Professional Level Rock Physics for Seismic Amplitude Interpretation
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1.1 Introduction The aim of rock physics in the oil and gas industry is to provide models with which to predict and interpret seismic effects related to lithology and fluid. A key aim (and one that has been justified in many areas) is to enhance the efficiency of oil and gas production as well as impacting the risk on drilling outcomes. The initial part of the course presents the broad context of 'rock physics' including background theory, analysis techniques, the practice of calibration and issues in applying rock physics in prospect evaluation. The philosophicai standpoint adopted here is to start simple and increase the complexity as needed. Applying rock physics in seismic interpretation requires a knowledge of numerous disciplines (geology, geophysics, petrophysics and rock physics (sensu strictu), see figure 1.1) and consequently It is a vast subject area. The possibilities for an advanced treatment of rock physics interpretation are considerable. Each area (e.g. Processing for AVO, Inversion, Well ties etc) really requires a separate course. Building on the basics the latter part of this course focuses on a deeper understanding of the elements of creating seismic models and workflows that can rock physics knowledge into practice.
Averaged log data
Quantitative Calibration
Single Interface First Order Modelling
Prediction of seismic diagnostics
1 D Rock Physics AVO
Simple
"'''"''00
VS predictiOn
interference mOOels
Facies Characterisation Probability
Wedge modelling
Matching Goodoes of fit Error estimation
Seismiclo-Well Ties
[==-{~~~~~ Depth to Time
Fine
layer
__ -
models Layered models Quantitative Calibration
----j Refteclion series ONset synthetics AIEl
Off>elto_
Figure 1.1. Rock physics elements in seismic interpretation.
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J1;o ?
Well with water bearing reservoir
I Vp
rhob $
Reservoir and fluid parameters
~
.----
/
Gassmann Vp,
~s, p
Vs Prediction
~ Real rock QC
Water, 011, gas bearing reservOir
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Reflectivity Model
PredIcted Effects
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-
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Angles and offsets
""_~.~ --_._.,-~ .........- ..... -
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Seismic Interpretation
Figure 1.2. Quick/ook workflow,
The basic level of using rock physics in interpreting seismic signatures is the 'Quick look' workflow (see figure 1.2), This involves single interface (half space) modelling with no wavelet or propogation effects is a useful approach for understanding the primary rock physics elements of the model, it is fast and can be applied in situations where the target reservoir is reasonably thick (in terms of the seismic resolution), The example in figure 1.3 shows a situation where the application of the 'Quicklook' workflow proved invaluable in recognising seismic diagnostics related to the presence of hydrocarbons.
0.15 0.10.J.------J---+---+----+------j 0.05
Ii.
k~~=;;:::=+--+-===I====t
Top Reservoir Response water
oil
o.oo.J----f_=-+----.:::::::O+-===*=-c:::.--j 00
03
04
05
Legend: -0.15 L _ _---l
-L
L _ _---l_ _---.J
Shale ==> Oil sand Shale ==> Wlr sand Oil sand ==> Wlr sand
sin 2(theta1}
Figure 1.3. An example of the application of the 'quick/oak' workflow to identify an oil accumulation. ~),
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The next level is to make models that have thin layers and that not only address reflectivity but also impedance (figure 1.4), thereby addressing the prediction of rock properties.
Log based rock physics ~
Real rock QC and rock modelling
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Figure 1.4. Seismic Modelling for Reflectivity and Impedance Interpretation. ~lI. GEOSCIENCE 0:.Q'TRAINING
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Professional Level Rock Physics for Seismic Amplitude Interpretation
2. Fundamentals
Rock Physics Associates
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2.1 Seismic Basics 2.2 Approach to Seismic Modelling 2.3 Elastic Parameters 2.4 Modelling Reflectivity 2.5 Types of Seismic Models 2.6 Relating Seismic Data to Models
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Fundamentals
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Fundamentals 2.1 Seismic Basics
2.1 Seismic Basics The figure below (figure 2.1) shows a conventional surface-towed gun and streamer arrangement typical of seismic acquisition in the marine environment. Each shot sends a wave of sound energy into the subsurface. Each receiver on the cable records energy that has been refiected from geological interfaces, and the path of the sound energy from source to receiver is described by rays that are perpendicular to the seismic wavefront. Notice that the reflections recorded on the near receivers have lower reflection angles (termed 'angles of incidence') than the far receivers. The lower part of the figure illustrates the recorded energy from the blue and red reflections in terms of distance between the source and receiver (offset) and the time taken to travel from the gun to the receiver via the reflecting boundary. This is called a 'shot gather' display. The reflected energy is shown as a 'wiggle' display and the reflection from the isolated boundary is describing the shape of the seismic pulse (or 'wavelet') at the boundary. Owing to the differences in travel time, the energy related to the geological boundary has a curved or hyperbolic form with the energy recorded on far offsets shown at greater times. Seismic Geometry ~
~
Far
Near Receiver cable
l:"'dGi~'-----~-----~--
Ray paths .' perpendicular to wavefronts
.~; /
Angle of incidence increases with offset
8i
Shot-receiver offset Reflection hyperbola time
----
Amplitude of reflection related 10
1. rock contrast across boundary, and 2. decrease in amplitude due to spherical divergence (squared function of time)
Figure 2.1 The Origin of the Seismic Gather.
The magnitude of the energy in the reflection (or 'amplitude') is related to the contrast in acoustic parameters across the boundary but also to the fact that energy decreases with increasing distance travelled (a phenomonen called 'spherical divergence').
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Fundamentals 2.1 Seismic Basics
Seismic acquisition comprises many shots and receiver recordings, with each receiver recording every shot. Figure 2.2 illustrates that each receiver is recording reflections from different subsurface locations for every shot. Thus a 'shot gather' is a mix of energy from different subsurface locations. As such it is of minimal value to the interpreter. If it is assumed that the earth is made up of flat lying layers then it is possible to re-arrange the reflection energy in terms of line location or 'common mid point' (figure 2.2). A common mid point (CMP) gather is made up of traces that relate to the same subsurface point.
Acquisition
CMP record
....
Figure 2.2. Marine Seismic Geometry and the Common Mid Point (CMP). offset
offset
- --
• Apply gain function 10 remove effect of spherical divergence
• Remove noise and mute out unwanted data • Apply spatial/geometric corrections (pre-stack migration)
~
• Calculate velocities 10 (Iallen gather (NMO)
Raw gather Figure 2.3. Overview of the Processing of Seismic Gathers.
4
In order for the seismic data to be interpretable the gathers need to be processed. Figure 2.3 gives a generalised overview of the various steps that are taken to give good quality seismic gathers. These issues are discussed in further detail in Section 11.
© Rock Physics Associates Ltd 2007
The goal of the processor and the desired output for the interpreter is a gather which shows amplitude variation with offset (AVO) that is related only to geology.
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Fundamentals 2.1 Seismic Basics
When seismic gathers have been correctly processed, seismic sections can be generated from 'stacking' the traces (i.e. summing and normalising). Stacking is a very useful process as it improves the signal-to-noise (S:N) ratio of the data. Figure 2.4 illustrates a stacking methodology which is very popular for seismic AVO (Amplitude Versus Offset) analysis. Seismic sections have been created by stacking traces within defined zones (the way these zones are defined is discussed in Section 2.6). In this case a 'near' and 'far' set of traces have been stacked. The benefits of this approach in AVO analysis are described in Section 11. In many cases there is only one seismic section available. This is usually derived from all useable traces in the gather and this is referred to as a 'Full Stack'.
Figure 2.4. Gather Display and Near (81O-1800m) (Top) and Far (1960-3710m) (Bottom) Stacks.
One of the first questions that an interpreter asks when beginning an interpretation project is 'What do the troughs and peaks represent?' The answer to this question is not always as straightforward as might be imagined. A part of the answer lies in the 'Polarity convention' used to display the data.
fe6U<.. " rOli/!VL l){/tE~ '7
!(/twt-W
SEG (American) Polarity Convention
!!hCfe. - 4Jtaf Jir
"Normal"
Geological Interface Model
Causal (recorded) wavelet
"Reverse" Causal
Symmetrical (processed) wavelet
(recorded) wavelet
Symmetrical (processed) wavelet
soft
I
hard
Trough
"Reverse"
"Normal"
North Sea UK Polarity Convention Figure 2.5 Reflections, Wavelets amd Polarity.
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Fundamentals 2.1 Seismic Basics 2.2 Approach to Seismic Modelling
The term 'Polarity Convention' effectively describes the way that compressional energy is displayed. In Europe, 'normal' polarity is commonly understood to mean 'negative number on tape = a compression = a trough seismic loop' (note that colour is not part of the convention). 'Reverse polarity' describes the situation where a peak represents a compression. European reverse polarity is normal according to SEG (American) polarity. Some interpreters simplistically approach the problem in terms of 'does a trough represent a soft to hard or hard to soft boundary?'. This approach is valid if the wavelet has a reasonable degree of symmetry. As is described in Section 5, polarity convention is no guarantee of wavelet shape in the data.
2.2 Approach to Seismic Modelling The propagation of seismic energy is a complex phenomonen. Sheriff's (1975) diagram (figure 2.6) is a useful illustration of the numerous factors involved. The problem with this complexity, so far as the seismic interpreter is concerned, is that even if a model could be built that accurately described all the complexity of seismic propogation, the data would generally not be available to parameterise it. Thus the approach to interpreting seismic in terms of a model has been to use a simple model that be readily parameterised.
Superimposed Noise
Geophone Sensitivity
Instrument Response
Source Strength and Coupling Array Directivity
Absorption
Spherical Divergence
Scattering
Reflector interierence
Reflection
~c=o=eff~iC~ie~n~t __~~,L.:""'_/~;(F-_-=RefieClorCurvature and Rugosity Small scale horizontal layering
O
Transverse Isotropy
Elasti~ Isotropy
~aB
Figure 2.6. Factors Affecting Seismic Amplitude (modified after Sheriff 1975).
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Aspects of Seismic Amplitude Interpretation
R=I,-1 1 I, + II
/, = II 1+ R
l-R
Reflectivity (Isotropic/elastic)
Impedance
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Geology
Seismic Data
Tools
I
Minerals
Pre-stack data quality
I
Porosity
Well Ties Amplitude/angle projections Net pay analysis Trace inversion Coloured inversion Gassmann modelling fluid substitution Rock modelling lithology substitution 1D and 2D modelling
Zoeppritz Aki-Richards (3 term) .......3 term EI
Pore geometry
;)
:1)
Shuey (Aki-Rich 2 term) ... 2 term EI Modified Shuey............... EEI
I
Layering Scaling Fluid fill
Elastic properties
AI,SI,PR,A.p,llp
/
~
Calibration to wells (wavelet shape) (matching statistics)
G'dePrl.ecl Eriulk /u-FQA/C£. -= E'El Av!~- W~fw~ttM~en~
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Fundamentals 2.2 Approach to Seismic Modelling
The simple model that underlies most seismic interpretation effectively has two components. The first describes rocks as isotropic (i.e. they have the same properties irrespective of the direction in which these properties are measured) and elastic (i.e. deformation of the rock is linearly and instantaneously related to the stress applied). Thus the stress induced on a rock by a seismic wave will result only in a momentary deformation or particle displacement. This model has the benefit that, in addition to density, only two elastic parameters are required to describe the behaviour of a rock.
Isotropy
Elasticity
Parameters measured in any direction give same results
C33
stress
The Convolution Model
+
*
noise
Wavelet Reflection Series from well data
Seismic Trace
Figure 2.7. The Components of the Interpreters Model.
The second component of the simple model is what is called the 'convolutional model'. This describes the seismic signal as the convolution of the seismic wavelet and the reflection coefficient (a scaling function related to the contrast of rock properties across a boundary, see later in this section). Thus for example, boundaries that have very soft rocks lying over very hard rocks will have high positive reflection coefficients. This concept has already been implicitly introduced in Section 2.1. and is central to well ties and seismic inversion (discussed in Sections 7 and 10). As will be seen, although simple this model is actually very useful.
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Fundamentals 2.3 Elastic Parameters
2.3 Elastic Parameters There are a variety of parameters that describe the behaviour of rocks in the presence of stress. Two parameters that will be central to the discussion of rock physics modelling (Section 8) are the bulk modulus and the shear modulus.
l'po;kCl ~hI'21/t'ht 1/ J Mvk. (I!) (j
Stress (S) = Force (kg-m/sec 2 ) I Area (m 2 )
7'
Shear stress = stress parallel to a surface
,,
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f - T'---f----(
.,
\
no change in volume
\
V
\
\
------
\
t
Figure 2.8. Volume and shape changes in rocks under stress.
S
Equation 2.1. Bulk modulus.
K=-(!'.V/V)
compressibility
1
=K
shear stress J1 = shear strain
The bulk modulus controls the response of the rock to compressive stresses (figure 2.8 and equations 2.1 and 2.2), and as such it is an indicator of the extent to which the rock can be squashed. The shear modulus (equation 2.3)controls the response of a rock to shear translational stresses (e.g. parallel to bedding surfaces) and as such it indicates the rigidity of the rock. Bulk and shear moduli increase with compaction.
Equation 2.2. Bulk modulus and Compressibility.
Equation 2.3. Shear modulus.
A more intuitive way for most exploration geoscientists to understand the role of elastic moduli on rock properties is to reiate them to rock velocity and density, parameters that are commonly measured in the borehole (equations 2.4 and 2.5).
Vp2 = Ksat + 'Ill P
Equation 2.4. Compressional velocity: a function of bulk and shear modulus and density.
Equation 2.5. Shear velocity: a function of shear modulus and density.
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Fundamentals 2.3 Elastic Parameters
Compressional velocity, shear velocity and density are the 3 key parameters that are needed to understand AVO behaviour. Compressional velocities are related to particle displacement in the direction of the propagation of the wave whereas shear waves are related to particle displacement perpendicular to the direction of wave motion. Rock bulk density is simply the addition of the various density components (i.e. fluid and matrix as shown in equation 2.6). Bulk Density (Pb) Shear Velocity (Vs)
Compressional Velocity (Vp)
-
Matrix (ma)
time
~
~
-
Particle motion in direction of wave propagation
Porosity (fluid)
Particle motion perpendicular to wave propagation
Figure 2.9. Vp, Vs and Density.
/
Pb = (q>PfI) + «1-q» Pma) .
Equation 2.6 Density Equation.
Below are shown some of the other elastic parameters described in terms of both bulk and shear
(:,gW;)/U..l51~t.,
moduli and Vp, Vs and density.
Youngs Modulus (E) =
Stress (S)
=
9Kfl
Strain (e)
-:t!V,vc.t iu7J
Lambda (J,,)
=K-2ll!3 = (Vp'-2Vs')p
Equation 2.8. Lambda.
Equation 2.7. Youngs Modulus.
Awlw
Poisson ratio(cr)
= ----1'1111
M modulus (M) = K+4fl/3 =Vp'p
Transverse strain
=
Longitudinal strain
=
3K-2fl 2(3K+fl)
Equation 2.9. M Modulus. Equation 2.10. Poisson Ratio. ~l& GEOSCIENCE &~TRAINING
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Fundamentals 2.3 Elastic Parameters
( eJ .X (Xp J
05- Vs
<J = 3K - 211 =
pI(
2(3K + 11)
1-
Equation 2.11. Poisson Ratio
v
2(1-0) (1-20)
= I_VLP2---,(---,1-_2---,0)
2(1-0)
s
Equation 2.12 VS from Vp and a
Equation 2.13 Vp/Vs from a
Poisson ratio is an important parameter in AVO as the contrast in Poisson ratio across a boundary can have a large control on the rate of change of amplitude with offset. Some interpreters prefer to refer to the Vp/Vs ratio rather than Poisson ratio. For most purposes it doesn't matter which paramater is used. The relationship of Vp/Vs and Poisson ratio is shown in figure 2.10. 11 10 9
(/)
~
>
8 7
-
6 5 4
I
3 2 1
.-'
-/-
a a
0.1
0.2
0.3
0.4
0.5
Poisson Ratio Figure 2.10. Poisson Ratio vs Vp/Vs.
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Fundamentals 2.4 Modelling Seismic Reflectivity
2.4 Modelling Seismic Reflectivity The acoustic impedance contrast across a boundary is an important control on seismic reflectivity. The contrast in impedance defines the reflection coefficient (equation 2.14). In practical terms, equation 2.14 describes the reflectivity only when seismic waves are normally incident (i.e. perpendicular) to the boundary. To describe the seismic reflectivity recorded with source and receivers in different locations requires further equations.
Rc
Al -AI,
z =----''---'Al z + AI,
Equation 2.14. Reflection Coefficient.
Receiver cable
Amplitude Varying with Angle (highly non-linear)
r:/"
Crilical Angle
R,fl,
T"Mm'"od Compressional
Iu.-=---- I
h I~ l-.L. I
{!.vi-· ~
~
0'
I
9,
.,
"'D'
9,
Reflected Shear
Transmitted Shear
Vp 12800fUs Vs 8000fUs Rho 2.4g/cc
Vp 21000ft/s Vs 12000flfs Rho 2.65g1cc
After Dobrin 1960
Figure 2.12. Modelling the Seismic Response: Zoeppritz' Equations
(re-drawn after Dobrin, 1960).
The phenomonen of amplitude varying with angle (AVA) is described by the Zoeppritz (1919) equations. Figure 2.12 illustrates that these equations describe the partitioning of energy at a boundary into four types of energy (reflected and refracted compressional (or P wave) and reflected and refracted shear (or 5 wave) energy). For the purposes of P-wave seismic interpretation it is the reflected compressional energy that is important. However, both P-wave and S-wave models would be important for the interpretation of OBC (ocean bottom cable) data.
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Fundamentals 2.4 Modelling Seismic Reflectivity
The example in figure 2.12 shows a limestone overlying a granite, and although this is generally not a usual hydrocarbon target scenario it serves to illustrate some important points. The reflected compressional energy initially decreases but at a certain angle the amplitude dramatically increases. The angle at which this effect takes place is called the 'critical angle' (see equation 2.16). Notice also that the transmitted compressional energy is reduced to zero at the critical angle. At this point incident energy is converted into refractions that travel along the interface to re-emerge later at the critical angle. Figure 2.13 and equation 2.15 illustrate the relationships between the incident and transmitted angles as described by Snell's Law. Equation 2.15 shows that the critical angle (derived from Snell's law) is dependent on the velocity contrast across a boundary.
Vp,. VS 1, P1
Figure 2.13. Incident and Transmission Angles.
SinS 2
SinS,
V2
V, Equation 2.16. The Critical Angle.
Equation 2.15. Snells Law.
Unfortunately the Zoeppritz equations are complex and do not give an intuitive feel of how rock properties are impacting the change of amplitude with angle. For this reason many authors have made approximations to the equations. One of the best approximations is the Bortfeld (1961) approximation shown in equation 2.17. A comparison of the Zoeppritz equation with the Bortfeld approximation (figure 2.14) shows a close fit.
Rc
:::::: a.5ln
[
vP, P, cose,] + (Sine, -Vp, P,
case2
VPl
J[
In P2
]
VS,2_ VS 22
2+
(vp,
In -
Vp,
J-InP1 vP,vs, J ~VPl vS 2
Equation 2.17. Bortfelds Approximation.
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Fundamentals 2.4 Modelling Seismic Reflectivity
08 0.7 'E 06
I
I
zoeppritz bortfeld
.~ 0.5
!J
IE
"o 0.4 <.J 0.3 ,§ 0.2 ~ 0.1 0-0.1 0
/'
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-
0.1
0.2
0.3
0.4
0.5
0.6
Sin 28 Vp
Vs
Rhob
3901 6401
upper layer lower layer
2438 3658
2.4 2.65
Figure 2.14. Comparison of Bortfelds approximation and the Zoeppritz Equations.
A more readily understandable approximation was derived by Aki and Richards (1980) and this is shown in equation 2.18. The approximation comprises 3 terms, with the 'A' term bein9 the zero angle reflection coefficient related to the contrast of acoustic impedance. The non-zero offset component of the reflectivity is given by the 'B' and 'C' terms.
R(O) = A + Bsin ~
e + Csin ~ (} tan
Vpp = Acoustic Impedance
1 (}
Zero angle of incidence
A=..!-(f::..VP +8P ) 2 Vp P
- 2V,.
RO
L\V.
= VP2P2
- VPIPI
Vpzpz
+ VPIPI
!:!.p
_ 2 V.
Non-z.," compon.nts
I
~ ~ation
=..!.- f::..Vp
to Zoeppritz because it is more intuitive and leads the way 10 linearizing AVO
Vp
2
""
(V,. )' (V,) -l()' V,.) ~ I
B _ f::..V/, -4 V,
C
_
Equation 2.18. The Aki-Richards (1980) 3 Term Approximation.
A
II./J.tf~ ee()f
,/V
____ . [?,:=.
~
-
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Fundamentals 2.4 Modelling Seismic Reflectivity
A further approximation, that led to the dramatic use of AVO technology in the 1980's, was suggested by Shuey (1985). Basically Shuey's equation (equation 2.19) comprises the first two terms of th Aki-Richards approximation previousiy discussed.
R(e) = A + B sin 2e Equation 2.19. Shueys Equation (2 term Aki-Richards).
Slope=B or Gradient
+ AorRO
Sin'8
Fi9ure 2.15. 2 Term Linearized AVO
The important aspect of this equation is that it describes amplitude as a linear function of Sin 2S (fi9ure 2.15). The linear regression of Sin 2 S and seismic amplitude defines two AVO parameters, the intercept and gradient. For reference figure 2.16 shows the relationship between angle and sin squared of the angle. The rise in the use of AVO technology in the 1990's was built on the rapid computation, and subsequent analysis, of the intercept and gradient.
1.00
/'
0.90
/
0.80 0.70
/
0.60
/
(0 N
<::
i:ii
0.50
/
0.40
/
0.30 0.20
/
0.10
/'
0.00 o
10
20
30
40
50
60
70
80
90
Angle (e) Figure 2.16. Incidence Angle vs. Sin'S.
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Fundamentals 2.4 Modelling Reflectivity
Another, rock property oriented, approximation to the Zoeppritz equations has been derived by Hilterman (2001. Equation 2.20). This approximation is effectively the same as the 2 term Shuey equation but it is arranged to highlight the fact that reflectivity is related to two components, an acoustic impedance contrast and a Poisson ratio contrast.
Rc(9)
/
\
Zero incidence (Acoustic impedance) component
'/)ou, ,',ve:l.eo! ~
"t/.uU
1!J}u,/0,<.)(.,#
i
Non-zero incidence (Poisson ratio) component
Equation 2.20 Hiltermans (2 Term) Approximation.
The reader needs to be aware that this approach to linearizing AVO is generally applicable over only a limited range of angles (figure 2.17). Although the angles at which the 2 term approximation deviates from the 3 term and Zoeppritz depends very much on the nature of the contrasts across a boundary, it is generally assumed that the 2 term approximation holds to about 30' angle of incidence. Whilst this has generally been appropriate for conventional cable lengths it may not be for the long offset cables that are now being widely used in the industry. Usual range of seismic acquisition angles
..
0.2
1:: Q) 'u IE Q) 0
0 c:
0.1 0
--...
-0.1 -0.2
0
U -0.3 Q) <= Q)
0::
f,
........... ~
f ~
-0.4
-
Aki-R 2 term
-
Aki-R 3 term
-
Bortfeld
-
Hilt. approx
~
-0.5 -0.6
o
10
20
30
40
50
60
Incidence angle
Shale Gas sand
Vp
Vs
Rhob
AI
2438
1006 1700
2.25 1.85
5486
2600
4810
Figure 2.17. Comparison of Bortfeld, Aki-Richards (2 and 3 Term).
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15
Fundamentals 2.5 Types of Seismic Models
2.5. Types of Seismic Models Offset algorithms such as the Zoeppritz equations and their various approximations are used to model the offset response. Various types of seismic models can be made and (with increasing time and effort) they are (figure 2.18): 1. Single interface model
-
vtJf..,d
/oR
1/.
,e4a,;,ItII~ 'fU,'d.-
I
uJ,0 AJr
J'
I
_
)
:t'N.et9 "1
h.O "- ()
2. Wedge Model 3. Layered model using log data
Single Interface Model Shale
+ Ampl.O f - - - - - -
Sand
Wedge Model
Layered Model
Figure 2.18. Types of Seismic Models.
The simplest model (and arguably the most important) is the single interface model, basically the result of inputting Vp, Vs and density for upper and lower layers into Zoeppritz or a similar numerical algorithm. Obviously in any modelling situation the effects of layering (interference and propagation effects) are important to understand but it is best to start with the simplest model. The wedge model is a very powerful tool that describes the interaction of reflections of two converging interfaces (see Section 6). Layered models address the interference effects of fine layering and various modes of sound propagation (see Section 9).
16
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Fundamentals 2.6 Relating Seismic Data to Models
2.6. Relating Seismic Data to Models In order to relate reflectivity models calculated in terms of angle to seismic data measured in offset, a conversion scheme for converting offset to angle is required (figure 2.19).
Amplitude Varying with Offset 10000
""00 '0000
•
5000
0
E
0
0. E -5000
•
"' .,,,,,,
.
·'0000
...•
·10000
0
'"
'000
''''
2000
."-t
''''
3000
Amplitude Varying with Angle 03 0.2
Model from well data
0'
-
r--.. ·0.2 ~.3
o
0.05
r-.
035
0.'
0.15
0.'
Sin2e
Figure 2.19. The Issue of Relating Offset to Sin'(J.
Converting seismic offset information to angle requires data from a velocity model. This velocity model is generally taken from seismic time and velocity measurements. Equation 2.21 is a widely used calculator for converting offset to angle. Figure 2.20 shows a corrected gather with angle 'mutes' generated using equation 2.21.
.... .,., .... •.
offset
210
3110
'.>00
....... .... ,.. "., ~
.m 0.100
..
,>00
, ,., .m
.... ..
1.600
5
'.>00
,
where: x=offset (metres) To=zero offset two way travel time (sees) Vrms=rms velocity at To (m/s) Vi=interval velocity at To (m/s) Equation 2.21. Angles from Offsets via Velocities.
,, "., ,>00 ".,
,~
'.m u., 'lOO
.......
,
,,
Figure 2.20. A Gather with Angle Mutes Displayed.
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Fundamentals 2.6 Relating Seismic Data to Models
The following illustrations provide background to the inputs of equation 2.21.
V
The RMS velocity is a function of the travel time through multiple layers (equation 2.22) and is similar (but generally faster) than the average velocity (equation 2.23)
_[Iv;2!;]!
rms -
~
""'~
Equation 2.22. RMS Velocity
Equation 2.23. Average Velocity
Equation 2.21 is related to the description of a reflection hyperbolae (Figure 2.21). Figure 2.21 shows the simplest case for understanding the description of reflection travel times, where the target depth is greater than the cable length (the 'small spread approximation' of Yilmaz (1987).
o
o
Offset 2000
1000
500
Tx=
1000
~
T02+~2 Vrms
-
TO '" lime at zero offset Tx "lime at offset )( Vrms" the foot mean square velocity
,
/
2000
_
TO=2~00ms
X
,
llT,(NMO)= To +--, -To
--------
2500
3000
Where
x" offset
I
1500
In order to flatten the reflection (i.e. perform normal moveout (NMO)) the hyperbolae equation is re-arranged (equation 2.24).
4000
3000
V rms
---..
Equation 2.24. Normal Moveout Equation (assuming simple geology).
Vrms - 2000 mls
Figure 2.21. Description of Reflector Hyperbola (assuming simple geology).
In practice, velocities are picked so that the gather is flattened and the maximum coherency is achieved (figure 2.22). The maximum coherency stacking velocities are a first order approximation for RMS velocities given limited offsets and simple geology. The reader is referred to AI-Chalabi (1974) for a detailed discussion of seismic and well velocities. Interval velocity can be derived from seismic velocities using the Dix (1955) equation (equation 2.25), although it should be applied to a time window of greater than 200ms.
_.
NMO Corrected Gather
-
,~
--
Velocity Spectra
OIP_ "'0
- '~III~"ii\nrrmmr_mrrmrmJ " ••
'U '1M
•••••
,
UM
••
•• 'M
,. ,~
'M
,-
,~
'M
Figure. 2.22 Velocity Analysis
2
V; = T,V,ms' -T,Vnns, [
18
T2 -T,
2 ]0,5
Equation 2.25. The Dix (1955) Equation.
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Fundamentals 2.6 Relating Seismic Data to Models
Figure 2.23 illustrates an approach to the calculation of offsets from angles.
Z
=
twt (ms) * Vp (m/s)
2000
Figure 2.23. Converting Angle to Offset (e.g. using checkshot surveys).
Once the offsets have been converted to angles then the corrected gathers can be combined in a number of ways. Figure 2.24 illustrates the derivation of intercept and gradient (using the 2 term linear AVO equations). The analysis of RO and G is a subject for Section 11. 2000
4000
Amp = RO + Gsin 2
6000
~
10000
Rfl
I
t
5000
e
•
y= -77725x - 3768.8 0
.E
I...
• • •
to '" -10000
~
~
"
'0
0. -5000 E
.
c-=- ~ K.0j I~
~ ....., • "
-15000
"". •
Sin
.......
.~
-20000
o
0.05
0.1
0.15
0.2
0.25
Figure 2.24. Deriving Intercept and Gradient from Seismic.
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Fundamentals 2.6. Relating Seismic Data to Models
An alternative approach is to stack the data according to angle ranges. Figure 2.25 shows an example of angle' stacks. It is common to stack the data into near and far angles, although the use of 3 angie ranges is also popular (of course, regressions using 3 points are likely to be more accurate than using 2 points). In many instances it is the number of available traces with good S:N that dictates whether to use 2 or 3 stacks. Seismic Gather
Near Angle Stack
Far Angle Stack
Near traces Far traces
50
15°
5-15°
35°
15-35°
Figure 2.25. Angle Stacks.
Figure 2.26 presents an overview of the modelled relationship between the AVO plot and seismic sections at various angles. For the purposes of calibrating seismic angle stacks to the AVO plot it can be considered that each angle stack represents reflectivity at a particular (effective) angle. Theoretically the average angle of a stack can be derived by averaging the Sin'S values of each trace in the stack (Connolly (1998)). Given the accuracy of the velocity model that is used to predict angles, in practice it can usually be assumed that the mid angle of the range of angles included in the angle stack is the effective angle of the stack.
