG DONGt, and ODDVAR LOTSBERGt Norwegian University of Science and Technology, Department of Telecommunications/Acoustics, O. S. Bragstads pi 2b, N-7491 Trondheim, Norway Received 14 June 1999 Revised 9 March 2000 This study is a part of a project to develop a borehole sonar for acoustic imaging of the geological structure of the rock formation near to a deviated or horizontal borehole performed while drilling. The purpose of the sonar is to provide a direct measure of the distance and the direction to bed boundaries parallel to the borehole. This paper gives a theoretical analysis of the effect of the borehole and the drillstring on the received response on sensors positioned on the drillstring and proposes a method for processing the received signal to enable the determination of the direction of an incoming plane wave and time of arrival. In the first part of this paper, the response at any position in a fluid filled borehole is determined for an incoming plane P-wave. It is shown that the response is quite complicated and consists of several vibrating modes with resonance structure. Secondly, the paper presents how the received signals can be decomposed and the individual modes can be resolved by utilizing the orthogonal properties of the mode functions. The individual mode functions are resolved by performing a spatial Fourier transform of the sensor signals. A requirement is that the sensors are uniformly distributed around the circumference of the drillstring and that the number of sensors is at least two times the number of significant modes. It is demonstrated that the spatial and temporal characteristics of the resolved modes can then be exploited to determine the time of arrival and the angle of direction of the incoming reflected waves.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy. t Permanent address: Institute of Theoretical Physics, Northeast Normal University, Changchun 130024, P. R. China. * Present address: Statoil, B & B project, Forus, Stavanger.

6 International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © MACS

/$&£\ | g | INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

INFORMATIONAL CAPACITY OF ACOUSTIC MEASUREMENTS*

EUGENE LICHMAN Lichman Research L.L.C.,

11634 Manor Park Dr., Houston, lichman@attglobal. net

TX 77077, USA

Received 16 June 1999 Revised 14 July 2000 Presented is the theoretical model for extracting the system response from measurements of the acoustic wave propagating through the linear system. Based on the results of this analysis, measurements are described as a convolution of the impulse response of the system with the mixed-phase-lag nonstationary forward wavelet (or source-generated wavefield). The source-generated wavefield includes all multiple terms generated within the system as well as the energy source signature and the detector characteristics. It is shown that the decay ratio of the source-generated wavefield can be used to separate the energy spectrum of the source-generated wavefield and the energy spectrum of the impulse response from the measurement function. The level of separability of energy spectrum of the source-generated wavefield and the impulse response reflects the amount of information about the measured system, which can be obtained from experimental data. In particular, if the source-generated wavefield does not decay during the propagation through the system, or, if the effective distance of the decay is comparable with the size of the measured system, the impulse response cannot be extracted from the result of measurements. Based on the theoretical conclusions, the computational procedure is proposed for one-dimensional deconvolution algorithm. The application of this algorithm is illustrated using seismic data as an example. The forward wavelet is extracted from seismic data itself. The deconvolution of data with the extracted wavelet provides surface-consistent scaling along with peg-leg and short-period multiples attenuation.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

7 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

RESONANCES OF ACOUSTIC WAVES INTERACTING WITH AN ELASTIC SEABED*

MARGARETE S. FOKINA Institute of Applied Physics, Russian Academy of Sciences, 46, Ulyanov Str., Nizhny Novgorod, 603950, Russia fok@hydro. appl.sci-nnov.ru VLADIMIR N. FOKIN Institute of Applied Physics, Russian Academy of Sciences, 46, Ulyanov Str., Nizhny Novgorod, 603695, Russia fokin&hydro. appl.sci-nnov.ru Received 8 July 1999 Revised 7 September 2000 An exact expression for the reflection coefficient is obtained with the Thomson-Haskell technique for the geoacoustical model of an ocean bottom consisting of an elastic homogeneous sediment layer overlying an elastic half-space. Characteristic equations for explicit determination of the position of each individual resonance contribution to the reflection coefficient are derived. Analytical expressions for the angular and frequency resonance positions are found. The resonance expression for the reflection coefficient is written in the form of a sum of resonance terms. Comparison between resonance theory and exact calculations for the elastic layer covering the elastic half-space is presented. The results of resonance formalism show excellent agreement with exact theory in all the cases.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

8 International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS

/iSfex g g | INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

MODELED VELOCITY AND REFLECTIVITY PROPERTIES OF ANISOTROPIC HYDRATED SEDIMENTS*

M. JAKOBSENt, T. A. JOHANSEN*, and B. O. RUUD§ Institute

of Solid Earth Physics, University of Bergen, Allegt. 41, N-5007 Bergen, Norway 'Morten. [email protected] ^TorArne. Johansen@ifjf. uib.no §BentOle. Ruud@ifjf. uib.no Received 17 July 1999 Revised 29 June 2000

The potential of mapping the extent gas hydrate from seismic data relies on the micromechanical model linking the actual material properties to the relevant observational data. We here consider four-phase sediment models consisting of hydrate, fluid, quartz (grains) and clay (platelets). The hydrate may occur in two ways when the pore volume is partially saturated, either in the pore voids without grain contact (unconnected), or as a grain coating, i.e. acting as a cementation of the grains (connected). In this model, the spatial orientations of the clay platelets are taken into account. By considering a model with a dominant horizontal grain distribution, we find that the elastic stiffnesses and velocities increase with an increasing proportion of hydrate. Both P and S velocities are largest for connected hydrates. Furthermore, the P wave anisotropy is largest for connected hydrates, while the S wave anisotropy is largest for the unconnected hydrates. If we consider the hydrate model as unconnected for low saturation (less than 50%) and connected for higher saturation, the reflectivity properties of the bottom simulating reflector (BSR) are similar to those found by other investigators considering no preferred grain orientation.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

9 International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

REFLECTION/TRANSMISSION COEFFICIENTS AT A PLANE INTERFACE IN DISSIPATIVE AND NONDISSIPATIVE ISOTROPIC MEDIA: A COMPARISON*

JOHANA BROKESOVA Department of Geophysics, Charles University, Ke Karlovu 3, 121 16, Praha 2, Czech Republic Received 12 July 1999 Revised 15 June 2000 The problem of reflection/transmission of plane waves in homogeneous isotropic dissipative media is investigated. In dissipative media, the elastic moduli, seismic velocities and slowness vectors are complex-valued and frequency-dependent. Results of extensive computations of R / T coefficients for plane waves incident at a plane interface are presented and discussed. In all cases, the "reference R / T coefficients" are considered, computed for a fixed frequency equal to the reference frequency fr, for which the elastic moduli are specified. The influence of angle of incidence i and attenuation angle 7 of the incident wave on the coefficients is studied in detail. In general, the differences between the moduli of the R / T coefficients for dissipative and nondissipative models are usually small for realistic Q's and 7's. These differences are more distinct in critical and postcritical regions for the reflection coefficients, particularly for small Q's, large contrast of Q's across the interface, and for large |7|'s (say, j—yj > 50°). The differences between the phases of R / T coefficients for dissipative and nondissipative media may be larger. For some 7's, the signs of the phases for dissipative and nondissipative media may be roughly opposite, even for very high Q's.

"Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

10 International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS

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ANALYSIS OF THE REFLECTION AND TRANSMISSION COEFFICIENTS IN THREE-PHASE SANDSTONE RESERVOIRS*

CLAUDIA L. RAVAZZOLI Facultad de Ciencias Astrondmicas y Geofisicas, Universidad National de La Plata, Paseo del Bosque S/N (1900) La Plata, [email protected]. edu. ar

Argentina

Received 2 July 1999 Revised 10 April 2000 As it is well-known, seismic and acoustic data play a very important role in the characterization of hydrocarbon reservoirs. The correct interpretation of the anomalies observed in seismic wave velocities, quality factors and reflection coefficients in such environments makes necessary to use accurate models taking into account the main petrophysical features of the rocks. This also brings into play the importance of adequately describing the in situ properties of the reservoir fluids. This work investigates the influence of gas saturation and excess pore fluid pressure on wave energy splitting at plane interfaces within a Biot-type porous medium saturated by a liquid-gas mixture. Using laboratory measurements made on a wide variety of sandstones, we incorporate in the model the effective pressure dependence of rock matrix properties such as bulk and shear modulus, porosity and pore space compressibility. Also, using empirical laws, we estimate the properties of real hydrocarbon gases, oils and brines of different compositions under variable pressure and temperature conditions. We present analytical computations of the amplitude reflection and transmission coefficients to study the combined effect of the forementioned variables, aiming at a further AVA trend analysis.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

11 International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

FRACTIONAL DIFFUSIVE WAVES*

FRANCESCO MAINARDI Department

of Physics,

University of Bologna, Via Irnerio 46, 1-40126 Bologna, [email protected]

Italy

PAOLO PARADISI DIENCA, Engineering, University of Bologna, Viale Risorgimento, 1-40136 Bologna, Italy [email protected] Received 25 June 1999 Revised 6 March 2000 By fractional diffusive waves we mean the solutions of the so-called time-fractional diffusion-wave equation. This equation is obtained from the classical D'Alembert wave equation by replacing the second-order time derivative with a fractional derivative of order /3 6 (0,2) and is expected to govern evolution processes intermediate between diffusion and wave propagation when j3 e (1,2). Here it is shown to govern the propagation of stress waves in viscoelastic media which, by exhibiting a power law creep, are of relevance in acoustics and seismology since their quality factor turns out to be independent of frequency. The fundamental solutions for the Cauchy and signaling problems are expressed in terms of entire functions (of Wright type) in the similarity variable. Their behaviors turn out to be intermediate between those found in the limiting cases of a perfectly viscous fluid and a perfectly elastic solid. Furthermore, their scaling properties and the relations with some stable probability distributions are outlined.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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ACOUSTIC EXCITATION OF SCHOLTE-STONELEY AND LAMB WAVES ON A REINFORCED CYLINDRICAL SHELL*

O. PONCELET, A. GERARD, and M. DESCHAMPS Laboratoire de Mecanique Physique,

Universite Bordeaux I, F-33405 Talence, France A. GURAN

Institute

of Structronics,

275 Slater Street, 9th Floor, Ottawa, K1P-5H9, Canada and Laboratoire de Mecanique Physique, Universite Bordeaux I, F-33405 Talence, France^ B. BELINSKIY and J. DAUER Department of Mathematics, University of Tennessee, Chattanooga, TN 37403-2598, USA H. UBERALL Laboratoire de Mecanique Physique, Department

of Physics,

Universite Bordeaux I, F-33405 Talence, France^ and Catholic University of America, Washington, DC 20064, USA Received 12 July 1999 Revised 24 April 2000

The scattering of sound from a submerged elastic cylindrical shell, evacuated and bare of reinforcements, is known to excite the pseudo-Lamb So wave propagating circumferentially around the shell, and also the Scholte-Stoneley (A) wave, but the latter only in a limited frequency region. For thin shells (of less than 10% thickness), excitation of the Ao wave has not been observed in a distinct resonant fashion, at least at moderate frequencies around and above coincidence. (Its excitation in a nonresonant fashion, i.e., immediately beyond the locus of its generation, has, however, recently been observed experimentally. 1 ) We show here that even the presence of internal attachments to the shell will not cause the excitation of the Ao wave, while greatly extending the excitation region of the A wave, however. A modification of resonance frequencies by the internal attachments ("frequency doubling") is discussed, and is explained by the phase matching principle of resonance excitation.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy, t'-tVisiting Professor

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ON THE ADIABATICITY OF ACOUSTIC PROPAGATION THROUGH NONGRADUAL OCEAN STRUCTURES*

E. C. SHANG and Y. Y. WANG CIRES,

University of Colorado/NOAA/ETL,

Boulder, Colorado,

USA

T. F. GAO Institute

of Acoustics,

Chinese Academy of Sciences, Beijing,

China

Received 9 February 2000 Revised 24 August 2000 To assess the adiabaticity of sound propagation in the ocean is very important for acoustic field calculating (forward problem) and tomographic retrieving(inverse problem). Most of the criterion in the literature is too restrictive, specially for the nongradual ocean structures. A new criterion of adiabaticity is suggested in this paper. It works for nongradual ocean structures such as front and internal solitary waves in shallow-water.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

14 International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

FERROMAGNETS AND KELVIN'S MEDIUM: BASIC EQUATIONS AND WAVE PROCESSES*

ELENA F. GREKOVA Laboratory of Dynamics of Mechanical Systems, Institute for Problems in Mechanical Engineering of Russian Academy of Sciences, Bolshoy pr. V.O., 61, St. Petersburg, 199178, Russia [email protected] Received 13 June 1999 Revised 20 April 2000 The nonlinear constitutive equations of Kelvin's medium (a nonlinear elastic polar medium consisting of rotating particles) are obtained. We establish the analogy between basic equations of saturated elastic ferromagnetic insulators and basic equations of Kelvin's medium. The most general way of taking the couplings of magnetic and elastic subsystems into account is suggested. Wave processes are investigated from this point of view. All results are interpreted both in terms of mechanical medium and ferromagnets.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

15 International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

PROPAGATION OF ULTRASONIC WAVES IN NONLINEAR MULTILAYERED MEDIA*

V. CHIROIU, C. CHIROIU, and C. RUGINA Institute

of Solid Mechanics, Roumanian Academy of Sciences, Ctin Mille 15, Bucharest, Romania P. P. DELSANTO and M. SCALERANDI

INFM, Dip. di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129, Torino, Italy Received 4 October 1999 Revised 22 June 2000 In the framework of the Local Interaction Simulation Approach (LISA), iteration equations are derived for the simulation of the propagation of ultrasonic waves in nonlinear multilayered 1-D media. The numerical results are compared with analytical solutions obtained in a perturbation treatment. The method is then applied to study several problems of nonlinear propagation, including the distortion of pulses, the formation of shock waves and, in the case of cw's, anharmonic effects and coupling between extended and localized vibration modes.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

16 International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

OPTIMAL MODEL FOR THE DIFFRACTION EFFECT IN THE ULTRASONIC FIELD OF PISTON TRANSDUCERS*

ABDELLATIF BEY TEMSAMANlt, STEVE VANDENPLAS, and LEO VAN BIESEN Vrije Universiteit

Brussel, Department of Fundamental Electricity Pleinlaan S, B-1050 Brussels, Belgium t abtemsa0vub.ac.be

and

Instrumentation,

Received 18 June 1999 Revised 3 March 2000 In this work, the analytical and experimental examination of the problem of diffraction effect is treated. In the laboratory, the diffraction phenomena have been mainly due to the beam spread of the ultrasonic plane wave propagating through a viscoelastic material. In fact, this effect has been found to be related, essentially to the attenuation and dispersion losses on a viscoelastic material. In this work, a frequency domain system identification approach is applied to determine an optimal function correcting the beam spread effect in both the normal and oblique incidences for a large frequency band (300 kHz-3 MHz). The Maximum Likelihood Estimator is applied to the magnitude and phase of the measured beam patterns of the used transducers in order to determine the model parameters. The calibration procedure is also discussed. Once the proposed model is established, the propagation through a viscoelastic plate is described and a comparison with measurements is done to validate the investigated model. The obtained longitudinal and shear attenuation and dispersion of the ultrasound in the viscoelastic plate are compared with those obtained by applying the complex harmonic plane waves combination model.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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OBLIQUE ACOUSTIC AXES IN TRIGONAL CRYSTALS*

V. G. MOZHAEV Faculty of Physics, Moscow State University, 117234 Moscow, Russia F. BOSIA and M. WEIHNACHT Institut fiir Festkorper- und Werkstofforschung, Helmholtzstrafie 20, 01069 Dresden, Germany Received 5 August 1999 Revised 6 April 2000 A general analysis on the subject of acoustic axes for bulk acoustic waves in trigonal crystals is presented. It is shown that the effect of piezoelectricity increases the maximum allowable number of acoustic axes in the plane of elastic symmetry from three to five for trigonal crystals of class 3m, and from 3 to 7 for trigonal crystals of class 32. The theory of acoustic axes of general orientation developed by Khatkevich (1962) is revised. A new, simpler and more general derivation of the conditions for the occurrence of acoustic axes of general orientation in crystals is presented. It is found that the previous analytical results and conclusions stating the absence of such axes in trigonal crystals are incorrect. New correct equations for acoustic axes of general orientation in trigonal nonpiezoelectric crystals are derived and confirmed by independent numerical calculations. Acoustic axes of general orientation oblique to the elastic symmetry planes are found to exist in berlinite (class 32) and in nonpiezoelectric lithium niobate (class 3m), however piezoelectricity eliminates these axes in the latter crystal. Some illustrative examples of the relationship between leaky surface acoustic wave branches and acoustic axes in trigonal crystals are given.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

18 International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

ACOUSTIC TIME SERIES VARIABILITY AND TIME REVERSAL MIRROR DEFOCUSING DUE TO CUMULATIVE EFFECTS OF WATER COLUMN VARIABILITY*