,
The Convolution Model
-
-
-
• -
-
+
noise
=
Wavelel
-
Reflection Series from well data
~
•
Figure 2.26. The AVO Plot and Seismic Reflectivity.
Seismic
~
o
"".".. ".. "I
oo;~l'~' 1".
•
O. 15
r--+---+----j
_ 0.10 t---+--~t---1
;;
/--------'----1 Ii 0.00 t--~-~-~-___1
~ 0.05
150;~~1
~10 ==-"S;;::-----'1
0
),005 • ,0 10
~ 15 ~20
300;~1
, 15
0.20 / - - - - ; - - - - - - - ,
". " - - - - - - - -
20
30
,~.
20
30
---"''',<::''''--
-----angle of iocidence 0
Lithology
VsNp
shale gas sand
0.413 0.654
© Rock Physics Associates Ltd 2007
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Fundamentals 2.6 Relating Seismic Data to Models
AI
--+
Rc
AI --+
Rc
If the processor has been successful!!!. .... Figure 2.27. Scaling - the key to seismic calibration
The ultimate goal of the seismic interpreter is to relate the changes in seismic amplitude to changes in rock properties that can then be used in planning successful drilling locations. A key aspect of this is to appreciate the scaling of reflection coefficient to seismic amplitude (figure 2.27). This is done principally through well ties (section 7). Correct scaling is critical for seismic inversion (chapter 10). Problems with scaling can seriously compromise the quantitative interpretation of seismic amplitude.
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Professional Level Rock Physics for Seismic Amplitude Interpretation
3. Rock Properties and AVO 3.1 AVO Response Description 3.2 Rock Property Controls on the AVO Response Rock Physics Associates
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Rock Properties & AVO
2
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Rock Properties & AVO 3.1 AVO Response Description
3.1 AVO Response Description There are a number of terms that are generally applied to AVO responses. First of all we need to establish the difference between negative and positive AVO and negative and positive gradients. As shown earlier, gradients are calculated as the difference in reflection coefficient divided by the difference in sine squared of the angles. On the AVO plot negative gradients are inclined from upper left to lower right, whilst positive gradients are inclined from upper right to iower left (figure 3.1). 'Positive AVO' describes the situation where there is, in an absolute sense, an increase in amplitude with offset irrespective of the sign of the reflection, whereas 'negative AVO' describes the situation where amplitudes are decreasing with offset.
AI Contrast /
+ve AVO +ve gradient
-ve AVO - - - -ve gradient
o ~
+veAVO -ve gradient -veAVO +ve gradient
Figure 3.1. Some AVO Terminology.
Fundamental to the use of the AVO plot in interpretation is the characterisation of different types of response, depending on lithology and fluid type. Rutherford & Williams (1989) first classified shale/brine sand AVA responses into three types (I,ll & III) depending on the impedance contrast between the shale and the sand. Type I responses are characterised by a positive contrast in impedance (i.e. the sand impedance is larger than the shale impedance), together with a decreasing amplitude with angle. Class II responses have small normal incidence amplitudes (positive or negative), but the AVO effect leads to high negative amplitudes at far offsets.
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Rock Properties & AVO 3.1 AVO Response Descriptions
Ross and Kinman (1995) have suggested that the small positive Class II responses should be termed Class IIp, owing to the phase reversal that is inherent in this response, and that the term Class II should apply to the small negative impedance contrast response. Class III responses have large negative impedance contrasts and the negative gradient leads to increasing amplitude with angle (see figure 3.2 and table 3.1).
Acoustic Impedance Contrast
RO - Controlled by contrast of acoustic impendance across the boundary
+ •
/
Class 1
0
Ql
"0 :J
e (deg)
""c-
o
E
/
/J/
IF'
..
Class 3
~
Class 4
Figure 3.2. The AVO Classes (modified after Rutherford and Williams, .1989)
A further class of AVO response (Class IV) was introduced by Castagna and Swan (1997). This response has a strong negative reflection coefficient with decreasing amplitude with angle.
Class
Gradient
Absolute Amplitudes
Notes
Far < RO
May have phase
+ve RO,
-
I
reversal +ve RO,
lip
-
Far> RO
Phase reversal
II
-
Far> RO
No amplitude atRO
III
-
Far> RO
Relatively high amplitude at RO
IV
+
Far < RO
Very high amplitude at RO
Table 3.1. Characteristics of Top Sand AVO Responses.
4
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Practical Polarity Conventions and AVO Classes
_ Rock Physics Associates
Hard response AI
:. ~r .: -.
SEG normal '+'
v.e
11
~ //~ive
+ve standard polarity
UK normal polarity
Ref!. -
+
+ Class 1
w
o
::J
I...J
a.. ~
Soft response
AI
-.
SEG normal +ve standard polarity
UK normal polarity
Ref!.
.: ~ l :. -
SEG normal=+ve no=peak=compression=hard response UK polarity = -ve no=trough=compression=hard response SEG normal = UK reverse UK normal=SEG reverse
«
Class 3
+
Class 4
Note - colour is strictly not part of the polarity definition - presented here are the usual use of the colours - but eg in South Africa they use SEG normal but colour the peak red
Rock Properties &. AVO 3.1 AVO Response Description
G
RO
r
./ \
Class I
~II ~IIP Figure 3.3. Introducing the AVO Crossplot.
It was realised that the crossplot of intercept and gradient provided a useful tool for describing and analysing responses (Castagna 1993, Foster et al 1993). The Rutherford and Williams (top sand) classes (I-IV) plot in distinct areas of the plot (see figure 3.3). The use of the plot for analysing seismic AVO is discussed in detail in Section 11.
Class lip
Class 111111
Offset
Near traces Far traces
• f--- Top Oil sand
Top Brine sand
Class IV
Class I
Top Limestone
• Figure 3.4. Some Examples of Different AVO Responses.
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Rock Properties & AVO 3.1 AVO Response Description
Figure 3.4 illustrates some real examples of the different classes of AVO responses. It must be noted that there is nothing unique about these responses in terms of them being related to specific geological scenarios. As will be discussed what is important in AVO analysis (section 11) is not the Class of the response but relative differences in AVO responses. Rutherford and Williams (1989) effectively only classified the AVO responses with the top of sand units. There are other responses related to the base of the sands and to hydrocarbon contacts. AVO modeis of hydrocarbon contacts always have positive intercepts and show increasing amplitude with angie (figure 3.5a). In real data, contacts can be difficult to interpret due to interference with bedding reflections.
".,
A. Hydrocarbon contacts
"~~-------I
+
Top Gas sand (red)
Gas waler contact (blue)
B. Base of sand response +
Figure 3.5. Other types of AVO responses. /(
/.JlL
{I
5'f
Figure 3.5b shows a base of sand AVO response
Class Vp If Rutherford and Williams had thought of other lithological boundaries other than shale/sand interfaces and had had the AVO crossplot as an analysis tool they would probably not have stopped at 4 classes. Figure 3.6 illustrates the additional types of AVO responses that in sand/shale sequences are related to base sand and hydrocarbon contact responses.
Class V
~\~ G
Ii ~~~VI RO
Figure 3.6. Incorporating Other Responses into the AVO
Crossplot.
6
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Rock Properties & AVO 3.2 Rock Property Controls on the AVO Response
3.2 Rock Property Controls on AVO 3.2.1 Ranges of Parameters for Common Sedimentary Rocks The AVO phenonomen is driven by contrasts in acoustic impedance and Poisson ratio. Figure 3.7 gives a variety of piots that illustrate the ranges of elastic parameters for commonly occuring sedimentary rocks.
A
8 -,_,--_---r"''''_--,-::-,..,,------'-Aj''n'''hyc;dc-;'ite
7
Dol mite
·•· ...16 ....
-'.
"
B
-I-'c..,,·..et.---+---+"-'D".,I,,/;.,",eS".l{o"'.~o!.--"'-'I,;1f::'",-/j -. /
I:
Sail
···...
1~.
/
andst
n·~······ / .
_"E, 25+--+-+-:r"S1' 3: ++===:===:===::~"~"'~f.(::A:·~~.::~:0=.4=. .~.
/ /
Z....
... /..< .......
...~
1.5
.
2
2.2
2.4
2.6
2.8
+---+''''f''''..-..zl~.....c:...I-",..r.."'---+---+---1 !r./"
+--,,,>1"t---+--+--+--+--+---I O+--+--+--+--t---+---+----I 1
3.0
345
2
Density (glee)
.2
7
8
(dashed lines = Poisson ratio)
0.5 Coal
-:\
'"
0.4
OJ
0:
c 0.3 0
'"
'" '0 Q.
6
Vp (km/s)
(dashed lines = AI (km/s.g/cc)
C
045
..t-.."..-. ' 4----1
0.5
o +--+--+--+--+--+--+----1 1.8
....•.<J-I'?
~ 2+--+--..:.-,>..+J~"'..+ .--,,.-f-.-...-
1+--t---1--+-+-+--t---1 1.6
n··';uz",-"",'!-·_·-:o/-",-"-1"--:cl
.
~
8
"7't~7"'/c_:l4:-.::c---Fsh=al.::...e j-;--+.._...-l ....
2 +'_':;...1-.-+.'"" .. Coa /'
+--+----1--+---+-.../-,"".'d..7'-:;""~.'-1 ,
4
+-:----11-'...-=<":+..__----=-+----"'-+-/..-,";.:."/'7 -. ...'-...-...17'..'-...-1
3
,--,--,--,-----.--.--,.-:O .. 0-3--:l ....
4.5 -I-'--I-'-+-+-+---I-;o".t7 .... ..·-+'.""./.:"'0;-;;1.3 ..
6+--+----"+-:-,---+--+----f7>..,.,-j't--+i
~
5
"•..20
~
Salt
0.2
V
\< """"
Limestone
.2: . Anhydrite I
~ Dolomite
~Shale
1-0.
0.1
I Sandstone
I
o o
5
10
15
20
25
Acoustic Impedance (km/s.gfcc)
Figure 3.7. Ranges of Parameters for Common Sedimentary Rocks (brine-bearing). After Castagna, 1993.
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Rock Properties & AVO 3.2 Rock Property Controls on the AVO Response
Several points can be made regarding Figure 3.7: The various rocks have a large degree of overlap in terms of veiocity and density o Coais are generally very low density and velocity, and would usually be represented on seismic by high amplitude negative reflections o On the other hand limestones, dolomites and anhydrites usually have very high densities and velocities. One exception is chalks where the range of velocity and density can be similar to those of sands and shales. o In terms of Vp versus Vs, sands and shales show a similar (high angle) trend, but with sands having higher shear velocities for the same compressional velocity than shales o On the Vp versus Vs plot limestones, dolomites and anhydrites have lower slopes and higher Poisson ratios at low porosities (i.e. at high Vp) than sand. o First order sands and shales show increasing Poisson ratio with increasing porosity (decreasing acoustic impedance). o Limestones, dolomites and anhydrites either show decreasing Poisson ratio with increasing porosity or a relatively invariant Poisson ratio across a range of porosities. o
3.2.2 The Effect of Burial Probably the most important control on the elastic parameters of sedimentary rocks is porosity. Figure 3.8 illustrates several first order effects of compaction (i.e. porosity reduction with increasing depth of burial). Firstly there is always a first order relationship between acoustic impedance (AI) and porosity, the exact form of the relationship being dependent on mineralogy and pore geometry. In most basins there is a relative change in acoustic impedance between shales and sands with depth. In the shaliow part of a basin the shales compact rapidly and have higher acoustic impedances than the sands, whereas in the deeper section the reverse is found. + "b"
AI
,.-1"fOlN, t
I'
&iliuJj
--\+-_'a' __ crossover
z
S)~3g% (
"a"
81.wat~. ~ "!(JI)'j Ii'
Q. " Sand a
Poisson
Ratio
....
Shale a
'
'e, '
Shale b
AI
-~'eQuartz Acoustic
Impedance Figure 3.8. The Effect of Compaction (depth) on Brine-filled Sandstones and
Shales.
8
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Rock Properties & AVO 3.2 Rock Property Controls on the AVO Response
Thus, at a certain depth (dependent upon the sedimentology and history of the basin) there is a crossover in the impedance of sands and shales. This means that a shallow (high porosity) sand will have a Ciass III top sand response, whereas a deep (low porosity) sand will have a Class I response (figure 3.B). Class IIp responses characterise the zone of crossover. The decrease in acoustic impedance with depth (for both sands and shales) is also usually associated with a decrease in the Poisson ratio (figure 3.7).
,
500 -
Mech anica!
1000
camp action domin ales
-
The general trends shown in Figure 3.8 are seldom seen so clearly. Often, variations in AI related to sedimentological variability are superimposed on the overall trend.
~
E
~
-
.<:
c- 1500
D
t-
Ol
Sa nd/shale Vp cro ssover
Sand
0
Shale
2500
Onset of
~-..
2000 I-
1
\
cementation Che mical camp action domi nates
)
I
,
2
3
At a certain depth, cementation serves to reduce the porosity of the sands dramatically. Consequently the compressional wave velocity dramatically increases (figure 3.Bb).
4
Vp FIgure 3.8b. Velocity Depth Trends for Sands and Shales Palaeogene offshore Norway (modified after Avseth 2000)
3.2.3. The Effect of Fluid Fill The effect of adding gas (or indeed any hydrocarbon) to the sands described in figure 3.8 is to reduce the acoustic impedance and the Poisson ratio. Usually gases have a bigger effect than oils, although in many deep basin situations the effect of light oils and condensates is very similar to gas (the effects of various fluids is discussed in more detail in Section B). Notice in figure 3.9 that the reduction in AI and PR becomes less with decreasing porosity. Water
Q
....•
--'-
Poisson Ratio
.
Shale 'a'
~ Shale 'b'
Sand ./a.•
Gas sand 'a'
....
Sand 'b'
;-
Gas sand 'b'
".
Porosity
/
········.oual1z
Acoustic Impedance Figure 3.9. Porosity
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Fluid Fill in Sandstones ©Rock Physics Associates Ltd 2007
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Rock Properties & AVO 3.2 Rock Property Controls on the AVO Response
Figure 3.10 illustrates the AVO responses for a shallow sand which changes in its porosity. This illustration basically describes the rock property reasoning behind AVO analysis. The effect of increasing porosity in a brine saturated (clean) sand is to increase the Poisson ratio. If the overlying shale is the same in each case the higher porosity sand will have a lower slope on the AVO plot (due to a lower contrast in Poisson ratio) than the lower porosity sand. If the brine is replaced by gas in the lower porosity sand then the effect is to increase the (negative) amplitude and steepen the AVO gradient (owing to the increased contrast in Poisson ratio).
•
Water
• PR
Porosity
Water
•;'
Gas sand
Porosity
•
Quartz
AI +
Shalel brine
sand responses Decreased contrast in PR flattens the gradient
Increased contrast in PR steepens the gradient
Figure 3.10. The Effect of Fluid Fill in Shallow Sandstones.
G + +
RO
/
Lithological trend
Theoretically, then, the porosity and gas effects are different. Chiburis (1992) noticed that the ratio of the AVO response and the background response decreases with angle (or offset) in the case of the high porosity sand but it increases in the case of the gas sand. Another way of visualising this differential AVO effect is to use the AVO cross plot (figure 3.10).
AVO Anomaly
aM dW~l
.'/<-Of/e
/o;A-:f N fi..,
Figure 3.11. AVO Crossplot showing the definition of an AVO anomaly.
Figure 3.11 illustrates that if it were possible to define a 'background trend' which defines brine saturated responses, then the gas sand would show up as an AVO anomaly (i.e. the gas sand response falls to the lower left of the background trend). This is fine in theory; in practice (Section 11) seismic noise and other lithological effects can complicate the picture significantly. 10
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Rock Properties & AVO 3.2 Rock Property Controls on the AVO Response
0.75 0.50 0.25 f -
-"
r:: 'C
34% porosity shallow sand
0.00
"'
•
~
t:l
-0.25
~
• Brine sand
.
/
• Gas sand
••.....
-0.50
r-....
18% porosity (deep) sand -0.75 -0.75
-050
-0.25
0.00
0.50
0.25
0.75
Intercept Figure 3.12. Magnitude of an AVO Anomaly is Related to Porosity.
r{/.(G; !ii!ylk.e.
!~
If/O
f.;ivil J.R
aAl7 S,!~-,
tfO'
The magnitude of AVO anomalies is directly related to porosity. Figure 3.12 shows that the magnitude of the separation of the brine and gas points on the AVO crossplot is much less in the case of the deep (compacted) 18% porosity sand. Thus it is potentially much more difficult to use AVO analysis techniques with low porosity rocks.
Interlaces upper shale shale shale shale 9 . . . . 34 18
•
0.3
o
30
0.4
0.5
0.6
0.7
0.8
0.9
45
9
lower
18 w 189 34w 349 18 w 34 w
1.0
90
Angle of incidence Figure 3.13. A 3 term AVO Model of North Sea Chalks with Different Porosities. (Note that the reflectiVity curves are terminated at the critical angle)
It is generally held that AVO techniques are less useful in areas of carbonates. From a theoretical
point of view, however, it is possible to demonstrate that there are significant differential AVO effects in many carbonates (figure 3.13).
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Rock Properties & AVO 3.2 Rock Property Controls on the AVO Response
n
¢
ofiYIJ-RCiA fDfl.O>
ell;;, Ii' ,J 110 Q.,ijoiy J-.I f
/(c/pj'e ,tOf/(;
r'/;/ ve,e)" tlOlv£
wrll k!tbJ k- /1-(' - IU-Y0 0IVl.{/
0.75 0.50
• Brine sand
0.25
34% porosity chalk
'E
" 0.00 '6
'"
I
~
C)
-0.25
•
-0.50 -0.75 -0.75
-0.50
-0.25
•
0.00
• Gas sand
I
18% porosity ch alk
•
~
0.25
0.50
0.75
Intercept
RO and G calculated from 0-30 0 Figure 3.J4. AVO Crossplot of Chalk Data in Figure 3.13.
A crossplot derived from the data in figure 3.13 is shown in figure 3.14. Notice that the magnitude of the anomaly at 34% porosity is much less than the sandstone model in figure 3.12., but the anomaly associated with the 18% chalk case is greater than the sandstone model.
Tight Ims Porous Dolomite (phi=20%)
Rc
0 -0.05
-0.15 -0.25 -0.35
Brine bearing dolomite
I_---~ ~-----_-........Gas bearing dolomite 10
20
30
40
50
Angle of Incidence Figure 3. J5. A Carbonate Example from Onshore Canada (redrawn after Li et ai, 2003).
12
Another carbonate example with a demonstrable differential AVO effect is shown in figure 3.15, based on the work by Li et al (2003) who discuss the application of AVO techniques in the hard rocks of Western Canada. The problem with carbonates is that while gradient differences due to fluid are often less than for clastic sediments, the petrographic (lithological) variations can be far greater than clastics. In practice this gives rise to interpretation ambiguity (see Eberli et ai, 2003, for a discussion of carbonate fabrics).
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Rock Properties & AVO 3.2 Rock Property Controls on the AVO Response
3.2.4. The Effects of Pore Geometry and Rock Fabric Pore geometry and rock fabric are important factors in addition to porosity. Flat or crack-like pores make the rock softer, whereas rounded or equant pores make the rock harder (figure 3.16). This is true for all rocks, including fractured limestone and granite. Soft sands have more compressible (flatter) pores
stiff AI
PR soft
Porosity
Porosity
"5'0'
Figure 3.:16. Pore Geometry Effects on AI and PRo
s'l>lI e01e
'1
iJl
'! Y
I'
II
4fUe..
A common manifestation of this generai effect is the differences between cemented and uncemented sands (figure 3.17). Cement gives the pores greater stiffness whilst uncemented sands are characterised by less stiff pore geometries and a greater number of flatter pore types (such as microcracks). U
"'"
8000
~ e
6000
~
0.5
10000
'\
•
~
§
4000
u
',5\
0.4
"
o
~
-Uncemente
-Cemented
~
£
£
2000
0.3
,;-
e
/
0.2 0.1
o
:I
o
o
o 0.2
04
06
o
0.2
Porosity
.....-
---
04
06
Porosity 0.5
----+- Water
0.4
"-
0.3
1"'-
02
.............
0.1
• Quarrz o
o
10000 15000 5000 Acoustic Impedance (mls.glee)
20000
Figure 3.17. Cemented versus Uncemented Sands (data from Dvorkin et aI, 2002).
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Rock Properties & AVO 3.2 Rock Property Controls on the AVO Response
Figure 3.17a. Velocity vs porosity characteristics of brine bearing siliclastic
6000
sediments (modified after Avseth et al 2005) Voigt average
5000
<>
W
]. 2:-
4000
-
~
" '" a.
08
°0
~
'u g >
o
3000
-
2000
-
~
'.~ROCk stiffening through 0
o§J <>
The broader context for the effects of pore geometry and rock fabric is illustrated in figure 3.17a. On the porosity vs compressional velocity plot, rocks fall within an envelope defined by an upper Voigt bound (arithmetic averaging of mineral and pore space parameters) and a lower Reuss bound (harmonic averaging of mineral and pore space parameters) (see section 8 for more discussion on mixing approaches). With changing porosity, rocks tend to fall along either harmonic (Reuss type) mixing lines (related to sorting) or linear (modified Voigt) trends (related to diagenesis).
I
•
compaction and diagenesis
·~crea5e in sorting ~~\ ~itical porosity for sand
.1.
f Reuss average
<>
1000
0
20
o
60
40
100
60
Porosity %
•
Suspensions Sand-day mixtures
•
Sand
•
Clay-free sandslone
o
Clay-bearing sandslooe
Another example of the role of pore geometry as well as rock fabric is the effect of the shale component on sandstones. Shales can occupy different iocations within sandstones (figure 3.18). This fact is very important when trying to forward-model the velocities of sandstones (Sams & Andrea, 2001).
o •
Sandstone Clay
7.2
AI
Laminated
• •.
8
Vshrws 1.
•
••
llJl: ":4)( ~><"x x1a 'Ax
0.• 0.8
x
0.7
::.: 11'/
6.4
Dispersed 5.6
0.6 0.5
Adding shale softens the rock
0.4
- Ie rock becomes more
0.3
compressible decreases bulk
4.8
0.2 0.1
modulus
Framework Structural
Grain boundary
'0.
0.1
0.2
0.5
0.'
O.
Porosity
Figure 3.18. Shale Types and Location
(after Minear, 1982).
0.3
Figure 3.19. Effect of Framework Shales in a Jurassic Reservoir Sand.
Structural shales or framework shales have the effect of reducing the strength of the rock frame. Acoustic impedance decreases with increasing shale content in this situation (figure 3.19). The Poisson ratio would be increased relative to a clean sand with a similar porosity.
14
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Rock Properties &. AVO 3.2 Rock Property Controls on the AVO Response
However when the porosity of a sandstone is decreased due to the fact that shale is occupying the pore space there is no simple relationship between acoustic impedance and porosity. The experiments of Marion et al (1992) illustrated what happens in this situation (figure 3.20).
Sandy, Shaley Sand ..
Sandy Shale, Shale
Ii
c=
7500
.y
..
7000
I
~
6500
\
6000 5500
" "-...
't
_ Sandy shale
I
Shaley sa nd I
San d
5000 4500
•
sha'i
4000
o
0.3
0.2
0.1
0.4
Phi Figure 3.20. The Effect of Dispersed Shale on Sandstone Properties (modified after Marion et ai, 1992).
The effect of the initial increment of shale in the pore space is to reduce the porosity and increase the acoustic impedance. When the pore space is fUlly occupied with shale the trend changes as further increments of shale add to the rock frame and serve to soften it, thereby reducing the acoustic impedance (figures 3.20 and 3.21). In terms of Poisson ratio, the sandy shales have a much flatter rate of change of Poisson ratio with porosity than a clean sand. In fact the trend can become negative (figure 3.22). AI
PHIT 0.4
1.
0.9
0.35
Clean sands
0
Effeclof dispersed shale in increasing
0.6
impedance
0.6
0.3 0.25
0.5
0.2
Vsh RPA
I
•4
-
.Q
16
'"w
o
o. 3
~
0
w '0
011111
a. o. 2
8'~ a
"
.4
I
Shaley sand trend 0 0
0
0 .3
~ :'
vr-'
0 .2
Clean sand trend - -
0.4
0.15 0.1
•,
VSHGR
0.3
1--+-4"e-p--+=--
0.05
Shales
-+--+-......+--+>--";d!i"'*'"""'=-. 0.1
o 5.
6.
0.2
7.
a
a
0 10.
11.
12.
13.
14.
1
'. .,
15.
0.2
03
Porosity
.
os 0
Acoustic Impedance
AI
Figure 3.21. An Example of the Effect of Dispersed Shales.
0 .1
•
Figure 3.22. An Example of Clean Sand and Dispersed Shale Trends.
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Rock Properties & AVO 3.2 Rock Property Controls on the AVO Response
3.2.5. The Effects of Pressure Variations in pressure can have a profound effect upon the AVO response. Figure 3.23 defines some of the terms associated with pressure. In a 'normally' pressured situation the reservoir (or pore) pressure follows the hydrostatic gradient. If the sand becomes enclosed and is buried, the fluid bears part of the load and the reservoir pressure increases. The difference between the reservoir pressure and the overburden pressure (effectively related to the weight of sediment above the reservoir) is the 'effective' pressure. Overpressuring of the reservoir leads to a lowering of the effective pressure.
Pe Pp Depth
\---,,'-"<:--- Top overpressure
::sa c PR
Brine sand Gas sand
Overburden gradient -1 psi/ft
Pe Hydrostatic gradient -0.43psi/ft
Pp Figure 3.23. The Effect of Pressure.
Laboratory experiments have shown that compressional velocity is directly related to effective pressure but in a non-linear way. Overpressuring will lead to a dramatic decrease in compressional velocity (and acoustic impedance). Poisson ratio is relatively insensitive to effective pressure in the case of brine saturated sands, but is very sensitive in the case of gas sands (Dvorkin et ai,
1999). Thus, if it were possible to invert the seismic for Poisson ratio (see Section 11), this might be one way of detecting hydrocarbon sands where a preViously consolidated rock has been overpressured. Experience shows that this is possible only with good quality seismic and appropriate well calibration. In terms of reflectivity, it would be wrong to assume that the differential avo effect would be greater in an overpressured situation. Figure 3.24 illustrates a modelled case where, owing to lithology as well as fluid changes the differential AVO (indicated by the separation of the blue and red curves) is less for the overpressured case.
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Rock Properties & AVO 3.2 Rock Property Controls on the AVO Response
.
•
.,
0
Normally pressured sand
000 0
Shale/brine sand
"
Shale/gas sand .~
000
Overpressured sand 0.10 ~
000
,
,
,
,
.(1,10
•.00
..,
•
, ___ Shalelbrine sand
""Shale/gas sand
Figure 3.24. An Example of the Effect of Overpressure on AVO Response.
In concluson, there are many parameters that can influence the AVO response. The reader is encouraged not to make assumptions about the probable relationship between rock properties and AVO response, but to make models.
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Professional Level Rock Physics for Seismic Amplitude Interpretation
4. Rock Physics, AVO and Seismic Interpretation
Rock Physics Associates
4.1 Seismic Interpretation and AVO 4.2 Trend Curves and the Stratigraphic Context of AVO Models 4.3 Some Examples
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Rock Physics, AVO &. Seismic Interpretation
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Rock Physics, AVO &. Seismic Interpretation 4.1. Seismic Interpretation and AVO
4.1. Seismic Interpretation and AVO In order to interpret amplitudes on seismic sections the interpreter needs to understand the likely effects of lithology and fluid. Modelling therefore is an important component of the interpretation as is understanding the relationship between the seismic data available (range of offsets etc) and the AVO models. Several examples are shown in figure 4.1 of single interface models and the predicted relative amplitudes around an anticline model.
...,
.,.
Impedance
..,. ..,•
• tJ.
Gas sand &ine sand
~.~
1iJ'
J JI JjjJJJjJJJJJJJJJJJJJ]JJ1J 11111
II
I•
0.00
Gas water contact
40-
II
•..•
....,.,.
..-v
20
I'
•
•
0
ShaleJbrine sand
Shalelgas sand
jJjjJ
1111!1 11111 Blue=hard response
Figure 4.1. Class II! Gas Sand - Bright Spot Scenario.
Figure 4.1 illustrates the relationship between the AVO plot of a shallow shale/brine and shale/gas sand and the relative amplitudes evident on two angle stack sections. The model sections show that the brightening response of the gas is evident on both sections but is more evident at greater angles. This is also true of the gas water contact. In fact as a rule, an interpreter is more likely to see fluid-related effects on the far angle stack. The amplitude of the brine sands will be very low on both sections.
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. .' ....
Rock Physics, AVO & Seismic Interpretation 4.1 Seismic Interpretation and AVO
30
. 10
"
Imped~
I
" .~
•• •• •.• " " •
M-
Oil waler contact
I
/'
,
--. '--- ,
:-----.
--
.'.
•
Shalelbtine sand
•.,
Shale/oil san d
-,
Phase reversal
30 degrees
Figure 4.2. Class IIp Oil Sand - Dim Spot and Phase Reversal Scenario.
Class IIp scenarios can give rise to dramatically different seismic sections depending on the average angle of the stack. Figure 4.2 shows a situation where the shale/brine sand response is effectively Class I whereas the effect of oil in the sand is to create a Class IIp AVO response. On the 10 degree section the effect of the oil is to create a subtle dimming of the amplitudes. However, owing to the AVO effects the top of the reservoir on the far angle section is represented by a 'soft' reflection (i.e. there is a phase reversal effect). As with the bright spot case (figure 4.1) the hydrocarbon contact is most evident on the far angle section.
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Rock Physics, AVO & Seismic Interpretation 4.1. Seismic Interpretation and AVO
10
30
" I '0
Impod-
c0 j
l
Shale Oil sand
,~:::- ___
• •" • •"'
"" ,",
Brine sand
/ ../
r--. •
Shale/brine sand
"'
Shale/oil sand
., '"
•"
Oilwaterconlad
I
~
I ~'.
Positive reflection 'Dim spot'
Figure 4.3. Class I Oil sand - Dim Spot Scenario.
In figure 4.3 the shale/brine and shale/oil sand are both Class I AVO responses, with the shale/oil sand response having a steeper gradient and a lower intercept. The fluid effects are very subtle on the near angle section, with a slight lowering of the amplitude. Reflectivity on the far angle section is very weak. In fact owing to the AVO effect the top reservoir is not evident as a clear reflection. It is relatively easy in these instances for the interpreter to pick across the oil-water contact and miss the hydrocarbon effect.
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Rock Physics, AVO & Seismic Interpretation 4.2 Trend Curves and the Stratigraphic Context of AVO Models
4.2 Trend Curves and the Stratigraphic Context of AVO Models In exploration it is important to understand the AVO responses in the context of the basin being explored. A useful tool is the trend curve illustrating the general relationship of rock properties and lithology with depth (figure 4.4). Acoustic Impedance
Poisson Ratio
o SOOO 10000 o """',,------,
~ <':
o
1000
f-----\c----\Ir------1
1000
2000
f------'He-----1
2000
3000
f---t++----1
4000
f---t-\-1c-1
5000
o
0.1
Total Porosity
0.2 0.3 0.4 0.5
o
1/1
I
1000
VI
/
0204060
II /
2000
!
3000
4000
4000
f---I------\-tH
5000
5000
6000 ' -_ _"-_---..J
6000
6000
.......
1/
-
brine sands
-
shales
-
gas sands
Figure 4.4. Trend Curves for an area of the Gulf of Mexico (constructed from Gregory, 1977).
Care needs to be taken when generating these types of curves, particuiarly with regard to the integrity of the input data and the averaging procedure adopted. Stratigraphy, pressures and rock fabric are all factors that need to be taken into account.
+ Stack Response Brine
Oil
Gas
;.
~
>
---.--..
•
G
gas
oil
Sand 1
Sand 2 Brine
-
,
~
....
Stack Response Brine
Oil
~
,
Stack Response
bnne
Oil
~
£
Gas-
Sand
+
Sand
2
3
Gas / ' / , ~
~
0. Q)
o
Sand 3
Sand 1
RO Figure 4.5. An Example of Rock Physics and Stratigraphy.
The example in figure 4.5 (from a passive margin setting) illustrates the effect of compaction and local overpressuring on the AVO response. Three sands are located at different depths, with the shallowest and deepest of the sands being normally pressured whereas the middle sand is located in an overpressured zone.
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Rock Physics, AVO &. Seismic Interpretation 4.3. Some Examples
The importance of understanding the stratigraphic framework cannot be stressed too highly. Any uncertainty in the stratigraphic context of AVO responses reduces the interpreter's ability to attach significance to observed seismic effects.
4.3 Some Examples The examples discussed below are all related to migrated full stack interpretation
4.3.1. Classic Gas Sand Bright Spot Figure 4.6 shows a classic gas sand bright spot from a sand/shale sequence. The top brine sand reflection is Class I (hard reflection shown as red) whereas the gas sand is Class III (soft reflection shown as black). A phase reversal marks the edge of the gas accumulation and the gas-water contact is significantly brighter than the brine sand reflection. Notice that the gas water contact is pushed down in time owing to the extremely slow velocity of the gas sand
•
Top brine sand
I Effective Angle
+ Interpretation model
!
GWC
E::::=:::::::::~""" Top Brine Sand Top Gas Sand
Figure 4.6. Bright spot gas sand with phase reversal at the contact and a time sag (after
Cowan et at 1998)
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Rock Physics, AVO &. Seismic Interpretation 4.3 Some Examples
4.3.2. Class IIp Oil Sand Class IIp scenarios are among the most subtle situations to interpret, and it is quite easy to get it wrong. Figure 4.7 shows an example where the top of the reservoir reflector is very weak owing to to the presence of hydrocarbons. Without the rock physics model as a gUide it is possible to pick the top sand across the oil water contact reflector and in the process significantly underestimating the size of the potential trap. The presence of reflector terminations as weil as an apparent thickening of the isochore between the two continuous black peak reflections are additional indications of the presence of hydrocarbons. II';
+
Effective Angle
1
rl.-~?__;;;;:;==-owc ~
..... Brine sand
~in2e Oil Sand
Figure 4.7. An example of a Class Illl Dim Spot.
Hydrocarbon contacts are not always very clear. They may be spiit up into segments (owing to interference effects) and sometimes the main seismic effect is the presence of terminations. In the case of oil water contacts, they should be flat or nearly so in two way time, but obviously depth conversion needs to be taken into account before making a contact interpretation
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Rock Physics, AVO &. Seismic Interpretation 4.3. Some Examples
4.3.3. Phase Reversal in Chalk The chalk example in figures 4.8 and 4.9 shows the role of lithology variations in the seismic response. The interpreter is primarily looking for indicators of porosity. A phase reversal of the top chalk reflector is one diagnostic for recognising the presence of high porosity chalks, aithough it is not always obvious exactly where it occurs. Owing to the large possible variation in porosity, a hydrocarbon interpretation on the basis of amplitude alone is not really possible. Figure 4.8. Seismic Section and Acoustic Impedance Inversion showing
Phase Reversal in High Porosity Chalks (after Pearce and Ozdemir, 1993).
• Relatively large change in impedance related to porosity
Effective Angle
r--:1
18% porosity (brine)
Sin1Q
~===~~ Relatively small change in impedance related to pore geometry and fluid fill Lower limit of data " points Impedance of
overlying Shale Top Chalk
=Trough Porosity
/
~
40% porosity (brine) 40% porosity (oil)
First order trend of AI and PHI
I,.~~~
-35%
Figure 4.9. Rock Model Explaining Top Chalk Phase Reversal
(based on Campbell & Gravdal, 1995).
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Rock Physics, AVO & Seismic Interpretation 4.3 Some Examples
4.3.4. Amplitudes and Structure Given the fact there are many reasons why a particular amplitude or set of amplitude relationships may be present on seismic, additional confidence in a hydrocarbon interpretation is usually sought in terms of the fit of the amplitude changes in relation to structure.
Low amplitudes
High amplitudes
\
~
Figure 4.10. A Far Offset Amplitude Map shoWing a Class I Dim Spot Corresponding to Structural Closure.
In some situations there is a clear coincidence of amplitude changes at the top reservoir and a hydrocarbon contact at a particular depth. Locally these effects may be coincident with the time structure (figure 4.10). Determining the correspondence of amplitude with structure is more practicable in 4-way dip rather than stratigraphic closure scenarios. Figure 4.11 shows two trapping scenarios with similar rock physics models (but different seismic diagnostics). stack ampitude - brine sands
stack amplilude
- bme sands
.1""-------R0
.... 1 -
brine sand
~2"",_-=;;;:::::Sj=n2~e 1
-
brine sand
oil sand
slack amplitude
- 011 sands
apparent thickerW1g 01 iSOChOte
top reservoir dim spot
~----
~~1--~ ~
tarmlnatiOfls
high amplitude biine sands
flat spot (owe
~ :::::-r ~~"pdIP.""'OOI ___
I
phase change
level of contact
low amplitude brine sands
Figure 4.11. Amplitude Diagnostics in Class II and IIp Scenarios - 4-way Dip and Stratigraphic Closure.
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Rock Physics, AVO & Seismic Interpretation 4.3. Some Examples
The example on the left in figure 4.11 shows a 4-way dip structure with a Class IIp oil sand response. The hydrocarbon accumulation is revealed by at least three separate effects on the seismic. The example on the right Is from a different basin and a slightly higher porosity of the sand that results In a Class II oil sand. In this case the trap is stratigraphic and is revealed by a phase reversal from a positive brine reflection to a negative oil sand reflection which has a consistent down-dip location around the structure. So there tend to be fewer diagnostic indicators with stratigraphic traps, and in practice it is more straightforward to demonstrate amplitude consistency with closure in the 4-way dip case. With 2D data It can be an impossible task to show consistency of amplitude and closure on stratigraphic traps.
Schematic depth structure (contours at 100ft intervals) (modified after Newton and Flanagan. 1993)
Figure 4.J2. A Flat Spot associated with a Stratigraphic Trap.
The most difficult situation in which to interpret the significance of amplitudes is where there is a localised (stratigraphic) bright spot that may be related to sand (see figure 4.12), but where there may be limited indicators of a hydrocarbon origin such as change in down-dip amplitudes or clear conformance to structure.
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Rock Physics, AVO & Seismic Interpretation 4.3 Some Examples
NW
..
W~I
lOCation
SE
Even with 3D data, care must be taken to account for possible lithological explanations before assigning high significance to an amplitude conformance effect (e.g. Luchford, 2001, figure 4.13).
Well location
Figure 4.J3. Bright spot - showing amplitude conformance? (after
Luchford, 2001).
Although the well encountered a 10ft oil column the bright spot in figure 4.13 shows locally very strong correspondence of amplitude with structure, but this is probably related to the presence of a channelised sand that is draped by a very hard shale. There is no apparent up-dip correspondence to structure.
SW
NE
SE
NW
Figure 4.J4. A bright spot showing good conformance to structure (after Luchford, 2001)
This is contrasted with a similar type of bright spot in which there is a high degree of conformance of amplitude to the time structure map in a area that has a prominent culmination (figure 4.14). A hydrocarbon interpretation is supported by the clear difference in amplitude of the channelised sands as they trend down-dip.
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Rock Physics, AVO & Seismic Interpretation 4.3 Some Examples
4.3.5 Single Interface Models - a word of warning The examples discussed in this section so far have shown a straigthforward connection between a simple model (the single interface AVO model) and the seismic interpretation. In many instances the AVO response is more complicated. An example in figure 4.15 has a Class IIp AVO effect at the 'top sand' when the seismic has relatively low resolution (30Hz case) but it has a Class II AVO response when the wavelet has higher resolution (50Hz case). The difference is due to the presence of a thin hard unit at the top of the sand.
Vsh
AI
PR
30Hz Syn
50HzSyn
25ms
Figure 4.15. Variation in AVO response with frequency - due to thin bed effects
Thus the interpreter needs to check the applicability of a single interface model before using it in an interpretation. More discussion on resolution issues is given in sections 7, 9 and 11.
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Professional Level Rock Physics for Seismic Amplitude Interpretation 5. Characteristics of Seismic Wavelets
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5.1 Bandwidth and Phase 5.2 Zero Phase and Minimum Phase 5.3 Wavelet Shape (Phase) and Depth 5.4 Idealized Wavelets 5.5 Wavelet Phase and Seismic Processing 5.6 Zero Phasing 5.7 Enhancing Frequency Content
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Characteristics of Seismic Wavelets
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Characteristics of Seismic Wavelets 5.1 Seismic Data - Bandwidth and Phase
5.1 Seismic Data - Bandwidth and Phase The seismic trace is composed of energy that has a range of frequencies. For example if we consider the seismic wavelet below, then the form of the wavelet is the result of the addition of the sine wave functions at each frequency. Another representation of the wavelet is in terms of the amplitudes of of the various frequency components (the 'amplitude spectrum'). The 'Bandwidth' of the wavelet (or seismic trace) is the range of frequencies above a given amplitude threshold (usually taken to be half the maximum amplitude).
Zero Phase wavelet and selected frequency
components
o3
4072Hz
Amplitude Spectrum
180r-----------, Phase
0
-I
~~~
angle ·,80r-~-~-~-~---'
20
60 Frequency Hz
Bandwidth (7-55Hz) Amplitude
H~~-----",,-
Half power point
o+-~-~-~_;~
20
60 Frequency Hz
Figure 5.1 Seismic Data: Frequency, Amplitude and Phase.
IU Frequency
Reflection Refraction Transmission Attenuation
Earth Filter
24
Phase Spectrum
Source Signature
~
612
I'"~" ~~ E
«
,
Unfortunately, the amplitude spectra do not provide enough information to uniquely define the shape of the wavelet. The other piece of information that is needed is the relative shifts of the waveforms at each frequency (i.e. the phase). Figure 5.1 shows a wavelet in which all the frequency components have a trough aligned at time zero. This is referred to a 'zero phase'.
It is a characteristic of seismic data that the bandwidth of the input signal is modified by the earth filter. Thus shallow targets will generally be characterized by good bandwidth whilst deeper targets will have poorer bandwidth. The extent to which individual geological layers can be resolved (i.e. vertical resolution) is in part controlled by the bandwidth (see Resolution section).
Frequency
Seismic Trace Figure 5.2. Seismic Bandwidth and the Earth Filter.
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Characteristics of Seismic Wavelets 5.2 Zero Phase and Minimum Phase
5.2 Zero Phase and Minimum Phase Wavelets are often described in relation to two different theoretical descriptions, notably minimum phase and zero phase. Common usage of minimum and zero phase as descriptors is based on the fact that sound sources such as explosives and air guns have minimum phase signatures, but zero phase wavelets are the most desirable for interpretation. As shown in the previous figure the zero phase wavelet is symmetrical, with the amplitude equally distributed around time zero. As the zero phase wavelet is not a naturally occurring phenomena seismic data has to be processed to achieve this wavelet form. 'Minimum phase' is a condition of a wavelet rather than a description of its shape. Minimum phase is used to describe a 'causal' wavelet (i.e. no energy before zero) in which the phase is closest to zero but which displays the most rapid build up of energy. Thus there is a unique minimum phase wavelet for a given amplitude spectrum.
o ---,.1-----twt
Figure 5.3 Two minimum phase wavelets with the same polarity
o
30
60
90
Most wavelets extracted from seismic data have mixed phase. A particularly useful aid in describing and discussing wavelets is phase rotation. The figure opposite illustrates the concept with respect to a zero phase wavelet. As the phase rotates, the relative amplitudes of the peak and trough loops of the wavelet change. At 90 degrees the two loops have the same amplitude; in practice this is not a useful concept for the interpreter as it does not prescribe a particular shape. As shown in the following figure minimum phase wavelets can have shapes in which either the leading or the following loop are the dominant parts of the wavelet. The subject of determining the wavelet in the data is described in section 7.
Figure 5.4. Phase Rotating a Zero Phase Wavelet.
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Characteristics of Seismic Wavelets 5.3 Wavelet Shape (Phase) and Depth 5.4 Idelaized Wavelets
5.3 Wavelet Shape (Phase) and Depth The earth filter can have quite dramatic (and largely unpredictable) effects on the phase of the seismic data. The example below shows a seabed response similar to a -120' phase rotated zero phase wavelet, whereas at the target the optimum wavelet for the wei! tie is symmetrical.
Seabed Response
Extracted wavelet at 3000 ms
450
-50
500
, 50
Figure 5.5. An Example of Change In Wavelet Shape with Depth.
5.4 Idealized Wavelets There a number of idealized wavelets that can be defined. A selection are shown below. Hosken (1988) has noted that Ricker wavelets have different spectral characteristics to those of real seismic and should not be used for synthetic ties. Butterworth and Ormsby filters are more applicable. Butterworth 18dBlOcl12Hz 12dBlOCt40Hz
Ormsby
Ricker
5-15-4G-60Hz
20Hz
Zero Phase
Minimum Phase
Figure 5.6. 3 Different Types of Zero Phase Idealized Wavelets and Zero and Minimum Phase Ormsby Wavelets (S-10-3S-60Hz).
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Characteristics of Seismic Wavelets 5.5 Wavelet Phase and Processing
5.5. Wavelet Phase and Processing It is a well known fact that various seismic processing steps can also have significant effects on wavelet shape. The figures below illustrates the effects of different processes and filters on the wavelet shape. Some companies adopt the approach of determining phase correction fiiters based on measured and calculated effects of the various filters applied in seismic acquisition and processing. The uncertainty in the effects of the earth filter and the processing sequence is a good reason for adopting a quantitative and target-oriented approach to well ties (see Section 7).
Figure 5.7a. Processing Affecting Waveiet Shape (after Bariey 1985).
~
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3.6
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2 Minimum phase wavelets with similar bandwidth but slightly different low-cut responses
Figure 5.7b. Processing
18dbJoct low-cul
Affecting Waveiet Shape
18+24 db/oct low-cut
o r---..;o---
(Courtesy R.E.White). 50
50
100
100
150
150
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Amplitude spectra
10.2
0
6
50 Frequency Hz
© Rock Physics Associates Ltd 2007
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Characteristics of Seismic Wavelets 5.6 Zero Phasing 5.7 Enhancing Frequency Content
5.6 Zero Phasing In order to generate a seismic section that has the best wavelet for interpretation (i.e. a symmetrical wavelet that is centred on time zero) the data has to be 'zero-phased'. This involves convolving the seismic data with an inverse filter that converts the estimated wavelet in the data to a zero phase equivalent.
~avelet I
I
I
100
0
"
Convolve with inverse operator 0
·w
-
·20
dB
..... .. ~-
I
I
·100
·30
Zero phase wavelet
60
30
I
50
",
40
15
I
0
Hz I
-50
...
I
0
..
I
50
Figure 5.8. Zero Phasing.
5.7 Enhancing Frequency Content Amplitude
Phase
Amp
Frequency
TWT
Frequency
~
Inverse Filter
Some workers attempt to broaden (whiten) the frequency spectrum through the zero phasing process. This is a rather dated approach to the problem of trying to enhance the frequency content of seismic data but it has been successful in some areas.
~ Amplitude
TWT
Phase
Amp
Frequency
Frequency
Figure 5.9 Zero Phasing and Whitening (broadening of frequency
spectrum).
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Characteristics of Seismic Wavelets 5.7 Enhancing Frequency Content
A more up-to-date approach to enhance the frequency content of seismic data is to design inverse operators that shape the reflectivity spectra of the seismic to the equivalent spectra displayed by well log data. A commercial implementation of this technique has been termed 'Spectral Blueing' (see below). It is based on the work of Walden and Hosken (1985) who showed that different rock sequences display different reflectivity characteristics. Average reflectivity spectra - seismic
Jf' 1\
...
••,
r\
•
\
Average reflectivity spectra· wells
Spectral blueing operator
----.
1\ V
1/\ V
! ." f .ro
.•
,
n
IJl' fll
,I
VI
Figure 5.10. Spectral Blueing. (The blueing operator converts the seismic reflectivity spectra to
the spectra of the synthetic reflectivity at the well). Courtesy ARK CLS.
Before
....,.....
_
- 3000
After 30:10
-3000
.Figure 5.11. An Example of Spectra/ Blueing (after B/ache-Fraser and Neep 2004)
The illustration above shows an example of blueing that served to enhance the resoiution and correlation of sands, as well as provide better definition of fluid reiated flats pots.
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Professional Level Rock Physics for Seismic Amplitude Interpretation 6. Resolution
Rock Physics Associates
6.1 The problem of Interference 6.2 Temporal Resolution 6.3 Estimating the tuning thickness and vertical resolution from seismic data 6.4 Vertical Resolution and Depth 6.5 The Effect of Wavelet Shape and Filter Slopes on Resolution 6.6 Thickness Prediction from Seismic 6.7 Net Pay Prediction in Isolated Thin Beds 6.8 Lateral Resolution 6.9 Resolution - Sections vs. Maps
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Resolution
2
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Resolution 6.1 The Problem of Interference
6.1 The Problem of Interference The modelled seismic trace in figure 6.1 illustrates the fact that a seismic section is a complex interaction of the wavelet and the reflecting surfaces (i.e. geology). It is clear that the major reflections are associated with distinct changes in impedance. However, owing to the fact that seismic wavelets are generally longer than the spacing between impedance contrasts, the presence of a reflection is dependent not only on the magnitude of the reflecting interface but also on the layering close to the boundary. For example the top and base of zone 5 are clearly identified on the trace but the reflections from the thin sands in zones 3 and 8 destructively interfere. The amount of interference is controlled by the length of the seismic pulse in milliseconds and the spacing of the contrasts (a function of the interval velocity). The question arises therefore how thin would zone 5 need to be such that it would not resolved on the seismic trace? TIME
Vsh (dec)
Phle (dec)
-2050 II1I 2100 III1 2150 IIII 2200 IIII 2250 IIII 2300 IIII 2350IIII -2400 IIII -2450 1III -2500 IIII -2550 1111 2600 I11I 2650 1111 2700 IIII 2750 IIII 2800 IIII 2850 IIII 2900 IIII 2950
AI()
3000. -
MS
------
____ ..
--
Ref Series ()
--
SynthetiC 0
10000. -0.175 - - 0.175 .(\.175 -
-
0.175
++-+-t-+-t+-Wo+-f-+4eH--H..."F-t-l
..I-++-f-+-HH--k-JH-+-tol++-+-t-W-t-I
Figure 6.1. A synthetic seismogram illustrating how geology fits with seismic.
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Resolution 6.2 Temporal Resolution
6.2 Temporal Resolution The issue of temporal (or vertical) resolution is addressed by considering a 2D seismic model of a simple wedging unit. Figure 6.2 illustrates the interference effects of two reflections from the top and base of a sand enclosed in shale. The following features can be recognised:
1. At 'A' the two reflections are resolved. 2. As the unit is thinned the two reflections begin to interfere, resulting in a composite response that progressively increases in amplitude to the 'tuning thickness' at 'B'. 3. Progressive thinning of the unit results in destructive interference and the composite reflection decreases in amplitude. 4. The reflections never get much closer together in time than the 'tuning thickness'. 5. For thicknesses below 'tuning' the time separation measured from the traces would greatly overestimate the thickness. 6. Interestingly, the amplitudes in the zone below tuning are approximately linearly related to the actual time thickness of the layer. 7. In the zone of constructive interference (between A and B), the time separation of the trough-peak is more or less a reasonable gUide to thickness. The trough-peak separation may slightly underestimate or overestimate depending on the shape of the wavelet. 2050
--------1-------- -------- -------- ------- -------- -------- ---------t-------- -------- --------
A
B
2100
_"Of-"''''--2250
2300
-
-- -------- -------- --------- -------- -------- -----
------
---- -------- --------
B
Amp
0.06
60
0.05
50
A
0.04
40
0.03
30
0.02
20 /
0.01
10
/
:»
u uQ) Cil
~
-<
:T
Ii"
Note that with a zero phase wavelet the tuning curve shape is half the wavelet.
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!!2-
/
0 0
20
40
0 60
60
Wedge Thickness (ms) Figure 6.2. The Wedge Model.
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Resolution 6.2 Temporal Resolution
Figures 6.3 and 6.4 give examples of tuning phenomena from the Rossetta Field.
,
--<# .....
Figure 6.3. Rossetta Field: An Example of Tuning Phenomena.
FWL MDT measurements in wells extrapolated to FWL's
courtesy BG Group
Figure 6.4. Rossetta C Sand.
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Resolution 6.3 Estimating Tuning Thickness 6.4 Vertical Resolution and Depth 6.3 Estimating the Tuning Thickness and Vertical Resolution from Seismic Data The tuning thickness is fundamentally determined by the thickness and compressional velocity of the unit and the wavelength of the seismic pulse. A first order approximation appropriate for making qUick calculations (equation 6.1): Tuning thickness = A I 4
Equation 6.1. Tuning thickness approximation.
A = Vp (m/s) / Fd (Hz) Fd
= 1 IT
A = wavelength (m) Fd = predominant frequency T = seismic period = peak-to-peak or trough-to-trough twt separation (Note that the 'peak' frequency (e.g. associated with defining a Ricker wavelet) is defined as Fp=Fd/1.3 (Kallweit and Wood, 1982)). In theory the temporal (or vertical) resolution (i.e. the point at which the two reflections become a composite) is slightly less than the tuning thickness and is defined as Tr = 1/(2.31Fd). Table 6.1 summarises this information. Period (T) Dominant frequency (fd) Peak Frequency (fp) Tuning thickness (twt)
Wavelenqth Vertical Resolution (!wt)
trough to trough 1fT secs Fd/1.3 1/(2.6fp) 0.0135s 1/(2fd) @2220m/s Tunina*4 0.0117s 1/(3fp) 1/(2.31fd) ®2220m/s
0.027s 37Hz 28.5Hz 13.5ms 15m 60m 11.7ms 13m
Table 6.1. A worked example of estlmatmg tumng thickness and vertical resolution from seismic.
6.4 Vertical Resolution and Depth A common first order effect evident on seismic data is the decrease in frequency content with depth (figure 6.5). This is due to the various effects of the earth filter. In the shallow part of the section the seismic loops are close together whilst in the deep section they are further apart. This change in frequency combined with the general increase in velocities with depth clearly has an effect on vertical resolution.
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Resolution 6.4 Vertical Resolution and Depth 6.5 Wavelet Shape, Filter Slopes and Resolution
High frequency loops close logelher
17<':~~ T :21 ms Fd "48Hz
Tr "9ms Vp" 2500 mlS vertICal
feso!ull(lfl "
113m
Low frequency loops futher apar1
T=27ms Fd=37Hz Tr=1l7ms
Vp "3000mIs Vef!1(:a1 resolution " 17 6 m
Figure 6.5. Frequency, Velocity and Vertical Resolution.
6.5 The Effect of Wavelet Shape and Filter Slopes on Resolution The work of Koefoed (1981) was instructive in illustrating the fact that wavelets with the same bandwidth can give different seismic traces and differences in perceived resolution. Figure 6.6 shows two zero phase wavelets with different slopes on the amplitude spectra. The wavelet with steep slopes has a narrow main lobe but significant side lobe energy, whereas the wavelet with shallower slopes has a broad main lobe and minimal side lobe energy. Koefoed (1981) made the point that neither wavelet is better than the other - it depends on what you want to interpret. In practice there is always a trade-off between the desire for a narrow main lobe and the effects of reverberations due to high filter slopes.
Narrow central lobe Significant Side lobes
""-. Resolves closely
Steep slopes on spectra
spaced events
d same polarity
~P'lfr ~ ~p·a f
Figure 6.6. The Effect of Filter Slopes on Wavelet shape and Vertical Resolution (re-drawn from Koefoed, 1981). ~)~
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---L r
Sh,'.~' -""" ,,,,,,,~ 00
Better appreciation of _ _ dosely spaced events of opposite polarity
Wide cenlrallobe Minimal side lobes
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Resolution 6.6. Thickness Prediction from Seismic
6.6 Thickness Prediction from Seismic It is useful to consider creating a volumetric case using the seismic alone as an alternative/addition to the more conventional mapping of the top time structure and depth conversion. Calculating thicknesses from seismic data in 'thick' bed areas is straightforward. Using the top and base picks the thickness is defined by (equation 6.2):
Thickness (m) = (Time thickness (ms) I 2000) * Vp (m/s)
Equation 6.2. Thickness from seismic.
However, calculating the thickness of a unit using the peak and trough picks in figure 6.7 will lead to big errors in the 'thin' bed (below tuning). To address this situation the tuning thickness can be estimated directly from seismic by crossplotting the trough-peak or peak-trough separation against amplitude (upper pick amplitude or composite amplitude, see figure 6.8).
Wedge Thickness (ms)
Figure 6.7. The Tuning Curve and Tuned Seismic.
Q)
"0
The tuning thickness is used to define the thin and thick bed areas. Thicknesses are calculated for the 'thin' bed areas from the amplitude map. Of course this involves drawing in the thin bed part of the tuning curve on seismic tuning curve and errors can arise if the relationship is not correct. It is easy to overestimate the thicknesses of thin beds. The 'thin-bed' thickness map can then be combined with the thickness estimated from the thick bed areas. In addition it must be remembered that below a given thickness (that varies with frequency, magnitude of reflection coefficients and noise content) the thin bed is essentially invisible to seismic.
Potential errors in making assumpions about the relationship between amplitude and thickness 3000 +--~--+----+----+----f----
~
Ci
~
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12
~
2000
-:\=====;~~~---+------ii~--+------.:~~:n :
.'.
1000 -l---""';'~~---I-----+-"""----l-----+----I
5
10
15
20
25
Time Separation Trough-Peak (ms) Figure 6.8. Tuning Curve from Seismic.
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Resolution 6.7 Net Pay Prediction in Thin Beds
6.7 Net Pay Prediction in Isolated Thin Beds The basis of net pay prediction in thin beds (i.e. below tuning thickness) is outlined in the diagram in figure 6.9. The tuning curve associated with a clean sand (N:G=l) is shown in red. In the subtuning zone amplitude is more or less linearly related to thickness and therefore amplitude can be used to predict thickness (in the case of N:G=l, thickness = net pay thickness). If it is assumed that to first order the effect of N:G is linear in terms of reflectivity then the tuning curve associated with a sand N:G=O.S (blue line) will have half the height of the clean sand tuning curve. If we then consider an amplitude 'a', the gross thickness predicted for the N:G=O.S sand would be twice that of the ciean sand but the net pay thickness would be the same. Thus the only curve that is required to give an estimate of the net pay thickness of thin beds is the clean sand curve. Of course such an analysis can only be done with confidence when pay is known to be present.
Impedance N:G=O.5
N:G=1
Cl..
:2
«
I\\:..&J/.
'a'
,/ Net Pay thickness
Thickness . Gross sand Thickness = 2*net pay thickness for sand with 50%N:G
Figure 6.9. The basis of net pay estimation in thin beds
(i.e. below tuning thickness).
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Resolution 6.8 Lateral Resolution
6.8 Lateral Resolution Lateral resolution is not independent of vertical resolution as it is a function of the frequency of the seismic. Reflections are the result of constructive interference over an area of the wavefront. The area is termed the 'Fresnel zone' (figure 6.10). The reader is referred to a useful discussion of the Fresnel zone by Lindsey (1989). For an unmigrated seismic image the Fresnel zone diameter is defined (by Sheriff, 1977) as (equation 6.3): For Spherical Waves: Equation 6.3. Fresnel Zone diameter.
Where z=depth and A = wavelength. Un-migrated seismic objects that are smaller than the Fresnel zones are not uniquely identified. However migration plays a large role in enhancing lateral resolution. Figure 6.11 shows how the Fresnel zone is compressed in the inline direction for a 2D migration. 3D migration collapses the Fresnei zone to a small circle (approximately one half of the wavelength). Key factors in lateral resolution for 3D seismic surveys are migration aperture, geometry, fold, and sampling.
a) .;- First Fresnel Zone -..;
{ For
{For
~~ b)
:: :
: I
:
:
low Frequency:
:
:
Zone
: - Low Frequency Zone ------:
Figure 6.10. The Fresnel Zone (Sherrif ,1977).
Post migration fresnel zone Pre migration fresnel zone
Figure 6.11. The Effect of Migration on the Fresnel Zone for a 2d line (after Lindsay, 1989).