KEVIN D. LEPAGE SACLANT Undersea Research Centre, Viale San Bartolomeo 400, 19138 La Spezia, Italy Received 2 July 1999 Revised 8 November 2000 The variability of the arrival structure of narrow band waveforms is derived propagation in a fluctuating ocean channel. Expressions for the expected signal intensity are obtained for sound speed fluctuations characterized moment sense over range, depth and time. Similar expressions are obtained intensity of a time reversal mirror.

for adiabatic value of the in a second for the focus

'Presented as "Acoustic time series variability due to cumulative effects of perturbative sound speed fluctuations" at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

NUMERICAL AND EXPERIMENTAL TIME-REVERSAL OF ACOUSTIC WAVES IN RANDOM MEDIA*

ARNAUD DERODE, MICKAEL TANTER, ARNAUD TOURIN, LAURENT SANDRIN, and MATHIAS FINK Laboratoire Ondes et Acoustique, ESPCI, 10 Rue Vauquelin, 75005 Paris, France arnaud. derode @espci.fr Received 29 June 1999 Revised 13 April 2000 In classical mechanics, a time-reversal experiment with a large number of particles is impossible. Because of the high sensitivity to initial conditions, one would need to resolve the positions and velocities of each particle with infinite accuracy. Thus, it would require an infinite amount of information, which is of course out of reach. In wave physics however, the amount of information required to describe a wave field is limited and depends on the shortest wavelength of the field. Thus we can propose an acoustic equivalent of the experiment we mentioned above. We start with a coherent transient pulse, let it propagate through a disordered highly scattering medium, then record the scattered field and time-reverse it: surprisingly, it travels back to its initial source, which is not predictable by usual theories for random media. Indeed, to study waves propagation in disordered media theoreticians, who find it difficult to deal with one realization of disorder, use concepts defined as an average over the realizations, which naturally leads to the diffusion approximation. But the corresponding equation is not time-reversal invariant and thus fails in describing our experiment. Then, to understand our experimental results and try to predict new ones, we have developed a finite elements simulation based on the real microscopic time-invariant equation of propagation. The experimental and numerical results are found to be in very good agreement.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

20 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © MACS

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FLUCTUATIONS OF ELASTIC WAVES DUE TO RANDOM SCATTERING FROM INCLUSIONS*

V. A. KORNEEV and L. R. JOHNSON Center for Computational Seismology, Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720, USA [email protected]; [email protected] Received 25 June 1999 Revised 28 March 2000 Exact solutions for elastic compressional and shear waves scattered from a homogeneous sphere are used to obtain formulas for fluctuations of velocity and attenuation of plane waves propagating through a layer of randomly distributed inclusions over a broad range of frequencies. The size and contrast of the inclusions are arbitrary, but interactions between scatterers are not considered and the concentration of scatterers is assumed to be small. The analytical solutions are also compared with numerical simulations and it is demonstrated that they satisfactorily explain the effects of scattering on both the mean and variance of the phase and the mean and variance of the attenuation. The need for spatial averaging of observational data and methods of interpreting such averaged data in terms of the material properties of the scattering medium are discussed.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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NUMERICAL STUDY OF THE WAVE INSTABILITY PROBLEM WITH THE EFFECT OF THE TRANSVERSE VELOCITY COMPONENT*

B. S. ATTILI Mathematical Sciences Department, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia Received 2 July 1999 Revised 14 October 2000 We will numerically investigate the wave instability problem with the effect of the transverse velocity component. An accurate and easy to program finite difference scheme will be developed for this purpose. The eigenfunctions will be normalized and computed simultaneously with the eigenvectors. Numerical results will also be presented.

* Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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Sound Propagation, Vibrations and Noise

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AIRBORNE ACOUSTICS OF EXPLOSIVE VOLCANIC ERUPTIONS*

MICHAEL J. BUCKINGHAM Marine Physical Laboratory, Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0213, USA Also affiliated to: Institute of Sound and Vibration Research, The University, Southampton SO 17 IB J, England MILTON A. GARCES University of Hawaii, Manoa, P.O. Box 1599, Kailua-Kona,

HI 96745-1599,

USA

Received 6 October 1999 Revised 16 April 2000 A recently developed theoretical model of the airborne acoustic field from an explosive volcanic eruption of the Strombolian type is described in this article. The magma column is assumed to be a circular cylinder, which is open to the atmosphere at the top, and which opens into a large magma chamber below. The magma itself is treated as a fluid, and the surrounding bedrock is taken to be rigid. An explosive source near the base of the magma column excites the natural resonances of the conduit. These resonances result in displacement of the magma surface, which acts as a piston radiating sound into the atmosphere. The source is modeled in much the same way as an underwater explosion from a high-explosive chemical such as T N T , although in the case of the volcano the detonation mechanism is the ex-solution of magmatic gases under extremely high hydrostatic pressure. The new theory shows compelling agreement with airborne acoustic signatures that were recorded in July 1994 at a distance of 150 m from the western vent of Stromboli volcano, Italy. The theoretical and observed power spectra both display the following features: (1) four energetic peaks below 20 Hz, identified as the first four longitudinal resonances of the magma column; (2) a broad minimum around 30 Hz, interpreted as a source-depth effect, occurring because the source lay close to nulls in the fifth and sixth longitudinal resonances and thus failed to excite these modes; and (3) radial resonance peaks between 35 and 65 Hz. On the basis of the theory, an inversion of the acoustic data from Stromboli yields estimates of the depth (w 100 m) and radius (~ 16 m) of the magma column as well as the depth (ss 83 m), spectral shape and peak shock-wave pressure (ss 1 GPa) of the explosive source. Most of the parameters estimated from the acoustic inversion compare favorably with the known geometry and source characteristics of Stromboli.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

26

SOUND GENERATION OF INTERACTING PERTURBED VORTEX RINGS*

C. C. K. TANG and N. W. M. KO Department of Mechanical Engineering, The University of Hong Kong Pokfulam Road, Hong Kong, People's Republic of China R. C. K. LEUNG Asia Pacific Engineering Center, Copeland Corporation 10/F, Pioneer Building, 213 Wai Yip Street, Kwun Tong Kowloon, Hong Kong, People's Republic of China Received 20 August 1999 Revised 15 December 2000 A numerical study of interaction of the vortex rings is carried out. The vortex ring is modelled by using a slender vortex filament in unbounded space. The motion of the vortices is simulated by the Biot-Savart Law. The present investigation studies the sound generation of vortices with phase differences of A 7 = 0 and 3TT/4. Results show that the phase differences influence the shapes of the vortices and their associated instability, thereby affecting the generation of sound.

"Presented at ICTCA'99 the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

27 International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

A WIDE-ANGLE PARABOLIC EQUATION FOR ACOUSTIC WAVES IN INHOMOGENEOUS MOVING MEDIA: APPLICATIONS TO ATMOSPHERIC SOUND PROPAGATION*

LAURENT DALLOIS, PHILIPPE BLANC-BENON, and DANIEL JUVE Laboratoire de Mecanique des Fluides et d'Acoustique, U.M.R. C.N.R.S. 5509, Ecole Centrale de Lyon, B.P. 163, 69131 Ecully Cedex, France Received 17 June 1999 Revised 24 March 2000 Two new derivations of "vector" parabolic equations (PE) for use in acoustic propagation have recently been published. In these cases, PEs have been derived from first principles and incorporate velocity fluctuations of the medium as two additional vector terms. In the simpler case, large spatial-scale velocity fluctuations can be accommodated. In the more general case, multi-scale velocity fluctuations can be accommodated. In this paper we report on a series of two-dimensional numerical experiments which compares sound propagation predicted from traditional PEs with sound propagation predicted from these two "vector" PEs. Two types of velocity fields are simulated. One, suitable for approximating an atmospheric boundary layer, is a field in which velocity has only a horizontal component, but whose magnitude can depend on height, i.e., v = vx(z). The other is a field having random spatial fluctuations over a range of length scales and could be suggestive of atmospheric turbulence. In both cases celerity inhomogeneities are also included. Results suggest that at least, in two dimension, the standard P E using an effective index of refraction is not accurate to describe the effects of the mean and turbulent velocity on sound propagation near the ground. We suspect that in three-dimensional problems, the added terms in the "vector" PEs will significantly increase in importance.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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ACOUSTICS OF KINEMATICALLY COMPLEX SHEAR FLOWS*

ANDRIA ROGAVAt Centre for Plasma Astrophysics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Heverlee, Belgium Abdus Salam International Centre for Theoretical Physics, Trieste 34014, Italia STEFAAN POEDTS* Centre for Plasma Astrophysics, Katholieke Universiteit Celestijnenlaan 200B, 3001 Heverlee, Belgium

Leuven,

SWADESH MAHAJAN Institute for Fusion Studies, The University of Texas at Austin, Austin 78712, Texas, USA Abdus Salam International Centre for Theoretical Physics, Trieste 34014, Italia Received 18 June 1999 Revised 14 June 2000 A new nonasymptotic method is presented that reveals an unexpected richness in the spectrum of acoustic fluctuations in a shear flow with nontrivial (kinematically complex) mean kinematics. The usefulness of the method is illustrated by analysing three different specific cases of compressible hydrodynamic shear flows. The temporal evolution of perturbations spans a wide range of nonexponential behavior from shear-modified oscillations, transitions between oscillatory and nonperiodic (vortical) modes of motion to monotonic growth. The principal characteristic of the revealed acoustic phenomena is their asymptotic persistence. Exotic regimes like "Echoing" as well as unstable (including parametrically driven) solutions are identified. Further areas of application, for both the method and the new physics, are outlined.

'Presented at ICTCA'99, the 4th International Conference on Theoretical Computational Acoustics, May 1999, Trieste, Italy. tOn leave from Department of Physics, Tbilisi State University, Tbilisi 380028, and Abastumani Astrophysical Observatory, Tbilisi 380060, Georgia. 'Research Associate of the Belgian National Fund for Scientific Research (NFWO).

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ULTRASOUND PROPAGATION THROUGH A ROTATIONAL FLOW: NUMERICAL METHODS COMPARED TO EXPERIMENTS*

SEBASTIEN MANNEVILLE, CLAIRE PRADA, MICKAEL TANTER, and MATHIAS FINK Laboratoire Ondes et Acoustique, ESPCI, CNRS UMR 7587, 10, rue Vauquelin F- 75005 Paris, France [email protected] JEAN-FRANCOIS PINTON Laboratoire de Physique, ENS-Lyon, 46, alUe d'ltalie F-69364 Lyon Cedex 7, France Received 2 June 1999 Revised 6 July 2000 Sound propagation through a vortex is studied numerically using two different techniques: ray-tracing and finite-differences. Geometrical acoustics and ray-tracing are shown to yield a good picture of the interaction between a sound wave and a vortex when the ratio of the vortex radius to the acoustic wavelength is larger than one. In particular, this technique allows to take into account finite-size effects such as edge waves and the results are compared to experimental data. The interest of the finite-difference approach is demonstrated for cases where sound scattering occurs. We show the ability of such a simulation to account for both sound scattering and finite-size effects. Those two numerical techniques are compared and their validity is investigated.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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WAVE PROPAGATION ON AN ELASTIC BEAM TRAVELING IN A TUBE: LINEAR THEORY OF AERODYNAMIC LOADING*

N. SUGIMOTO Department

of Mechanical Science, Graduate School of Engineering University of Osaka, Toyonaka, Osaka 560-8531, Japan

Science,

K. KUGO Department

of Mechanical Science, Graduate School of Engineering University of Osaka, Toyonaka, Osaka 560-8531, Japan

Science,

Received 16 November 1999 Revised 24 August 2000 Linear theory is developed of flexural wave motions of an elastic beam of circular crosssection traveling along its axial direction at a constant speed in an air-filled, circular tube placed coaxially. The beam is constrained to deflect in a plane and is subjected to a restoring force in proportion to the magnitude of deflection. Both beam and tube are assumed to be long enough for end effects to be ignored. Taking account of aerodynamic loading on the lateral surface of the beam, wave propagation is examined under a longwave approximation that a characteristic wavelength of flexural waves is much longer than the tube's radius. Using the lossless, acoustic wave equation for the velocity potential of the air, and the classical, flexural wave equation for the deflection of the beam, an asymptotic-expansion method is applied based on the long-wave approximation. A linear wave equation for the deflection is derived and its dispersion relation is examined by comparing with the exact one derived previously without any long-wave approximation. Higher-order effects of the axial curvature of the beam and the compressibility of air on the aerodynamic loading are also discussed.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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ON THE VIBRATION OF MEMBRANE PARTIALLY PROTRUDING ABOVE THE SURFACE OF LIQUID*

GEORGE V. FILIPPENKO Institute of Mechanical Engineering of Russian Academy of Sciences, Vasilievsky Ostrov, Bolshoy Prospect 61, St. Petersburg, 199178, Russia [email protected] DANIIL P. KOUZOV Marine Technical University of St. Petersburg, Department of Applied Lotsmanskaya, 3, St. Petersburg, 190008, Russia [email protected]

Mathematics,

Received 27 July 1999 Revised 12 July 2001 The problem of free oscillations of membrane partially submerged into the layer of liquid is considered in the rigorous mathematical statement. The exact analytical solution of the problem is constructed. The eigen frequencies and the eigen functions of vibrating membrane basing on analyses of exact solution are calculated. The influence of liquid's level on eigen frequencies and on eigen functions is analysed.

* Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

32 International Journal of Computational Acoustics, Vol. 11, No. 1 (2003) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

VIBRATIONAL ANALYSIS OF SHIPS WITH COUPLED FINITE AND BOUNDARY ELEMENTS*

CHRISTIAN CABOS and FRANK IHLENBURGt Germanischer

Lloyd, Vorsetzen 32, D-20459 Hamburg,

Germany

Received 10 August 2000 Revised 20 September 2002 The vibrational analysis of ships involves the solution of a coupled fluid-structure interaction problem in order to simulate the inertia response of the water to the structural vibrations. The paper describes a coupled FE-BE procedure for the computational solution of this problem. Regarding the structural equations, special emphasis is put on the modeling of damping. Various models of damping, in particular local damping, are discussed and implemented into the FE-model of the ship structure. The computational results are compared to data from large-scale measurements.

•Presented at ICTCA'99. •Corresponding author. Present address: ISKO Engineers AG, Knorrstrafie 142, 80937 Munich, Germany.

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International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © MACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

TRANSVERSE RESONANT OSCILLATIONS IN ACOUSTIC DUCTS*

P. VAINSHTEINt Department

of Mathematical Physics, University Belfield, Dublin 4, Ireland

College Dublin,

Received 28 June 1999 Revised 9 March 2000 A theoretical study is made of the flow induced by a piston, performing rotational sinusoidal vibrations in a uniform two-dimensional planar duct. A frequency of the forced vibrations is close to a cut-off frequency. It is shown that exactly at a cut-off frequency the steady-state response represents a transverse periodic shock wave, propagating between duct walls and decaying algebraically in the far field.

* Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy. T Permanent address: Faculty of Mechanical Engineering, Technion - Israel Institute of Technology, Technion City, Haifa 32000, Israel.

34 International Journal of Computational Acoustics, Vol. 8, No. 3 (2000) © MACS

,42te\ ( | | g INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

NOISE SHIELDING BY SIMPLE BARRIERS: COMPARISON BETWEEN THE PERFORMANCE OF SPHERICAL AND LINE SOUND SOURCES*

D. OUIS Department

of Engineering

Acoustics, Lund Institute S-221 00, Lund, Sweden

of Technology Box 118,

Received 13 July 1999 Revised 29 February 2000 This study is concerned with the theoretical solution to the problem of sound screening by simple hard barriers on the ground with special emphasis given to the type of wave incidence, namely a comparison between the use of either a spherical or a cylindrical sound source. For a receiver at the shadow of the noise source, the field may be assumed to be due to the edge wave and for this, exact solutions are used. Regarding the wave reflection on an impedance ground, exact formulations are also used, and finally, some calculations are made on the performance of a hard noise barrier on a two-impedance ground. As a conclusion, it is found that although the sound level at the receiver may show some small differences depending on the frequency and on the geometry of the problem, the overall insertion loss of the thin hard barrier is almost the same for the spherical and the line source, and the differences are found to amount to less than 1 dB for geometries of practical occurrence.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

WAVE PROPAGATION THROUGH HOLLOW BODIES AND NOISE REDUCTION*

SYLVAIN GERMES and CHRISTOPHE STAWICKI PSA Peugeot Citroen, Division of Research and Automobile Innovation, 2, cherain de Gisy, 78943 Velizy-Villacoublay Cedex, France [email protected] DENIS AUBRY Ecole Centrale de Paris, Laboratoire de Mecanique Sols-Structures-Materiaux, Grande Voie des Vignes, 92295 Chatenay-Malabry Cedex, France [email protected] Received 16 June 1999 Revised 13 March 2000 Low frequency noise (2-200 Hz) reduction in the passenger compartment has emerged in the past few years as a crucial subject of research in the car industry. This kind of noise is mainly due to the panels' vibrations, therefore our aim is to decrease the part of structural energy that reach them, i.e., we want to increase the part of energy that dissipates while propagating in the car body frame. This approach requires the understanding of structural wave propagation through the beam like structure (pillar, cross members...) as well as reflection and transmission at the structural joints. This is the physical problem that we want to address in this paper. Since car body frames are much too complex for physical understanding, we focused on simpler representative academic structures. We developed a numerical tool for the prediction and visualization of wave propagation, based on finite element models (FEM). Our FEM are first validated by comparison with experimental modal analysis, and then used for transient analysis. In both cases, the good agreement between calculations and experiments shows the reliability of our model and allows us to use it for wave propagation visualization. We illustrate our results by making a movie that helps to understand how waves propagate through a two hollow bodies junction.

"Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

36 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) IMAC

©

/i2r$\

S

g | | INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

GENERATION OF GROUND ELASTIC WAVES BY ROAD VEHICLES*

VICTOR V. KRYLOV Department of Civil and Structural Engineering, The Nottingham Trent University, Burton Street, Nottingham NG1 4BU, UK Received 23 June 1999 Revised 16 June 2000 Ground elastic waves, or ground-borne vibrations, represent one of the major adverse environmental impacts of road vehicles, especially of heavy lorries. In the present paper, ground elastic waves generated by road vehicles are investigated theoretically. Two main generation mechanisms are considered. The first one is associated with vehicles traveling on rough or bumpy road surfaces, in particular over road humps and speed cushions installed by local authorities at some sensitive road locations as a simple method of traffic calming. The second mechanism of generation is associated with acceleration and braking of road vehicles. General analytical results are illustrated by numerical examples and are compared with the existing experiments.

* Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

Underwater Acoustics

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39 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

BROADBAND MATCHED-FIELD LOCALIZATION PERFORMANCE IN UNCERTAIN ENVIRONMENTS USING A SHORT ARRAY*

BRIAN F. HARRISON Naval Undersea Warfare Center, Submarine Sonar Newport, RI 02841, USA harrison.bf@ieee. org

Department,

Received 25 June 1999 Revised 20 February 2000 Typical applications of matched-field localization use low frequency signals received on large aperture vertical-arrays. However, small aperture arrays are much more practical for real-world systems and must be considered. Additionally, any practical localization algorithm must also be robust to environmental mismatch. In this paper, we present the broadband Loo-norm estimator for robust matched-field localization of mid-frequency signals (e.g., 800-4000 Hz) received on very short aperture vertical-arrays. Realistic simulation results are presented using broadband signals in the band of 1000-3000 Hz received on a 3 m vertical array which demonstrate the substantial performance gains in using the Loo-norm estimator over the asymptotically-optimal maximum a posteriori estimator and the conventional Bartlett processor. Experimental data results in an uncertain shallow-water environment using a 2.13 m vertical array in the band of 3000-4000 Hz are also presented.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

40 International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

A FREQUENCY DOMAIN INVERSION METHOD APPLIED TO OBLIQUE REFLECTED SIGNALS FROM A WATER-SEDIMENT INTERFACE*

S. VANDENPLASt, A. B. TEMSAMANI, Z. CISNEROS, and L. VAN BIESEN Dept. ELEC, Vrije Universiteit Brussel, Pleinlaan 2, B-1050, Belgium *[email protected] Received 30 June 1999 Revised 6 March 2000 Due to the complexity of the seafloor as an acoustical system, it is very important to validate wave propagation models and test inversion methods first in the laboratory. A known sediment is placed in a water-filled tank, in such a way that a smooth watersediment interface is obtained with minimal air bubbles retained in the sediment. Two broadband piston transducers are used to carry out reflection experiments at oblique incidence. The placement of the emitter and receiver is symmetrical with respect to a vertical plane perpendicular to the sediment surface. The aim of this work is to find physical parameters of the sediment from the reflected signals. A general viscoelastic model that considers losses due to absorption and dispersion along the propagation of the wave through the sediments is proposed. A rational transfer function is used to model the viscoelastic modulus of the bulk sediments and a comparison with constant Q viscoelastic modelling is performed. The estimation of the model parameters is elaborated using a Maximum Likelihood Estimator in the frequency domain.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

41 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

APPLICATION OF A THREE-DIMENSIONAL TWO-WAY PARABOLIC EQUATION MODEL FOR RECONSTRUCTING IMAGES OF UNDERWATER TARGETS*

DONG ZHU 0degaard & Danneskiold-Sams0e A/S, Titangade 15, DK-2200 Copenhagen N, Denmark dong.zhu&nokia. com Received 5 July 1999 Revised 3 February 2000 A three-dimensional, two-way parabolic equation model developed for solving threedimensional backscattering problems in previous work is applied incorporating a focusmarching procedure to study the image reconstructions for underwater targets. Intensive numerical simulations are performed in this paper. Targets in the water are formed by objects with simple shapes. The "experimental data" of the return signals from targets are simulated by the backscattered sound calculated at a short distance from the source. These simulated return signals are processed by reversing their phases, and numerically propagated back to the place of the targets. It is due to the conjugating process that the target image may be reconstructed with less deformation at a distance near the target surface. This realistic study demonstrates an encouraging technique that may be utilized for studying underwater target imaging in many sonar applications.

* Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

42 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

DETERMINATION OF A BURIED OBJECT IN A TWO-LAYERED SHALLOW OCEAN*-t

ROBERT P. GILBERT Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA MICHAEL W E R B Y Naval Research Laboratory, Code 7181, Stennis Space Laboratory, Stennis, MS 39529,

USA

YONGZHI XU* Department

of Mathematics, University of Tennessee at Chattanooga, TN 37403, USA

Chattanooga,

Received 1 July 1999 Revised 22 June 2000 In this paper, a method for solving the unknown object problem is presented for a twodimensional object buried in a fluid seabed lying over a rigid basement. The algorithm makes use of a regularized Born approximation. Several examples are provided which demonstrate the utility of the algorithm.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy. tThis research was supported in part by the NRL Stennis Grant # N00173-99-1-G903. *This author's research was supported in part by CECA Scholarship and UC Foundation Faculty Research Grant of University of Tennessee at Chattanooga.

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International Journal of Computational Acoustics, Vol. 8, No. 3 (2000) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

NEW SCHEMES OF OCEAN ACOUSTIC TOMOGRAPHY*

E. C. SHANG, A. G. VORONOVICH, Y. Y. WANG, K. NAUGOLNYKH, and L. OSTROVSKY Cooperative Institute for Research on Environmental Science, University of Colorado, NO'A A/ERL/Environmental Technology Lab, Boulder, Colorado 80303, USA Received 1 June 1999 Revised 17 August 1999 Ocean acoustic tomography based on modal horizontal refraction/phase difference measurement has been developed in recent years. In this paper, potential opportunities for remotely sensing various interesting ocean dynamic structures by using the modalhorizontal-refraction tomography and modal-phase tomography are discussed, including: (1) retrieval of the 3-D structure of a mesoscale eddy, (2) monitoring of the transverse component of the current, (3) retrieval of ocean frontal parameters, and (4) acoustically diagnosing internal solitary waves (ISW) in the coastal zone.

*This paper has been presented at the 4th ICTCA in May 1999, Trieste, Italy, as a keynote address.

44 International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS

/^Efex | g g j INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

NUMERICAL SIMULATION OF TRANSVERSE CURRENT MONITORING IN THE FRAM STRAIT*

K. A. NAUGOLNYKH, YUN-YU WANG, and E. C. SHANG University of Colorado, CIRES/NOAA,

Environmental

Technology Lab., USA

Received 10 June 1999 Revised 18 April 2000 The horizontal refraction method (HRM) of transverse current acoustics monitoring in the Pram Strait environment is modeled numerically. The current profile was constructed on the basis of experimental data on the West Spitsbergen Current (WSC) structure and the complex environment of the region presented by the sound speed profiles, which were derived from the experiments. The HRM is based on the measurements of the deflection of the horizontal modal rays due to the gradient of the refraction index produced by the transverse current. The signals received by the antennas in a receiving plane perpendicular to the propagation axis have a modal phase difference in proportion to the average transverse velocity, which is due to the different orientation of the acoustical path of the current. The interesting result is that even in a strong mode coupling environment the numerically obtained phase difference is quite close to its value as calculated by adiabatic approximation. The physical reason behind this is most likely that the mode coupling impact can be canceled at the sound signal propagation along the two very close paths.

•Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS

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PROSPECTS FOR MEDIUM-SCALE DIFFRACTION TOMOGRAPHY ON THE SHELF*

I. P. SMIRNOV Nizny Novgorod State University, 23 Gagarina Nizhny Novgorod 603600, Russia ivansm@mail. ru

Avenue,

A. I. KHILKO Institute of Applied Physics, Russian Academy of Sciences, 46 Ulianov Street, Nizhny Novgorod 603600, Russia [email protected] J. W. CARUTHERS Naval Research Laboratory, Stennis Space Center, MS 39529, jwc ©nrlssc.navy. mil

USA

Received 10 June 1999 Revised 1 March 2000 Acoustical tomographical reconstruction of the location and sizes of spatially localized, random perturbation in a shallow-water oceanic waveguides is developed for mid-range distances. As examples of such perturbations, clouds of bubbles arising due to breaking wind waves and shoals of fishes are discussed. The ray approximation is used for the acoustical field description. The oceanic environment is presented as a medium with a background of uniformly distributed volume and surface random inhomogeneous fluctuations. Complex acoustical repetitive pulses are used as the probing signal. The receiving system consists of an array of spatially distributed hydrophones. The signals received from all hydrophones are processed on the basis of a tomographic algorithm including matched-filter processing in the spatial and frequency domains for reconstruction of the random time-delay statistical moments (average value and dispersion), which are descriptors of the observed random spatially localized inhomogeneity. As a specific model of random perturbation, a three-dimensional Gaussian cloud of fluctuations associated with parameters of a fish shoal is investigated. A vertically distributed array of receivers and a directed source of LFM-pulses are tested as the prototype of the tomographical system in a shallow waveguide with typical hydrology. Computer simulations of the tomographical reconstructions are conducted taking into account investigation of the influence of the level of additive noise on the accuracy of the reconstructed parameters.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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Engineering Seismology

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International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

APPLICATIONS OF THE MODAL SUMMATION TECHNIQUE TO THE THEORETICAL SITE RESPONSE ESTIMATION*

F. ROMANELLI+'t, F. VACCARlt-t, and G. F. PANZA*'§ t Dipartimento

di Scienze delta Terra, Via E. Weiss 4, 3^127 Trieste, Italy t INGV, Rome, Italy § The Abdus Salam International Centre for Theoretical Physics, Miramar, Italy Received 15 July 1999 Revised 8 March 2000 A practical definition of site effect, that accounts for both the seismological and engineering point of view, is the one given by Field': "the unique behavior of a site, relative to other sites, that persists given all (or most) of the potential sources of earthquake ground motion in the region". This definition implicitly indicates the difficulties connected with a correct estimate (or prediction) of the site effect. We estimate theoretical site responses adopting several techniques and using different seismic motion types. Our results confirm that the identification of the site behavior with a set of resonance frequencies can be a very difficult task, especially when the amplification levels seem to be "azimuthally" dependent. We show that the adoption of simplified models can lead to misleading conclusions concerning the seismic response of sedimentary basins. The results suggest that, in order to perform an accurate estimate of the site effects in complicated geometries, it is necessary to make a parametric study that takes into account the complex combination of the source and propagation factors.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

50 International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

EARTHQUAKE GROUND MOTION SIMULATION THROUGH THE 2-D SPECTRAL ELEMENT METHOD*

ENRICO PRIOLO Istituto Nazionale di Oceanografia e Geofisica Sperimentale

(OGS),

Borgo Grotta Gigante 42/c, 1-34010 Sgonico {Trieste), [email protected]

Trieste,

Italy

Italy

Received 20 July 1999 Revised 22 November 2000 The application of the 2-D Chebyshev spectral element method (SPEM) to engineering seismology problems is reviewed in this paper. The SPEM is a high-order finite element technique which solves the variational formulation of the seismic wave propagation equations. The computational domain is discretised into an unstructured grid composed by irregular quadrilateral elements. This property makes the SPEM particularly suitable to compute numerically accurate solutions of the full wave equations in complex media. The earthquake is simulated following an approach that can be considered "global", that is all the factors influencing the wave propagation — source, crustal heterogeneity, fine details of the near-surface structure, and topography — are taken into account and solved simultaneously. The basic earthquake source is represented by a 2-D point double couple model. Ruptures propagating along fault segments placed on the model plane are simulated as a finite summation of elementary point sources. After a general introduction, the paper first gives an overview of the method; then it concentrates on some methodological topics of interest for practical applications, such as quadrangular mesh generation, source definition and scaling, numerical accuracy and computational efficiency. Limitations and advantages of using a 2-D approach, although sophisticated such as the SPEM, are addressed, as well. The effectiveness of the method is illustrated through two case histories, i.e. the ground shaking prediction in Catania (Sicily, Italy) for a catastrophic earthquake, and the analysis of the ground motion in the presence of a massive structure.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

THE VARIATIONAL INDIRECT BOUNDARY ELEMENT METHOD: A STRATEGY TOWARD THE SOLUTION OF VERY LARGE PROBLEMS OF SITE RESPONSE*

FRANCISCO J. SANCHEZ-SESMAt and ROSSANA VAlt.t t Instituto

de Ingenieria, UNAM; Cd. Universitaria, Apdo 70-472; Coyoacdn 04510; Mexico D. F., Mexico

* Instituto Mexicano del Petrdleo; Eje Central L. Cardenas 152; Gustavo A. Madero 07730; Mexico D. F., Mexico [email protected] [email protected]. unam.mx ELINA DRETTA ADK SA; Themistokelous 106; 10681 Athens; Greece [email protected] Received 26 June 1999 Revised 30 March 2000 Boundary integral equation approaches and their discretization into boundary element methods (BEM) have been useful to obtain solutions for numerous problems in dynamic elasticity. Well documented advantages over domain approaches are dimension reduction, relatively easy fulfillment of radiation conditions at infinity, and high accuracy of results. In spite of dimension reduction, the computational cost at high frequencies may easily exceed the capacity of computing facilities. To overcome this problem, Galerkin's ideas may be used. The Indirect Boundary Element Method (IBEM) equations are the starting point of the proposed methodology. The boundary force density is expanded in terms of a complete set of functions. Weighting functions from the same complete set are used to minimize the error of this approximation. Once a significant subset is selected, the size of the resulting linear system is much smaller than that of the IBEM method as currently applied. Moreover, with appropriate trial functions, some matrix operations can be reduced to Fourier transformations. In what follows, the formulation and some examples for scalar problems are presented. Simple 2-D topographies are studied, but the extension to 3-D realistic configurations may well be treated on the same basis.

* Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

52 International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS

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EFFICIENCY AND OPTIMIZATION OF THE 3-D FINITE-DIFFERENCE MODELING OF SEISMIC GROUND MOTION*

P E T E R MOCZO, J O Z E F KRISTER, and ERIK BYSTRICKY Geophysical Institute, Slovak Academy of Sciences, Dubravskd cesta 9, 842 28 Bratislava, Slovak Republic. geofpemo @savba. sk Received 6 July 1999 Revised 15 January 2000 We present a tutorial introduction to the 3-D finite-difference modeling of seismic ground motion in elastic and viscoelastic media with special emphasis on its computational efficiency. We consider four basic types of the finite-difference schemes — the displacementstress, displacement-velocity-stress and velocity-stress schemes on a staggered grid, and displacement scheme on a conventional grid. Their memory requirements in the case of perfectly elastic medium, elastic medium with aposteriori approximate attenuation correction, and realistic viscoelastic medium are reviewed. We also present application of the powerful optimization techniques to the 3-D fourth-order displacement-stress and displacement-velocity-stress modeling in the case of viscoelastic medium whose rheology is based on the generalized Maxwell body. Description of a medium using material cell types and use of a discontinuous grid with combined memory optimization makes it possible to simulate earthquake ground motion in realistic large-scale models.

•Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

THREE-DIMENSIONAL GROUND MOTION SIMULATIONS FOR LARGE EARTHQUAKES ON THE SAN ANDREAS FAULT WITH DYNAMIC AND OBSERVATIONAL CONSTRAINTS*

KIM B. OLSEN Institute for Crustal Studies UCSB, Santa Barbara, CA 93016-1100,

USA

Received 4 October 1999 Revised 4 September 2000 I have simulated 0-0.5 Hz viscoelastic ground motion in Los Angeles from M 7.5 earthquakes on the San Andreas fault using a fourth-order staggered-grid finite-difference method. Two scenarios are considered: (a) a southeast propagating and (b) a northwest propagating rupture along a 170-km long stretch of the fault near Los Angeles in a 3D velocity model. The scenarios use variable slip and rise time distributions inferred from the kinematic inversion results for the 1992 M 7.3 Landers, California, earthquake. The spatially variable static slip distribution used in this study, unlike that modeled in a recent study, 1 is in agreement with constraints provided by rupture dynamics. I find peak ground velocities for (a) and (b) of 49 cm/s and 67 cm/s, respectively, near the fault. The near-fault peak motions for scenario (a) are smaller compared to previous estimates from 3D modeling for both rough and smooth faults. 1 ' 2 The lower near-fault peak motions are in closer agreements with constraints from precarious rocks located near the fault. Peak velocities in Los Angeles are about 30% larger for (b) 45 cm/s compared to those for (a) 35 cm/s.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

54 International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

MODIFICATIONS OF THE GROUND MOTION IN DENSE URBAN AREAS*

DIDIER CLOUTEAU and DENIS AUBRY Laboratoire de Mecanique des Sols-Structures-Materiaux, CNRS UMR 8579, Ecole Centrale de Paris, Grande Voie des Vignes, 92295 Chatenay-Malabry CDX, France Received 18 January 2000 Revised 12 July 2000 The main motivation of this work is to analyze whether or not the presence of buildings is able to modify the seismic field significantly. We first present a numerical method able to account for a three-dimensional building distribution resting on a layered elastichalf-space. The proposed method is based on a variational coupling between Boundary Elements and modal representation for the buildings. Provided with the hypothesis of a stochastic homogeneous distribution of these buildings or a deterministic periodic one, a realistic model of an entire city may be accounted for. This method is applied to practical situations and it is shown that modifications of the incident field occur mainly for soft layered soils. However from an engineering point of view, it appears that the amplification levels are not significantly modified even in these extreme cases. Nevertheless, a strong scattering of the response inside the city depends on the nearby buildings can be observed.

•Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

N U M E R I C A L SIMULATIONS OF S T R O N G G R O U N D MOTION DURING DESTRUCTIVE EARTHQUAKES IN H O K K A I D O , J A P A N *

MITSUKO FURUMURAt Hokkaido Univ., Kita-ku N10W8, Sapporo 060-0810, [email protected]

Japan

TAKASHI FURUMURA* Hokkaido Univ. Edu., Midorigaoka 2-34-1, Iwamizawa [email protected]

068-86^2,

Japan

Received 11 October 1999 Revised 26 April 2000 Seismic wave propagation in Hokkaido, Japan, for large destructive earthquakes are simulated by the 3-D finite-difference method. The simulation results indicate that the peak ground velocity distribution for an inland earthquake is nearly circle, but for a plate-boundary earthquake it is irregular, due to influence of lateral heterogeneity in the crust and upper mantle beneath the Hokkaido region.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy. tPresent address: Earthquake Research Center, Association for the Development of Earthquake Prediction, Sarugaku-Cho 1-5-18, Chiyoda-ku, Tokyo, 101-0064, Japan, E-mail: [email protected] 'Present address: Earthquake Research Institute, University of Tokyo, Yayoi 1-1-1, Bunkyo-ku, Tokyo, 113-0032, Japan, E-mail: [email protected]

56 International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

APPLICATION OF THE INTEGRAL LAGUERRE TRANSFORMS FOR FORWARD SEISMIC MODELING*

G. V. KONYUKH, B. G. MIKHAILENKO, and A. A. MIKHAILOV Institute of Computational Mathematics and Mathematical Geophysics, Siberian Division Russian Academy of Sciences, Pr. Lavrentieva, 6, Novosibirsk, 630090, Russia [email protected] Received 19 July 1999 Revised 2 August 2000 The paper presents some efficient algorithms based on the application of the integral Laguerre transform for approximation of temporal derivatives. Some specific features of employing this algorithm for the first and the second order equations with respect to time are considered. A few examples of calculation of seismic fields for the layered medium model with drastically contrast elastic parameters and for the 2-D heterogeneous medium model are presented.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

57

PARALLEL 3D FOURIER SPECTRAL SIMULATION OF STRONG GROUND MOTION IN OSAKA BASIN DURING THE 1995 KOBE EARTHQUAKE

TAKASHI FURUMURA Hokkaido University of Education, Midorigaoka Iwamizawa 068-8642, Japan [email protected]

2-34-1

Received 15 August 1999 Revised 19 December 2000 Numerical 3D simulation of strong ground motion in Osaka basin during the 1995 Kobe (Hyogo-ken Nanbu) earthquake is conducted by using a parallelized Fourier spectral method. During the parallel computing the 3D wavefield are separated into threecoordinate system, and the calculation is conducted concurrentry with a use of interprocessor communications via a computer network. The simulation results for the Kobe earthquake clearly demonstrate that the complex 3D subsurface structure, and the relation to source fault location, plays an very important role on the generation of strong ground motion on the surface.

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Ultrasonic Field Synthesis and Modelling Guest Editor: M. Pappalardo

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61 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

SPEED-ACCURACY TRADE-OFFS IN COMPUTING SPATIAL IMPULSE RESPONSES FOR SIMULATING MEDICAL ULTRASOUND IMAGING

J 0 R G E N ARENDT JENSEN 0rsted , DTU, Build. 348, Technical University of Denmark, DK-2800 Lyngby,

Denmark

Received 7 October 1999 Revised 7 August 2000 Medical ultrasound imaging can be simulated realistically using linear acoustics. One of the most powerful approaches is to employ spatial impulse responses. Hereby both emitted fields and pulse-echo responses from point scatterers can be determined. Also any kind of dynamic focusing and apodization can be incorporated, as has been done in the Field II simulation program. Here the transducer is modeled through a set of either rectangles, triangles, or bounding lines, so that any geometry can be simulated. The response from the transducer is found by summing the spatial impulse responses from the individual elements. One of the problems in using spatial impulse responses is the abrupt changes in the responses due to the sharp transducer boundaries. Sampling the responses directly therefore have to be done at very high sampling frequencies to keep the shape and energy of the response. The high sampling frequency is unnecessary in the final signals, since the transducers used in medical ultrasound are band limited. Approaches to reduce the sampling frequency are, thus, needed to make efficient simulation programs. Field II uses time integration of the spatial impulse responses using a continuous rather than discrete time-axis. This preserves the energy in the responses and makes it possible to make sub-sample interval delays for focusing. The paper discusses the consequence of the integration for the rectangular elements that uses an approximative calculation of the spatial impulse responses. Data for the accuracy as a function of sampling frequency is given, and it is shown how a sampling frequency of 100 MHz gives similar results to using 2 GHz sampling of the analytic solution for rectangular elements. The spatial impulse responses for the triangular and bounding line elements are found analytically, and an iterative integration routine has to be used. The Romberg integration routine is used, and the accuracy versus sampling frequency for bounding line is shown. An increased accuracy is attained for the lines compared to the rectangles, but the simulation times are significantly higher. Line elements should therefore, in this implementation, only be used very close to the transducer, and if a very high precision is needed in the calculation.

62 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001)

/d2fe>\

© IMA CS

(|g| INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

MECHANISM OF ACOUSTIC WAVE PROPAGATION: A REAL ROLE OF VIRTUAL SOURCES

HENRYK LASOTA Technical University of Gdarisk, ul. G. NarutovAcza 11/12, 80 952 Gdaiisk,

Poland

Received 7 October 1999 Revised 18 April 2000 The Huygens problem of self-regeneration of the acoustic wave crossing a liquid medium is discussed in the paper. Equal weight of both elastic and kinetic aspects of mechanical waves in fluids is stressed. Two types of virtual surface sources are defined, reflecting local action of the pressure and particle velocity, respectively. They are applied by the author in calculations of secondary radiation from the wave front of the plane wave. The Dirac delta impulse has been used as a waveform, the wave thus being reduced to its own front. T h e results have been obtained analytically, thanks to some particularly "friendly" features of the operation of convolution with the delta distribution. The paper gives formal proof to Fresnel's intuitive explanation of the mechanism of the forward-only propagation of the wave with no backward effects.

63

International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

SYNTHESIS OF UNEQUALLY SPACED ARRAYS WITH ASYMMETRIC BEAM PATTERNS

ANDREA TRUCCO Department of Biophysical and Electronic Engineering (DIBE), University of Genoa, Via Opera Pia 11, 16145 Genova, Italy trucco@ieee. org VITTORIO MURINO Dipartimento Scientifico e Tecnologico, University of Verona, Ca' Vignal 2, Strada Le Grazie, 37134 Verona, Italy murino@ieee. org Received 19 November 1999 Revised 18 March 2000 In this paper, a novel method that is able to synthesize a desired asymmetric beam pattern by a fully optimized linear array to be used together with a narrow-band beamforming system is proposed. Generally, the methods presented in the literature optimize only the weight coefficients and do not consider the element positions. Therefore, when half-wavelength-spaced arrays are concerned, the optimized weight coefficients are valid only for a fixed steering angle. If the steering angle changes, it is necessary to recompute a new set of weight coefficients to keep the desired asymmetric beam pattern profile. The main feature of the method proposed here is that the synthesized weight coefficients keep their validity in any steering direction. This is attained by acting on both the element positions (in order to generate an aperiodic array) and the weight coefficients. To this end, a well-suited energy function has been defined and several conceptual mechanisms have been devised in order to minimize the energy function by the simulated annealing algorithm. As a result, a very flexible method is achieved to synthesize array configurations that yield asymmetric beam patterns that keep their validity in any steering direction without need for any update.

64 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS

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REAL-TIME DECONVOLUTION IN ULTRASONIC IMAGING SYSTEMS

G. CINCOTTI*, R. CAROTENUTO, G. CARDONE, P. GORI, and M. PAPPALARDO Dipartimento di Ingegneria Elettronica, Universitd degli Studi Roma Tre, via delta Vasca Navale 8^, 00146 Roma, Italy *g. [email protected]. it Received 12 June 1999 Revised 10 January 2000 We address the problem of improving the lateral resolution of ultrasonic images by a regularization technique in the wavelet domain. With a very low additional computational cost, the proposed approach increases the efficiency of the standard regularization technique because it efficiently remove the additive noise. Under the assumption that the point spread function is known, we applied our restoration technique to both synthetic and real ultrasonic imaging data. Moreover, experimental results show that the proposed method reduces also speckle artifacts, which generally are enhanced by the deconvolution.

65

TIME REVERSAL IN ACOUSTICS*

MATHIAS FINK Laboratoire Ondes et Acoustique, ESPCI, CNRS UMR 7587 10, rue Vauquelin F-75005 Paris, France [email protected] Received 22 September 1999 Revised 29 September 2000 The objective of this paper is to show that time reversal invariance can be exploited in acoustics to create a variety of useful instruments as well as elegant experiments in pure physics. After a description of time reversal cavities and time reversal mirrors, a comparison between time reversal techniques and phase conjugation methods will be given. To illustrate the robustness of time reversal mirrors, several experiments conducted in multiply scattering media, in waveguides and in chaotic cavities will be presented. Finally, various applications of time reversal mirrors in medical therapy and in non-destructive testing will be discussed.

* Invited Lecture given at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

66 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

COMPUTATION OF THE ULTRASONIC FIELD RADIATED BY SEGMENTED-ANNULAR ARRAYS

O. MARTINEZ and L. G. ULLATE Institute

de Automdtica

Industrial (CSIC), Ctra Campo Real, Km. 0,200 - La Poveda, 28500 Arganda del Rey (Madrid), Spain F. MONTERO

Instituto

de Acustica (CSIC), CTEF, Torres Quevedo, C/ Serrano 144> 28006 Madrid, Spain Received 19 September 1999 Revised 20 March 2000

A method for computing the ultrasonic field radiated from segmented annular arrays is presented. Using the well known convolution-impulse response approach, an analytical expression for the spatial impulse response velocity potential from a segmented annular transducer valid for all spatial points is obtained. The array field is then calculated by superposition. The proposed solution allows us to predict transient and continuous wave pressure fields from segmented annular arrays without requiring any far-field or paraxial approximation. In order to evaluate the proposed method, an analysis of efficiency versus accuracy of the computational results is also incorporated.

67 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

NUMERICAL TECHNIQUES FOR MODELING DOPPLER ULTRASOUND SPECTRA SYSTEMS

M. GRAQA RUANO Adeec, Uceh, Universida.de do Algarve, Campus de Gambelas, 8000 Faro,

Portugal

Received 27 August 1999 Revised 1 March 2000 Evaluation of blood-flow Doppler ultrasound spectral content is currently performed on clinical diagnosis. Since mean frequency and bandwidth spectral parameters are determinants on the quantification of stenotic degree, more precise estimators than the conventional Fourier transform should be seek. This paper summarizes studies led by the author in this field, as well as the strategies used to implement the methods in realtime. Regarding stationary and nonstationary characteristics of the blood-flow signal, different models were assessed. When autoregressive and autoregressive moving average models were compared with the traditional Fourier based methods in terms of their statistical performance while estimating both spectral parameters, the Modified Covariance model was identified by the cost/benefit criterion as the estimator presenting better performance. The performance of three time-frequency distributions and the Short Time Fourier Transform was also compared. The Choi-Williams distribution proved to be more accurate than the other methods. The identified spectral estimators were developed and optimized using high performance techniques. Homogeneous and heterogeneous architectures supporting multiple instruction multiple data parallel processing were essayed. Results obtained proved that real-time implementation of the blood-flow estimators is feasible, enhancing the usage of more complex spectral models on other ultrasonic systems.

68 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

INFLUENCE OF THE INTER-ELEMENT COUPLING ON ULTRASOUND ARRAY RADIATION PATTERNS

P. GORI*, A. IULA, and M. PAPPALARDO Dipartimento

di Ingegneria Elettronica, Universita degli Studi Roma Via della Vasca Navale, 84, 00146 Roma, Italy *p.gori@ele. uniroma3.it

Tre,

N. LAMBERTI Dipartimento d'Ingegneria dell'Informazione ed Ingegneria Elettrica, Universita di Salerno, Via Ponte Don Melillo, 84O84 Fisciano (SA), Italy F. MONTERO DE ESPINOSA Instituto

de Acustica,

CSIC, Serrano 144> 28006 Madrid,

Spain

Received 20 June 1999 Revised 3 March 2000 It is well known that the performances of the acoustic imaging arrays are degraded by the inter-element coupling sustained via the backing, the matching layers, and the kerf filler. The filling material inserted between the elements gives mechanical robustness to the array, but acts as a path of interaction, transmitting, between the elements, shear and lateral compressional forces. In this work, the effect on the array radiation pattern of the cross-coupling due to the filling material is investigated. A hybrid experimentalnumerical technique is used. Two groups of five elements of a commercial array transducer were isolated and in one group the kerf filling material was removed. The crosscoupling waveforms, captured with a mechanical probe of small dimensions in contact with the emitting surfaces of the elements, were recorded for filled and unfilled groups of elements when: only the central element of the group was driven; all the elements were driven with the same pulse applied at the same time; all the elements were driven with the same pulse, but inverting the polarity alternately. This latter case refers to the worst coupling situation caused by the shear forces exerted between the elements. Fourier transforming the temporal signals, the cross-coupling transfer function of each element was computed and the radiation pattern was simulated by a numerical model based on the Rayleigh-Sommerfeld integral. Comparing the radiation patterns for filled and unfilled groups of elements, for the three cases mentioned above, a good estimation of the influence of the filling material is obtained.

Computational Methods

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71 International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

A DIRECT DISCRETE FORMULATION FOR THE WAVE EQUATION*

ENZO TONTI Department Civil Engineering, University of Trieste, Piazzale Europa 1, 34127 Trieste, Italia [email protected] Received 10 June 1999 Revised 7 September 2000 T h e paper shows how to give a direct discrete formulation of the wave equation starting directly from physical laws, i.e. without passing through differential formulation. Using global variables instead of scalar and vector field functions, a close link between global variables and spatial and temporal elements immediately appears. A preliminary classification of physical variables into three classes: configuration, source and energy variables and the use of two cell complexes, one dual of the other, gives an unambiguous association of global variables to the spatial and temporal elements of the two complexes. Thus, one arrives at a discrete formulation of d'Alembert equation on an unstructured mesh.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

72 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

AN HEXAHEDRAL FACE ELEMENT METHOD FOR THE DISPLACEMENT FORMULATION OF STRUCTURAL ACOUSTICS PROBLEMS*

ALFREDO BERMUDEZt and PABLO GAMALLO* Departamento de Matemdtica Aplicada, Universidade de Santiago de Compostela, Spain t [email protected] * [email protected]. es RODOLFO RODRIGUEZ Departamento

de Ingenieria Matemdtica, Universidad de Concepcidn, [email protected]

Chile

Received 23 June 1999 Revised 6 March 2000 Several finite element methods for the numerical computation of elastoacoustic vibrations are compared. They are applied to two formulations based on different variables to describe the fluid: presssure and displacement potential in one case, and displacements in the other. While the first one is discretized by standard Lagrangean finite elements for both variables, the second one is solved by "face" Raviart-Thomas elements. In each case we consider both tetrahedral and hexahedral meshes. Elastoacoustic eigenmodes have been computed for a test example by means of MATLAB implementations of all these methods. T h e numerical results allow us to compare all of them in terms of error versus number of degrees of freedom and computing time.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

73 International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

A COMPARISON OF NUMERICAL METHODS FOR ACTIVE SONAR ARRAY PERFORMANCE*

SUSAN MORGAN and DAVID J. W. HARDIE DERA

Winfrith,

Winfrith Technology Centre, Winfrith Dorchester, Dorset. DT2 8XJ, UK

Newburgh,

PATRICK C. MACEY SER Systems Ltd, 39 Nottingham

Road, Stapleford, Nottingham,

NG9 8AD, UK

Received 22 July 1999 Revised 7 November 2000 Low frequency active sonar (LFAS) arrays are complicated devices requiring careful design. Prototype LFAS arrays are expensive to construct and test. Accurate prediction of acoustic and electrical performance is therefore of great interest to LFAS designers. This generally involves solving a fully coupled problem relating the electrical drive to the resulting acoustic field. To derive results a numerical solution method is clearly the only recourse. This paper compares various numerical techniques in terms of accuracy, efficiency and overall applicability for the solution of LFAS problems. These are based around finite element (FE) and boundary element (BE) descriptions of the surrounding acoustic medium. Here we consider a pure F E approach based on wave envelope elements and a combined F E / B E scheme using an approximate BE formulation. These are contrasted with a pure BE approach that has been demonstrated to provide accurate predictions of LFAS array performance over a number of years. A piston stack transducer and a line array of free-flooding ring projectors are considered as example LFAS problems. The acoustic, structural and electrical responses are considered.

* Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

74 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

ON THE EFFICIENT IMPLEMENTATION OF THE INTEGRAL EQUATION METHOD IN ELASTODYNAMICS*

EVGENY V. GLUSHKOV and NATALYA V. GLUSHKOVA Kuban State University,

P. O. Box 4102, Krasnodar 350080, [email protected]

Russia

Received 18 June 1999 Revised 15 June 2000 The authors deal with low-cost computer implementation of the integral equation method in application to wave excitation, propagation and diffraction phenomena in solids. Typically these are frequency domain problems of seismic and physical acoustics and of nondestructive testing. Fast codes are obtained basing on analytical extracting and taking account of singular and slowly converging components of the solution beforehand. The present paper gives ideas of several such approaches, which have already proved their efficiency in practical applications. More details including numerical examples and discussion of similar methods known from the literature can be found in the surveyed 1—12

papers.

"

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

A GENERALIZED MODE MATCHING METHOD FOR SCATTERING PROBLEMS WITH UNBOUNDED OBSTACLES*

A.-S. BONNET-BENDHIAt and A. TILLEQUIN* ENSTA,

SMP, URA 853-CNRS,

32 bd Victor, 75739 PARIS [email protected] HillequWensta.fr

Cedex 15, France

Received 16 September 1999 Revised 6 June 2000 The two-dimensional time-harmonic acoustic scattering by a semi-infinite waveguide composed of two parallel rigid plates is considered. An original mode matching method is developed to avoid the use of the Wiener-Hopf technique, generalizing usual mode matching methods to the case of unbounded media. A brief description of the method is given by means of Fourier decomposition leading to a well-posed variational problem with unknown being the trace of the solution on a well-chosen interface. From the numerical point of view, a local approximation is first considered by using Lagrange P I finite elements on a segment of the interface. This leads to the computation of oscillatory integrals involving Fourier transform and complex square root functions. As a matter of accuracy, a special function is added to the finite element space, in order to take into account the asymptotic behavior of the solution. Finally, this method is extended to deal with local perturbations of the media by coupling the previous method to a classical integral one.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

76 International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

AILU FOR HELMHOLTZ PROBLEMS: A NEW PRECONDITIONER BASED ON THE ANALYTIC PARABOLIC FACTORIZATION*

MARTIN J. GANDER Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, QC H3A 2K6, Canada mgander@math. mcgill. ca FREDERIC NATAF CMAP,

CNRS UMR 7641, Ecole Poly technique, 91128 Palaiseau Cedex, France [email protected] Received 15 July 1999 Revised 3 October 2000

We investigate a new type of preconditioner which is based on the analytic factorization of the operator into two parabolic factors. Approximate analytic factorizations lead to new block ILU preconditioners. We analyze the preconditioner at the continuous level where it is possible to optimize its performance. Numerical experiments illustrate the effectiveness of the new approach.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

77 International Journal of Computational Acoustics, Vol. 8, No. 3 (2000) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

APPLICATION OF A DOMAIN DECOMPOSITION METHOD WITH LAGRANGE MULTIPLIERS TO ACOUSTIC PROBLEMS ARISING FROM THE AUTOMOTIVE INDUSTRY*

FREDERIC MAGOULES ONER A, 29 avenue de la Division Leclerc B.P. 72, 92322 Chatillon Cedex, France KARL MEERBERGEN and JEAN-PIERRE C O Y E T T E t LMS International, Interleuvenlaan 3001 Leuven, Belgium

70,

Received 12 July 1999 Revised 29 February 2000 The Finite Element Tearing and Interconnecting method for the Helmholtz equation is a recent nonoverlapping domain decomposition method for solving linear systems arising from the finite element discretization of Helmholtz problems in bounded domains. This method was validated on two-dimensional external problems with first-order absorbing boundary conditions. The purpose of this paper is to study the robustness and efficiency of iterative methods for the solution of the associated interface problem for three-dimensional interior problems arising from the automotive industry.

* Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy. tPresent address: Free Field Technologies, 5 rue Charlemagne, 1348 Louvain-la-Neuve, Belgium.

78

VISUALIZATION OF THE ENERGY FLOW IN AND AROUND A FLUID LOADED ELASTIC SPHERE*

CLEON E. DEAN Department of Physics, Georgia Southern University, P.O.B. 8031, Statesboro, Georgia 30460-8031, USA cedean @gsvms2. cc.gasou.edu JAMES P. BRASELTON Department of Mathematics and Computer Science, Georgia Southern University, P.O.B. 8093, Statesboro, Georgia 30460-8093, USA [email protected] Received 10 July 1999 Revised 15 December 2000 The energy flow in and around a fluid loaded elastic sphere can be visualized by the instantaneous elastodynamic Poynting vector field and its time averaged complex cognate. The instantaneous field can be used to animate and follow the energy flow around the sphere much as one can follow the ripples of wind through a wheat field. The real and imaginary parts of the complex elastodynamic Poynting vector field can be used to show the traveling and standing wave components of the energy field, respectively. Special attention is given to the fluid/elastic boundary and energy coupling between the solid and fluid media. Numerous vector field plots and several animations will be shown.

'Presented at ICTCA'99 the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

79

NOISE PREDICTION BASED ON THE SPECTRAL METHOD FOR SOLVING A DISSIPATIVE BOUNDARY VALUE PROBLEM IN ACOUSTICS AND ITS NUMERICAL REALIZATION*

EUGENE SVIAGENINOV Institute for Mechanical Engineering Problems of the Russian Academy 61, Bolshoj ave., 199178, St.Petersburg, Russia

of

Sciences,

Received 20 July 1999 Revised 3 October 2000 With intensive progress in noise control engineering it is necessary to solve diverse and highly complicated problems on vibrations of dissipative acoustical systems. The mathematical problems can be realized exactly in the specific cases only. Among approximate ways for solving the problems on dissipative acoustical vibrations of compressible gas or liquid the spectral method, based on the variational principle, is presented. The paper deals, first of all, with a new approach to noise prediction, i.e. forced vibration of a compressible gas. As a polyharmonic vibration, noise consists of the set of monoharmonic oscillations. There were no variational principles for stationary forced oscillations of dissipative distributed parameter systems when complex displacement amplitudes exhibit phase lag relative to pressure amplitudes due to the energy loss. Such a principle is stated in the paper. The starting boundary value problem has mixed nonhomogeneous conditions. The approach is illustrated by the modelling of compressible gas oscillations inside a device for producing resonance acoustical vibrations by means of steady excitation of the gas. This sonic generator, incorporating a resonator is under consideration as an example of the variational approach fitted to the problem quite adequately.

'Presented at ICTCA'99 the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

80

SINC SOLUTION OF THE SHALLOW WATER EQUATIONS*

KAMEL AL-KHALED Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan applied@just. edu.jo Received 12 August 1999 Revised 17 May 2000 A sinc-Galerkin procedure is developed to approximate the solution of the shallow water equations. An integration of the shallow water equations with respect to the time variable leads to a nonlinear Volterra integral equation. Sine approximations to both derivatives and indefinite integral reduce the integral equation to an explicit system of algebraic equations. Applications of the scheme to the variable-depth shallow water equations (thus having a source term) are given.

'Presented at ICTCA'99 the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

Finite Elements for Wave Problems Guest Editors: R. J. Astley, K. Gerdes, D. Givoli, and I. Harari

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83 International Journal of Computational Acoustics, Vol. 8, No. 1 (2000) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

NUMERICAL STUDIES OF CONJUGATED INFINITE ELEMENTS FOR ACOUSTICAL RADIATION

R. J. ASTLEY and J. A. HAMILTON Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand Received 3 August 1999 Revised 15 October 1999 Aspects of conjugated infinite element schemes for unbounded wave problems are reviewed and a general formulation is presented for elements of variable order based on separable shape functions expressed in terms of prolate and oblate spheroidal coordinates. The formulation encompasses both "conjugated Burnett" and "Astley-Leis" elements. The performance of the two approaches is compared for steady multipole wave fields and the effect of the radial basis on the condition number of the resulting equations is discussed. Transient formulations based on these elements are derived and methods for solving the resulting transient equations are discussed. The use of an implicit time stepping scheme coupled with an indirect iterative solver is shown to give fast transient solutions which do not require matrix inversion.

84 International Journal of Computational Acoustics, Vol. 8, No. 1 (2000) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

A REFLECTION FREE BOUNDARY CONDITION FOR PROPAGATION IN UNIFORM FLOW USING M A P P E D INFINITE WAVE ENVELOPE ELEMENTS

WALTER EVERSMAN University of Missouri-Rolla,

1870 Miner Circle, Rolla, MO, 65401, USA

Received 15 June 1999 Revised 23 November 1999 Variable order mapped infinite wave envelope elements are developed for finite element modeling of acoustic radiation in a uniformly moving medium. These elements are used as a nonreflecting boundary condition for computations on an infinite domain in which a radiating body is immersed in a moving medium which is essentially undisturbed outside of the near field. The mapped elements provide a boundary condition equivalent to element stiffness, mass, and damping matrices appended to an inner standard FEM mesh. A demonstration of the performance of mapped elements as influenced by element order is given in the context of acoustic radiation from a turbofan inlet and exhaust.

85 International Journal of Computational Acoustics, Vol. 8, No. 1 (2000) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

A REVIEW OF INFINITE ELEMENT METHODS FOR EXTERIOR HELMHOLTZ PROBLEMS

KLAUS GERDES Department

of Mathematics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden Received 15 June 1999 Revised 2 November 1999

This work is devoted to review infinite element discretizations for the Helmholtz equation in exterior domains, which have become popular in recent years, as many research papers on this topic have appeared in the literature. The early contributions were mostly motivated by engineering considerations and the variational formulations have, in general, not been stated in a mathematically precise way. Only recently, theoretical aspects of the infinite element methodology have been analyzed and helped to put the different formulations into a mathematical framework. We build upon this, and present and compare the infinite element formulations within this context.

86 International Journal of Computational Acoustics, Vol. 8, No. 1 (2000) © IMACS

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ON FUNDAMENTAL ASPECTS OF EXTERIOR APPROXIMATIONS WITH INFINITE ELEMENTS

FRANK IHLENBURG Germanischer

Lloyd, Vorsetzen 32, D-20459 Hamburg,

Germany

Received 15 June 1999 Revised 16 October 1999 Over the last years, infinite elements have become a popular method of exterior approximation in scattering problems. Addressing the scalar case (Helmholtz equation), this paper gives a state-of-the-art review on the convergence theory for the approximation used in radial infinite elements. The focus is on the stability of different variational formulations that were proposed in the context of this approximation. Exterior approximation on partitions with finite and infinite elements is also considered. The review is preceded by an outline of the relevant general theory. Open questions are listed in the conclusion of the presentation.

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International Journal of Computational Acoustics, Vol. 8, No. 1 (2000) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

FINITE ELEMENT SOLUTION OF TWO-DIMENSIONAL ACOUSTIC SCATTERING PROBLEMS USING ARBITRARILY SHAPED CONVEX ARTIFICIAL BOUNDARIES

RABIA DJELLOULI, CHARBEL FARHAT, ANTONINI MACEDO, and RADEK TEZAUR Department of Aerospace Engineering Sciences and Center for Aerospace Structures, University of Colorado at Boulder, Boulder, CO 80309-0^29, USA Received 30 June 1999 Revised 12 October 1999 For elongated scatterers such as submarines, we show that the generalization of the Bayliss-Turkel nonreflecting boundary conditions to arbitrarily shaped convex artificial boundaries improves significantly the computational efficiency of finite element methods for the solution of acoustic scattering problems.

88 International Journal of Computational Acoustics, Vol. 8, No. 1 (2000) © IMACS

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THIRD-ORDER DOUBLY ASYMPTOTIC APPROXIMATIONS FOR COMPUTATIONAL ACOUSTICS

THOMAS L. GEERS and BRADY J. T O O T H A K E R Center for Acoustics, Mechanics and Materials, Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309-0427, USA Received 9 July 1999 Revised 3 November 1999 A fully and symmetrically matched, third-order doubly asymptotic computational boundary (DAA3) is presented in both operator and matrix forms. Its performance is then compared with that of other DAA boundaries for the spherical geometry, which admits an exact series solution. Based on stability, accuracy and passivity as performance criteria, DAA3 is found to be superior to all other DAAs formulated to date. However, there are other third-order forms t h a t are nearly as good, and are easier to implement in boundary-element form. The existence of both DAA2 and DAA3 boundaries enables the analyst to assess solution accuracy for a given problem through the comparison of results produced with these higher approximations of different order.

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ANALYTICAL AND NUMERICAL STUDIES OF A FINITE ELEMENT PML FOR THE HELMHOLTZ EQUATION

ISAAC HARARI and MICHAEL SLAVUTIN Department of Solid Mechanics, Materials and Structures, Tel Aviv University, 69978 Ramat Aviv, Israel ELI TURKEL School of Mathematical Sciences Tel Aviv University, 69978 Ramat Aviv, Israel Received 3 June 1999 Revised 4 November 1999 A symmetric PML formulation that is suitable for finite element computation of timeharmonic acoustic waves in exterior domains is analyzed. Dispersion analysis displays the dependence of the discrete representation of the PML parameters on mesh refinement. Stabilization by modification of the coefficients is employed to improve PML performance, in conjunction with standard stabilized finite elements in the Helmholtz region. Numerical results validate the good performance of this finite element PML approach.

90 International Journal of Computational Acoustics, Vol. 8, No. 1 (2000) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

CONTINUED-FRACTION ABSORBING BOUNDARY CONDITIONS FOR THE WAVE EQUATION

MURTHY N. GUDDATI Department of Civil Engineering, North Carolina State University, Campus Box 7908, Raleigh, NC 27695-7908, USA JOHN L. TASSOULAS Department

of Civil Engineering, The University of Texas at Austin, TX 78712, USA

Austin,

Received 25 June 1999 Revised 1 October 1999 Absorbing boundary conditions are generally required for numerical modeling of wave phenomena in unbounded domains. Local absorbing boundary conditions are generally preferred for transient analysis because of their computational efficiency. However, their accuracy is severely limited because the more accurate high-order boundary conditions cannot be implemented easily. In this paper, a new arbitrarily high-order absorbing boundary condition based on continued fraction approximation is presented. Unlike the existing boundary conditions, this one does not contain high-order derivatives, thus making it amenable to implementation in conventional C° finite element and finite difference methods. The superior numerical properties and implementation aspects of this boundary condition are discussed. Numerical examples are presented to illustrate the performance of these new high-order boundary condition.

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International Journal of Computational Acoustics, Vol. 8, No. 1 (2000) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

OPTIMAL LOCAL NONREFLECTING BOUNDARY CONDITIONS FOR TIME-DEPENDENT WAVES

IGOR PATLASHENKO Hummingbird Communications LTD., 1 Sparks Avenue, North York, Ontario, Canada MSH 2W1 DAN GIVOLI Department of Aerospace Engineering, and Asher Center {or Space Research, Technion — Israel Institute of Technology, Haifa 32000, Israel Received 5 July 1999 Revised 5 July 1999 Nonreflecting Boundary Conditions (NRBCs) are often used on artificial boundaries as a method for the numerical solution of wave problems in unbounded domains. Recently, a two-parameter hierarchy of optimal local NRBCs of increasing order has been developed for elliptic problems, including the problem of time-harmonic acoustic waves. The optimality is in the sense that the local NRBC best approximates the exact nonlocal Dirichlet-to-Neumann (DtN) boundary condition in the L2 norm for functions which can be Fourier-decomposed. The optimal NRBCs are combined with finite element discretization in the computational domain. Here this approach is extended to time-dependent acoustic waves. In doing this, the Semi-Discrete DtN approach is used as the starting point. Numerical examples involving propagating disturbances in two dimensions are given.