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Resolution 6.9 Resolution - Sections and Maps
6.9 Resolution - Sections vs. Maps There are different ways of looking at the resolution of seismic. Vertical resolution as defined above is definitely not the same as the resolution of 3D seismic. 3D seismic resolution is defined by the character and continuity of seismic amplitude and associated attributes on maps. The distinction is important as decisions can be made on the basis of simple 1D trace modelling that may be totally erroneous. An example of the enhanced resolution of maps is shown in figure 6.12. It is a 4D modelling example. The figure shows a 3D model of a gas water contact in a formation (defined by two bounding surfaces). 3D synthetic models are generated to simulate the seismic before and after the raising of the contact. Differenced data sets are also generated. The effect of the contact variations cannot readily be seen on difference sections to which a realistic amount of seismic noise is added. However on maps generated from the same dataset the effect is very clear. Difference Section Model Contact movement of 25 m
COP 10
M
~
15
~
,. S:N=1.5 mTttit-t-tt'i'rmffi-ttifflrt+tm" S:N=1.5
,
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2 118 .ll..LllL"'-'CLU-LU.LllLLLLLLULu..u-LULUilll
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Signal only
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~ "+++++++++++++++++++H-I+H-I+++I+++I+++I-Jh..- - - ,
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2.118.ll..LLLLLW.LLI-LU.LLLllLLLLLWLW-LU.LLLilll
u"" 20
30
40
10
u.... 20
30
40
Signal only
After Archer et al 1996 40
Signal only
Difference Maps Figure 6.12. Resolution: Sections V5. Maps.
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Professional Level Rock Physics for Seismic Amplitude Interpretation 7. Well Ties
Rock Physics Associates
7.1 The Well Tie Process 7.2 A Quantitative Approach to Well Ties 7.3 The Need for Precision in Well Ties 7.4 Practical Issues
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Well Ties
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Well Ties 7.1 The Well Tie Process
7.1 The Well Tie Process In order to pick seismic or invert seismic for rock properties, seismic data needs to be calibrated to the geology encountered in a well (figure 7.1). This calibration process (often referred to as 'making a well tie') involves the comparison of a synthetic (or modelled) seismic trace with the reai seismic. If the correlation is good then the seismic can be interpreted in terms of the geology. If it is poor there will remain significant uncertainty in the seismic interpretation. Stlale
Porosity
Impedance ReI CoeK
Wavelet
SynlhcHc
SeismIC
- - - --\-1---',-1--/--1--+-1 -'-. -
-l---Ii--I
3000
30W
3'"
'1---1---{'- ---\-1--1--1--1....-1' Figure 7.1. An example of a well tie.
In theory the well tie process (following the concept of the convolutional model) is very simple, involving a time calibration of the sonic log to the checkshots, a convolution of the time reflection series with a wavelet and a comparison to the seismic (figure 7.2).
Log Calibration (depth to time)
+
Time Reflection Series
+
Convolution ......1 - - Wavelet
+
Compare to seismic Figure 7.2. The Well Tie Process.
Despite the simplicity of the concept, well ties can present considerable problems, usually in the area of the wavelet estimation. ~l). GEOSCIENCE ~.BTRAIN'NG ...., ALLIANCE
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Well Ties 7.1 The Well Tie Process
7.1.1 Log Calibration Prior to use in the synthetic, velocity logs need to be upscaled. It is generally accepted that the best way to do this Is through Backus averaging (figure 7.3). The Backus average departs from an arithmetic average when there are strong contrasts of velocity.
1. Determine Il and Ksat from Vp Vs and P
"te-J >l<.{/c /law eIe'j'i~
WVs'p
I~
Ksat=p(Vp'·4/3Vs')
2. For selected sample r nge (ie operator length, usually %·1/51c
II
Calculate the arithmetic Average of p and
I
'600
the harmonic average of Il and Ksat
I
e.g. Ilb'= 1/(sum of (fraclll)) 3. Reconstitute velocities Vp' =(Ksatb.,g +((4/3)llba,g))/Pa,g) Vs'= (llba,g!Pa,g)
Original tog
Figure 7.3. Backus Averaging
t.J~4/' -cbc"@t Ie .uy'4-vu.~, u{Cl-,NI;; ,-
-
r.od
Arithmetic average
Backus average
Ine
Log calibration seeks to analyse and resolve the differences in times from the sonic and the checkshots (figure 7.4). The sonic log is hung on the top checkshot or other time reference point and integrated. The differences between log time and seismic time are then plotted and some form of minimised fit made to the data. Common ways of deriving the fit are linear trends with 'knee' points, polynomial fits. Spline fits can generate artifacts and are not recommended.
::11 . Interval Velocity (mls)
2000
.....,,,."... ...,"...
3000
4000
~
Figure 7.4. Log Calibration
Time Log· Time Checkshol (ms)
6000
•
201$1050
Function to minimise difference S (i.e. less than
,
Integrated Transit Time (ms)
1000 1200 14(1(1 1600 1800 2000
L
V
!• 1~
...
b~
~ "
- resolving differences in
seismic and sonic travel times.
_2ms)
!
(linear spli no
polynomial )
t~!/'0 iN t- I.M~ i ~
/ /
~-!I~lUcf ",,/0.1
l'
~
Apply to sonic log (Le. changes log values)
Integrated Log hung on top checkshot
This fit is then used as a correction factor to the sonic log or as a means of creating a detailed time-depth curve (figure 7.5). The difference between the fit and the difference data should be no more than ~2ms. If the corrections are applied to the sonic log then the log velocities are changed. Care should be taken in applying linear fits as there is the possibility of introducing false reflections. To minimise this problem the 'knees' of the linear fits should be located at major changes in acoustic impedance. It is important to remember that drift is strongly related to geology. 4
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Well Ties 7.1 The Well Tie Process
TL-TC us Sonic uslft
-30 -20 -10
0
10
20
30
o
\
-
Top of log tied to first check shot
"00
f--t--t g
r;..o-- Log velocity> checkshot velocity
2000
~
~
HL---l~ %. ~
f---/'--t
~ ~
4000
5000
... _ _. • ..... _
Courtesy Read Geophysical
Figure 7.5. An Example of linear fits to Sonic/Seismic Time Difference Data.
7.1.2 The wavelet The wavelet that gives an optimum tie of a well log to a seismic section has a characteristic length, shape and timing. The problem is how to estimate it. The well tie example in figure 7.6 illustrates that the best tie is with a trough-dominated wavelet that has a time lag of about 20ms. The correct pick on the seismic is 20ms below the calibrated two way time of the horizon. Synlheli
-
Matching
trace
Seismic AI
Rhob
vp
\ (J/!-J/,r4..Q.
!~fae.;'; V
,,~
Wavelet ,~
-so
t'~
r~t
\v;y~
TWT 0
~
f'~ .Yj ~ \..J? .~V.l
~"1
so
-
,- - - -
Figure 7.6. Another example of a weN tie.
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"
5
i
Well Ties 7.2 A Quantitative Approach
7.2 A Quantitative Approach to Well Ties In order to estimate the correct filter (i.e. wavelet) for the purposes of picking seismic or designing zero phase or inversion operators the best approach is to estimate the wavelet directly from the seismic data. The technique described here is that of White (1980). The wavelet is extracted from the data through a ieast squares technique (figures 7.7 and 7.8).
Seismic Trace
Reflection Series
Wavelet
Figure 7.7. Schematic illustration of least squares
/
filtering to obtain the wavelet.
Least squares filter
!
Theory imposes constraints on wavelet length and filter parameters Wavelets usually extracted over 500ms gate
PEP.4Jelay Plot
'00
3002
00
60
40
20
Well Position
+
around the well - this plot shows percentage of energy predicted
Selected Trace
Plot:
6
I
Figure 7.8. Wavelets are
extracted in a cube of data
o
2922
X
if
~
PEP _> Defay
© Rock Physics Associates Ltd 2007
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Wavelet Phase Description
When describing wavelet shape it is often convenient to use the concept of a phase rotated zero phase wavelet. The diagram below illustrates that the description depends on the reference polarity convention.
o
180
30
-150
120 -60
150 -30
·12060
-90
Phase description reference
90
60
-120
90
·90
-150 30
-60
SEG standard +ve
© Rock Physics Associates 2007
130
-30
150
UKOOA normal polarity
Well Ties 7.2 A Quantitative Approach
Following White and Simm (2003):
Matching involves extracting a filter (l) from a time
Seismic segment
window of seismic data (T) (figure 7.9) The Time segment length should be around 500ms - any longer and the stationarity assumption starts to
Wavelet length
fall down - any shorter and the chance of a statistically valid tie
-100 .
are reduced. T= 500ms
l
100
Figure 7.9. Seismic segment (T) and wavelet length (L)
For statistical validity where L = 1.704 be 1.704T
b=bandwidth c = 0.4 - 0.5 = 5 - 12
L
Generally Til = ~3 with relatively low bandwidth data (~25Hz) Til = ~6 with high bandwidth data (~50Hz) For low bandwidth data and short time segments it may not be possible to get a valid estimation of the wavelet.
'/"n.J -I Quality of tie re.R.evJ 'i.f ~I 'l!"veo/l V'M (JJ'r;1 l.olJ 1. PEP Amount of seismic energy that is /7'
1)
rr-=- 0 1-
PEP
A-
f7)
J
0, (
,
2.
predicted in the synthetic (P) where P=R' and R=cross correlation coefficient (Goodness-of-fit) Estimated error in wavelet (NMSE)
NMSE=~·I-P cT
Approximate phase error =
where c= 1. 704
P
in radians
Good Tie PEP >0.6 and NMSE 0.1 - 0.2 ~l) GEOSCIENCE ~.BTRAINING ALLIANCE
©Rock Physics Associates Ltd 2007
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Well Ties 7.2 A Quantitative Approach 7.3 The Need for Precision
Wavelet length
I
too short
I too long
Goodness-ol-fit
\ \ \
. . . . . - - Wavelets that are tOO long are matching noise in the seismic
\
Wavelets thaI
\
are too short are being distorted
\ \
,,
,
-
-- _ - - - §;limated error in wavelet
Optimum wavelet length
Wavelet Length Figure 7.10. Goodness of Fit and Accuracy in Well
The reason lor deriving the error in the wavelet (figure 7.10) is that the goodness-of-fit alone is not a definitive measure of accuracy. The cross-correlation increases with increasing wavelet length, but the longer the wavelet gets the more chance that noise is being matched. The NMSE has a minima, effectively defining an optimum range of wavelet length (i.e. where noise being matched at a minimum and there is minimum distortion of the wavelet).
7.3 The Need for Precision in Well Ties - two examples Wavelet B
~ 1-60ms
-I 5
1.9
10
Response with Wavelel"A" (10-40 Hz. BandpaSS)
2.0
15
20
25
30
35
40
45
-H--H-t-t-t-t-H-1--H--H-tt-t-t-t-ttt-H-t-t-H-H-1--H--H-tt-t-t-t-t-H-t-t-t-
H-HI+H-HH-+++H-+-t+H-+++t-++++t-++++
t+-H-++++++++++++++++++-H+++++++++++++++++++++++ Response \0 Wavelet "B" (Actual Seismic Wavelet)
Figure 7.11. Modelling - the need to understand the wavelet (after Neidell et
ai, 1977).
8
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Well Ties 7.3 The Need for Precision 7.4 Practical Issues
The shape of the wavelet is important for the results of seismic modelling. For example, Both wavelets used in the modeling in figure 7.11 are peak-dominated but the reflectivity characteristics are quite different. The wavelet on the left is a processed zero phase wavelet and on the right and air-gun signature. Figure 7.12 shows an example where understanding the polarity of the data is vital to identifying the loop which carries the amplitude information about the top reservoir.
High amplitude
sands
Red Pick Amplitude
Blue Pick Amplitude
Figure 7.12. Which loop to pick - it can matter!
7.4 Practical Issues 7.4.1 Workflow The recommendation here is that the interpreter begins the well tie process by making no assumptions about the phase and timing of the data and performs a quantitative tie. Sometimes the results are not especially stable and other assumptions need to be employed. An order of well tie investigation for the interpreter might be: 1. Quantitative wavelet estimation - no phase and timing assumptions 2. Quantitative wavelet estimation but assume constant phase 3. Select idealized wavelet and phase rotate until reasonable match is made. Note that stretching and squeezing the synthetic to match is an absolute last resort.
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Well Ties 7.4 Practical Issues
7.4.2 Reasons for Poor Well Ties In the event of poor well ties there are likely to be some very good reasons. Some of them are listed below: • • • • • •
different propagation paths for sonic and seismic (including AVO) relative scales of measurement frequency of measurement spatial sampling errors in seismic migration problems in the log measurement (e.g. borehole effects and invasion).
Experience has shown that the most important factors in the well tie process are not the algorithm that is used to match the seismic and well reflection series but the understanding of the processing of the seismic (and well-seismic) data and log conditioning. In many practical situations there will remain ambiguity as to the correct phase and polarity of the data. In these situations the interpreter needs to keep an open mind (possibly even work up two interpretations) and check all available observations for their consistency.
7.4.3 The Problem of Poor Bandwidth Seismic wavelet I
Selsmk:wavel1l12
0.'
"0.'
"
!
Ii.o.:::f-------..~AVl'lw.r-V
0.1
1'1.",,--"'.'~ \
'& o.of--~,.
,
..,
".(1.1
1
.,
.(l:~\;;---:;;.,,,.-------;;__,;;;;,,;---,;,,,
Bandwidth has a significant role to play in well ties. The poorer the bandwidth of the data the more there is ambiguity as to wavelet shape. Poor bandwidth data can be tied equally well with wavelets that have different phase and timing .
~
Matdl w~h syr(hetie seismogtllm 1 . --_ . . . _.
2500
"
''''
.
""
""
.
Figure 7.13 shows a data example in which equally good ties can be made with wavelets that have almost 90 degree difference in phase.
'000 .
-
_
2650
.
.§ nOll
.
!
f
i '000
.*1""
'000
Figure 7.13. Wavelet Ambiguity with Poor
""
"" o.
10
27SO
Bandwidth Data 10
15
20
(From White and Simm, 2003).
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Well Ties 7.4 Practical Issues
Figure 7.14 illustrates the ambiguity in terms of linear fits through data with standard error estimates on a frequency vs. phase plot. Phase is defined by the intercept whilst timing is defined by the slope. In the poor bandwidth case there are greater possbilities for different phase and timing to fit the data. High bandwidth data
Low bandwidth data
radians
~
radians
-- -
•
~
&.
&. ,
• .,
.,
.,
,
,
•
~!!!"i~Jt. e
--_
---
?
• ~
~
~
H,
H,
Frequency
Frequency
Figure 7.14. Wavelet Phase and Timing (From White and Simm, 2003).
wdl f/e
7.4.4 Well Ties and AVO
-/vA/ek;. wid rf)(!;
For Class I and III situations the reflectivity of near and far angles is similar, just varying in the magnitude of the amplitude, and the AVO effect has little effect on well ties of vertical incidence synthetics to migrated stack seismic. However this is not the case with Class IIp responses. Figure 7.15 shows that for Class IIp situations the reflectivity of near and far angles is very different. Thus, it is very difficult to tie vertical incidence synthetics to migrated stack seismic in these situations. Reflection Series
Estimated Wavelet
Seismic Trace
Synthetic
<~
Seismic Trace
<
~
Residuals
<
~
0
2000
~
... ~
TWT ms
~b
"::~
:::: :...
~
<
~-
=,
2300
......, ~
... ;,
~l):
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<~
""
~
~-
0...,
~
<~~- <.
"
<:
In the example shown in figure 7.15, an initiai tie was made to a conventional migrated stack using a normal incidence reflection series. Reflectivity at the reservoir level is characterised by a phase reversal owing to the effect of oil in the pore space. The tie is not a good one and the top reservoir is not definitively identified on the migrated stack.
~
• Figure 7.15. Initial Tie-Migrated Stack and
<:
Normal Incidence Synthetic (after Simm et al 1999).
©Rock Physics Associates Ltd 2007
11
Well Ties 7.4 Practical Issues
Reflection Series
Estimated Wavelet
Seismic Trace
Synthetic
Seismic Trace
Residuals
Waveleltime ZerO ~ 1950 ms
'2000
.:: TWT
ms
~
C;;
--
~
-=: 2300
-~
='"
..,; ~< =
<~
~
<
-
~
<:
Figure 7.16. Improved Tie - Zero Offset (Intercept)
Stack and Conditioned Normal Incidence Synthetic.
Subsequent re-processing of the seismic (creating an intercept stack) and log conditioning to remove the effects of fluid invasion yield the tie shown in figure 7.16. The Top reservoir is now clearly tied from synthetic to seismic.
7.4.5 No Well Calibration - What Then? When there isn't a well the problem of determining wavelet shape and timing becomes more problematic. In theory the answer is to look at the reflection response of 'unique' reflectors of 'known' impedance contrast, such as the hard sea bed or the top reflections of seismically 'thick' igneous intrusions or thick sequences of carbonates overlain by basinal shales. In practice there is usually a great deal of ambiguity arising from: 1. the change of wavelet shape with depth (in response to attenuation and the effects of interbed reflections) 2. tuning effects. One approach that can be useful in situations where there is little well data is the method of phase rotation and measurement of amplitudes (Figure 7.17) on a distinctive (single reflector) horizon (such as the sea bed) . The idea is that the phase rotation that gives the highest amplitude establishes the seismic close to zero phase. There are a number of issues 1. In order to assign polarity you need to be confident of the impedance contrast across the boundary. 2. Care need so be taken that the techniques is applied as close as possible to the target of Interest owing to the effects of time variant phase rotation of seismic. 3. If this approach is used in the vicinity of a well then the reflector boundaries in the well can be shifted to match the seismic events.
12
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Well Ties 7.4 Practical Issues
j)H~\I~I) J,
":,:
.~
F~( l f .
I I
I
~
~~ .
.~,!
'.
Ilii
1J
~;,
I.:
'll
ftt lIt 'it I "
\.\1.,
\\
0.020,---,---,----,----,----,-----,-----.----.----.-, 0.020
O.015i--+--=-t-r-<-h-r-l-hrr"lr-hr=:-l::::,-----+---+--+-f 0.015 w
o=>
0.010
0.005
::::; 0.005 a.. :;;
0.000
0.000
f-
f-
::::; a.. :;;
w o ::>
0.010
«
«
-90
o
90
Phase rotation Figure 7.17. The method of determining near zero phase through phase rotation and amplitude measurement (after Roden & Sepulveda, 1999).
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©Rock Physics Associates Ltd 2007
13
Exercise - Well Ties Rock Physics Associates
The well tie is the experiment that tests the model against the seismic data. As such it gives the interpreter critical information on which to base, for example, decisions as to horizon picking, relative scaling for AVO studies and assessing whether or not seismic inversion is likely to work. The well tie experiment is best performed (at least initially) using no phase and timing assumptions. This exercise will introduce the method of White (1980) described in the manual in section 7. Two wells are available to perform well ties (Well 1 and Well 2). Near and far angle stacks have been defined with effective angles of 15 and 35 degrees. The RokDoc project is located in a folder called 'well tie dataset' on the memory stick.
Well Tie Workflow 1. Open RokDoc by clicking on the. bat file in the RokDoc folder on the USB memory stick 2. Click on 'well l' 3. Click on 'well ops' then 'wavelet extraction' 4. select reflectivity log (5 degrees) 5. select survey (well 1 near) 6. accept defaults a. 'use all selected traces' b. 'find the best fit location' 7. set start time to 1400ms ____ 8. set segment length to 500ms 9. accept default for wavelet length 10. hit 'calculate' button 11. look at the 'QC' tab and a. assess the location of the tie (it looks like the closest reasonable tie is around inline 8090 xline 1460) b. evaluate the nature of the tie (statistics and character/amplitude match, good - poor) c. compare your results to those shown overleaf 12. Wavelets can be viewed in the 'results' tab 13. For the far stack repeat steps 3-12. 14. For well 2 repeat steps 2-12 for near and far datasets a. choose a start time of 1487ms b. time segment of 500ms c. the closest reasonable tie is around inline 8130 xline1472
© Rock Physics Associates 2007
1
Exercise - Well Ties Rock Physics Associates
Typical results from the exercise are shown below (more results are shown in the 'well tie exercise.ppt' file on the memory stick). Well
Well 1
Well 1
Well 2
Well 2
Tie Inline
8090
8090
7140
7140
Tie xline
1460
1460
1044
1044
15
35
15
35
near
rar
near
Far 1487 500
Log angle Survey/stack Start time
1400
1400
1487
Segment T
500
500
500
Wavelet L
124
124
124
124
Dominant Loop
Trough
Trough
Trough
Assymetric
Approx Phase
-120
-150
180
120
8
4
0
0 47%
Time Delay
PEP
60%
55%
58%
Cross corr
0.83
0.8
0.78
0.75
Approx Phase Error
13'
14'
13'
17'
-
bT
6.8
6.8
6.8
6.8
biB
0.35
0.33
0.36
0.31
39
41
38
43
B (Hz)
Well 1
Well 2
.• Near
I I
. ,
Far
. ,
Extracted wavelets
Well Tie
5 tatistics
Lr; 1I.e£jJ- !~d,'tt'" 1'1( Q;...d ,j."e Wi:.
"'4/ fOt.
~~ . t3 t
~
~
~
.- . .
.
~
.
,
~
-
Questions to Consider 1. Are the well ties good enough for a. horizon picking? b. seismic inversion? 2. Are the data correctly scaled for AVO studies? 3. What factors might be responsible for poor ties? © Rock Physics Associates 2007
2
0Jf
'1~
1
Professional Level Rock Physics for Seismic Amplitude Interpretation 8. Deriving Inputs for Seismic Models
Rock Physics Associates
8.1 Introduction 8.2 Gassmanns Equation 8.3 General Comments on Gassmann Inputs and Workflow 8.4 Practical Gassmann Scenarios 8.5. A Note on Shales 8.6 A Discussion of Rock Models 8.7. Log Editing
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Deriving Inputs for Seismic Models
2
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Deriving Inputs for Seismic Models 8.1 Introduction 8.2 Gassmanns' Equation
8.1 Introduction This section deals with the basics of rock physics and its implementation on log data. The input data to offset reflectivity equations generally comes from wireline logs. Velocity and density data are usually available from most wells in the form of borehole compensated sonic and density logs. Shear wave velocities can also be logged, for example by running dipole sonic or array sonic logging tools. Even if the full suite of logs is available, however, it is not a simple matter of taking the values off the logs and inputting to the AVO algorithm. There are a number of issues that need to be borne in mind to QC the data prior to AVO modelling. These include: 1. Petrophysical QC (log edits, borehole corrections etc). Indeed much of what is written here presupposes that a petrophysicist has had a good look at the data prior to it being used for rock physics. 2. The need for a consistency check of the parameters with regard to the properties of known rocks. 3. The fact that the Vp, Vs and density measured in the hole may not relate to virgin fluids but to the effects of drilling fluids - particularly in flushed hydrocarbon zones.
8.2 Gassmann's Equation Gassmann's Moduli Relations Gassmann's Equation (Gassmann, 1951) is the most applicable model at seismic frequencies (equation 8.1). It is an approximation to real rocks (Wang and Nur, 1992) describing a rock in terms of the Incompressibilities of a two-phase medium. It is applicable to rocks with intergranular porosity and more or less uniform grain size.
~Kso,
K o - K so,
where: K", = saturated bulk modulus of the rock Ko = bulk modulus of the matrix K, = bulk modulus of the dry rock frame K, = bulk modulus of the pore fluid 0= porosity Equation 8.1. Gassmanns equation.
Given that shear waves do not propagate through fluids the second part of the equation states the condition that shear modulus (>I ) is the same irrespective of pore fill.
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Deriving Inputs for Seismic Models 8.2 Gassmanns' Equation
In oil and gas exploration Gassmanns equations are the workhorse of the seismic modeller. They are both a description of rock behaviour and the engine for modelling the effect of changing fluidfill on Vp, Vs and density (Fluid Substitution). Whilst this sounds straightforward the way that the equations are applied depends on the type of rock, the available data and their quality. Presented here is a pragmatic approach. With careful thought the standard gassmann equation can be applied successfully to determine an appropriate magnitude of fluid substitution effect in all reservoir rocks.
Gassmann - Practical Equations Figure 8.1 illustrates the Gassmann rock components and practical equations (derived from Gassmann's relations) that can be used in log analysis. Batzle and Wang (1992) equations or locally derived
if! = Po -
Pb Po - Pfl
"'" -----....
Mineral tables and mixing rules
,
and mixing rules
~
/
Kd
Ko
\,
K o = Vpo Po -3 flo
'"
Pore space stiffness
K.
'K,a,
= VI'
, Pb
sa,
K
Shear modulus (Fluid independent)
IJI=V,'Pbl
KOK jl
if! 1
1
K so1
Ko
~ I--'
K o -Kfl
¢
K.=
1
1
Kd
Ko
---
Saturated bulk modulus
-3 j.J.
= V pjl Pfl
----
I--
V
4
K.=
Ko
-'
v
2
fl
vi'
Mineral Porosity Dry rock frame Fluid
4
,IK
data
~ f'-.
f.l
K Saf
=
1
¢
1
-+ Ko
K.+
KoKfI K o -Kfl
K=GPa, V=km/s, p=g/cc Figure 8.1. Gassmann - Practical Equations
Gassmann Assumptions Importantly, key assumptions in the model are that (Wang and Nur 1992) (figure 8.2) 1. the solid is homogenous and isotropic 2. all the pore space is in communication 3. there is limited coupling between fluid and matrix (low frequency assumption) 4. fluid that fills the pore space is frictionless (ie low viscosity) the shear modulus is not affected by interaction with the pore filling fluid.
4
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Deriving Inputs for Seismic Models 8.2 Gassmanns' Equation
In the strictest sense then Pore space totally interconnecting
Fluid is frictionless (ie low viscosity)
with moderate to high porosity.
No coupling between solid and fluid phases
Shear modulus unaffected by pore fluid
'Low' frequency model
Ld,da:it<
Figure 8.2. Gassmann Model - Assumptions
Seismic
o
Gassmann's model is likely only to apply to clean sandstones
Solid phase: homogenous and isotropic
?
Sonic
LO~ frequency I
Ultrasonic 10kHz O.1mHz
100Hz 1kHz 500Hz
At high frequency (eg in the laboratory) brine filled rocks show 1mHz
100kHz
I High frequency
?
High porosity/permeability rocks with low viscosity fluids
Gassmann -----------Biot-Gassmann-toLow/mod. porosity/permeability sands with high viscosity fluids
Biot-Gassmann Gassmann
dispersion effects (ie velocity increasing with frequency). In these situations Gassmann needs to be extended using additional models (such as Biot and squirt theory, see Mavko et al 1998) (figure 8.3). It is unclear whether rocks with low porosity and permeability may be dispersive at seismic frequency (figure 8.4).
+
?
Squirt flow Figure 8.3. Acoustic frequency and Rock Physics Models
Sandstones and Carbonates with moderate to high porosity
Tight Sands
Gassmann OK
Gassmann
At logging frequencies: Velocities may be dispersive Patchy saturation may characterise low saturation gas scenarios At seismic frequencies:
application requires
uncertaintv over fluid modulus
~
>-
Shaley Sands and Laminated Sands
care
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Figure 8.4. Gassmann
and Various Rock Types
Common Gassmann pitfall of exaggerated fluid substitution effect
~
Rocks with Fractures or Dual Porosity Systems
Considered thai sonic log responses in these rocks are essentially low frequency and Gassmann is applicable
Gassmann needs to be 'fudged' to achieve intuitive result
Other models required
©Rock Physics Associates Ltd 2007
5
,'.
Deriving Inputs for Seismic Models 8.2 Gassmanns' Equation
Fluid Substitution The workflow shown in figure 8.4 introduces the idea of fluid substitution. This workflow would be appropriate in a scenario where there are clean blocky sands with reasonable porosity and good quality log data.
Central to this approach would be the QC of the various log inputs as well as a comparison of the dry rock parameters with published data on real rocks.
,
2
f.l = V, Pb
3
K ¢-
¢
KoKfll
1
1
Ksaf1
Ko
----
4
K
$(112
=
5
6
Ph2
=
Vs2 =
Pb -
K o -Kfll
K¢+
=¢
1
The approach in Figure 8.4 can be described as 'data driven', in as much as the dry rock and pore stiffnesses used in the fluid substitution come from the input log curves. In some situations (for example where the log quality is not very good or there are inconsistencies between various log curves) then achieving a reasonable fluid substitution effect on the velocity curve may require a modelled approach (figure 8.5). The details of how this is done will be discussed in the following sections.
I
-+-
Ko
K¢
1
¢
1
-+ Ko
Kd
QC
K oKfl2 Ko-Kfl,
({¢.pfll)- (¢'Pf/2))
~ J.1
Pb2
~
Pfl_' = (p"S,.)+(l-S,.)p" Pb_' = (pp_,¢)+((l-¢)Po)
7
Figure 8.4. Fluid Substitution Workflow Log Data
Initial fluid Vp Vs Pb
I
Rock Model (stiffness) (eg Phi vs KiKO)
~,
"I;",,;J .... ......... _-
~---
H
KO
_
Initial fluid Kfl, P.
I
Gassmann inversion for
IInitial and Final fluids Sw1, Sw2, Kfl, P, Figure 8.5. Two approaches to Gassmann fluid substitution with log data
pore stiffness
r-
and dry rock
Final fluid Kfl, P. '---
Forward
tNp tNs
Gassmann (fluid sub)
~Pb
~
Model Driven
6
I
© Rock Physics Associates Ltd 2005
Substituted logs Vp.Vs, Pb
J Data Driven
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Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
8.3 General Comments on Gassmann Inputs and Workflow The workflow that will be discussed is as follows: 1. Estimate virgin fluid parameters (Kfl and Pfl) and Sx (invaded zone saturation) 2. Calculate matrix parameters (K O and PO) 3. Derive porosity (0) 4. Check relationship between porosity and Vp 5. Derive or evaluate shear velocity (Vs) 6. Input parameters to Gassmanns equation and invert for the dry rock properties (Kd' QC values
~,
ad) and
7. Perform fluid substitution Figure 8.6 shows a schematic illustration of the workflow. I Press Temp and fluid properties I
1
I Virgin fluid pO and Kfl I calculation
I
Mineralogy Components
~
I
I Log Editsltransforms I
IK.LogandflUid,P. I Reconcile density components and porosity
Real rock QC
I
~
Vp, Vs,
+. Ko ,Po ' K... P.
I Gassmann inversion ~ I dry r~k:~~jes
I
I
I I
Fluid substitution
1
I Water Vp.Vsandpb I Oil and gas i
Figure 8.6 Gassmann with log data - a workflow.
.11
iF'1>. .....,
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Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
8.3.1 Fluid Parameters Virgin Fluid parameters One of the first steps in rock physics analysis is to derive the properties of the 'virgin' fluids (i.e. the fluids that would relate to the petrophysicists saturation (Sw) calculation). The properties of virgin fluids at reservoir temperature and pressure can be estimated using the Batzle and Wang (1992) equations that relate fluid velocities and densities to fluid properties and reservoir conditions. These equations have been shown to give a good ballpark estimate. Care needs to be taken however with very light hydrocarbons and condensates. For these fluid types it is recommended to obtain compressibility data from the reservoir engineer. The inputs required for the Batzle and Wang (1992) calculation of fluid parameters are: • • • •
Res. Temperature (C), Res. Pore Pressure (MPa) Brine salinity (ppm), Gas index for brine (0-1) Density of gas relative to air 'l,<., ,.Jf.tcuVfL
q. d·=
• Oil gravity (API), Gas-oil-ratio (III). The units of the calculated fluid parameters are kmls for velocities, GPa for moduli, and glcc for density. As an illustration, Figures 8.7 and 8.8 show some relationships of fluids based on North Sea data. Gases are more compressible than brine and live oils. With high API and GaR live oils may have properties similar to gases. It is common to find relationships between oil API and depth. In the North Sea oil API generally increases with depth, owing to effects of bio-degradation at shallow depths. High API oils generally have higher GaR. Time should be taken to accumulate relevant fluid information for the basin that is being investigated.
0
Density (gIc:c) 0.5 1
1.5
0
0
:§: ~
8
Fluod mod~ (OPa) 1 2
3
0
500
500
1000
1000
relationships based on
1500
1500
a generalised North Sea
2000
:§:
2500
!
JOOO
2000 2500 JOOO
3500
3500
'000
'000
'500
'500
5000
5000
Figure 8.7. Modelled
-""'"
_
dataset.
mediumoil
-,..
Based on 3 depths 5000. 15000. 15000 ft 0.022 Flfl" temp grad 0.45 psiJIl pressure grad
""m
50000 gas gravily 0.7 medillm Oil 38 API 500 scflslb
8
© Rock Physics Associates Ltd 2007
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Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
API
o
o
20
40
300
500
I '"C.
,.
250
'0
150
~
100
/. // "/ . /
~ 200
1000
•
1500
x
•••
~
0
60
2000
::;
••
2500
•
•
V
50
o
5000 ft 10 000 ft 15 000 ft
a
20
40
60
Oil API
3000
Figure 8.8. API vs Depth and Oil API vs Maximum GOR - Central North Sea.
In most exploration situations the Batzle and Wang (1992) equations are perfectly adequate for modelling the expected differences between different fluid types. In production situations there is usually more data to consider, including PVT data generated by the engineers. PVT data include laboratory measurements of pressure, coefficients of compressibility, relative volume and reservoir fluid density. It must be remembered that PVT measurements are isothermal whereas those calculated using the Batzle and Wang (1992) equations are adiabatic. It is possible that the isothermal bulk modulus of a fluid can differ from the adiabatic by more than a factor of 2 (Batzle and Wang, 1992), although this is unusual. Discuss the relevance of the PVT data with the reservoir engineer before proceeeding. Since the publication of Batzle and Wang (1992) there has been a joint project of HARC and the Colorado School of Mines funded by 21 industry sponsors, investigating properties of reservoir fluids and their variation with the change of in situ conditions due to production. This has resulted in a free software release called FLAG. It presents the Batzle and Wang calculations along with some other methods detailed in Han and Batzle (2000). The program can be used to evaluate fluid parameter sensitivity.
Fluid Mixing The density of a mixture of fluids is simply the weighted addition of the densities of the various fluids. The fluid modulus of a fluid comprising two fluids requires a mixing model. For the purposes of modelling the effect of fluid substitution on rock properties it is generally assumed that Woods law applies (equation 8.2):
1 Kfl
Sw Kw
1-S Kh
- = - + - -w
Equation 8.2. Wood's or Reuss' law.
This equation essentially describes the situation where the relative proportion of each fluid (i.e. the saturation) is the same in each pore (i.e. it is a homogenous mixing model). Such an assumption is generally held to be valid for modelling at seismic frequencies for rocks which satisfy the Gassmann assumptions.
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Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
Invaded Zone Fluid Parameters Given that the density log measures just a few millimetres into the borehole wall, the appropriate fluid density to calculate porosity is the fluid density of the invaded zone (figure 8.9). The sonic tool is considered to be less prone to invasion effects than the density log.
~_-"v"",O'--'1. 2 . _00 _ 0 -20. HMO
100. SW(1to) SlCO("4)
0
Uninvaded zone
2.---20. 100.--0 ",,0
2.---".
•
Hydrocarbon
•
Formation water
near borehole schematic mudcake Invaded zone Transition zone Uninvaded zone
•
Hydrocarbon
•
Mud filtrate
' ........-
Invaded zone Figure 8.9. An illustration of the invasion issue.
Invasion is a complex process, resulting from the movement of filtrate from the drilling mud into the borehole wall under pressure, until mudcake builds up and the process stops. It is a volume process and the depth of invasion in high porosity rocks can be quite limited. In moderate porosity rocks, in holes which have been left open a long time or which have been drilled over-balanced the invasion can extensive.
The various issues that are involved in invaded zone fluid parameter estimation are:
•
• • •
Calculation of filtrate elastic parameters J P, th,,;k "'l!~ Batzle and Wang equations ~K ·nw 0' I' KCI mud filtrate density < NaCI mud density (owing to lower molecular weight of potassium) Sx - invaded zone saturation Resistivity interpretation (Sxo from Petrophysicist) Sx/Sw rules of thumb Decide on end-member fluids I
~ ~:v-,..
•
Use core porosity information if available Fluid modulus mixing Try Reuss first
•
Use stiffer mixing models to account for patchy satuCapon Trial and Error May need to perform fluid substitution and re-iterate
10
J/IuuIJ i
, - - '( (~
jj
p
f.!t
71' r
lU
~
to:?
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Filtrate properties Estimation of invaded zone fluid density requires consideration of the fluid properties of mud filtrate
as well as an understanding of the relative amounts of different fluids in the invaded zone. The most straightforward situation is where water bearing sands are drilled with water based muds (WBM). Where the saline component of the WBM is sodium chloride (NaCI) the Batzle and Wang (1992) equations may be used to calculate density. In this instance water properties derived from the Batzle and Wang (1992) equations would be a reasonable starting point for the fluid properties input to Gassmann's equation. Note that the filtrate density of potassium chloride drilling muds is likely to be slightly lower than that of NaCI muds owing to the lower molecular weight of potassium.
Invaded zone saturation Relative saturations in the invaded and virgin zones are calculated by the Petrophysicist through
the analysis of resisitivity logs with differing depths of investigation (figure 8,9).
In some WBM situations the following rules of thumb may be useful
= Sw+IF
S
I+IF
x
Where IF
~2
(after Production Geoscience Ltd)
Equation 8.3. Invaded zone
saturation (WBM) - 1
Sx
=S
0.2 IV
After Dewan (1983) Equation 8.4. Invaded zone
saturation (WBM) - 2
Oil based mud filtrate invading water sand is likely to reduce the density of the water sand. The filtrate part of oil based mud is up to 50% water with the rest comprising refined oils and other additives. Typical values for oil filtrate are about 0.75g/cc. A rule of thumb sometimes used in OBM situations is Sx (invaded zone saturation)=Sw if Sw<0.5 otherwise Sx=0.5. Talk to your petrophysicist before using these types of ruie of thumb.
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Deriving Inputs for Seismic Models
Invaded zone fluid densities in hydrocarbon situations are likely to be more uncertain where filtrate mixes with both water and hydrocarbon. The greatest uncertainties are likely to be in flushed gas sand situations. Use of core information to constrain fluid density In many instances fluid density estimation may involve a certain degree of trial and error. Certainly core porosity and grain density data from core analysis can be helpful to constrain fluid density (figure 8.10). In wells where there are multiple fluid zones and limited variations in reservoir lithology, comparison of fluid substitution results from the different zones may lead to a refinement of the fluid densities that are appropriate for each zone.
3.
t~P' l)'Yl JiU ~
RhoO 2.5
0
2. 0
:I:
'"
1.5
: I:
1.
0.5
O.
O.
20.
60.
4lJ.
60.
100.
CeRE Figure 8.l0. A forced regression of (depth calibrated) core porosity against the density log
Invaded Zone Fluid Modulus From a practical point of view once the invaded zone saturation and end member fluid properties are established it is straightforward to calculate fluid density. However, for the fluid modulus there is the issue of how the fluid should be mixed. It is advised that initially a Reuss mix is used and if this fails to give a reasonable answer then other modes of mixing can be invoked.
12
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The argument for using other modes of mixing apart from the Reuss average in the invaded zone is based on a physical concept of how the sonic interacts with the pore space. It is possible that in the invaded pore space the saturations are not homogenous (owing to variable permeability). Given that sonic travels the qUickest route through the rock (figure 8.10) it may be biased to the pore spaces with the highest moduli (ie high water saturation) and the velocity will be higher than the 'average' for the whole rock. This effect can be accommodated in Gassmanns equation by varying the stiffness of the fluid through the mixing of the moduli.
Sonic finds fastest route through rock - ie via stiffest pores
Hydrocarbon
water
, ,,
Measured velocity at logging frequency will be higher than the whole rock (low frequency) velocity Can be compensated for by increasing the fluid modulus in Gassmann
Different saturations on pore or sample scale Figure 8.11. Patchy saturation and velocity at the pore scale.
The empirical mixing relationship presented by Brie et al (1995) is useful to account for the effect of patchy saturation:
where 'e' is a number between 1 and 10 (figure 8.12) Equation 8.5. Fluid modulus mixing - Brie et al (1995)
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Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
3
Kfl = (Kw-Kg)*Swe+Kg
2.5 (/) ~
:; '0
0
2
1
E :2 ~
u..
2
1.5
3 5
Q)
>
:g
1
10
Q)
'l::
w
0.5 0 0
0.2
0.4
0.6
0.8
1
Sw Figure 8.12. Fluid Moduius Estimation (after Brie et ai, 1995
In a practical situation the modulus would be varied until the 'likely' dry rock parameters are matched.
8.3.2 Mineral Parameters Tables from the Literature Generally, values for the matrix density (Po) and the mineral bulk modulus (K o) are based on values from the literature (table 8.1). Obviously information is required on the various minerals that are in the rock. Very often the petrophysicists shale volume calculation is used as the basis for the relative volume of sand and shale. Sometimes, very detailed log analyses may be available (such as the Schlumberger ELAN analysis) where the logs have effectively been inverted for a range of minerals and fluids. Mineralogical reports can also be useful, particularly if there are exotic minerals with densities and moduli very different from quartz and shale.
Presented in table 8.1 are typical values of elastic constants for various minerals. Whilst the mineral properties of quartz are known reliably within a certain range, for dry clay they are not. The parameters of dry clays vary dramatically (table 8.2). Wang et al (2001) has shown that dry clay densities can vary between 2.2g/cc to 2.84g/cc and the bulk moduli (K) can vary between 10GPa and 70GPa, while the shear modulus is roughiy equal to 0.47K.
14
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Youngs Density Modulus Quartz Chert Calcite Doiomite Aragonite Magnesite Na-Felspar K-Felspar Ca-Felspar Glays (a~flFox) Muscovite Biotite Halite Anhydrite Gypsum Pyrite
2.65 2.35 2.71 2.87 2.94 3.01 2.62 2.56 2.73 2.eB 2.82 3 2.16 3 2.31 5.02
95.756 67.682 84.292 116.574 92.559 169.659 71.253 61.878 99006 4a.Q17 78.731 70.223 38.3 87.034 77.114 338.68
Bulk Modulus
36.6 26 76.8 94.9 47 114 55 48 85 41 52 50 25.2 66.5 58 158
Shear Modulus
45 32 32 45 39 68 28 24 38 17 31.5 27.5 15.3 34 30 149
Vp
Vs
Poissons Ratio
6.0376 5.4 6.6395 7.3465 5.8 8.2 5.9 5.6 7.05 4.9 5.8 5.4 4.6 6.15 6.75 8.4
4.1208 3.7 3.4363 3.9597 3.6 4.75 3.3 3.05 3.75 2.6 3.35 3 2.65 3.4 3.7 5.45
0.064 0.058 0317 0.295 0.187 0.247 0.272 0.289 0.303 8.324 0.25 0.277 0.252 0.28 0.285 0.137
Table 8.1. Examples of Solid Mineral Elastic Properties., After Simmons & Wang, 1971.
Clay mineral Smectite Illite Kaolinite
Chlorite
K (GPa)
u.{GPa)
17.5 39.4 1.5 37.9 12 95.3
7.5 11.7 1.4 14.8 6 11.4
Table 8.2. Examples of Dry Clay Elastic Parameters (After Avseth et al 2005)
Mineral Mixing Single 'effective' mineral densities are derived on the basis of the combination of the densities of the different minerals in the rock. An effective modulus (Ko) of the mineral composite is calcuiated by mixing the moduli according to a mixing scheme. There are a number of mixing schemes (see Mavko et ai, 1998). The Voigt-Reuss-Hill (VRH) average (Hill, 1952) and the Hashin-Shtrikman (1963) mixing schemes are the most commonly used. The mixing scheme appears not to be a critical factor in the process. The VRH average scheme is shown in figure 8.13.
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Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
Voigt modulus
Kr Reuss modulus
VRHav modulus
1 Valqtz + Valclay K qtz K clay K vrh
K +K v
r
2
Figure 8.13. Voigt, Reuss, Hill Average mixing
8.3.3 Porosity The porosity of a rock is the ratio of the volume of pore space to the volume of the rock and is expressed as a decimal or percentage. As discussed previously porosity is simply described in terms of the fluid, mineral and bulk densities (equation 8.6): Where: Po = matrix density, Pn = fluid density, Pb = measured bulk density Equation 8.6. Porosity.
Once the mineral and fluid parameters have been calculated the porosity calculation is straightforward (as it is related to the various density components). For the rock physicist this consistency between density and porosity is important given that bulk density is an output of the fluid substitution process. It is worth saying that a good density log is a key requirement to perform meaningful rock physics analysis. Shaley sand porosity Most sandstones commonly have shale as part of the rock (figure 8.14), introducing the concept of an effective part of the porosity where fluids can freely move in and out of the rock, and an ineffective part with water bound to clay minerals. It is common for petrophysicists to calculate effective porosity as it is a key parameter in determining the volume of hydrocarbon. In terms of the simple porosity equation, the effective porosity is calculated when the mineral density is considered as a mix of quartz and shale. Whether Phie or Ph it is input to Gassmann doesn't really matter too much for rocks with porosities above ~15% so long as the saturation is consistent with the porosity. As shall be seen in section 8.4 care needs to be taken when applying Gassman in shaley formations with less than 15% porosity.
16
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1>1
Quartz grains
::::::
Dry shale
•
Clay bound water (cbw)
D
Effective porosity
Total porosity r_----A----~"
Quartz
'-
>?v - PklT
/
V
Shale
C1Ii?
)wc: -PkfE I
0.2
L--~M
sf,;v fl
£ wJ/S{> .fe~d 0.15
(I-S,J¢e =(I-SwtM UJ
Xl.1
tl.
Swt =1-
(I-SweMe ¢t
005
0'0.
005
0.1
015
0.2
PHIT
Figure 8.14. Shaley sandstones - definition of effective and total porosity
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The issue of connectivity / permeability It is critical to understand the connection between porosity and saturation when performing fluid substitutions. A simple illustration considers the effect of packing of spheres on the porosity (figure 8.15). In the case of regular packed spheres the porosity needs to be about 30% before it becomes connected throughout the rock. The connected (or 'effective') porosity is closely linked to the permeability (i.e. the ability of fluids to flow through the rock). Thus each rock will have its own porosity cut-off below which the porosity is 'ineffective' and the rock is essentially impermeable. This is an important issue for Gassmann modelling as there is no point trying to model the effect of saturation changes in a rock that comprises only ineffective porosity. An example of water saturation relationships to porosity and shale content is shown in figures 8.16 and 8.17. The data is from a discovery well and effectively illustrates the irreducible water saturation characteristics of the reservoir. /-",
o
/-"" ,-,---/
" .i-'/--,
••••• •••••••••• •••••• '".--/
~
Cubic packing 47.6 % porosity
•••••
Rhombic packing 39.6 % porosity
Tetrahedral packing 25.9 % porosity
Figure 8.15. Sphere models illustrating the effect of packing arrangement on porosity.
1.0
PHJE 0.5
1.0
"" 0.•
OA5
0.•
0.•
0.4
"""
0.7
.
0.6
0.6
I
0.3
"R
~ 0.5
'"
0.35
0.4
w
0.4
0.25
~'?
0.2
;. t~_l "
0.3 0.2
0.2 0.1
~
o
O. O.
0.05
0.1
0.15
0.2
\ ." ~~
0.0
0.2
0.1 0.05
" "
0.4
0.0 0.6
0.•
1.0
sw
PHIE
Figure 8.16. Sw vs
"
0.15
''It •
Figure 8.17. Sw vs Vsh &
Obviously grains in sands are rarely spherical and the porosity will be a complex function of grain size distribution and packing as well as the effects of cementing material and mineral diagenesis. As a rule of thumb when sandstones approach 35-40% porosity the grains become suspended. This point at which a rock loses all strength has been termed the 'critical porosity' (Nur et ai, 1998). 18
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8.3.4 Compressional Velocity and Porosity The initial rock physics analyses on log data should comprise crossplots of the key parameters. One of these is the porosity vs. compressional velocity plot. Unless something strange is occuring there should be a first order relationship between porosity and compressional velocity. As porosity decreases the rock becomes harder and the compressional velocity increases. Also the data should fall within certain bounds. Figure 8.18 is a collation of data from the literature that illustrates a number of aspects of the porosity vs. compressional velocity relationship. 6000 ,,,-----,----,------,--------, \'\, Wir 5500 \ " y Ie ~ Han et al 1986 (40MPa) dataset Vp 5000 \ I \
\~\ ~1\
.
4500 +-¥----=--tL-..--.;-+---_+_ Reuss _~4~02l00~=~~~~;:,;:~~::~1--~= } . , JJ f) d --= 3500 Oseberg Qtz cemented /lq:WWIC Uu X '7 '-\' IU/ '
/)./Tf< 2000 +----~---_+---"_'_'I--._'<_---1 Gulf Coast example o 0.1 0.2 0.3
04
l
r sity
-r
Shallow unconsolidated example
Figure 8.18. Brine bearing San stones: Porosity V5. Compressional
• The first order relationship between porosity and velocity is only locally linear. • There appears to be a lower bound at relatively low porosities (black dashed line). • For a given porosity there is a range of possible velocity. This is an effect of pore shape. Flatter pores give rise to slower velocities as they are more compressible than more equant shaped pores. Pore geometry distributions are dependent not only on the state of consolidation but also on the lithology. The inclusion of shale (clay and silt with bound water) into a sand has a similar effect to increasing the number of crack-like pores in the rock. • Wyllies equation (see following section) is relevant for compacted sands (i.e. those in which all the flatter cracks and pores have been closed due to consolidation). • Presence and type of cement are factors in velocity. Quartz cemented Oseberg sands have higher velocities than clay cemented sands, and these in turn have higher velocities than uncemented Troll sands. • Effective pressure is a key factor in the velocities of high porosity sands.
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Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
8.3.5 Wyllie's Equation Wyllie et al (1958) described the fundamental correlation of velocity and porosity in consoli ated sediments. Wyllie's time-average equation relates the sonic transit time (in us/ft) to the dition of the transit times through the pore space and the matrix (equation 8.7):
1= ljl.lr + (1 - ljl).lma Where: t = transit time of rock t f = fluid transit time t m, = matrix transit time Equation 8.7. Wyllie's equation.
Sometimes petrophysicists use the equation as one way to calcuia
the porosity (equation 8.14):
ljl = (I - Ima ) / (If - Ima ) Equation 8.8. Porosity from Wyllies Eq
tion
An empirical correction to Wyllies equation in relati ely unconsolidated rocks commoniy used by petrophysicists in determining porosity is to mul . Iy the time average equation by a compaction correction factor (equation 8.9):
where Bop
Equatio
Wyllie's equation has been m 1980).
transit time shale/100.
8.9. Compaction correction factor.
ified to improve the quality of the prediction (e.g. Raymer et ai,
Equation 8. O. Raymer Hunt Gardner (1980) Equation (for porosities <37%)
Care must e taken, however, in using any sonic/porosity relation without calibration. For excellent introduc . ns to the rock physics context of empirical sonic/porosity relations and discussion on physic models that describe velocity in terms of rock components (including pore geometry) the read r is referred to Wang and Nur (1992) and Castagna et al (1993).
20
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8.3.6 Shear Velocity The shear velocity input to Gassmann can come from: 1. Predictions based on empirical models 2. Direct measurements of shear.
8.3.7 Vs Prediction based on Empirical Models: Linear Regressions There are two empirical approaches that might be used. The first is based on relationships derived from measured data (in the laboratory or from logs). It is a fortunate fact that there is a strong linear correiation between compressional and shear velocity. Table 8.3 below shows some of the commonly used Vp/Vs relationships.
• mudline • sandline vllfI.V S.4~ ~ Quartz Line • • • •
gas sands shale dolomites limestones
• rock salt • anhydrite • coals
Pv t (/'c,v{LI) ~ (' rG
.) c
-
~
Vs=0.8621Vp-1.1724 Vs=0.8042Vp-0.8559 Vs=0.8029Vp- 0.7509 (based on Murphy et al 1993)) VpNs -1.4-1.8 Vs=0.77Vp-0.8674 VpNs =1.8 VpNs=1.9 (if V!,,<1.6I\fl'I/a) Vs=Vp2(-0.05509)+1.0168(Vp-1.305) (Vp> 1. 5km/s) VpNs =1.7 VpNs=1.8 VpNs - 1.9-2.2
Figure 8.19 shows an example where
Table 8.3. Vp/Vs Relationships (V=km/s).
/1 /?_A I, .. 11.
L~vMU-<
I -
SfbSu, 0
/.n. '/
11000 9000
Castagnas
sandline~
8000
. (). i the 'sandline' is a close approximation
fA.. I
'7fJ -
W
V
0
g: ~
7000
Vs 6000
~
~
:>'
0;1 rpo
5000 4000
r
8000
10000
12000
14000
16000
vp Figure 8.19, Saturated Laboratory Data and Castagnas
S~.
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For clastic sand/shale sequences commonly used lines for brine saturated rocks are Castagnas 'mudline' (an average VpfVs relationship for sand/shale rocks based on in-situ and field measurement data) and the 'sand line' (based on numerous consolidated sand samples). The data used to derive these particular relationships comes from the Gulf of Mexico and the continental United States (see Castagna et ai, 1993).
2.1:1-/0
18000
fA ti(!,j,
to the brine-filled velocities of some North Sea sand samples (dry properties were measured in the laboratory and saturated using Gassmann's equation). However not all sands behave in accordance with Castagna's sandline. For example high porosity sands can have higher Vs than predicted from the 'sandline' (Dvorkin and Nur, 1996). It must be remembered that Vs is an intricate part of Gassmann and that its consistency with other inputs needs to be checked.
Z
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Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
A popular approach to the interpolation problem was published by Greenberg & Castagna (1992, figure 8.20). Vs prediction is based on several linear regressions and estimates of the mineralogy. The Vs is the average of the harmonic and arithmetic averages.
4500 400
./-. ij'/
3500 3000
Vs
-
&'
2500
A
2000
..--:W
1500
sand shale limestone dolomite
-
/'/.:?
1000
Sand Vs = 0.80416Vp - 0.85588 Shale Vs = 0.76969Vp - 0.86735 Lim~stone Vs = -0.05508Vp2+1.01677Vp-1.03049 Dolomite Vs = 0.58321Vp-0.07775
/'
500
o 1000
2000
3000
4000
5000
6000
7000
Vp
Figure 8.20. Greenberg-Castagna Linear Relations and Vs prediction.
There has been a large amount of work done on Vp/Vs transforms, for example some workers have constructed simple equations that include the effects of clay and effective pressure (see Mavko et ai, 1998). However, care needs to be taken when employing these relations that they are relevant to the specific rock types under investigation. In both exploration and production situations a small amount of shear log data can be invaluable in both determining the validity of published regressions and in establishing those that are formation-specific. Figure 8.21 illustrates an example where the Greenberg Castagna relatiO{'s do not adeuqately describe the Vp vs Vs
tf""{..L WI./
relationship.
\j,
n
~
X-V.o~
7000 1~-;::~==::::::;-~Castagna
~.••:
Saodlio. 6000
\, c..
, ......
.",
Q,~J
:'
t,~/ V-\
(!
i
C(i.yR.
~ It
Olv
•
Figure 8.21. An example of
sandstones which do not fof/ow the Greenberg castagna Model
5000
I
Vs ftIs 4000
3000
• oil sand, sand::: 0.5, Sw < 0.5 • wet sand, sand ~ 0.5, Sw ::: 0.5 • shale. shale::: 0.5
2000
/ 22
o
:5 M Vp ftIs
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In some basins sands and shales can fall on the same Vp vs. Vs trend line and there may be significant differences between hot and cold shales (figure 8.22).
3OOO.r------L~
'normal' shale
VSH
CJ(
1.
0.9
Organic rich 'Hot' shale
0.8 0.7 0.6
!!Z 2000.
0.5 0.4 0.3
1500. 0.2
e Smd
0.1
1~.----::3000=.---""4000""""'.
-----.,5000=.---"""6000.°·
VP
Figure 8.22. vp vs Vs for 'hot' and 'cold'shakes - North Sea
In very shallow sediments (i.e. where Vp is <8000'/s) it is likely that the simple linear regressions breakdown and the Vp/Vs is highly dependent on the state of consolidation of the sediments. At the sea bed the Vp!Vs ratio is infinite (as Vs does not travel through water) and reduces with depth as compaction increases. The trend of Vp!Vs with depth in this shallowest layer is highly variable and largely unknown. One worker (A. Hook formerly of Magnetic Pulse Inc.) has developed an equation (called the consolidation model) which attempts to incorporate the effect of poor consolidation into the relationship between Vp and Vs (equation 8.11):
Equation 8.11. The
Where: VPc = pwave velocity at critical porosity VPm = matrix p-wave velocity, VS m = matrix 5 wave velocity and
Consolidation Modei (after MPI).
y can be approximated by (1.9-(vs!Vsmf))'
V Y = V Y+ V Y VpmY-VpoYJ p
pc
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s (
V Y sm
©Rock Physics Associates Ltd 2007
23
Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
Figure 8.23 provides useful templates for assessing Vp/Vs ratios in sand/shale sequences. It illustrates that in general with increasing velocity (i.e. depth) the Poisson ration decreases. 4500
-,--r---,--,---,----,-----,----,----,---,--r----,
Quartz
- - - alz cemenled
4000
+--+--+-+-+-+-+-+-+---F-+---j
3500
-1----1---1---1-----J--I--l--+--l--+:~:;,.~--.j
- - - Iro 115 MPa -
lrolll0MPa
-1----1----I---l---l---l--+--I---I--+-+---.j
-
troll20MPa
3000
2500
claycemenl
Calcite
.....
- - - Castagna 55
- - - aIrline
Cays
-1----1---1---1---1--."-..
- - - Castagnas Mudline • •••••• - 0.45
.'
••••• _-- 0.4
•••••• _- 0.3
.'
·0.4
-_ •••• _- 0.2 -_ •••••• 0.1
..
0.45
._--_ ••• 0.49 _ _ _ oon501
'
• ,u
1000
500
-1----:'1;t:'J.'-.. .--.+.-.-..-.!-.~.~.·...I--0-.4~9'-J-:-"---l---1---1-----J--I---1
•
calcite
•
days
_ _ _ shales
o-l--.!-l-----1--+--l---l---l---I--l--+--J----J 1500
2000
2500
000
3500
4000
4500
5000
5500
6000
6500
7000
vp
- - - Qtz cemented
- - - Castagna 55 2000
+----+----+-----,--IL--;2.:,40-~;.e:~
clay cement - - - Iroll5MPa -
\rolll0MPa
- - - Iroll20 MPa
0.4
..
Vs
- - - Qtzline
.'
- - - Castagnas Mudline ••• ----- 0.45
'
0.45.....· .. ,
.. , .. , .. , ..
•••• _--- 0.4
••••• _-- 0.3 ._ ••• _-- 0.2
,
-------- 0.1 -------- 0.49
SOD
-1--_-4~~---J------1---.,d,;.0:__.4:.:;9~ ..~..::..:.:j. .--' . .. _.. . ... -- .. -.. ..
--
--
,
- - - ooosol •
qlz
•
calcile
clays • _ _ _ shales
o+--'---+----J------1----+-----.j 1500
2000
2500
3000
3500
4000
vp
Figure 8.23. Vp/Vs (dashed lines represent Poisson ratio).