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MIXED FINITE ELEMENTS WITH MASS-LUMPING FOR THE TRANSIENT WAVE EQUATION

GARY COHEN and SANDRINE FAUQUEUX INRIA,

Domaine de Voluceau, Rocquencourt, B.P. 105, 78153 he Chesnay Cedex, Prance gary. [email protected] [email protected] Received 15 June 1999 Revised 30 September 1999

Solving the acoustics equation by finite elements with mass-lumping requires the use of spectral elements. Although avoiding the inversion of a mass-matrix at each timestep, these elements remain expensive from the point of view of the stiffness-matrix. In this paper, we give a mixed finite element method which provides a factorization of the stiffness-matrix which leads to a gain of storage and computation time which grows with the order of the method and the dimension in space. After proving the equivalence between classical spectral elements and this method, we give a dispersion analysis on nonregular periodic meshes. Then, we analyze the accuracy and the stability of Q3 and Q5 approximations on numerical tests in 2D.

93 International Journal of Computational Acoustics, Vol. 8, No. 1 (2000) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

SHORT WAVE MODELLING USING SPECIAL FINITE ELEMENTS

OMAR LAGHROUCHE and P E T E R BETTESS School of Engineering,

University of Durham, Durham DH1 3LE, UK Received 15 June 1999 Revised 2 November 1999

The solutions to the Helmholtz equation in the plane are approximated by systems of plane waves. The aim is to develop finite elements capable of containing many wavelengths and therefore simulating problems with large wave numbers without refining the mesh to satisfy the traditional requirement of about ten nodal points per wavelength. At each node of the meshed domain, the wave potential is written as a combination of plane waves propagating in many possible directions. The resulting element matrices contain oscillatory functions and are evaluated using high order Gauss-Legendre integration. These finite elements are used to solve wave problems such as a diffracted potential from a cylinder. Many wavelengths are contained in a single finite element and the number of parameters in the problem is greatly reduced.

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A NUMERICAL COMPARISON OF FINITE ELEMENT METHODS FOR THE HELMHOLTZ EQUATION

ASSAD A. OBERAI and P E T E R M. PINSKY Division of Mechanics and Computation, Room 262, Durand Building, Stanford

Department of Mechanical Engineering, University, Stanford, CA 94305, USA

Received 14 July 1999 Revised 14 July 1999 Three finite element formulations for the solution of the Helmholtz equation are considered. The performance of these methods is compared by performing a discrete dispersion analysis and by solving two canonical problems on nonuniform meshes. It is found that: (1) The scaled L2 error for the Galerkin method, using linear interpolation functions, grows as k{kh)2, indicating the pollution inherent in this method; (2) The Galerkin least squares method is more accurate, but does display significant pollution error; (3) The residual-based method of Oberai & Pinsky, • which was designed to be almost pollution-free for uniform meshes retains its accuracy on nonuniform meshes; (4) The computational cost of implementing all these formulations is approximately the same.

95 International Journal of Computational Acoustics, Vol. 8, No. 1 (2000) © IMACS

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EFFICIENT COMPUTATION OF MULTI-FREQUENCY FAR-FIELD SOLUTIONS OF THE HELMHOLTZ EQUATION USING PADE APPROXIMATION

MANISH MALHOTRA* and P E T E R M. PINSKY Department

of Mechanical Engineering,

Stanford

University,

CA 94305-4040,

USA

Received 19 July 1999 Revised 7 December 1999 For many problems in exterior structural acoustics, the solution is required to be computed over multiple frequencies. For some classes of these problems, however, it may be sufficient to evaluate the multiple frequency solutions over restricted regions of the spatial domain. Examples include optimization and inverse problems based on the minimization of a functional defined over a specified surface or sub-region. For such problems, which include both near-field and far-field computations, we recently proposed an efficient algorithm to compute the partial-field solutions at multiple frequencies simultaneously. In this paper, we consider the particular case of far-field computations and simplify the recently proposed algorithm by exploiting the symmetry of linear operators. The approach involves a reformulation of the Dirichlet-to-Neumann (DtN) map based finite-element matrix problem into a transfer-function form that can efficiently describe the far-field solution. A multi-frequency approximation of the transfer function is developed by constructing matrix-valued Pade approximation of the transfer function via a symmetric, banded Lanczos process. Numerical tests illustrate the accuracy of the approach for a wide range of frequencies and cost reductions of an order of magnitude when compared to commonly used factorization based methods.

•Present address: Sun Microsystems, UMPK24-201, 901 San Antonio Road, Palo Alto 94303.

96 International Journal of Computational Acoustics, Vol. 8, No. 1 (2000) © IMACS

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AN ITERATIVE TIME-STEPPING METHOD FOR SOLVING FIRST-ORDER TIME DEPENDENT PROBLEMS AND ITS APPLICATION TO THE WAVE EQUATION*

GEZA SERIANI Istituto Nazionale di Oceanografia e di Geofisica Sperimentale Borgo Grotta Gigante 42/C, I-S4010 Trieste, Italy [email protected] Received 18 July 1999 Revised 2 December 1999 Equations describing dynamic problems, after spatial discretization by using the finite element or spectral element method, lead to solve large systems of ODE in time. A family of new time integration algorithms based on an iterative time-stepping (ITS) approach is proposed for solving these systems. The method is developed for first- and second-order differential equations, and applied, in particular, to wave equation. It is an implicit time marching method in which, at each time-step, the solution is computed by a fixed-point scheme. The analysis show that the method is accurate, unconditionally stable and that it allows for efficient and parallel implementations because no matrix inversion is required and only matrix-vector multiplications and vector scaling operations are involved.

'Presented at ICTCA'99 the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

Wave Propagation Modeling

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99 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © MACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

FICTITIOUS DOMAINS, MIXED FINITE ELEMENTS AND PERFECTLY MATCHED LAYERS FOR 2-D ELASTIC WAVE PROPAGATION*

E. BECACHEt, P. JOLY*, and C. TSOGKA§ INRIA, Domaine de Voluceau-Rocquencourt, BP 105, F-78153 Le Chesnay Cedex, Prance t eliane. [email protected] ' [email protected] § [email protected] Received 23 September 1999 Revised 21 April 2000 We design a new and efficient numerical method for the modelization of elastic wave propagation in domains with complex topographies. The main characteristic is the use of the fictitious domain method for taking into account the boundary condition on the topography: the elastodynamic problem is extended in a domain with simple geometry, which permits us to use a regular mesh. The free boundary condition is enforced introducing a Lagrange multiplier, defined on the boundary and discretized with a nonuniform boundary mesh. This leads us to consider the first-order velocity-stress formulation of the equations and particular mixed finite elements. These elements have three main nonstandard properties: they take into account the symmetry of the stress tensor, they are compatible with mass lumping techniques and lead to explicit time discretization schemes, and they can be coupled with the Perfectly Matched Layer technique for the modeling of unbounded domains. Our method permits us to model wave propagation in complex media such as anisotropic, heterogeneous media with complex topographies, as it will be illustrated by several numerical experiments.

"Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

100 International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

HIGHER-ORDER MASS-LUMPED FINITE ELEMENTS FOR THE WAVE EQUATION*

W. A. MULDER Shell International Exploration and Production BV, P. O. Box 60, NL-2280 AB Rijswijk, The Netherlands w. a. mulder&siep. shell, com Received 20 July 1999 Revised 29 March 2000 The finite-element method (FEM) with mass lumping is an efficient scheme for modeling seismic wave propagation in the subsurface, especially in the presence of sharp velocity contrasts and rough topography. A number of numerical simulations for triangles are presented to illustrate the strength of the method. A comparison to the finite-difference method shows that the added complexity of the FEM is amply compensated by its superior accuracy, making the FEM the more efficient approach.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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NUMERICAL STUDY OF ELASTIC WAVE SCATTERING BY CRACKS OR INCLUSIONS USING THE BOUNDARY INTEGRAL EQUATION METHOD*

ENRU LlUt British Geological Survey, Murchison House, West Mains Road, Edinburgh EH9 SLA, Scotland, UK [email protected] ZHONGJIE ZHANG Institute

of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100101, China zjzhang&mail. c-geos.ac.cn

11 Datun Road,

Received 1 July 1999 Revised 30 August 2000 In this paper, we use a 2-D elastodynamic boundary integral equation or boundary element method (BEM) to solve multiple scattering problems due to existence of cracks or inclusions. The method is based on the integral representation of a scattered wavefield by assuming a fictitious source distribution on the scattering objects or inclusions (i.e. mathematical description of Huygens' principle), and the fictitious source distribution can be found by matching appropriate boundary conditions at the boundary of the inclusions. The method is called indirect boundary element method. Three numerical examples are presented to demonstrate the versatility of the BEM method. The first example shows that different spatial arrangements of the same scatters lead to profound differences in scattering characteristics, in particular the frequency contents of the transmitted wavefields using the method of time-frequency analysis. The second example shows the effects of power-law or fractal distribution of scalelengths on transmitted wavefields, and we conclude that frequency characteristics, such as the frequency of the peak attenuation, can be related to spatial size parameters of the model. In the third example, we show that orientated inclusions with aspect ratio less than unity have strong effects on the amplitudes of transmitted waves, and this has an important implication in characterizing inclusions and fractures using azimuthal variation in amplitudes (or attenuation anisotropy).

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy. t T h e work was done while the author was at Institute of Geology and Geophysics, Chinese Academy of Sciences, 11 Datun Road, Beijing 100101, China.

102 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

FINITE-DIFFERENCE MODELING IN MEDIA WITH MANY SMALL-SCALE CRACKS*

GERBEN B. VAN BAREN and GERARD C. HERMAN Department of Applied Mathematics, Centre for Technical Geoscience, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands WIM A. MULDER Shell International Exploration and Production BV, Postbus 60, 2280A B Rijswijk, The Netherlands Received 26 May 1999 Revised 28 February 2000 We discuss a finite-difference modeling technique for scalar, two-dimensional wave propagation in a medium containing a large number of small-scale cracks. The embedding medium can be heterogeneous. The boundaries of the cracks are not represented in the finite-difference mesh but the cracks are incorporated as distributed point sources. This enables the use of grid cells that are considerably larger than the crack sizes. We compare our method to an accurate integral-equation solution for the case of a homogeneous embedding and conclude that the finite-difference technique is accurate and computationally fast.

* Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

103 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

SCALE AND ANGLE DEPENDENT REFLECTION PROPERTIES OF SELF-SIMILAR INTERFACES*

JEROEN GOUDSWAARD and KEES WAPENAAR Delft University of Technology, Centre for Technical Geoscience, P.O. Box 5028, 2600 GA Delft, The Netherlands Received 30 June 1999 Revised 6 March 2000 We propose an alternative parameterization of seismic reflectors in the subsurface, in terms of self-similar singularities, which are generalizations of stepfunctions. This parameterization captures the multi-scale behavior of real sonic P-wave velocity logs, as can be derived by performing modulus maxima analysis on wavelet-transformed welllogs. Results on synthetic seismic reflection data, modeled in real well-logs, show that a singularity parameter can be retrieved, that is consistent with the parameter derived directly from the well-log.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

104 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

ELASTIC WAVES GENERATED BY HIGH-SPEED TRAINS*

AUKE DITZEL and GERARD HERMAN Department of Applied Mathematics, Centre for Technical Geoscience, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands PAUL HOLSCHER GeoDelft, P.O. Box 69, 2600 AB Delft, The

Netherlands

Received 2 June 1999 Revised 12 April 2000 High-speed trains can generate vibrations that propagate away from the track. We present an accurate and efficient method for computing the vibrations in an elastic half-space at both small and large distances from the track. The method takes possible oscillatory behavior of the train into account. We conclude that vibrations, generated by oscillating trains, can be observed at large distances from the track, even if the train speed is lower than the Rayleigh wave speed.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

ADAPTIVE FINITE ELEMENT TECHNIQUES FOR THE ACOUSTIC WAVE EQUATION*

WOLFGANG BANGERTHt and ROLF RANNACHER* Institute of Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 293/294, 69120 Heidelberg, Germany "wolfgang. bangerth@iwr. uni-heidelberg. de ^rannacher@iwr. uni-heidelberg. de Received 2 July 2000 Revised 31 March 2000 We present an adaptive finite element method for solving the acoustic wave equation. Using a global duality argument and Galerkin orthogonality, we derive an identity for the error with respect to an arbitrary functional output of the solution. The error identity is evaluated by solving the dual problem numerically. The resulting local cell-wise error indicators are used in the grid adaptation process. In this way, the space-time mesh can be tailored for the efficient computation of the quantity of interest. We give an overview of the implementation of the proposed method and illustrate its performance by several numerical examples.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

106 International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

WAVE PROPAGATION IN 2-D ELASTIC MEDIA USING A SPECTRAL ELEMENT METHOD WITH TRIANGLES AND QUADRANGLES*

DIMITRI KOMATITSCHt Harvard University,

Cambridge, Massachusetts,

USA

ROLAND MARTIN Institute) Mexicano del Petrdleo, Mixico D.F.,

Mexico

JEROEN T R O M P t Harvard University,

Cambridge, Massachusetts,

USA

MARK A. TAYLOR and BETH A. WINGATE Los Alamos National Laboratory, Los Alamos, New Mexico,

USA

Received 8 October 1999 Revised 25 May 2000 We apply a spectral element method based upon a conforming mesh of quadrangles and triangles to the problem of 2-D elastic wave propagation. The method retains the advantages of classical spectral element methods based upon quadrangles only. It makes use of the classical Gauss-Lobatto-Legendre formulation on the quadrangles, while discretization on the triangles is based upon interpolation at the Fekete points. We obtain a global diagonal mass matrix which allows us to keep the explicit structure of classical spectral element solvers. We demonstrate the accuracy and efficiency of the method by comparing results obtained for pure quadrangle meshes with those obtained using mixed quadrangle-triangle and triangle-only meshes.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy. tNow at: Seismological Laboratory, California Institute of Technology, Pasadena, California, USA.

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A COMPARATIVE STUDY OF EXPLICIT DIFFERENTIAL OPERATORS ON ARBITRARY GRIDS*

MARTIN KASER and HEINER IGEL Institut fur Allgemeine

und Angewandte

Geophysik, Miinchen,

Germany

MALCOLM SAMBRIDGE and JEAN BRAUN Research School of Earth Sciences, Canberra,

Australia

Received 20 July 2000 Revised 13 March 2000 We compare explicit differential operators for unstructured grids and their accuracy with the aim of solving time-dependent partial differential equations in geophysical applications. As many problems suggest the use of staggered grids we investigate different schemes for the calculation of space derivatives on two separate grids. The differential operators are explicit and local in the sense that they use only information of the function in their nearest neighborhood, so that no matrix inversion is necessary. This makes this approach well-suited for parallelization. Differential weights are obtained either with the finite-volume method or using natural neighbor coordinates. Unstructured grids have advantages concerning the simulation of complex geometries and boundaries. Our results show that while in general triangular (hexagonal) grids perform worse than standard finite-difference approaches, the effects of grid irregularities on the accuracy of the space derivatives are comparably small for realistic grids. This suggests that such a finite-difference-like approach to unstructured grids may be an alternative to other irregular grid methods such as the finite-element technique.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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A HIGH-ORDER FAST MARCHING SCHEME FOR THE LINEARIZED EIKONAL EQUATION*

JONATHAN B. FRANKLIN Stanford University, Mitchell Building Rm. 453B, 397 Panama Mall, Stanford, CA 94305, USA JERRY M. HARRIS Stanford University, Mitchell Building Rm. 321, 397 Panama Mall, Stanford, CA 94305, USA Received 14 July 1999 Revised 10 April 2000 We present a high-order upwind finite-difference scheme for solving a useful family of first-order partial differential equations, of which the linearized eikonal equation is a member. Fast solutions of the linearized eikonal equation have applications in traveltime tomography and residual migration algorithms. The technique, besides being both accurate and stable, escapes aperture limitations inherent in static marching schemes. We use a time-sequential evaluation method similar to Sethian's Fast Marching strategy to insure causal operator evaluation. We apply our technique to several complex slowness distributions, including the Marmousi model. We also use an adaptation of our technique to compute Cartesian-to-Ray coordinate transforms for the same slowness models.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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FREQUENCY DOMAIN WAVE PROPAGATION MODELING IN EXPLORATION SEISMOLOGY*

PATRICIA M. GAUZELLINO and JUAN E. SANTOSt Departamento de Geofisica Aplicada, Facultad de Ciencias Astrondmicas y Universidad National de La Plata, Paseo del Bosque s/n, La Plata (1900),

Geofisicas, Argentina

DONGWOO SHEEN Department

of Mathematics,

Seoul National

University,

Seoul 143-747,

Korea

Received 24 June 1999 Revised 17 April 2000 To evaluate the wavefield for realistic 2-D and 3-D models we used a parallel computer, employing algorithms designed specifically to profit from the parallel architecture. The numerical procedures are iterative domain decomposition algorithms employing a nonconforming finite element, which are used to discretize the viscoacoustic and viscoelastic wave equations describing wave propagation in a porous medium saturated by either a single-phase or a two-phase compressible inviscid fluid and subject to absorbing boundary conditions at the artificial boundaries. Our purpose is to establish the effect of gas, brine or oil and gas-brine or gas-oil pore fluids on seismic velocities. Numerical examples showing the implementation of the algorithm to compute crosshole seismic response of simple 2-D and 3-D hydrocarbon reservoirs are presented.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy. ^Department of Mathematics, Purdue University, West Lafayette, Indiana 47907, USA.