24
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Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
8.3.8 Dry Rock Poisson Ratio Method of Gregory (1977) and Hampson Russell Another empirical approach that can be used is here termed 'the dry rock Poisson ratio approach'. The dry rock poisson ratio is defined as
(Yd
=
,
Equation 8.12. Dry rock
M=Vp P
poisson ratio
S = 3(I-O'J 1+0'" It follows from the relationship of Vp and dry rock Poisson ratio within Gassmann that Gassmann can be re-written
a=S-l
to input Vp and dry rock Poisson ratio (ad) and to derive the shear velocity (Vs) (equation 8.13):
y= -b+(b' -4ac)" 2a K,,=(l-y)K o
Figure 8.24 shows that this approach can have equally good results to the empirical sandline of Castagna et al (1993). Also owing to the fact that parameters such as porosity are included it can be used effectively to establish a consistency of the inputs to Gassmanns equation. One drawback is that it requires total porosity to calculate the Vs for the shales and it can be difficult to stabilize.
f.L=
3KAl-2O') 2(1 + a)
Equation 8.13. Workflow for VS calculation via the dry rock
poisson ratio method
11000
11000
10000
m
9000
1Ji'" m
8000
y = 1.0831x· 626.02 R' = 0.9491
.!f0
c
U
6000 5000
~ 6
.¥
7000
~
>
~
iO
°~
~ v
4000 4000
9000
g"
8000
~
7000
~
6000
e-
y=x+33.478 R' = 0.934
10 000
~
>
5000
+---+---+---+-----1
6000
8000
10000
12000
4000 4000
6000
Vs Gassmann
8000
10000
12000
Vs Gassmann
Figure 8.24. Vs prediction comparison of Castagnas sandline and Vs from dry rock poisson ratio method. ~)!.! GEOSCIENCE
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25
Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
Hilterman (1990, figure 8.25) used this technique with log data and modeiled the dry rock Poisson ratio as a function of Vshale. In practice there is a limitation to this technique, (for example where porosity is zero the formula becomes unstable).
"'6 g
DRP ratio varies for shales depending on compaction history
0.35
i!' c
o
V> V>
'0
0.
13
e
c:-
Sand
0.1
o
Clean sand
Clay rich
100
~
~~
Figure 8.25. Modelling dry rock poisson ratio as a function
of Vshale (modified after Hi/terman, 1990).
8.3.9 Using Linear Regressions to Predict Vs in Hydrocarbon Zones In order to use the Greenberg-Castagna type approach to predict Vs in hydrocarbon sands the hydrocarbon effect first has to be backed out of the Vp log. In order to do this properly requires some prior knowledge of an appropriate stiffness model. The approach described by Mavko et al (1995) uses the critical porosity model (a stiff rock model). This may underestimate the substitution effect in rocks which are relatively 'soft'. Mavko et al (1995) construct the Gassmann fluid substitution model graphically (Figure 8.26). The effect of fluid substitution on the saturated modulus is understood as the difference between the straight lines drawn from the mineral point to the Reuss mixing curve at critical porosity.
1.0,..-------------, Reuss (waler)
Reuss mixing curve for
c
0E: ~
walerand mineral
~
0'--_-+_ _'----------'
o
~R
1.0
Porosity ("') Figure 8.26. Graphical solution of Gassmann fluid substitution using the critical porosity model
26
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Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
If K is replaced with the M modulus in the graphical solution then the following workflow will yield Vp with hydrocarbon substituted for brine (equation 8.14). This approach might be termed 'Modified Gassmann'.
¢R =
¢M.' - Mo(l + ¢)M/I + M,a,M/I (Mo -Mro,XMo -M/I)
P=Po(l-
:.J
4 K$'l' =M,o,-'3 p ~
K.... =
K$o/'
1
1 ---K,
---
K,,"
I
=
I Ko
Vpl =~
K S(I/2
¢
-+
K¢So, +
Equation 8.14. Fluid
I
I Ko
K/lIKo
K Fal
K o -KJ/l
Vp '
Pbl
IVp_wet
=
=1
substitution without VS
¢
-+
+~P
K,o"
---
K,a"
(modified after Mavko et
K/I,K o + K-K o
a11995)
/I'
R. Shu
+~ P
,j UOI2,ud !2kJE loll 1A/1la--',:n<J 7.) Met aJ ~ (,//0 !.Alii') '?)ea-!~. D~ DUe- j'-iJ~f{llv.,
P"
if
Vp2 - Vpll
I
The value of critical porosity can be optimized through forward modelling to hydrocarbon bearing Vp (Figure 8.27). Of course the success of this approach depends on Greenberg-Castagna being the appropriate Vs prediction tool.
v p2-- 1i.v pi
2
-(K
fli
_K
1 ).1.-._
Jl2,/,2
P2
@ p
'f'R
Modified Gassmann (no Vs)
I Optimise on Vp (minimise errOl by changing Q<)
Minerals %, Kma
p
~)~ GEOSCIENCE
& .... T ~I
R A I N I N G
ALLIANCE
Brine Vp. P Greenberg-Castagna
Vs Log fluids
SXQ
Porosity from density
I
~ Vs
P2
Figure 8.27. Modified Gassmann to Predict VS - Optimizing on critical
porosity
I
Inverse Gassmann
Full Gassmann
I
Dry parameters
©Rock Physics Associates Ltd 2007
27
~
eJ,u!t.. _
Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
8.3.9 Measured Shear Data Interpreted compressional and shear sonic are provided from the interpretation of sonic waveform data. The interpreter needs to understand where the data has come from - is it rig-site processing or subsequent lab processing? Rig-site results usually are less reliable. The processing of shear log data is interpretive and there are several methods of computing shear and compressional slownesses. For information concerning the operation of dipole logging tools and their interpretation the reader is referred to in Schlumberger (1994). It is always worth getting trained personnel to review the waveform data. Crossplots can be used to identify some of the bad data situations. Monopole tools have a welldocumented limitation where the shear velocity of the formation (e.g. shale) is less than the compressional wave velocity of the drilling mud (figure 8.28). In these instances the mud arrival obscures the shear arrival from the formation and this is detected on a Vp vs. Vs plot as a trend parallel to the Vp axis. The data is clearly in error and should not be used for modelling.
5 500
5000
Log Data
500
•
000
500
3 000
7500
• •
....... .. . :,. ~
","
--- ---
•
~
•• • •• ~
~
----
~Shale Line
8000
8500
9000
P Wave Velocity (fUs)
Figure 8.28. North Sea Shales: The Problem of Monopole Shear 6000 , - - , - - , - - , - - , - - - - , - - - - , - - - - , - - - -
•
5500
5000
Vs 4500
(\f' ~+-e,.----+-
Castagnas Mudline
Figure 8.29 shows where the shear velocity of the shale has been measured properly. However, the interpreted results of dipole waveforms analysis are not immune to the problems with direct mud
arriva~/C~1 ! Cl:efl111
2V.-vb.l, tf
fuAJe!
3500 +--+--iti
l·';t-)C1;~
?-< bu4... £oj
3000 +_-+-~~-+_-+_-+_-+_-+_-+____1 7000 7500 8000 8500 9000 9500 10000 10500 11000 11500
Vp
28
Figure 8.29 Dipole Sonic Data: Shale Example.
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Figure 8.30 shows a dipole example from a sand section where the effect of mud arrivals is clearly seen .
7000
6500
•
•
•
•
Castagnas Sandline
•
•
•
6000
~
5500
~
>
5000
4500
• •• • •
4000 9000
10000
11000
12000
Vp (fUs)
Figure 8.30. Dipole Shear Log Example - Sands.
There are some effects which are not possible to categorically recognise simply by looking at crossplots. For example mode interference from Stoneley waves can bias the Vs to lower velocities. Figure 8.31 shows an example of processing from brine sand data that have this bias. Such effects can only be picked up with careful phase analysis of the waveform data (eg Kozak et
£A::LJ
al 2006).
I:;:,..)
<'
,) UrR - f(),v;'C
Sok(r C!q;!q 2500.
2500.
2000.
2000.
/0
/
J
,1~
P.
'1'~t.M-! fit1lf-;i.D~ i.A-J
LOtH!. (? Wf-
~ ",I 1500.
~ 1500.
>
1000.
1000. Sand
Sand
Shalo
Shale
""i1lOO!:::-.----,2000=.---:3OOO=.---:4000=-.---::::'. 5000. V,
Original processing Stoneley interference creates bias to lower Vs
""iooo.
3000. Va reo
2000.
4000.
5000.
Re-processing Re-processed data consistent with offset wells that show close agreement with GreenbergCastagna Model
Figure 8.31. Brine sand data example - original data Vs was biased by Stoneley
contamination
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Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
8.3.10 Dry Rock Frame Moduli Sandstones Once the dry moduli have been derived then the numbers should be QC'd in much the same way as described with porosity and compressional velocity. Presented in figures 8.32 and 8.33 are plots of porosity vs. dry moduli showing the generai range of values encountered in real rocks. The dry moduli vary systematically with porosity. Murphy et al (1993) derived best fit functions for clean sands based on iaboratory analyses (equations 8.15 and 8.16):
Kd =38.18(1 - 3.39<1> + 1.95<1>2)
Equation 8.15. Dry bulk modulus trend in consolidated clean sandstones (after Murphy et al
1993)
Equation 8.16. Shear modulus trend in
Jl = 42.65(1 - 3.48<1> + 2.19<1>2)
consolidated clean sandstones (after Murphy et al
1993)
These results are similar to the critical porosity model of Nur et al (1998). Essentially they apply to compacted sands with mid-range porosities. As with compressionai veiocity there are variations in the moduli range at a given porosity owing to the presence of clay or microcracks.
45 40 +----=.:---_/_
-
Murphy et al1993 - - - - I
35 30 25
Kd 20 ~-+---
15
North Sea Tertiary Trend
.-----,7"-
10
Gulf Coast example
5 -t----+--=--=--"'f-...=....-"----= "",,~::::::::t- Troll 0 0
0.1
0.2
Porosity
0.3
0.4
Shallow unconsolidated example
Figure 8.32. Porosity vs. Dry Bulk Modulus
30
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Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
45...,------.-------r------..,.----, 40 ~~---l- -
Murphy et al 1993 ----l
35 -1--....:..~~___+_----I-----1-------I 30 -1------'~~----I------l-------I 25
Jl
North Sea Tertiary Trend
-l--,......'--+~~-~_!'=-------+_....:...--___<
20 -1--~~~-*~----=~-I-----1-------I 15 -I--~:--=
....Ib:::;I:Ii~~~---_I__-
Oseberg
10 +----""I..:r-t~;t&I
Troll
5 +----+----=-~'!'-==---:
oL------J---L---L~s;::r o
0.1
0.2
0.3
0.4
Shallow
unconsolidated example
Gulf Coast example
Porosity Figure 8.33. Porosity vs. Shear
66
Porosity vs Dry Rock Poisson Ratio sands 0.35
Vsh
..e
0.25
.~
0.2
·1Jir rr
0.3
x· _:l.
c
~ 0.15
• ~
8'1..
x •
o
•
0.1
':
I ..
.0-0.05
~t~. t
.0.05-0.1
--
X 0.15-0.2
.-
0.1-0.15
#l-
x 0.2-0.3 • :>0.3
~
-
0.05
o o
0.1
02
0.3
0.4
Porosity
A rule of thumb for particular sand types is : Clean consolidated 0.1 - 0.2 (average 0.15) Unconsolidated 0.1-0.35 (Spencer et al 1994)
Figure 8.34. Porosity vs. Dry Rock Poisson Ratio (data from Han et at 1986)
Figure 8.34 illustrates that the dry rock poisson ratio for consolidated sands can vary widely between 0.1-0.3. Notice that with increasing shale content the dry rock poisson ratio of the sand increases. Cleaner sands tend to have lower dry rock poisson ratios. Spencer et al (1994 and Zimmer et al (2002) also note that the dry rock poisson ratio of unconsolidated rocks varies between 0.1 and 0.35. If the dry moduli and the dry rock Poisson ratio fall outside the expected range the shear velocity and the fluid modulus are generally the first parameters to check.
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Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
({;;;1!~oIu au j;/!tIU.~-I ~ cllUv7c J d.
(
7J
u . tI..u.. s
/I-Uod. 1<- tJ7U. Ii /I.{.#,fJ et,a.,;CIA " t2 vq ICi-U Carbonates (/ If -Figure 8.35 shows the dry properties of selected carbonates. In general the shear modulus is always less than the dry bulk modulus (owing to the effect of mineralogy) uniike sands where the shear modulus can be higher than the bulk modulus at low porosity. Some carbonates can show strong trends in dry rock poisson ratio whilst others do not.
!
80
80 ,---,....------,------,
70 60 50
70 - 1 - - - - + - - - - 1 - - - - - 1 60 - 1 - - - - 1 - - 501----1----1----1
~ 40
30 20 10
r..·· ".~
---
=> 40
-.r:.~ .lIIIi
• -----. .
8~fJoo
0
0.000
30 20 1--=:::....' 'l'-""-~'H----I 10 -j----+----;-rr-C1n;OOO 0-1----+-....:...----''-1---''''-''=1 0.000 0.100 0.200 0.300
'b .n. 0'-'00'
o 0.100
0200
4-~~-t____---t____--_i
0.300
Porosity
o
~
0.5 0.4
I..
'"
n10
a..
... •"'lIt. ..
"" 0.2 ~"._ u
••
Ii.
1:' 0.1
u
00
·8-gl;...
~- • • • •
'0
c
o Chalk
Porosity
t.. :z 0.3~_··· g
elms • Anhydrite • Dolomite
-
•
0",-,
0
0
__I"Q,~
•
0-00 lO-
.
0
.lms • Anhydrite • Dolomite o Chalk
0-1----1----+-----4 0.000 0.100 0.200 0.300 Porosity
Figure 8.35. Carbonates - Frame Moduli (coloured points - data from Rafavich 1984, open circles - Chalk North Sea).
Owing to the high degree of pore geometry variabiiity within carbonates the reader is strongiy advised not to use generaiised models but to make specific analyses. A useful discussion is presented by Marion and Jizba (1997).
32
© Rock Physics Associates Ltd 2007
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Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
8.3.11 Aspects of Fluid Substitution Effect of Rock Stiffness on Magnitude of Fluid Substitution A useful way of understanding the mechanics of fluid substitution is to utilise the normalised bulkmodulus (K/K o) as a function of porosity (
Figure 8.36. Porosity
....""'''''''-~- -
, -,- ,
- - - - - - - -
, , T ,
vs normalised bulk
.
modulus- with lines of
- - - - - - - - -,- - - - - - - - - -
, ,
equal normalised pore modulus
o
~ 0.5
05 04
0,4
03
03 02
'-'-,,-',-J _ _:_ _ _ _
,
_ __ • __
,
0.1 - ----------:--------
,
~_--:_~_~_.._::_:_:-_-:_~_~_~
-+
,
- --
Ji
0.2
I
0.1
,,
o +-------i'-----+-----i--'- - - - - - - i 0.1 0.2 o 0.3 0.4 Porosity The following example was described by Avseth et al (2005) and shown in Figure 8.36. If the normalised fluid modulus change is 0.06GPa (for example in substituting water for air) then the substitution effect is 3 lines on the plot. Given the variability in the spacing between the lines the fluid substitution effect on a dry rock at A in Figure 8.36 will be much less than the effect at B. Thus, it is possible for low porosity rocks to have greater fluid substitution effects than higher porosity rocks. (The proviso here is of course that Gassmann actually applies to low porosity rocks).
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33
...
Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
As a guide to what to expect from an analysis of log data, it is useful to consider datasets from laboratory studies. For example Figure 8.37 shows dry lab data which appear to indicate that real sandstones may follow two possible trends; constant (normalised) pore stiffness or a linear, 'modified Voigt' trend (Nur 1992, Mavko and Mukerji, 1995).
Modified Voigt relationsip
Figure 8.37. Porosity vs normalised
~:: .~~~~~~J~~.~,=.~;,.+.l.l
0.7· .. o
0.6····
~
0.5
~
data from real rocks (Red points - Han et al (1986) 0-5% Vel samples, Blue - Han
.. Kq,/KO
et al (1986) 5-10% Vel, Green - Han et al (1986) >30% Vel, Purple points - North Sea
0.5
Palaeocene dataset)
0.4
0.4
0.3 0.2
bulk modulus crossplot showing
-
----------
0.1
--
:
•
--~------_. -----~----
------------~--
•
/. f.
0+---~---__j_---~~-__1
o
0.3
0.3
0.2
0.1
Porosity
0.4
>&K.li~ tf ;.p,
tU{.('IIA/1 (j These observations open the way to consider what might be termed 'model-based' fluid substitution. A model of KIKO is generated from the available dry data then this is used to calculate the difference in saturated bulk modulus. The difference in velocity is then applied to the original velocity log (figure 8.38).
{Ie<- a.id tf- 'JIUlfP$
Figure 8.38. Workflow for model based fluid substitution
V
1
V
2
Final Vp_sub = Log Vp - AVp
34
© Rock Physics Associates Ltd 2007
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Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow
Modulus vs Density Effects - the 'Fizz Gas' Phenomonen Figure 8395 shows an example of Gassmann modelling, illustrating the effect of fluid substitution in shallow and deep sands. The Sw vs. Vp plot in Figure 8.39(a) shows how a small amount of gas can have a dramatic effect on the compressional velocity of a high porosity shallow sand. The decrease in velocity is related to a significant effect of a small amount of gas on the bulk modulus. With increasing gas the effect on the modulus is negligible but the density decreases. As the density term is in the denominator, the velocity increases with increasing gas saturation. The acoustic impedance plot shows that most of the lowering of impedance occurs with the first 5% of added gas. This can explain why sands with low gas saturations can have significant amplitudes on seismic sections. However the addition of gas always serves to lower the impedance. The problem then in interpreting gas bright spots on seismic sections is that usually we don't have a good enough handle on the critical factors (e.g. rock properties and wavelet shape) in order to be able to distinguish 'fizz' from reasonable saturations of gas. Note that Poissons ratio does not discriminate the gas saturation.
B
A
sooo
2500
2000
~
~
>
-Oil
1500
1000 0 .000
0.200
0.400
0.600
0.800
1
4500
FG"l
~
>
~-o"
4000
'-----+---+----+---+------1
3500 0.000
po"
0.200
0.400
0.600
Sw
SW
sooo
10000
4500
9500
4000
9000
:;( 3500
~ " - Oil
3000
2500 2000 0 .000
-
-
-
8500 8000
7500 7000
0,200
OAoo
0.600
0.800
1000
0.000
0.200
Sw 0.5
0.400
0.4
~ ..
-
0300
0.400
0.600
0.800
1.000
Sw
0.500
a:
-Oil
0.200
0.3
~ -Oil
0.2 0.1
0.100
I
0.000
o.000
1.000
-
I
--
0.800
0.200
0.400
0.600
Sw
0.800
1000
0'----l-------I---+-----1-----1 0.000 0.200 0.400 0,600 0,800 1.000
.---z...1l1! ClhaA/f?\
~
SW
tvfW.,i/V ~s6
Figure 8.39. Saturation vs.Vp, Al and PR for A - shaiJow low pressure sand (34% porosity), 8- deep high temp/pressure sand (15% porosity). Note differences in Y-scales.
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35
Deriving Inputs for Seismic Models 8.3 Gassmann with Log Data - a General Workflow 8.4 Practical Gassmann Scenarios
The saturation vs. velocity and saturation vs. impedance effect of light oil is more linear. Indeed there is the potential for the prediction of saturation from seismic amplitude. Interestingly, in some rocks at low water saturations there may be little difference between gas and oil in terms of the compressional velocity. It is clear from figure 8.39b that pressure plays a signifcant role in the relationship between Sw and Vp. In the deep sand case the effect of high pressures is to flatten the Sw vs. Vp relationship.
and the relationship between AI and Sw is more linear. The 'fizz' phenomonen then should only be expected in relatively shallow sands (Han and Batzle, 2002).
8.4 Practical Gassmann Scenarios
8.4.1. Clean sands Of all the situations in which Gassmann's equation is employed probably the best understood is that of clean sands (eg Smith et al 2003). In this situation the mineral modulus and density are known reasonably well. In these situations scenario dry values can be derived which can be used to analyse the consistency of the various input logs and provide a means of QC. Water bearing sands drilled with WBM If a wet sand has been drilled with a water based mud, the fluid density (and therefore porosity) and modulus can be reasonably well constrained. It is unlikely In this situation that the difference between mud filtrate and formation water properties will be significant. Invaded Clean Sands Confident invasion correction is only really possible in clean sands in which there is good quality Vp, Vs, and density logs and porosity calibration (eg from core analysis). Without these data the problem is underconstrained. For example if there is no independent Vs measurement there is the problem that in order to predict Vs, knowledge of the fluid modulus is required.
Correction of the density log for invasion effects is straightforward. However there is usually an issue as to whether the sonic is reading the invaded or the virgin zone. In instances where there is a hydrocarbon contact then the dry rock properties above and below the contact should be compared. Unless there is some reason (such as preferential diagenesis in the water leg) then the dry rock properties should be similar.
36
© Rock Physics Associates Ltd 2007
~)/.! GEOSCIENCE
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~I
T R A I N I N G
ALLIANCE
Deriving Inputs for Seismic Models 8.4 Practical Gassmann Scenarios
Tight Sands Care needs to be taken when applying Gassmann in tight sands. Wang (2001) notes that in rocks which have medium to low aspect ratios, velocities at seismic frequencies may be closer to high frequency laboratory velocities than those predicted from low frequency Gassmann. Thus models in addition to Gassmann may be required for the analysis of tight sands (eg Biot, 1956, Mavko et al 1998). At laboratory frequencies (eg Domenico 1977, Gist 1994) there is a dispersive element to the velocity and in addition, there is potential for a patchy saturation effect in low gas saturation sands (Figure 8.40). The low frequency response of tight gas sands is an area of ongoing research.
Figure 8.40.
Dispersion of lab and Gassmann
velocity in brine sands
Dry velocity is independent of frequency
2400
experimental data
glass bead rocks.
o
Combination of Biot and Brie
flow (patchy)
Model fits by RPA Ltd.
appears to
.!!! 1800 E Q, > 1600
laboratory using synthetic
2200 2000
Domentco (1977)
•
account for dispersion and
I - - H patchy saturation 1--+-/---1 effects
1400
imbibition (homogenous)
-Gassmann+Reuss -Biot + Brie
1200 1000 0
0.2
0.4
0.6
0.8
Sw
Low Frequency Gassmann
Biot Figure 8.41.
=
K Id
Jv '-~ ,) ~P 3'
Biat extension of
v = p
Gassmann to High
Frequency (after
p=pV,2
Geertsma and Smit
1961 and Castagna b =(XY -t)t(x +Y -2) Y
=I+¢(:; -I)
1993)
v, =
X = K,,,, K~
..~~l'l/;. GEOSCIENCE ~_TRAINING
.1
ALLIANCE
=
k =1 for high frequency no solid-fluid coupling k = infinity for low frequency = perfect coupling K=1=high frequency
from Castagna 1993
©Rock Physics Associates Ltd 2007
37
Deriving Inputs for Seismic Models 8.4 Practical Gassmann Scenarios
Shaley sands and laminated sands To illustrate the use of Gassmann with sand/shale rocks the following discussion uses a model described in Skelt (2004a and 2004b). This model (figure 8.42) is in fact derived from a laminated sand scenario. Consequently the porosity in the shaley zones is slightly higher than is usually found in situations where the sand and shale are homogenously mixed. MD(m)
Volumes
: M[).lVDss
"1VDss·TWT
Por_and_Sat
Vp_Tlatk
VSh PHIE {fraeO 0 . 0 - - 1 0 0.0 ----s:;- 0." 00--0'
Vsh
~_Tr..(k
200'ffJ O!-I'9bSJo,Q aoo~81~(~~do.o
Phie/Sw
Vp
Vs
Rho_Track
fCObl00 (g}cmi~
Rhob
..
2,380
Pw
pg
2.390
-
2,400
- Psh
2,410
- Pqtz
2,420 2,430
2,UD
/
\
Kw K - o -
1\
-
2,450
-
2,460
'--
2,470
Ksh
Kqtz
1.001g/cc O.257g/cc 2.3g/cc 2.65g/cc 2.571GPa O.104GPa lO.25GPa 39GPa
-
2,480 2,490
1001
-
.
Figure 8.42. Sand shale model (from Skelt 2004)
A conventional approach to fluid substitution (section 8.2) has been used (sample by sample) for the substitution of gas into the initially water-bearing rock (Figure 8.42). Porosity input to Gassmanns equation is effective porosity (derived from the density log using a mix of shale and quartz) and the effective mineral modulus has been derived by mixing shale and quartz using the Voigt/Reuss/Hill average mixing approach (Hill (1952), Mavko et al (1998». Figure 8.43 shows that substituting from water to gas gives rise to a dramatically larger fluid substitution effect on Vp in the low porosity shaley sands than in the clean sands. When the dry data are plotted on the Phi vs K/KO crossplot (Figure 8.43) the low porosity data literally drop off the plot. At around 12% porosity, Kd becomes negative! Thus it must be concluded that the large change in Vp is the result of unrealistic inputs to Gassmann.
38
© Rock Physics Associates Ltd 2007
~l/.! GEOSCIENCE ~""'TRAINING
.,
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r
\.rr-
1- .
r
rr{
Invasion Correction Example/Exercise
_
AHll'
Rock Physics Associates
"""VN) Io.t...' . _ ,...... .. " ..... ' ,-",--,,--'''_'''Wl_.''''''y,_,.. ,.....,_...... , _.. ,~(U",,,,,,,,
,
""(.U<j,."
tnmmn ~::::;:::::;:::~::;
'-~J"(""
_,~
.
~'
?,f";) n o1c,,-("~
,,>,,"",'
....",
~~~ ,.,,""(-:~
.;'""-~
Data set includes GR, DT, DTS, Rhob, Core porosity, resistivity logs
drilled with WBM
"00
Virgin Fluid Properties Brine 1.005g/c 1638m/s Gas 0.156g/cc 610m/s
2.695GPa 0.058GPa
- ,
Minerals Sand;monomineralic;quartz Average Log data for Sand with Good Saturations Average log values at 2925m Vp 2654 Vs 1653 Rhob 2.17 Phi 0.285 tied to core porosity data Sw 0.241
o
i
-,
Invaded zone saturation (Sx) Given the porosity and the end member fluids: density of 2.17 fits with Sx;0.955 and Rho_fiuid;
0.967q/cc
Virgin fluid density (ie Sw;0.241) ;
0.361q/cc
o
Thus the density log is invaded Correcting the density log to in-situ conditions
To correct the density log to in-situ conditions: Rhob_corr; Rhob-«phi*0.967)-(phi*0.361)) So if measured density; 2.17
corrected density; 1.997q/cc
© Rock Physics Associates 2007
1
Invasion Correction Example/Exercise Rock Physics Associates .
Should the sonic logs be corrected for invasion? Using the spreadsheet 'RPA single value Gassmann' try the following scenarios (assume Reuss/Woods fluid mixing): 1) No corrections to sonic (Sw Vp Vs and corrected density) Vp Vs Rhob Sw
Kd
2654 1653 1.997 0.241
~\013
).1((7 /.l
"dry
0.176
Fluid substitution to brine filled (ie Sw=l) Vp
26(1.(
vs!U.s
Rhob
.':::1.
PR
O.IK3
2) Correction to sonic (Sx Vp Vs and measured density) Vp Vs Rhob Sx
2654 1653 2.17 0.955
Kd
s-,z.
/.l
(,1
"dry
D.Ort-
2.---
Fluid substitution to brine filled (ie Sw=l) vp
1"rr{ I'
Vs
16 'f 9
Rhob
?
COAt I.
IIt1
Is scenario 1) more probable than scenario 2) ? - what information would be useful to decide? Think about the invasion problem if porosity and shear ~nf~rmation were uncertain.
I.
t
/1,/0 (l./iI'1J/oA)
/pI! If,
/. 0
Cpf~U: ) ,J
Discussion Points fCC~?1(c'u.e.1 1. There is some guesswork in defining the end-member fluid parameters - in many cases simply using virgin fluid brine and hydrocarbon as the end members works well but in some situations mud parameters may be significantly different to formation brine parameters. 2. Whatever the means of deriving the invaded zone fluid parameters the first test is that these data fit with the other parameters in Gassmann 3. Without some idea of the porosity of the rock and a good shear log the problem of invasion correction is under-constrained. 4. This problem assumes importance in flushed gas sands where the impedance of the gas sands and overlying units are not too dissimilar (eg Class IIp AVO) 5. This procedure should be part of a feedback loop which includes quantitative well ties and seismic gather comparison to modelled gathers.
1
© Rock Physics Associates 2007
]
2
Gassmann Exercise - Shaley Sands Rock Physics Associates
.. -, .
p"'_...._,,,
li"'",'
'"-'''''
V'_T''''
~
..._"".
"00
Skelt (2004) pUblished a model to illustrate the issues arising from Gassmann fluid substitution in laminated sands. The model (left) serves as a useful template against which to discuss various approaches to Gassmann fluid substitution.
".
Model Parameters Brine Rho
~
I.r~ ••
~O~'O >O\1~'~~O ,.J'd'.22."1~, \"rr.,(lO("'1'~
,m "00
""
". "n
\/
vp Gas Rho
1.001g/cc 1603m/s
vp
0.257g/cc 637m/s
Minerals Rho_shale K_shale Rho_quartz
2.39/cc 10.25GPa 2.65g/cc
1"1
". lUI
".
".
Using the 'RPA single value Gassmann' spreadsheet, evaluate the results of the following scenarios:
1. Sand - substitution from wet to gas bearing Phie
0.31
Sw
0.23
Vsh
0.1
Vp
2486
Vs
1056
Rhob
2.115
crdry
Kd Gas bearing sand Vp Vp%change
Vs Vs%change
© Rock Physics Associates 2007
Rhob Rhob%change
1
Gassmann Exercise - Shaley Sands Rock Physics Associates
2. Sandy shale section - substitution from wet to gas bearing Phie
0.056
Sw
0.9
Vsh
Vp
2417
Vs
1028
Rhob
Kd
J.l
"dry
Vs
Rhob
0.84 2.28
Gas bearing Vp
Vs%change
Vp%change
Rhob%change
3. Sandy shale section - substitution from wet to gas bearing (total porosity approach)
Phit
0.236
Swt
Assumed dry clay parameters
Vp
Kd
2417
0.98
2.68g/cc
Vs
VcI
0.84
Rhob
2.28
Kclay 27GPa
1028
J.l
"dry
Vs
Rhob
Gas bearing Vp Vp%change
Vs%change
Rhob%change
Note how the magnitude of fluid substitution can change if you vary the Kclay parameter. There is significant uncertainty in the fluid substitution of sandy shale sequences the result of scenario 2 is clearly wrong whilst the result of scenario 3 is more intuitively correct but it is not the only possible answer! It is also noteworthy to point out that these results assume that the porosity/saturation relationship is known. In practice Gassmann substitution in these situations either uses a total porosity approach (and the dry clay parameters are assumed) or Gassmann is run with effective porosity but 'fudged' by either using a dry rock model to perform the substitution or by using a stiffened fluid modulus (eg Brie type of mixing). Beware of pressing the 'do fluid substitution' button in software packages when there is significant variation in shale content! © Rock Physics Associates 2007
2
Deriving Inputs for Seismic Models 8.4 Practical Gassmann Scenarios
".""
- ~·_·"I_'O", r-..:;;;;;~., ~,.:K'~~o~~~.f':f'~'l'f _fW1 I ~, . ".0"' !:!, .,:'I!-!'!.JI!',
lOM>Mo
••
•••
••
Figure 8.43. Fluid
~
subsUtution using
o.
Gassmanns equation
.. .... ..•
- effective porosity approach with no
/ 1\ /
·
. ..
constraints
\' , ""'---,---------,c----, '1'0 0.' 0.'
·
~::::~~~~.,
0.' 0] ~O.5 0.4
o
•. -
-- - -
0.3
. ..
L--.-.,
-
,-__ ~-
•• __ -
,
-
0.•
.-
0.3
0.2
'0
0.' 0.1' --- ----. ---
·
o o
0.'
0.1
0.'
0.'
Porollty
·
Such problems associated with effective porosity are usually remedied by applying cut offs (eg fluid sub is done only in porosity>X and Vsh
.- . ~' ""~"r'~':'~~illit~ltt"~'t I
.T'O""wr
~!!..
~
.-
.,:t~,.
•
Figure 8.44. Fluid
substitution using
..oo
Vp results for variable dry clay
..oo
"oo
I".
/
I
...
Gassmanns equation
39 23 13
- total porosity approach with varying mineral
modulus
..
' ----
0'
o··P\~&=
1"$
0.'
6 0°. ~ 0.5
"
..oo
0.3
I".
Ko
-
I
~
'.
--- -I
02
I
0.1
'·1
o +-----'----'-'''------'-----' o
•.,
0'
0.3
0,4
PorosIty
Figure 8.44 shows that the fluid substitution effect in the shaley sands depends on the value of KO for dry clay. If a high value is used then the dry rock parameters become unreasonable and there is a large fluid substitution effect in the low porosity shaley sands.
~)):
GEOSCIENCE
&3TRAINING
..I
ALLIANCE
©Rock Physics Associates Ltd 2007
39
Deriving Inputs for Seismic Models 8.4. Practical Gassmann Scenarios
It could be concluded that as 'artefacts' are less exaggerated, total porosity is the more appropriate system for gassmann fluid substitution. However we fundamentally don't know what
the real answer should be and the substitution focusses on attaining 'reasonable' or 'intuitive' results. In the total porosity case this would amount to tuning the result by varying dry clay KO. In the effective porosity case 'reasonable' results can be attained using two approaches. The first is to use a model based approach to fluid substitution (figure 8.45).
-
.~,
""
". ". ".
". IuS
".
". ".
".
-
Figure 8.45. Fluid substitution using model based approach with effective porosity
The second approach, which gives results very similar to model Bis to use a stiffened fluid mix (eg using the Brie et al 1995 mixing approach).
Of course some authors prefer to drop Gassmann in favour of a different model or separate models for different shale scenarios. The authors view is that owing to the fundamental uncertainties in the way shale behaves in conjunction with sand, alternative physical based models inevitably are more complex (and therefore probably more difficult to parameterise) and do not necessarily yield greater accuracy.
40
© Rock Physics Associates Ltd 2007
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Deriving Inputs for Seismic Models 8.5 A Note on Shales 8.6. A Discussion of Rock Models
8.5 A Note on Shales So far the discussion has centred around sands and the use of Gassmann in fluid substitution. We need to be equally careful when using the wireline data from shale sections: • • • •
Beware of sections of hole showing drilling damage (use caliper log) Other hole problems (e.g. swelling clays) Beware anisotropy (deviated wells) Look for consistency between wells.
Shear velocity for shales can be estimated from • Castagna mudline (or locally calibrated function) • Shear logs (beware of monopole tools). The anisotropic nature of shales is an interesting issue in seismic modelling. Logically we should be making our models by including the anisotropic effect of changing velocity with angle. However we (generally) don't, and this is simply because there are problems in parameterising the anisotropy (i.e. lack of relevant data at different scales). As yet the most reliable (seismic-scale) anisotropy (vertical transverse isotropy) measurements have come from expensive multi-component multioffset VSPs. Given current trends it is likely that practical workflows will evolve from work currently being done in seismic imaging. There are situations in which anisotropy can invalidate the conclusions from elastic/isotropic modelling. This uncertainty in the model should be addressed in the risking process (see section 12).
8.6 A Discussion of Rock Models As illustrated by the discussion so far, rock physics models are fundamental tools for data QC and rock characterisation. Rock physics models are of various types and a useful description is given by Avseth et al (2005): 1. Theoretical a. Para-elastic models - eg Biot - Gassmann, squirt flow models (Mavko et al 1995) b. Inclusion models - eg Kuster Toksoz c. Grain contact models (driven by Hertz Mindlin theory (Dvorkin and Nur (1996)) d. Bounds - VRH, HS e. Transformations (eg gassmann fluid substitution) 2. Empirical (using coefficients of fit) a. Eg Wyllie and Raymer-Hunt (Vp vs porosity), Greenberg-Castagna (Vp vs Vs), Gardner (Vp vs density) b. Neural networks or fuzzy logic 3. Heuristic - pseudo-theoretical - intuitive but non-theoretical - using physical reasoning that is not rigorously supportable a. Eg Wyllie In practice combinations of models are usually employed.
~'))
GEOSCIENCE
&3TRAINING
..I
ALLIANCE
©Rock Physics Associates Ltd 2007
41
Deriving Inputs for Seismic Models 8.6 A Discussion of Rock Models
Of course one of the goals of the use of rock physics models is, through understanding the variability of rock properties with acoustic parameters (eg acoustic impedance and poisson ratio), to gain an idea of the degree of non-uniqueness of seismic signatures and confidence in the lithological/fluid interpretation. Another use of rock physics models is prediction. For example Avseth et al (2005) state that "Rock physics models ailow for extrapolation of observed trends to depositional settings and depth ranges that are not covered by weil log data". The idea appears sensible but in practice assessing the confidence in such predictions can be difficult. Whilst understanding rock physics trends is critical to exploration, the results of exploration very often teil us that the likelihood of being correct in predicting outside the range of observations is usuaily quite low.
A simple approach to modelling the effect of changing porosity is to use Gassmann but with some assumptions about the moduli. Hampson and Russell (note in the AVO manual) showed that if it is assumed that the pore bulk modulus (K p) and the dry rock Poisson ratio (ad) stay constant then the dry rock bulk modulus (K d) and the shear modulus (~) can be estimated using the foilowing (equation 8.17):
1 new
Equation 8.17. Deriving dry rock properties with
a (small) change in porosity
The inherent assumptions in this approach are generaily valid for estimating a change in porosity in clean sands of about 5-10 p.u. (porosity units). Modelling changes greater than this usually require a greater understanding of the change of rock fabric with porosity. In this case porosity vs. moduli trends (based on theoretical models or on data generated from log sample Gassmann inversion) need to be used. An example of these types of trends is shown in figure 8.46.
42
© Rock Physics Associates Ltd 2007
~l~ GEOSCIENCE
0; ....
.1
TRAINING
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Deriving Inputs for Seismic Models 8.6 A Discussion of Rock Models
~
,--,---,---,----,---,
.. 1--+---+---+--+---1 ,
" I--"'~+---+---+--+---I , .. Clean sand trend
Kd
" 1--+'-'~,-+--+--1--1 ~ .. "
,
I.. ~:::
....
'" f-"~'......c+~. c,,'--,A+"~-..'01.-_+-_-1
,,L.
_~,L,
Figure 8.46. Examples of moduli
~
: .. ",~ __,"'.,__,"'.,_---"._---:' ,.• ,.,
.. ,,,,
Porosity
u
V5.
porosity trends that might be used to model sensitivities of Gassmann
,
modelling to porosity.
"
,,
" '" ,,. ... V'-
"
02
0.3
Porosity
"
"
Theoretical and laboratory based description of rocks has led to a plethora of rock physics models many of which have been deemed quite impractical. The reader is referred to Avseth et al (2005) who detail 11 models which describe differE;nt aspects of sand-shale sedimentology. Essentially these reduce to descriptors of clean sands with variabie cement and sorting and various sand shale mixtures. Two key models that help to describe the elastic relationships for high porosity as well as low porosity sands are the 'Contact cement' and 'Uncemented sand' models derived by Dvorkin and Nur (1996).The illustration in figure 8,47 published by Dvorkin et al (2002) shows the interesting fact that rocks in widely disparate geological basins can have very similar moduli vs. porosity relationships. Cemented and uncemented sands from the two basins appear to follow similar trends.
• 10
30
ro a-
ro a-
~ 20
, ... '•
•
~.
8
~ 6 0 4
~
~,J
2 .1
.2
.3
Porosity
,4
.1
.2 .3 ,4 {1~1 Porosity.....___ SoP-
tiJld
,f~.v)
Figure 8.47. Modulus (Vp2p) vs. porosity crossplots for North Sea (grey) and Gulf Coast (black) wells. Upper black curve is contact cement model. Lower black curve is the uncemented (friable sand) model (after Dvorkin et ai, 2002).
h()£'-'#= !./~oto!1 ~l~ GEOSCIENCE 0;_TRAINING
.1
ALLIANCE
©Rock Physics Associates Ltd 2007
9V/rhlvrtD /J 43
h-t J
Deriving Inputs for Seismic Models 8.6 A Discussion of Rock Models
Figure. 11.48 shows a schematic illustration of the dominant (empirical) trends in clean sands.
Constant cement
Kd/KO Variable cement
Porosity Figure 8.48. Schematic representation of the dominant (empirical) trends in clean sands
•
.
I/dP-
l/,Vtj1<..<..
As shown in Section 3 the relationship between acoustic parameters and porosity and clay content may be highly non-linear. In some cases relatively simple empirical models can be used to describe the variation of porosity, shale content and velocity.
,, ,, ,
14 ---
Raymer-Hunt Model ~--------------,
~
c
'"
E'<' <J) .-u-E U;'" :::J o
::f.
:
:
--~-----j---------------
12
"0 U <1> U 0.-
I
o:
Figure 8.49 shows a calibration of the Raymer-Hunt (1980) model (a variant on the Wyllie model described in Section 8.3.5)
10 8 6 Figure 8.49. Use of the Raymer-Hunt
4
Empirical Model to Model Changes in
o
10
20
30
Porosity and Clay Content (Ovorkin et ai, 2004).
Total Porosity 44
© Rock Physics Associates Ltd 2007
~l& GEOSCIENCE
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TRAINING
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Deriving Inputs for Seismic Models 8.6 A Discussion of Rock Models
The sand shale situation has been addressed in more sophisticated ways. One successful approach is that of Xu and White (1995) It is essentially a hybrid model combining theoretical (Kuster Toksoz (1974) inclusion model) and empirical aspects (ie matching the model through pore geometry coefficients) (figure 8.S0).The Xu-White model effectively creates a matrix of velocities, porosity, shale and quartz. 'm ,psf ~(.k7/(J( 1M
oW . ..
Vclf----, Aspect Ratio Model
·as
Mineral Parameters
ae
Fluid Parameters
Figure 8.50. The Xu-White Model (forward modelling flow).
When the Xu-White model is applied to log data ('I' and Vsh) the parameters of the model are tuned (to the measured sonic log) using a minimisation procedure. OWing to the numerous parameters that might be tuned (e.g. pore aspect ratios, mineral densities and moduli) the model is nonunique.
GR
Lilh
Phil
Vp
Vs
Rhob Commonly, single values for sand and clay related pores are used over logged sections of around 300m. Figure 8.51 is an example of a calibration to measured velocity data. The fit is not exact (it never will be) but the model can now be used to predict the effect of varying clay or porosity. Note, however, that the predicted is generally higher than the GreenbergCastagna prediction. This is related to the low values of dry rock poisson ratio that are calculated through the Kuster-Toksoz theory.
".
Figure 8.51. An example of the calibration of the Xu-White Model to
~ ~lb. GEOSCIENCE
~_TRAINING
.1
ALLIANCE
log data (predicted logs in red).
©Rock Physics Associates Ltd 2007
45
Deriving Inputs for Seismic Models 8.6 A Discussion of Rock Models
18000 ~ 16000
g
14000
~
12000
~
10000
~
Q.
8000
The illustration in figures 8.52-54 show some forward modelling results from the Xu-White model; figure 8.52 - effect of varying aspect ratio and porosity in sands, figure 8.53 - shaley sands showing a greater fluid substitution effect on vp than clean sands. figure 8.54 - Xu-White solution for a dispersed shale scenario.
,-
'""'0
/
~~ --;; \~ ~ I I ~ Equation I
\,~ ~ .,
-I " =0.01 I
6000
I
~~ "- ~" ~
""
~
----------= .~
"XlO
o00
r-
1'--1,,=0·13
010
020
030
Porosity
t"
j>o/G(/7~d ,eJio
000
/V
~D{"' d~.eu
Figure 8.52. Illustrating the Xu-White model. Sand
model with varying pore geometry and porosity.
7000 6000
Figure 8.53. Clean and Shaley
5000
Sands Modelled using the Xuc.
White Model.
~
4000
>
--+- brine sand
"""" ~,~~
3000
~,
2000 1000
~
____ gas sand Vsh 20% brine sand ~ Vsh
20% gas sand
o 0.000 0.100 0.200 0.300 0.400 0.500 Phi
3600
3200 ~ 2800
2600
-----
2200
2000 0.05
0.1
\,\ \ -
I
I
Increasing shale con tent ~ r--..... I I
.\
3000
2400
I
"I -
3400
~
0.15
~ '""i--...
=-j~'
0.2
....
Sa nd
-
Figure 8.54. A Xu- White solution
for a sand with dispersed shale
-
Shale 0.25
0.3
0.35
Phi
Theoretically the Xu-White model can also be used as an inversion scheme, for example predicting porosity from sonic and shale content. However it must be remembered that it is a volumetric model, taking no account of where the clay or shale is located within the rock. Sams and Andrea (2001) have shown that the type of clay distribution can be important in the forward prediction of P and S wave velocities from clay volume and porosity (particularly where the clay is dispersed) or when predicting porosities from velocity and clay volume. 46
© Rock Physics Associates Ltd 2007
~)~ GEOSCIENCE
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Deriving Inputs for Seismic Models 8.7 Log Editing
8.7 Log Editing Introduction Adverse hole conditions (borehole washouts and damaged formations) can lead to bad density and sonic logs. Indeed bad well ties are often caused by poor quality logs. Log editing is one of the most important elements of the well tie process but all too often enough time is not devoted to checking the logs and finding appropriate editing strategies. In addition to bad logs there are also the problems of how to fill in missing sections and multi-well tool calibration or scaling. Effects of Bad Hole on Sonic and density logs In many instances the caliper tool is a key to recognising bad hole. Figure 11.55 shows zones of caving shales that have led to errors in the density log. The density tool generally has low tolerance to poor hole conditions. In this instance a correction to the density log has been made simply by using the shale log with values for sand and shale density. Of course such a scheme is only appropriate where the fluid fill is invariant.
.,.
Black curve
-raw density log
200m
~ 0
"EJ ~ c
Red curvedensity log based on mineral mix of sand and shale densities
. "
. " . •
"
[1f:~
I', . ~';' . '. "'~;.~•. : .' ,.;' .' '.
.-
Caliper (ins)
Figure 8.55. Density log affected by bad hole
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Deriving Inputs for Seismic Models 8.7 Log Editing
In contrast to the density log, the conventional wireline sonic is usually quite tolerant of poor borehole conditions (Figure 8.56). However, in very bad holes attenuation of the sonic signal can mean that the amplitude of the compressional arrival is below the threshold for triggering the receiver. In these instances higher amplitude (possibly shear) arrivals are detected rather than the compressional wave giving sonic readings that are too high (this is usually referred to as 'cycle skipping'). Long Spaced Sonics (LSS), the use of which is now largely discontinued, are less tolerant of bad hole.
Figure 8.56. Sanies less
susceptible to poor hole than
SOm
Dipole sonic (Red Curve) appears less susceptible to poor hole than conventional sonic (Black curve)
density log
Signal attenuation (sonic log stretching) may occur in 1. Formations with low velocity - eg high porosity sands with poor grain to grain coupling or uncompacted shaley formations 2. Thin bedding - losses through reflection and refraction at bed boundaries 3. Altered formations - eg hydrated shales 4. Rugose borehole where the sonic sonde may be misaligned 5. Long spaced tools with large transmitter-receiver spacing 6. Fractured rock - reflection and mode conversion 7. Hydrocarbon bearing rocks (after http://www.hendersonpetrophysics.com/sonic_w_frames.html) Less common effects on sonic logs are noise spikes where the receivers are triggered for example by tool movement in the hole.
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Deriving Inputs for Seismic Models 8.7 Log Editing
Altered Formation Effects on the Sonic Log A common type of effect of formation damage on the sonic is the chemical reaction of shale with the mud filtrate. This results in an increase in the sonic transit time in shales (figure 8.57).
Sonic us/ft
DaYS ane~:rilling
~
'"~ ...
25 35
Figure 8.57. Progressive
change in sonic response as shales react to mud filtrate (redrawn after Blakeman 1982)
.s.c" a.
"
0
""
Burch (2002) describes a way of evaluating and correcting for the effect (figure 8.58). The relationship between deep conductivity and transit time is used to estimate scalars to reduce sonic slowness values.
I'!===::=::
120 .----,-----,-----;r-:----, , "
i ..........J.. :;
---------·t----------~--
g::
gj 100 Q)
E i= '00 c
~ I-
l
-
j-.........
t..
:'k*: I: ---f---------
----------~------- -~------
•
. '
ooYI!
200 Deep conductivity
First order for shale correction
:~:~~t~on
scalars
varying with conductivity
Figure 8.58. Using the resistivity log to correct sonic
affected by shale alteration (drawn after Burch 2002)
400
Altered shale effects can account for as much as -lOOms drift in a 10000ft well section (Burch 2002). Thus analysis of drift curves (as described in Section 7) and the comparison of raw and calibrated sonic logs should potentially highlight the effect.
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Deriving Inputs for Seismic Models 8.7 Log Editing
Invasion of mud filtrate into porous formations is another effect that can adversely affect density and sonic logs (see discussion in section 8.3) (figure 8.59).
Figure 8.59. Invasion corrected density and sonic
logs In a flushed gas zone. (Note that there is limited effect on the sonic as in this case velocity is similar at 95%
50m
water saturation and 20% water
saturation.)
Vasquez et al (2004) have shown that the scaling of extracted wavelets can be dependent on a correction for invasion (figure 8.60).
-100 Blue
~ TWT
Figure 8.60. Effect of invasion
using raw
correction on wavelet scaling
logs
(re-drawn after Vasquez et al
ms
o
wavelet-
<=:
~
,- -
~
~
2004)
I
Red
wavelet After invasion
correction
100
50
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Deriving Inputs for Seismic Models 8.7 Log Editing
Log Editing Tools The interpreter needs to carefully evaluate all data including composite and mud logs as well as comparisons with offset wells to help recognise bad data. Box et al (2003, 2004) describe a process in which log editing is approached from the perspective of multi-linear regression of a large number of wells including all relevant logs (Sonic, Density, GR, Resistivity, Depth, pressure). They note that recognising zones of damage, erroneous scales and other errors requires detailed QC. Using neural net or fuzzy logic prediction techniques without adequate QC is likely to be misleading. Log Transforms - Densitv from sonic In instances where the sonic is relatively unaffected by borehole issues density might be generated from the sonic log through a log transform. Gardner et al (1974) developed a general relation (figure 8.61, equation 8.18) based on data from different brine saturated rock types of the form:
Where Vp is km/s Equation 8.18. Gardner's Equation
Table 8.4. Coefficient for
Lithology
d
f
Ss/sh avg
1.741
0,25
Shale
1.75
0.265
Sandstone
1.66
0.261
limestone
1.55
0.3
Dolomite
1.74
0.252
Anhydrite
2.19
0.16
Gardners relations (modified after Castagna et al 1993)
Bulk densrty (glee)
4.5 ,---'j"i'-'~2'i.O,---,2r·2----,2T·4----,2T6'--'i2·r' _3 ·O'--,
T
30000
4.4
25000
4.3
20000
4.2
ROCkr
7.'t--+--+
15000
£ ;:: 4.1 ;;
12000
'04.0
10000
~ ~
.~
g
8000
3.9
General ralalian
~ ~ ~
~
7000 3.'
6000
'---+-------+----1--'------'
7 8000
10000
12000
14000
16000
18000
Velocity
3.7
5000
Figure 8.62. Density vs Velocity 3.6 L--'----,:'::---+-----;:L----'----:' 3980 0.2 0.3 0.4 0.5
with Gardners Relations (North Sea Example)
Logarithm of bulk density (glee)
Figure 8.61. Relationship between density and velocity (re-drawn after Gardner et a11974)
As with all empirical relations there is a need to check the applicability of Gardner's equation before applying it. The crossplot in Figure 8.62 shows an example of some consolidated sands where the general relation is clearly wrong but the sand specific relation is reasonable approximation. If at all possible it is advised to develop area specific density/velocity relations. ~)b. GEOSCIENCE 0:-TRAINING
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Deriving Inputs for Seismic Models 8.7 Log Editing
Log Transforms - Sonic from Resistivity Constructing a sonic curve from resistivity logs is reasonably accurate for the purposes of generating synthetic seismograms in areas of largely uniform sedimentation such as the Gulf Coast USA. A commonly used relationship based on the work of Faust (1951) is (equation 8.19):
I
Vp(ft / s) = K * {RZ)6" Equation 8.19. Faust's Equation
K= constant that is usually a simple function of depth or varying with formation type Z= maximum burial depth (feet) R=ohm/ft Vp=ft/sec
I
It
=
[~J *&r -t,J + 'm.
Another approach is to combine the Archie and Wyllie equations (ref. Henderson Petrophysics on the internet): Equation 8.20. Transit time from Resisitivity (after Henderson Petrophysics)
Burch (2002) also gives a recipe for creating sonic logs from resistivity logs. 1. Polynomial fit to sonic to remove first order compaction 2. Transform Resistivity to conductivity (ie reciprocal) 3. Filter the conductivity to match the spectra of the sonic log (High pass sonic is normally distributed but resistivity is logarithmically distributed) 4. Add low frequency trend Of course with all these methods care needs to be taken in hydrocarbon zones.
Physical Models Gamma ray
Models such as the Xu-White (1995) model (described in section 8.6) can also be useful in predicting missing sections (Figure 8.63).
Density
Resls1Mty
", I
-
~ [
Model (after Simm et a/1997)
~
~
Xu-Vvllite .
I ,
I
-
~
predicted using the Xu- White
~--
-
-
Figure 8.63. Missing section
-
I
Sonic
..
-
-:;: I
,
~
I
,F'
,
J-
-
~.
SCflic log
t..
I,~.
Hotethe 8rronltOu.log rudlngl at around 7175ft.
52
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Deriving Inputs for Seismic Models 8.7 Log Editing
Testing the Predictions - Well Ties If possible the log transform results should be tested through well ties. Figure 8.64 shows an example where the sonic was created from a transform of the density log. The resulting tie (figure 8.65) was acceptable for identifying the general phase of the data and unambiguous picking of seismic horizons.
Figure 8.64. Sonic log ~
200ft
f:.; ? 1 .f7
J ~
~ ?
..,...
" .,-
-J ~
~ "C
t
predicted from density.
11
Sonic log prediction=black curve
1 i
r Seismic
a ,
t
'"
-------
.
-
.( -"-
Seismic
) - -- -
Figure 8.65. Well tie Wavelel
--
using density log and
.
predicted sonic
-,
100ms
-t: :1:
~
,, .. I
1
I)'
~ml ~l/.!
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Professional Level Rock Physics for Seismic Amplitude Interpretation 9. Detailed Seismic Modelling
9.1 Discussion
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Detailed Seismic Modelling
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Detailed Seismic Modelling 9.1. Discussion
9.1 Discussion In addition to first order and wedge modelling the interpreter needs to consider the effects of the detailed interaction of thin layers (figure 9.1). This involves using log data to generate synthetic gathers. As with well ties, synthetic gathers are produced by convolving a wavelet with an offset reflection series.
_ -"
Vp Vs and Rho
- --
,.
............
Wavelet
... -
Reflectivity Algorithm
.•..•'-J.-----'\---!'----.+ _.
• ••••••
'"
::¥~
!§
:~ ..
::
t~2'"
\-,::-
~~
'" 2
,.........
............. _---
........
::----\,------+------j'-----rt J:. 'M
Offset Synthetic
.. ....
t-
:."
....... ,;
.
:::t:.,.
...j:::::
Zoeppritz Aki-Richards Full wavefield solution
~... ~:
Figure 9.1. Detailed Seismic Modelling.
Offset models can be used to: • attempt calibration with seismic gathers • model 'what if?' scenarios (for example bed thickness variations) • evaluate the effects of multiples or mode-converted energy (that may be misinterpreted as primary effects). There are a range of modelling algorithms, and commonly used ones are: • Approximations to Zoeppritz (e.g. Aki-Richards) - simple primaries only P wave reflectivity equation - requires 10 offset/angle algorithm • Zoeppritz - same as above except that other modes can be modelled • Full wavefield - all modes (e.g. converted waves, intrabed multiples, surface multiples) and acquisition geometry. It has been noted that in the presence of high contrast thin layers the Aki-Richards approximation may give a better result than Zoeppritz (Simmons & Backus, 1994).
The choice of model depends very much on the application. 10, 20 and 30 modelling software is available. Owing to its flexibility and ease for rapidly generating models 10 modelling is the most common.
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Detailed Seismic Modelling 9.1. Discussion
- - - Increasing Offset - - _
.",~
l\)\
II
~
I?!
Seismic Gather
Model Synthetic
Figure 9.2. The Problem of Calibrating Seismic Gathers (after Hall et ai,
1995).
Figure 9.2 shows that the synthetic gathers generally do not look like real data. This is due to the fact that the models are noise-free and the modelling algorithms are a gross simplification of the process of sound propagation. These models aim to match particular aspects of the gather (in this case a brightening with offset) to gain confidence in the interpretation. Certain modelling approaches can be very time-consuming. Figure 9.3 is an example of a workflow that attempts to forward model the gather using modelled shots and even processing of synthetic shots. Such a workflow is time-consuming and labour intensive and does not always help the interpretation. Gun signature modelling
I
Acquisition geometry
I
I
Earth Response (Attenuation, multiples etc.)
I
Layered model
Full wavefield modelling
I
Synthetic gathers
I
Processing :
Comparsion to real data
Figure 9.3. One approach to forward modelling.
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Detailed Seismic Modelling 9.1. Discussion
Real Gather
Synthetic Gather
Figure 9.4. An example of full wavefiefd modelling.
Figure 9.4 is an example where the final gather model (based on the workflow shown on the previous page) is significantly different from the real data. In instances where the model does not appear to explain real data observations (generally owing to the effects of noise), it may not be appropriate to perform AVO analysis or elastic inversion.
Figure 9.5. Near Stack.
Figure 9.6. Far Stack.
Data quality can be an important factor when attempting to connect models and real data. The illustrations in figures 9.5 and 9.6 show an area where data quality at the target on near stacks is very poor and it is impossible to say whether there is a positive AVO signature at the target. After drilling modelling was performed in an attempt to explain the seismic response.
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Detailed Seismic Modelling 9.1. Discussion
P·...."e m,; 2500 5000
Oen$~Y9'cc
20
30
0
Poisson p-Impeclance 025 050 4000 14000
-+lttftH+----1-HItt-f+-+H-ttttt-ftt---+-+t-fttt+_ """
-+Hl-HftH+----1-H-lH-H-+H-tt-H+H+---++!I--I++t+_ """ Figure 9.7. Primaries only (Aki-Richards) modeling.
P·W8"e...... 2500 5000
Denoilygcc 2.0 3.0
0
Poisson p-1~d8nc. 0.25 0.50 4000 14000
Brine Model
Gas Model
ttttttt--+ttttttt-"""-f-Htl'HtHtlfffi'rltl-ltt\tt'rtft'l"~-+fffiffiffl-
fWr\tfffl-HtttH+--
Figure 9.8. Full waveform modeling.
Simple primaries-only modelling (no noise) showed a weak positive AVO associated with the base of hydrocarbons (figure 9.7). It was clear, however, that the noise content of the near offsets made it impossible to connect the model with the seismic data with any confidence. Full waveform modelling (figure 9.8) gave some insight into the problems of noise and the best way to interpret the far stack. In the case of a brine sand it appeared that the multiple energy on the far offsets was totally obscuring target reflections, whilst reflections from a hydrocarbon sand persisted across the offsets. Thus owing to the effect of noise the far offsets appear to be a good discriminator for the presence of hydrocarbons. The connection between seismic models and real seismic data is not always obvious and the interpreter has some difficult decisions when assessing the appropriate modelling route to take.
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Detailed Seismic Modelling 9.1. Discussion
Probably the best advance on single interface modelling for the interpreter is to use 2D modelling as a guide to the validity of possible interpretation options. Figure 9.9 shows a simple 2D model based on an interpolation of log data with 4 brine-bearing sands. A simple anticline has been created and fluid substitution carried out to create a hydrocarbon flat spot. Interestingly the flat spot is cut up into segments owing to the interference effect of the thin hydrocarbon sands. It might be possible to interpret faults where in fact there are none.
Acoustic Impedance
Reflectivity at 15 degrees
Figure 9.9. The value of 2D modelling to the interpreter.
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Professional Level Rock Physics for Seismic Amplitude Interpretation
~l·~
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NAUTILUS
10. Seismic Trace Inversion
Rock Physics Associates
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10.1 Introduction 10.2 Seismic Data and Bandlimited Impedance 10.3 Towards Absolute Impedance from Seismic 10.4 Broadband Inversion for Absolute Impedance 10.5. Interpretation Issues
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Seismic Trace Inversion
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Seismic Trace Inversion 10.1 Introduction 10.2 Seismic Data and Bandlimited Impedance 10.1 Introduction By effectively applying the convolutional model in reverse it is possible to derive an estimate of impedance from seismic data (figure 10.1). There are a number of benefits to the interpreter in doing this: • Inversion simplifies the seismic picture by removing the effects of the wavelet and it commonly provides a clearer picture of stratigraphic, lithological and fluid changes. • Impedance is the geophysical link to geological parameters we need to know - e.g. porosity. • As a layer property impedance (or the derivatives of impedance) forms a common parameter between disciplines (geologists, engineers and geophysicists).