110 International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS

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THREE-DIMENSIONAL TIME DOMAIN MODELING OF ULTRASONIC WAVE PROPAGATION IN CONCRETE IN EXPLICIT CONSIDERATION OF AGGREGATES AND POROSITY*

FRANK SCHUBERTt and BERND KOEHLER* Fraunhofer-Institute for Nondestructive Testing (IZFP), Branch Lab Kruegerstrasse 22, D- 01326 Dresden, Germany 1schubertQeadq. izfp.fhg. de [email protected]

EADQ,

Received 20 July 1999 Revised 3 May 2000 Concrete as strongly heterogeneous and highly-packed composite material represents a very important but also very difficult object for ultrasonic nondestructive testing (NDT). Due to the high scatterer density, ultrasonic wave propagation in this material consists of a complex mixture of multiple scattering, mode conversion and diffusive energy transport. In order to obtain a better understanding of the effect of aggregates and porosity on elastic wave propagation in concrete and to optimize imaging techniques, e.g. synthetic aperture focusing technique (SAFT), 1 it is useful to model the wave propagation and scattering process explicitly in the time domain. In this paper, the three-dimensional EFIT-Code (EFIT: Elastodynamic Finite Integration Technique) 2 with periodic boundary conditions is used to model attenuation and dispersion of a plane longitudinal wave propagating in a synthetic three-dimensional concrete plate. Systematic parameter studies are carried out in order to demonstrate the effect of porosity and that of different aggregates. Finally, the simulation results are compared with former plane strain simulations, revealing significant differences in attenuation and signal-to-noise ratio between the two-dimensional and the more realistic three-dimensional case.

•Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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TIME DOMAIN MODELING OF AXISYMMETRIC WAVE PROPAGATION IN ISOTROPIC ELASTIC MEDIA WITH CEFIT — CYLINDRICAL ELASTODYNAMIC FINITE INTEGRATION TECHNIQUE*

FRANK SCHUBERT and BERND KOEHLER Praunhofer-Institute for Nondestructive Testing (IZFP), Branch Lab EADQ, Kruegerstrasse 22, D-01326 Dresden, Germany [email protected] [email protected] ALEXANDER P E I F F E R Presently at: ADtranz Daimler Chrysler Rail Systems, Am Rathenaupark, D-16761 Hennigsdorf, Germany peiffer@bigfoot. de Received 20 July 1999 Revised 3 May 2000 The Elastodynamic Finite Integration Technique (EFIT), originally developed by Fellinger et a/., 1 - 3 represents a stable and efficient numerical code to model elastic wave propagation in linearly-elastic isotropic and anisotropic, homogeneous and heterogeneous as well as dissipative and nondissipative media. In previous works, the FIT discretization of the basic equations of linear elasticity, Hooke's law and Cauchy's equation of motion, was exclusively carried out in Cartesian coordinates. For problems in cylindrical geometries it is more suitable to use cylindrical coordinates. By that, axisymmetric problems can be treated in a two-dimensional staggered grid in the r, z-plane. The paper presents an EFIT version for axisymmetric problems in cylindrical coordinates called Cylindrical EFIT (CEFIT). After demonstrating the accuracy of the numerical code by a comparison between simulation results and analytical solutions, different examples of application are given. These examples include modeling of sound fields of ultrasonic transducers, thermoelastic laser sources, geophysical borehole probes, impact-echo measurements in layered media, and load simulations of the European Spallation Source (ESS) mercury target.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

112 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

ON THE PROPAGATION OF ACOUSTIC PULSES IN POROUS RIGID MEDIA: A TIME-DOMAIN APPROACH*

Z. E. A. FELLAHt and C. DEPOLLIER* Laboratoire d'Acoustique de I'Universite du Maine UMR-CNRS IAM AveO. Messiaen, 72085 he Mans Cedex 9, Prance ^zine @laum. univ- lemans.fr ^Claude. [email protected]

6613,

Received 20 September 1999 Revised 10 March 2000 Wave propagation of acoustic waves in porous media is considered. The medium is assumed to have a rigid frame, so that the propagation takes place in the air which fills the material. The Euler equation and the constitutive relation are generalized to take into account the dispersive nature of these media. We show that the connection between the fractional calculus and the behavior of materials with memory allows to work out time domain wave equations, the coefficients of which are no longer frequency dependent. These equations are suited for direct and inverse scattering problems, and lead to the complete determination of the porous medium parameters.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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TRIANGLE-QUADRANGLE GRID METHOD FOR POROELASTIC, ELASTIC, AND ACOUSTIC WAVE EQUATIONS*

ZHANG JIANFENG Department

of Engineering Mechanics, Dalian University of Technology, Dalian 116023, P. R. China zjfhmOdlut. edu. en Received 20 September 1999 Revised 15 March 2000

A new numerical technique is developed for wave propagation in heterogeneous poroelastic media and mixed poroelastic, elastic and acoustic media. The scheme, based on a first-order hyperbolic Biot's system and a discretization mesh of triangles and quadrangles, solves the problem using integral equilibrium equations around each node, instead of satisfying Biot's differential equations at each node as in the finite-difference method. The surface topography and complex geometrical interfaces can be accurately modeled with the proposed algorithm by making the nodes of triangles and quadrangles follow the curved interfaces. The elastic (acoustic)/poroelastic interface conditions of complex geometry are introduced using the integral equilibrium equations around nodes at the interface based on the continuities of total stresses and velocities between the interface. The free-surface conditions of complex geometrical boundaries are satisfied naturally for the scheme. This work is an extension of the grid method for the heterogeneous elastic media to the heterogeneous poroelastic one. The proposed algorithm is successfully tested against an analytical solution for Lamb's problem when the algorithm is reduced to handle the elastic limit of the Biot's equations. Examples of wave propagation in a poroelastic half-space with a semi-cylindrical pit on the surface and mixed acousticporoelastic and elastic-poroelastic models with inclined interfaces are presented.

•Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

114 International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS

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ABSORBING LAYER VIA WAVE-EQUATION SPLITTING*

JOSE M. CARCIONE+ and FABIO CAVALLINI* Istituto Nazionale di Oceanografia e di Geofisica Sperimentale — OGS, Borgo Grotta Gigante 42/C, 1-34010 Sgonico {Trieste), Italy t [email protected] ' [email protected] Received 1 June 1999 Revised 22 January 2001 Modeling acoustic waves generated by a localized source is always vexed by the nagging problem of spurious reflections and wraparound arising when the wavefront reaches the boundary of the numerical mesh. This difficulty may be circumvented by using a very large computational domain, which is very inefficient, or can be tackled by using some kind of absorbing boundary technique, which has not yet found a universally satisfactory solution. In this work, the wave equation is modified by introducing a term that is nonzero only in a narrow strip near the boundary. Then, a splitting technique permits to compute part of the solution analytically (hence, at no computational cost), while an application of Weyl's formula for the exponential of a matrix leads to a secondorder accurate scheme that completes the algorithm. An application to SH seismic wave modeling shows that the performance of the present method is competitive with standard ones. Moreover, there is evidence for a potential application to the modeling of wave propagation in porous media, where stiff differential equations arise.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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OPTIMISED ABSORBING BOUNDARY CONDITIONS FOR ELASTIC-WAVE PROPAGATION*

A. LANGE, J. ZHOUt, and N. SAFFARI Department

of Mechanical Engineering, University College Torrington Place, London WC1E 7JE, UK aAange@meng. ucl.ac.uk N'[email protected]

London,

Received 29 June 1999 Revised 18 April 2000 Second-order absorbing boundary conditions for numerical modeling of elastic-wave propagation are studied. The corresponding reflection coefficients are derived, from which a necessary and sufficient condition for complete absorption at normal incidence is deduced. We define a family of absorbing boundary conditions from symmetrically specified zero reflection incidences. Conditions to avoid singular reflection coefficients are given for this case, these ensure that the solutions of the elastic wave equation also satisfy the boundary conditions. These are then optimised over a wide range of materials, and absorbing boundary conditions that give an efficient absorption for the whole range are obtained. We also compare the results with absorbing boundary conditions developed from the least-squares solution of the system requiring complete absorption at all incidences. The best set of conditions are presented and compared with Clayton and Engquist 6 (A2) condition.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy. tPresent address: Unigraphics Solutions Ltd., Parasolid Development, Cambridge, UK; E-mail: jianweiOugsolutions.com

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CONJUGATED INFINITE ELEMENTS FOR TWO-DIMENSIONAL TIME-HARMONIC ELASTODYNAMICS*

TIAGO PINTO and JEAN-PIERRE C O Y E T T E Civil Engineering Division, University catholique de Louvain, 1 Place du Levant, 1348 Louvain-la-Neuve, Belgium Received 15 July 1999 Revised 29 February 2000 Wave propagation problems in unbounded domains require the handling of appropriate radiation conditions (Sommerfeld). Various absorbing boundary conditions are available for that purpose. In a discrete finite element context, local and global Dirichlet-toNeumann (DtN) and infinite element methods have shown their efficiency for the scalar wave equation. The paper concentrates on the extension of an infinite element method to the elastodynamic vector wave equation. The extension is developed in the frequency domain for 2-D problems. The paper focuses on the development of a conjugated formulation using the Helmholtz decomposition theorem of smooth vector fields. The accuracy of the developed formulation is assessed through the study of benchmarks. The computed results are shown to be in good agreement with the analytical solution for a multi-pole field along a circular cavity and with the results produced by other numerical methods.

•Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

Inverse Problems and Tomography

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International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

RECONSTRUCTION OF LAYERED ELASTIC BOTTOM CHARACTERISTICS BY THE FREQUENCY DEPENDENCE OF SOUND REFLECTIVITY*

VLADIMIR N. FOKINt and MARGARETE S. FOKINA* Institute of Applied Physics, Russian Academy of Sciences, 46, Ulyanov Str., Nizhny Novgorod, 603950, Russia [email protected] [email protected] Received 8 July 1999 Revised 12 October 2000 The relation between the sound reflection losses measured at fixed grazing angles and the characteristics of the sediment layer and underlying half-space is considered. Based on this relation, a method of the reconstruction of the sea bottom characteristics is developed for a ocean bottom consisting of a single sediment layer overlaying a semi-infinite elastic half-space. Using this bottom model, the reconstruction of the characteristics of a layered elastic bottom is performed from the numerically simulated data with induced synthetic error.

* Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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International Journal of Computational Acoustics, Vol. 9, No. 4 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

JOINT 3D TRAVELTIME INVERSION OF P, S AND CONVERTED WAVES*

GIULIANA ROSSI and ALDO VESNAVER Istituto Nazionale di Oceanografia e di Geofisica Sperimentale — OGS, Borgo Grotta Gigante 42/c, 34010 Sgonico Trieste, Italy Received 18 June 1999 Revised 22 January 2001 Converted waves can play a basic role in the traveltime inversion of seismic waves. The sought velocity fields of P and S waves are almost decoupled, when considering pure P and S arrivals: their only connection are the possible common reflecting interfaces in the Earth. Converted waves provide new equations in the linear system to be inverted, which directly relates the two velocity fields. Since the new equations do not introduce additional unknowns, they increase the system rank or its redundancy, so making its solutions better constrained and robust.

•Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

COMPLETE FAMILIES AND RAYLEIGH OBSTACLES*

GIOVANNI F. CROSTAt Center for Electromagnetic Materials and Optical Systems, University of Massachusetts — Lowell, 206 Falmouth Hall, Lowell, MA 01854, USA crosta@galileo. eng.uml. edu Received 7 July 1999 Revised 31 January 2000 Complete families in a given function space are sets of linearly independent functions, a linear combination of which can approximate any other function with arbitrarily high accuracy. Outgoing cylindrical wave functions are one such family, used to represent the scattered wave in exterior boundary value problems for the scalar Helmholtz equation in two spatial dimensions. When the incident wave is plane and the scattered wave is represented by a series of said functions, which converges up to the boundary of the obstacle, the obstacle is said to be in the Rayleigh class. One shall further distinguish between Dirichlet-Rayleigh and Neumann-Rayleigh obstacles, according to the applicable boundary condition. Discs are trivial obstacles of these classes. Ellipses of eccentricity n such that rj2 < 1/2 were shown to be in the Dirichlet-Rayleigh class by Barantsev et al. in 1971, who used the saddle point method to asymptotically estimate the Fourier scattering coefficients. Herewith, another one parameter family of obstacles is constructed by the same method. It is also shown that the same obstacles are in the Neumann-Rayleigh class. The relevance of these results to the numerical treatment of scattering problems is briefly discussed.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy. tPermanent address: Dipartimento di Scienze dell' Ambiente e del Territorio, Universita degli Studi Milano — Bicocca 1, piazza della Scienza; I 20126 Milano, Italia, Lab. Phone: +39 02 64 47 47 34; Seer. Fax: +39 02 64 47 45 00. E-mail: [email protected]

122 International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

A SIMPLE REGULARIZATION METHOD FOR SOLVING ACOUSTICAL INVERSE SCATTERING PROBLEMS*

MICHELE PIANA INFM — Dipartimento di Fisica, Universita di Genova, via Dodecanese) 33, 1-16146 Genova, Italy Received 1 July 1999 Revised 17 April 2000 The problem of determining the shape of an object from far-field data is considered. We present a method, originally formulated in Ref. 1 and furtherly modified in Ref. 3, for the solution of this ill-posed nonlinear inverse problem whose main features are: • the method is exact, that is no low- or high-frequency approximation is considered; • it is not necessary to know the number of scatterers and whether or not the scatterers are penetrable by the waves; • if the medium is not penetrable, it is not necessary to know whether the obstacle is sound-hard or sound-soft; • in the case of an inhomogeneous scatterer, the method provides the shape of the inhomogeneity. The method is particularly simple since it requires only the solution of a linear Fredholm integral equation of the first kind whose integral kernel is the far-field pattern. T h e numerical instability due to ill-conditioning can be reduced by using regularization algorithms such as Tikhonov method where the regularization parameter is chosen by using Morozov's discrepancy principle generalized to the case where the noise affects the kernel of the integral operator.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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THE USE OF THE HERGLOTZ FUNCTION METHOD TO RECONSTRUCT OBSTACLES FROM REAL AND FROM SYNTHETIC SCATTERING DATA*

PIERLUIGI MAPONI Dipartimento

di Matematica

e Fisica, Universita di Camerino, [email protected]

62032 Camerino,

Italy

FRANCESCO ZIRILLI Dipartimento di Matematica "G. Castelnuovo", Universita di Roma "La Sapienza", 00185 Roma, Italy [email protected] Received 19 July 1999 Revised 4 March 2000 We consider the problem of the reconstruction of the shape of an obstacle from some knowledge of the scattered waves generated from the interaction of the obstacle with known incident waves. More precisely we study this inverse scattering problem considering acoustic waves or electromagnetic waves. In both cases the waves are assumed harmonic in time. The obstacle is assumed cylindrically symmetric and some special incident waves are considered. This allows us to formulate the two scattering problems, i.e. the acoustic scattering problem and the electromagnetic scattering problem, as a boundary value problem for the scalar Helmholtz equation in two independent variables. The numerical algorithms proposed are based on the Herglotz Function Method, which has been introduced by Colton and Monk. 1 We report the results obtained with these algorithms in the reconstruction of simple obstacles with Lipschitz boundary using experimental electromagnetic scattering data, that is the Ipswich Data 2 ' 3 and in the reconstruction of "multiscale obstacles" using synthetic acoustic scattering data.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

NONLINEAR INVERSION OF PIEZOELECTRICAL TRANSDUCER IMPEDANCE DATA*

LAURA CARCIONE, JOHN MOULD, V. PEREYRA, D. POWELL, and G. WOJCIK Weidlinger Associates,

4410 El Camino Real, Los Altos, California,

USA

Received 21 June 1999 Revised 8 March 2000 We describe a nonlinear least squares inversion algorithm for obtaining elastic and electromagnetic properties for piezoelectric materials from measured impedances. Richard Brent's PRAXIS, a general unconstrained minimization code is used for the nonlinear least squares fit. No explicit derivatives of the goal functional are required by this code. Bound constraints are imposed in order to limit the variability of the parameters to physically meaningful values. Since PRAXIS is an unconstrained optimization code, these constraints are introduced via a novel change of independent variables. The forward modeling is achieved by using a coupled finite element time domain code for the elastic and electro-magnetic parts of the problem. We also describe how a linearized sensitivity analysis can be used to suggest a priori which parameters can be calculated from impedances measured on a given sample. Numerical results are included.

'Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

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International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

AN ALGORITHM FOR THE FULLY NONLINEAR INVERSE SCATTERING PROBLEM AT FIXED FREQUENCY*

F. NATTERER Institut fur Numerische und instrumentelle Universitat Munster, Germany [email protected]

Mathematik,

Received 24 June 1999 Revised 5 April 2000 We reconstruct an object which is described by a complex valued function from the scattered waves generated by irradiating plane waves at fixed frequency. The scattering process is modeled by the Helmholtz equation and includes multiple scattering. We present numerical results from computer generated data.

•Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy

126 International Journal of Computational Acoustics, Vol. 9, No. 3 (2001) © IMACS

,<5?&\ | | g INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

MAXIMUM LIKELIHOOD INVERSION OF ACTIVE REVERBERATION FOR BOUNDARY LOCALIZATION ON A MOVING SONAR PLATFORM

ROBERT B. MACLEOD Naval Undersea Warfare Center, Newport R.I. 02841 USA macleodrb Gnpt. nuwc.navy.mil

This paper addresses the problem of determining the environmental parameters of an acoustic channel based on partially processed data in an active sonar system. The premise is that a system has been designed to detect and track targets and may not have an auxiliary sonar system available to make environmental assessments. In this case, the data available to the processor may be beamformed in an unfavorable direction for the assessment (or parameter estimation) that is sought. Two methods to make such an estimation will be explored, including an approximate method which can make a computationally inexpensive estimate by fitting the likelihood functions.

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International Journal of Computational Acoustics, Vol. 9, No. 2 (2001) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

MATHEMATICAL SIMULATION IN DIFFRACTION ACOUSTICAL TOMOGRAPHY WITH MULTIELEMENT TRANSCEIVER*

ALEXANDER V. OSETROV and ANDREW P. KHRENOV Electroacoustic & Ultrasonics Department, St. Petersburg State Electrotechnical University, Prof. Popov St., 5, 197376 St.-Petersburg, Russia osetrov<8osetr. usr. etu. spb.ru Received 21 June 1999 Revised 17 April 2000 The parameters of diffraction tomography methods for inhomogeneity reconstruction is investigated. For a two-dimensional case with linear multi-element transceiver one single frequency and two multi-frequency measurement schemes are introduced. For these schemes the data regions in the spatial frequency domain of inhomogeneities function are presented. The new two-stage approach is developed for resolution investigation and image quality estimation. In the first stage, it is proposed to find the resolution for ideal measurement conditions (infinite measurement aperture, ideal transducers). Then in the second stage for real measurement conditions, it is enough to determine only the degradation factor which is calculated for all measurement schemes dependent on measurement parameters. For examination of this approach also the images for complicated inhomogeneity model are calculated. It is shown that resolution and point spread functions cannot fully describe image quality, especially for complicated data regions in the spatial frequency domain of the inhomogeneities function. Many numerical examples are presented.

•Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy.

128

RADIAL ULTRASONIC TOMOGRAPHY TECHNIQUE AS A N E W METHOD OF FLAW IMAGING

ALEXANDER V. OSETROV Electroacoustic & Ultrasonics Department St. Petersburg State Electrotechnical University Prof. Popov St., 5, 197376 St.-Petersburg, Russia osetrov@osetr. usr. etu.spb.ru Received 25 July 1999 Revised 16 June 2000 The problem of a flaw position estimation in cylindrical homogeneous objects is briefly discussed. A number of SAFT algorithms for ultrasonic reconstruction are reviewed. A new method of flaw position determination is developed. Its main advantages are that this method does not require knowledge of the radius of the cylinder and of the time delay into the wedge transceiver. In spite of a lack of data it is possible to estimate with sufficient accuracy the radial position of a flaw from so-called radial tomogram. The theory of radial tomography is presented. A numerical algorithm based on Radon transformation is described. An example of a flaws radial position reconstruction is shown. The main possible application of the radial tomography technique is reconstruction of small cracks with radial orientation for cylindrical objects with unknown radii.

129

MULTIRESOLUTION IN 3D SEISMIC TOMOGRAPHY WITHIN PHYSICAL LIMITS

GUALTIERO BOHM, PAOLO GALUPPO, and ALDO VESNAVER Istituto Nazionale di Oceanografia e di Geofisica Sperimentale Borgo Grotta Gigante 4®/c, 1-34010 Trieste, Italy Received 28 July 1999 Revised 3 October 2000 In the parametric inversion of traveltime of direct and reflected arrivals, the design of the Earth model is a compromise between two opposite needs: on one hand, we look for the finest details of the geometrical and physical properties of rocks; on t h e other hand, the limited signal band-width and the mathematical ambiguities suggest us to reduce the sought unknowns. We compare here two different approaches to this problem, i.e. adaptive versus staggered grids. Adaptive grids can fit the local resolution according to different physical and mathematical criteria, as the Fresnel radius and the null space energy. Staggered grids are less flexible, but much simpler and potentially more efficient. We compare these methods both in 2D and in 3D by synthetic examples, including the E A E G / S E G salt model.

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Geoacoustic Inversion in Shallow Water Guest Editors: R. Chapman and M. Taroudakis

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International Journal of Computational Acoustics, Vol. 8, No. 2 (2000) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

OBJECTIVE FUNCTIONS FOR OCEAN ACOUSTIC INVERSION DERIVED BY LIKELIHOOD METHODS

CHRISTOPH F. MECKLENBRAUKER Forschungszentrum

Telekommunikation Wien, A-1040 Vienna, [email protected]

Austria

PETER GERSTOFT Marine Physical Laboratory, Scripps Inst. Oceanography, San Diego CA 92093-0704, gerstoft@mpl. ucsd. edu

USA

Received 13 August 1999 Revised 14 January 2000 Selection of a suitable objective function is an integral part of the inverse problem, and poor selection can have a strong influence on the inverse result. Objective functions are here derived for many practical occasions such as for single frequency and broadband, with and without knowledge of source strength, and with and without the received signal phase. These objective functions are all derived from a unified approach based on maximum likelihood and additive Gaussian noise models. The assumptions for the objective function are thus clear and the resulting estimator has good properties. From a Bayesian point of view, the solution to the inverse problem is the a posteriori probability distribution of the unknown parameters, which can be found from the likelihood function. Thus using objective functions based on likelihood functions facilitates computing the a posteriori distributions.

134 International Journal of Computational Acoustics, Vol. 8, No. 2 (2000)

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© !MACS

Igg INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

DEDUCTIVE MULTI-TONE INVERSION OF SEABED PARAMETERS

M. A. AINSLIE, R. M. HAMSON, G. D. HORSLEY, A. R. JAMES, and R. A. LAKER CORDA Ltd, Apex Tower, 7 High Street, New Maiden, Surrey, KT3 4LH, UK M. A. LEE, D. A. MILES, and S. D. RICHARDS DERA(W), Winfrith Technology Centre, Winfrith Newburgh, Dorset, DT2 8XJ, UK Received 6 August 1999 Revised 22 February 2000 An iterative matched field processing scheme is described for efficient inversion of geoacoustic parameters in shallow water using a vertical receiving array at three frequencies in the range 50-500 Hz. The method relies on the assumption that the acoustic data are sensitive to different geoacoustic parameters at different frequencies. First an exhaustive 2D search is carried out at high frequency to determine initial estimates for density and sound speed. A second 2D search follows at an intermediate frequency to determine sediment attenuation and sound speed gradient. An iteration is carried out over these first two phases until these four parameters converge. In a third phase, the low frequency data are used to search for the remaining unknown parameters (primarily sediment thickness, substrate density and substrate sound speed) with a differential evolution algorithm. Finally all three phases are repeated iteratively, in principle until a complete converged solution (a self-consistent set of all inverted parameters) is found, although for practical reasons the search is terminated before convergence is demonstrated. Tests on synthetic data are reported demonstrating the accuracy and stability of the method. Initial results for measured data are also presented.

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TOMOGRAPHIC INVERSION FOR GEOACOUSTIC PARAMETERS IN SHALLOW WATER

A. TOLSTOY ATolstoy Sciences, 8610 Battailles Court, Annandale atolstoy&ieee.org

VA 22003,

USA

Received 6 August 1999 Revised 3 December 1999 This paper examines the linearized tomographic inversion of simulated data for a shallow water, multi-array, multi-source scenario. The environments represented include simulations of (1) highly idealized constant regions as well as (2) the Haro Strait Test of June 1996 which displays range, depth, and azimuthal variability, i.e., 3-D dependence on environmental parameters where these parameters can include water depths and multiple sediment sound-speed profiles, densities, depths, and attenuations. This tomographic inversion method is independent of the number of parameters to be determined. However, the method does assume that some inversion method (such as RIGS, simulated annealing, genetic algorithms, etc.) has already estimated range-independent average source-to-receiver environmental parameters. These average parameters are then input into the tomographic inversion which relies on a matrix of path-cell distances. The matrix condition number, A, is a determining feature for the inversion accuracy where A is a function of source and receiver distributions and their subsequent path distances through the region cells. Additionally, the accuracy of the input estimates for the average geoacoustic properties is also an important factor in the final 3-D tomographic inversion accuracy. Results using this (linearized) tomography inversion method show a potential for excellent error estimates (much less than 1%) for the environmental parameters assuming exact, idealized input values. Errors are still quite reasonable (well under 10%) if more realistic, i.e., erroneous, input values are assumed. This paper will conclude with a discussion of upcoming future directions.

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INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

MATCHED FIELD TOMOGRAPHIC INVERSION TO DETERMINE RANGE DEPENDENT GEOACOUSTIC PROPERTIES

V. CORRE, N. R. CHAPMAN, and M. J. WILMUT School of Earth and Ocean Sciences, University of Victoria, P. O. Box 3055, Victoria B.C., V8W 3P6, Canada Received 5 August 1999 Revised 29 November 1999 T h e paper describes a new broadband tomographic matched field method for estimating the geoacoustic properties of a range-dependent shallow water environment. This method is designed for a multiple acoustic element configuration (several sources and vertical arrays deployed in an ocean region) in order to estimate the range and cross-range properties of the sediment over the region. The synthetic pressure fields (replicas) for the tomographic inversion are computed using a ray model. A linear processor operating in the frequency domain is used to quantify the match between replica and measured fields. This processor is based on coherent summations over frequencies and receiver pairs. The method is demonstrated for a geoacoustic ocean model simulating the environment of the Haro Strait experiment. The area is divided into cells in which the geoacoustic properties are range independent but can vary from one cell to another. The layer thickness can vary within a cell. Results are presented for the estimation of the compressional velocity and sediment layer thickness in the ideal case of a noise free synthetic data set.

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International Journal of Computational Acoustics, Vol. 8, No. 2 (2000) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

IDENTIFYING MODAL ARRIVALS IN SHALLOW WATER FOR BOTTOM GEOACOUSTIC INVERSIONS

MICHAEL I. TAROUDAKIS Institute of Applied and Computational Mathematics, Foundation for Research and Technology-Hellas, P.O. Box 1527, GR-711 10, Heraklion, Crete, Greece Department of Mathematics, University of Crete, 714 09 Heraklion, Crete, Greece [email protected]. gr Received 24 August 1999 Revised 4 January 2000 A mode identification process that can be applied to broadband acoustic transmissions in the ocean is presented. The process is associated with a modal travel time inversion scheme for geoacoustic or tomographic inversions. The process is based on the assumption that a reference (background) environment is known and the identification process is based on information on the group (modal) velocities of the reference environment only. Using two characteristic examples corresponding to shallow water environments it is shown that the identification process works well at least for the lower order modes.

138 International Journal of Computational Acoustics, Vol. 8, No. 2 (2000) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

GEOACOUSTIC TOMOGRAPHY: RANGE DEPENDENT INVERSIONS ON A SINGLE SLICE

GOPU R. P O T T Y and JAMES H. MILLER University

Department of Ocean Engineering, of Rhode Island, Narragansett, RI 02882, USA Received 24 June 1999 Revised 21 February 2000

A hybrid inversion scheme is used for the inversion of bottom geoacoustic properties using synthetic d a t a as well as broadband signals from explosive sources. This technique is shown to be effective for range dependent inversion on a single slice using synthetic and experimental data. The experimental data was acquired during the Shelf Break Primer Experiment. Time-frequency analysis was performed using wavelets. Group speeds obtained from the time-frequency scalograms were used as data for the inversion. The hybrid method consists of a Genetic Algorithm, which performs the global search, and a Levenberg-Marquardt method, which hastens the descent to the global minimum. Error estimates based on Hessians and a posteriori variances are also provided. Resolution is estimated using an a posteriori analysis.

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International Journal of Computational Acoustics, Vol. 8, No. 2 (2000) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

NONLINEAR SOLITON INTERACTION WITH ACOUSTIC SIGNALS: FOCUSING EFFECTS

O. C. RODRIGUEZ and S. JESUS UCEH-Universidade

do Algarve, Campus de Gambelas, 8000, Faro, Portugal Y. STEPHAN and X. DEMOULIN

EPSHOM/CMO,

BP426, F-29275, Brest, France M.PORTER

Science Applications

International

Corp., San Diego, USA

E. COELHO Institute

Hidrogrdfico, 1296, Lisboa,

Portugal

Received 6 August 1999 Revised 11 January 2000 The problem of nonlinear interaction of solitary wave packets with acoustic signals has been intensively studied in recent years. A key goal is to explain the observed transmission loss of shallow-water propagating signals, which has been found to be strongly time-dependent, anisotropic, and sometimes exhibited unexpected attenuation versus frequency. Much of the existing literature considers the problem of signal attenuation in a static environment, without considering additional effects arising from groups of solitons evolving both in range and time. Hydrographic and acoustic data from the INTIMATE'96 experiment clearly exhibit the effects of soliton packets. However, in contrast with reported observations of signal attenuation, the observed transmission loss shows a pronounced signal enhancement that behaves like a focusing effect. This focusing is correlated with peaks in current, temperature, and surface tide. That correlation suggests that the nonlinear interaction of solitary wave packets with acoustic signals can lead to a focusing of the signal. To clarify this issue, hydrographic data was used to generate physically consistent distributions of "soliton-like" fields of temperature and sound velocity. These distributions were then used as input for a range-dependent normal-mode model. The results strongly support the hypothesis that the soliton field causes the observed signal enhancement.

140 International Journal of Computational Acoustics, Vol. 8, No. 2 (2000) © IMACS INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION

SEAFLOOR PROPERTIES DETERMINATION FROM ACOUSTIC BACKSCATTERING AT NORMAL INCIDENCE WITH A PARAMETRIC SOURCE

ANDREA CAITI Environment ISME — Interuniversity Centre of Integrated Systems for the Marine & DII — Dip. Ing. Informazione, University of Siena ISME — c/o DSEA, Dept. Electrical Systems & Automation, University of Pisa, via Diotisalvi 2, 56100 Pisa, Italy Received 28 July 1999 Revised 9 December 1999 An inversion technique is proposed for the determination of the geoacoustic and morphological properties of the uppermost sediment layer. The methodology is based on the use of the backscattering acoustic return when the source is a parametric instrument steered at normal incidence with respect to the seafloor. The peculiarity of the parametric sonar (i.e., its narrow beam and the absence of sidelobes) allows for discriminating between the scattering effects due to surface roughness and those due to volume perturbations. The inversion procedure is based on the minimization of a discrepancy measure between d a t a and model predictions. Model predictions are obtained as time series realization of a stochastic process, modeling the backscattering process with the Kirchoff approximation for surface scattering and the small perturbation theory for volume scattering. The BoRIS code is used to generate the time series predictions. It is important to note that the model is stochastic, i.e., the model predicted time series with the same nominal parameters may differ from one realization to another. However, by use of wavelet transform of the signals involved, and measuring the data-model discrepancy in a generalized time-frequency domain, the stochasticity of the problem is greatly reduced. In particular, the wavelet transform is insensitive to different model realizations obtained with the same set of parameters, and sensitive to changes in the parameters. By appropriately weighing the discrepancy in the wavelet domain, and exploiting the properties of the parametric source, it is possible to separately recover the parameters influencing the surface backscattering (acoustic impedance and surface roughness) and those influencing the volume backscattering (P-wave attenuation and volume inhomogeneity), avoiding ambiguities and nonuniqueness problems. The approach proposed requires, however, a precise calibration of the parametric sonar, in terms of source level and beam pattern. Comparison of inversion results with independently measured ground truth at three different sites in the Mediterranean Sea are reported.

Theoretical and Computational Acoustics'99

The ICTCA conference provides an interdisciplinary forum for active researchers in academia and industry who are of varying backgrounds to discuss the state-of-the-art developments and results in theoretical and computational acoustics and related topics. The papers presented at the meeting cover acoustical problems of common interest across disciplines and their accurate mathematical and numerical modelling. The present book collects papers that were presented at the 4th meeting and printed in the Journal of Computational Acoustics. There are about 120 full research articles on various subjects, such as wave propagation theory and numerical modelling, sound propagation, vibrations and noise generation, underwater acoustics, engineering seismology, ultrasonic field synthesis and modelling, as well as computational methods, inverse problems and tomography, shallow water acoustics and environmental/bottom parameter extraction. A CD-Rom is attached that allows readers to browse through articles and print those of interest to them.

ISBN 981-238-447-2

v.worldscientific.com 5332 he

9 "789812"384478"