Impedance l""'IIIiiiiiii
There are many different approaches to trace inversion and no attempt will be made here to either outline them all or discuss which is best. The aim of this discussion is to outline the general concepts and raise the issue of quality control.
10.2 Seismic Data and Bandlimited Impedance When considering inversion of seismic data for impedance the first thing to understand is the nature of the impedance information that is actually contained in the seismic trace. As already discussed, the convolution of a wavelet with a reflection series is effectively a process which involves bandwidth reduction. Figure 10.2 shows that there is a loss of frequency information at both the low and high ends of the spectrum.
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Seismic Trace Inversion 10.2 Seismic Data and Bandlimited Impedance
lWT(mI)
__ .....
l\C1I(m)
'lIO-'MlIl
_.
POI_and_SII
O.O~I.OOO~U
NOs.1Wf
00
~ O.l
Ref Series
AI log
wavelet
Seismic trace
2._ 2,&03
2,110 2,8.3
2.nO 1,6S7
1,140 2,689
2,150 2.106
1,150 2.125 2,110 1,111
Figure 10.2. The
Bandwidth Issue in the
AI Log Broadband
Seismic Bandlimited
Convolutional Model
F
F
The low frequency component that is lost is effectively the D.C. component of the AI log, whilst the loss of high end frequencies effectively smooths the relative impedance (or A.C.) component (figures 10.3, 10.4 and 10.5). Figure 10.3. Impedance logs - Low frequency
(D.C.) and high frequency (A.C.) components
" . f /1£L c.!JU-7'';4.t.,vt 1,810 1,803
2,685
'.000
l,tiO
2,615
2,e9S
l,on
2,100
un
1,105
2,635
2.1\0
1.~J
Low frequency component (lost in seismic convolution)
(low f~1d.Pp)
Logs bandwidth
\
Seismic
bandwidth
'.~ 2.120 2M1
1,115
1.125 1,66(
V)O 1.172 1,135
'.000
1,140
'.~
1.1H
U"
2,150 2,106
High frequency component
F Low frequency log
component
U5S 1.716
2.110 1,115
UM 2.133 2.nO l,UI
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Seismic Trace Inversion 10.2 Seismic Data and Bandlimited Impedance
__ _
:llD-1VO" :T\Ot.. 1WT
AI log filtered with 8-10-40-50 bandpass
2,690 2.815
1.100 Ull
2,110 2,8.3
1,130 1.812
2,15D 2,108
1.160 1.125
2,110 1.1'1
Figure 10.4. Bandlimited impedance
So, the impedance component of seismic data is smoothed relative impedance (ie band limited). To obtain this information from the (zero phase) seismic effectively requires a -90 0 phase rotation and a high cut filter. Figure 10.5 illustrates the concept. Notice the similarity of the AI log with bandpass applied (column 4) and the bandlimited impedance trace in the last column (they are not exactly the same as the high cut filter needs fine tuning).
AI log
AI with band
pass
Seismic trace
I
Seismic Trace -90
I
Seismic Trace ·90 & high col
(
2.1190 2.615 2,100 2.&28
( l,7SO
t
2,106
2.710 2,U!
• I .
?f
Figure 10.5. Deriving Bandlimited Impedance from the Seismic Trace
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Seismic Trace Inversion 10.2 Seismic Data and Bandlimited Impedance
There are two documented approaches to bandlimited impedance from seismic. The first was published by Waters (1978). He described the SAIL (Seismic Approximate Impedance Log) approach which involved applying a -90 0 phase rotation and 6dB/octave high cut filter (from 2Hz) to a zero phase seismic trace. Integration of the trace gives a similar result. A technique which is an enhancement on the SAIL approach is 'Coloured Inversion' (figure 10.6), pioneered by BP (Lancaster and Whitcombe, 2000). The enhancement is that rather than assuming the filter characteristics to be applied to the data the bandlimited impedance from seismic is matched to the spectral characteristics of impedances from log data. Thus the coloured inversion operator to be applied to the seismic is that which maps the mean amplitude/frequency response from seismic to that of the impedance logs.
Amplitude spectrum of AI Logs
CIOperator
Seismic Data Mean response
-
Amp
Frequency
Amp
'" ••••••• fa._ '"
Log Frequency
Frequency
Time Series
-
+
I
Ph", ~-90'
Relative Impedance
-
--------------
Figure 10.6 Coloured Inversion.
Figure 10.8 illustrates a number of features of bandlimited impedance data. 1. note that the horizon pick is a zero crossing on the bandlimited impedance data rather than a maxima 2. the bandlimited impedance signature of the peak/trough doublet related to the topmost reflection is proportional to the magnitude of the real impedance contrast 3. where there is no signal (ie in thick homogenous units) the amplitude of the bandlimited impedance is zero 4. as the data is band limited it is affected by reflector interference (ie tuning). (See also figure 10.8). 6
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Polarity Conventions
+
'f.
'70°
Reflectivity
Bandlimited Inversion
-~ ~
SEG 'Normal' Polarity
(+vo standard polarity) ~
Reflectivity
_~ North Sea Normal pOlarit;
~
Bandlim.ited Inversion
~
Rock Physics Associates
Impedance Contrast
~r---~'--_ _
SEG normal polarity gives a band limited impedance signature with the appropriate sense of impedance change
Impedance Contrast
~
sP(+
For bandlimited impedance from UK polarity data need to apply -1 scalar to get the correct sense of impedance change
- (Wi (etc
'1-
i
Ca,v ["'J7d tv elf
:1
. ' t1act,'c!dff 5ik,,~ , !US /;z,' del Icrzt d 2v7J 'IJotl q WS'U!I( Me.
iJ
/'eM
lulled, 'VIIA
Seismic Trace Inversion 10.2 Seismic Data and Bandlimited Impedance
Zero phase wavelet
Rc
AI---+
Seismic Trace
Bandlimited Impedance Trace
~::::::::::----- -----::*::::r:::::::;;::::--------
Figure 10.7. Bandlimited Impedance using the SAIL (Waters 1978) Approach.
COP
•I
. I
Reflectivity
"I
. I
••I
.
,
I
•I
., .. I
I
so I
.. I
Bandlimited Impedance
...... ,.., ,
........ ..- ! .... I
.,..
" .... .... ....
-
Figure 10.8. A Wedge Model showing Reflectivity and Bandlimited Impedance Tuning
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Seismic Trace Inversion 10.2 Seismic Data and Bandlimited Impedance
Figures 10.9-10.12 shows an example where a simple SAIL 'inversion' works well. The data in Figure 10.9 has good bandwidth and the bandlimited impedance looks quite different to the reflectivity data (if the bandlimited impedance simply looks like a phase rotated version of the reflectivity it is likely that the inversion attribute wll not provide any additional useful information). In this case, the bandlimited impedance has helped in defining the presence of hydrocarbon (red colours in the culmination in figure 10.10 are relatively low impedance).
Reflectivity 1700
Impedance Attribute 1800
1700
1800
2600
2700
2800 Figure 10.9. An Example of a Bandlimited Impedance Attribute.
Figure 10.10. A Bandlimited Impedance
Slice Parallel to the Top Reservoir
A bandlimited impedance slice parallel to the top reservoir illustrates brine filled channels (blue - high relative impedance) and the presence of hydrocarbons (red - low relative impedance).
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Seismic Trace Inversion 10.2 Seismic Data and Bandlimited Impedance
G)
® ® @
Injection Halo Water Front Fault Barrier to flow
? Bypassed oil
Figure 10.11. Fluid Changes on a 8andlimited Impedance Attribute (after Simm et ai,
1996).
SE
NW 2600
2500
2400
2300
2200
2400
2500
2600
2700
2800
o
685m
Top Forties
-
OOWC
-
Base Pay
Figure 10.12. Section 8-8' (from Simm et ai, 1996).
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Seismic Trace Inversion 10.2 Seismic Data and Relative Impedance 10.3 Towards Absolute Impedance Bandlimited impedance inversion attribute approaches work well where there is: 1. predictable stratigraphy 2. a restricted target zone with reasonable reflectivity 3. good quality seismic data with good well ties Advantages of these approaches are that they are quick to apply with current workstation technology. However, tuning effects are not addressed and in areas of rapid lateral variations in impedance the results can be difficuit to interpret with confidence. Bandlimited impedance is a boundary attribute and as such is sensitive to impedance variations above the target as well as the target itself.
10.3. Towards Absolute Impedance from Seismic It is possible to convert a relative impedance trace to an approximation of absolute impedance by adding a low frequency model. This model needs to be created for example from an interpolation of well data. Before adding the two components the bandlimited impedance trace (which will have arbitrary seismic units) needs to be scaled (figure 10.13). Scalars can be derived by matching to well data (figure 10.14). AI
o
Zero phase seismic
Low frequency (-010Hz) model based on interpolated well AI or stacking velocity data
1 Relative AI volume
5000
10000
15000
2500
r-----r---r------j
2700
i----I-...- I -
2900 I---+--+-'~~
TWT
1
3100
j---[---$"I---I
scaling
1
3300 t---+-~-+---j
Merge
1
3500
Absolute acoustic impedance inversion
+----[-----;:~~
3700 ' - - - - - - - ' - - - - ' - - - - '
Low frequency model Scaled relative impedance Well log AI
Figure 10.13. A Simple Merge Workflow
Figure 10.14. Deriving Bandiimited
Impedance Scaiars by Caiibration to Weii
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Seismic Trace Inversion 10.3 Towards Absolute Impedance
Low Frequency Model
Seismic
AAI Result
Figure 10.15. An Absolute Impedance Result from Merging a Bandlimited Impedance Inversion
and a Low Frequency Model.
A colourful (believable?) example of the approach just described is shown in Figure 10.15. There are a number of potential problems with this result, notably 1) wavelets effects remain in the data 2) the low frequency has not been added effectively 3) the interpolated low frequency model is Iikley to be misleading (impedance pinch outs may be related to the model rather than the seismic data).
t/ welL!. vwl
:.J wd/s
32000 31000 30000
29000
28000 "000 26000 25000 2<000 23000 22000
Figure 10.16. Variability of Interpolated Low Frequency Models
Depending on Number of Wells Used.
The low frequency component is a very important element in the final result. In terms of absolute impedance numbers it is the low frequency component which effectively determines the impedance magnitude. Uncertainty in the propagation of the low frequency component (figure 10.16) will give uncertainty on the overall magnitude of impedance.
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Seismic Trace Inversion 10.4 Broadband Inversion
In most cases there appears to be little point in merging a low frequency model with a bandlimited impedance 'inversion' rather than performing a model based broadband inversion which attempts to remove wavelet effects and justify the seismic trace with an impedance model. The previous dscussion is largely for illustrative rather than practical purposes.
10.4 Broadband Inversion To generate a broadband inversion result (ie absolute impedance) requires knowledge of the seismic wavelet and a model of the low frequency component (figure 10.17). Of course solving for reflection spikes means that the final impedance result will be blocky. There are a wide range of approaches to broadband inversion (and of course each contractor has the best approach!!). Seismic Trace
Rc
Wavelet
AI---
Recursive formula
I
=
or iterative
-
modelling scheme (with constraints)
Blocky impedance result Figure 10.18. The Idea behind Broadband Inversion
One of the first adopted (and relatively simple) approaches involves generating a 'sparse' reflection series (ie sparse spike inversion), based on the idea that there are only a few major reflection coefficients that are needed to justify bandlimited seismic. This reflection series is then converted to impedance using the recursive formula (equation 10.1) (figure 10.18):
A/2
= Al1((1 + Rc)/(I- Rc))
~.I
Equation 10.1. The Recursive Formula. !'.J8
The recursive formula is are-arrangement of the reflectivity equation presented earlier. Provided an estimate of the impedance can be made for the top layer, the impedance for a lower unit can be calculated from the reflectivity. A spatial model of All is required to implement recursive inversion.
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....
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.................
------
---
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------
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Figure 10.19. An Example of Sparse Spike Inversion (Courtesy Western Geophysical).
12
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Seismic Trace Inversion 10.4. Broadband Inversion
More sophisticated broadband inversions are now popular which effectively justify the inverted impedance through an iterative forward model and comparison procedure (Veeken and Da Silva (2004) give a good introduction to the subject). Such 'model-based' inversions (figure 10.19) require a starting model that is subsequently perturbed and checked against the seismic.
Parameters: Seismic misfit Rc threshold deviation from starting m odel trace by trace variation term AI constraints
Seismic interpretation Log Data
IWavelet I
Seismic trace
•
Impedance estimate (model)
I
I model trace I
I
•
ICalculate error I Display impedan ce
I
I
Yes
~ Small enough?
I
Update impedance model
No
Figure 10.19. Model-Based Inversion.
The starting model In this inversion approach may be an interpolation of well data or a more general trend model. Either way there is the benefit of the result being a total solution (i.e. the impedance model has been checked against the seismic and the errors calculated and minimised). If the wavelet is adequately described then the problem of tuning can be addressed. Also it is possible to incorporate multiples and attenuation effects Into the solution if necessary. If the low frequency component is described adequately then the problem of lateral variability in reflectivity can also be addressed. Model based inversions find a minimum error in the data for the given starting model and imposed constraints. Unfortunately more than one model may fit the data - this is the so-called 'problem of non-uniqueness' and there are usually a number of different minima that might be found. 'Global minimisation' approaches seek to find the overall minimum for the dataset. This can take a long time (possibly days). Unfortunately it is possible that the minima may change depending on the constraints. Figures 10.20-10.24 show an example of a model-based inversion.
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Seismic Trace Inversion 10.4 Broadband Inversion
"'
~ 1.5
!!2. Q)
E
;::
1.8
1 km Figure 10.20. Initial Model.-Courtesy CGG.
Major reflection picks are used as a basis for establishing a macro layer model, the generalised starting model for the inversion (figures 10.20 and 10.21). The starting model might also be based on an initial band-limited inversion.
1200
-r-::;~~~-~L-_-----'-------l-
1400
"'..sw
::;;: f= 1600
1800
5000
5833
6667
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Impedance
Figure 10.21. Macro Impedance Model. Example-Courtesy CGG.
14
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Seismic Trace Inversion 10.4. Broadband Inversion
1300
-r--~"'-----'--;-----'---------,-
1400
1500
1600
1700
1800
---l:===::::;:::=~r:::::~====-L
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Figure 10.22. Micro Impedance Result with well AI.-Courtesy CGG.
The inversion is run with the wavelet, macro model and constraints. A micro impedance layering is the result of the model-based inversion (figure 10.22). This is compared to the AI at wells. At the target level in the section and map in figures 10.23 and 10.24, the results show tight (high AI) sands in red contrasting with porous sands in blue (low AI).
1.5
~ Q)
E
F
1.6
Figure 10.23. Final Impedance Section. Example-Courtesy CGG.
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Seismic Trace Inversion 10.4 Broadband Inversion
AI > 6500
6325 6150 5975 <
5800
"1- ?'CQ! CCC '<;a1<".-. 0r-t:/Mh~ cQ.A/"'.;:! 7fd R-,'llwft--Zwvf d' ",flwe//s fJ1"f~'Of Iiu f..u;f,,1'
Figure JO.24. Reservoir Distribution - Courtesy eGG
10.4.1 Wavelet Issues Understanding the wavelet in the data is essential for deriving reliable inversions. Figure 10,25 shows how inversion can be very sensitive to the wavelet used.
Figure 10.25. Sensitivity of Inversion to Waveiet Shape, (Two Wavelets were derived using different wavelet
extraction methods) (after Ozdemir et a11992)
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Bandwidth and low frequency component in Impedance Inversion
Rock PhysIcs Associates
Impedance inversion can be fraught with difficulties. A recent paper by Wagner et al 2006 highlights the problem of merging the low frequency with a sparse spike inversion result. Reference: Wagner, S.R., Pennington, Wand C. Macbeth, 2006.gas saturation prediction and effect of low frequencies on acoustic images at Foinaven Field. Geophysical Prospecting, 54 (1),75-87 )~O'Tl.<-)
(s'W/wj
The paper concerns a comparison of the inversion results from streamer and ocean bottomllJ Sf! hydrophone ( data. The streamer data has a reduced range of frequencies compared to the
Data processed to zero offset
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From Wagner at al (2006) Geophys. Prosp. 54
(1),75-87
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A comparison of the inversion results from the different surveys shows significant differences. The streamer data shows apparently greater resolution with more layers evident in the reservoi r section.
Apparent
greater resolution of streamer data
Sparse spike inversion
with merged
low frequency From Wagner at al (2006) Geophys. Prosp. 54 (1),7S.a7
fuo;.
~~----->
© Rock Physics Associates 2007
I
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)
Bandwidth and low frequency component in Impedance Inversion
Bandlimited wedge models using wavelets of different bandwidth Nole: positive side lobe
energy
,i:D
50msl
• • It " • " •
Bandpass 11,20,56,64 -3.5 octaves
Rock Physics Associates
It is probable that the apparent layering in the streamer data inversion is related to residual effects from the bandlimited impedance. The low frequency has not been correctly merged.
I 'I~--j I •
Bandpass 5,11,56,64
-4.5 octaves
Maps of the impedance results show dramatic differences between the streamer and aBH data.
Time lapse inversion maps (AI differences) show believable (geologically consistent) results in the case of the aBH data but not for the strea mer data. Unreasonable gas
saluration valueswhy would the gas be located downdip?
More reasonable values and makes geological sense From Wagner at al (2006) Geophys. Prosp. 54 (1 ),75-87
© Rock Physics Associates 2007
2
Seismic Trace Inversion 10.4. Broadband Inversion
Quantitative well tie techniques are invaluable in deriving a good approximation of the wavelet, When a number of wavelets are available, they may be averaged provided their amplitude and phase characteristics are similar (figure 10.26),
Phase
Amplitude
o TWT
Frequency
Amplitude 'Average' Wavelet
TWT Figure 10.26. Averaging Wavelets with Similar Phase Spectra
Actual Impedance
Wavelet in the data
Assumed wavelet for inversion
Inversion result
Figure 10.27. Step or Thin Bed? It all depends on the wavelet.
The wavelet can have a significant impact on interpretation, In the extreme case where the seismic wavelet is 90° phase rotated from that which is used in the inversion a step in impedance will be represented as a thin bed (figure 10.27), There is no general agreement on the accuracy of the phase estimation of the wavelet required for trace inversion but it is probably about 30°,
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Seismic Trace Inversion 10.4 Broadband Inversion
10.4.2 Prediction QC 1.4
A critical aspect of model based inversions is to QC the results (figure 10.28). For those inversions where the initial model is very general then a comparison between well data impedance and the inversion is required. Where the inversion uses a starting model based on interpolations of well data 'blind' well tests need to carried out (i.e. leaving out a well from the starting model and checking the results) .
15
1.8
19
2.0
~iii=iCiiijij::s~ II 5.5 6.0 6.5 1.0 1.5 8.0 8.5 9.0 9.5 10.0 10.5 AoollSlie Impedance (10' kg/(m' 811
3.0
AOOl>Slic Impedance
-
13.0
WelIl::>g (lal. 1,",~StOn'elUN
Figure 10.28. QC of Inversion Results-weii comparisons and biind tests (courtesy Odegaard).
10.4.3. The Role of Constraints
• ,,~----
-...
In model based inversions the choice of guiding horizons in determining the starting model can have an impact on the final result. Figure 10.29 illustrates the point using a simple wedge model with a pseudo-well giving impedance control. When only the upper horizon is used in the interpolation to create the starting model the inverted impedances around the pinchout have slight errors. When two horizons are used the inversion is more precise.
Figure 10.29. Inverted Tuning models using model based inversion (upper section - 1 horizon as constraint, lower sectrion- 2 horizons as constraint)
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Seismic Trace Inversion 10.5 Interpretation Issues
10.5 Interpretation Issues 10.5.1 Choice of Inversion Approach The choice of which inversion to perform is a difficult question to answer (although inversion salesmen will tell you that you need their latest and greatest!). No one approach is definitively better than any other, it depends on several factors including the aim of the interpretation, the nature of the geology, the quality of the well ties and the time available. In most instances it is wise to look at both band limited and absolute impedance inversions.
10.5.2. The Role of Scale in Inversion Interpretation The issue of scale is an important one for inversion interpretation. Well data analysis provides a guide to the discrimination of various lithologies in terms of AI (figure 10.30). This is usually done at a sampling rate of about 6ins. Very often the various lithologies overlap each other and it is tempting to draw the conclusion that inversion will not work. An example of such a histogram display is shown in figure 10.30. In fact this data display relates to the map in figure 10.11 where inversion is clearly a successful technique. (Be careful of making significant decisions on the basis of single crossplots or histograms.) >. 0.7
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In seismic data the impedance is usually averaged over tens of metres and consequently it has a different distribution of impedance values to the logs (figure 10.31). Very often the main lithologies will show an apparently greater separation at the seismic scale compared to log sampling. Facies prediction from seismic on the basis of AI should use models derived from time converted (upscaled) data.
Figure 10.30. An example of an AI histogram based on
well data.
Solid line· wells
Dashed line· seismic
, ,
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,
I I
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I I I
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Well data
n
.
Acoustic Impedance . 1.1 AI V f1/ >'fj '] 11.-"1 C CI--e/ t( ,u;, fJiufri.J7J ?JVfc/ L eM/UU/e&! M ?&vcl 1/t'' f·.4. /' tv/II oIeC/!.ttMe. Figure 10.31. Impedance Distributions - Wells Seismic. VS.
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Professional Level Rock Physics for Seismic Amplitude Interpretation 11. AVO Analysis
Rock Physics Associates
~l~
11.1 Introduction 11.2 'Conventional' Intercept! Gradient AVO Analysis 11.3 Seismic Processing Issues 11.4 Other Reflectivity Analysis Techniques 11.5 Elastic Inversion
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AVO Analysis
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AVO Analysis 11.1 Introduction
11.1 Introduction There is no single approach to AVO analysis (figure 11.1). 'Conventional AVO' is a term usually given to the analysis of intercept and gradient (the two terms from Shuey's equation) derived from reflectivity data. The central idea in this approach is to derive projections that highlight fluid and lithology. In recent years the use of inversion techniques in AVO (termed 'Elastic Inversion') has become popular in order to derive AVO related impedance attributes, which in turn are related to the elastic parameters of rocks. Given the limitations of 2 term fitting, as well as the limitations of combining separate inversions of (for example) near and far stacks, some workers have developed techniques which seek to give more stable pre-stack estimates of avo parameters such as P wave (Rp) and S wave (Rs) reflectivity. Recent developments include simultaneous inversions of prestack data directly for elastic parameters. AVO analysis is currently a rapidly developing area.
Zoeppritz Modelling seismic
Figure 11.1. Approaches to AVO
I Linearized 2 term
(Shuey)
I
I Conventional AVO I
I
I Aki Richards 3 term I
I Pre-stack Inversion
I
~ '~
I RO/G, Near/Far I
c
I
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I Rp Rs and Rp I
';?(" I AVO Projections , I Ref and band limited Imp
0
I
I
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Elastic Inversion
! lEI
! EEl I
.1 AI 81 AP !1P a
It is important to note that AVO interpretations requires not only seismic analysis but also an adequate rock physics model. It is part of the challenge for the interpreter to integrate models and seismic analysis in order to assess the level of confidence in the interpretation. Understanding the role of seismic data quality is a key aspect of this process (figure 11.2).
I
Geology+ earth filter + noise
AVO Modelling
Calibration / Confidence in Interpretation Dependent on seismic data quality
Figure 11.2. Modelling and Seismic Analysis in AVO
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AVO Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
S:N - Quality of Imaging -Relative Amplitude Control High
Reasonable
Calibrated Amplitudes Quantitative Elastic Inversion for rock properties
p
Bad
Anomaly hunting
No Go AVO
Qualitative amplitude interpretation
Geological/Structural Interpretation
anomaly Consistency with structural
closure
F/gure 11.3. Data Quality Controls on AVO
Data quality controls the extent to which AVO responses can be effectively calibrated (figure 11.3). Properly calibrated elastic inversion to rock properties requires exceptionally good data. In most cases the data is only good enough to give a qualitative (anomaly vs background) type of answer.
11.2 2 term AVO - Reflectivity Analysis 'Conventional AVO' usually refers to the analysis of seismic using the intercept and gradient attributes derived from curve fitting to the seismic amplitudes as described in Section 2.
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R
-6 0
0.05
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Figure 11.4. Gradient QC and robust fitting (after Walden, 1990).
In the 1980's and 1990's various workers combined intercept and gradient sections in different ways to create a variety of AVO attributes. Examples of these include: • product indicator - intercept x gradient (figure 11.5) • 'fluid factor' attribute - Smith and Gidlow (1987) • pseudo-poisson reflectivity - Verm and Hilterman (1995) • Rp-Rs - Castagna and Smith (1994) At the time there was a thought that there may be a universal AVO indicator. However with the advent of the AVO crossplot there has been a gradual understanding that reflectivity AVO analysis is best considered in terms of data adaptive projections (i.e. avo indicators based on the local data). Analysis shows that most of the 'hard wired' products such as those listed above can be understood as representing particular angle projections.
4
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AVO Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
Figure 11.5. Intercept x Gradient (P*G) Stack Identifying a Small Gas Filled Structure.
Figure 11.5 shows an example of the intercept x gradient attribute, commonly referred to as the P*G or AB attribute, that was used extensively in early Gulf of Mexico AVO analysis of 2D seismic sections (figure 11.5). This attribute effectively separates out reflections which have increasing amplitude with offset (usually shown in red) and decreasing amplitude with offset (usually shown in blue), and is useful for determining Class III AVO anomalies. In this case the red zones are indicating the presence of a gas sand.
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The discussion will focus on the use of the AVO crossplot introduced in Section 3. The AVO crossplot (figure 11.6) provides a useful way of generating projections to emphasise not only fluid effects but also lithological effects.
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Figure 11.6. The AVO Crossplot and the AVO Classes. ~)!i
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AVO Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
To explain the mechanics of the intercept/gradient crossplot and the definition of angle projections a simple model is used as the starting point (figure 11.7).
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Sin 2 e Figure 11.7. AVO plot
Given this AVO model, Figure 11.8 shows a simple anticline model (a) with modelled sections of what the interpreter might expect in terms of reflectivity signatures at 10 degrees (b) and 30 degrees (c) (these may represent, for example, the average angle of near and far stacks). On the near stack (b) the presence of oil causes a dim spot, whereas on the far stack (c) there is a soft 'bright' spot as well as a polarity reversal at the top sand reflection.
a
Shale Figure 11.8. Simple anticline
Oil sand
model (a) and Zoeppritz calculations at 10 and 30 degrees.
Brine sand
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AVO Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
II
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Figure H.9. AVO crossplot illustrating the concept of 2 term 0.4
0
AVO projection
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Figure 11,9 shows an AVO crossplot with the data from Figure 11.7, Note that the 36 degree projection can be visualised on the AVO cross plot as a trend drawn through the origin which intersects the shale/brine sand point, Projecting the data along this trend would make the shaie/ brine sand point zero and the shale/oil sand below the line would be negative, Shuey's equation (R=RO+Gsin'8) can be used to generate the projection, Note that owing to the fact that tanx=sin'8 (Whitcombe et al 2002) any trend drawn from the top left to bottom right quadrant through the origin (at an angle of 45 degrees or less) effectively represents a projected angle 'stack'.
o /Culd ~e.t 0
Given that Shuey's equation
,
is quite simply a projection of the data, it follows that the AVO responses could be projected to negative incidence angles. Generally, this would serve to subdue the AVO differences due to fluid variations (Figure 11.10).
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Sin'S Figure H.10. AVO plot illustrating Shuey projections at negative incidence
angies to highlight lithology and subdue fluid variations
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AVO Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
"'-V /
0.4
.
0.2
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l
o -0.2
-0.4 -0.4
--/ -0.2
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Figure 11.11. AVO Projection using Shueys equation where
o
sin'8=-0.36 - subduing the fluid
0.4
0.2
avo signature
RO This idea of a projection to negative values of sin'S can be illustrated on the crossplot as a projection of the data from the top right to bottom left quadrant (figure 11.11).
0.5 0.4 0.3 0.2 0.1
"
0.0
•
• shale/brine sand • shale/oil sand • oil water contacts
-0.1 -0.2 -0.3 -0.4 -O.S
$=28%
••• •• •
$=24% $=20%
-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5
RO Figure 11.12. AVO crossplot showing a variation in porosity
To investigate this further, Figure 11.12 shows a model where there is a variation in the sand porosity. There are two features to note: 1. the slope (ie lIG/lIRO) of the porosity variation is around -2. 2. the fluid vector between the different porosities is not parallel. This means of course that fluid and porosity are not completely independent avo variables. One consequence of this is that AVO anomalies can be associated with variations in porosity.
8
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AVO Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
0.8
0.6
--24% par wet
0.4
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0.2
,
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Sin'e Figure 11.13. AVO plot showing Shuey avo responses for various fluid fill and porosity
An avo plot showing the Shuey AVO responses of the various porosities (figure 11.13) reveals that the porosity variation is emphasised at negative values of sin'S whereas the fluid differences are emphasised at positive values of sin'S. Notice that the points at which the wet and hydrocarbon curves intersect varies slightly between porosities. This re-iterates the fact that fluid and lithology are not totally independent AVO variables. The effect of varying the shaliness of a sand on the AVO crossplot signature may differ depending on the role of the shale on the porosity of the sand. Figure 11.14 shows a dispersed shale model The slope of the trend (~-3) is slightly steeper than the sand porosity trend in Figure 11.12 but it is clear that the key variable in the crossplot response is the reduction in porosity associated with the introduction of shale.
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RO Figure 11.14 Dispersed Shale Trend. ~l& GEOSCIENCE ~_TRAINING
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<JAva Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
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8200
8000 7800
.,...
C::;;S=::::;:;S==7.2
x 10'
"
"''' 0000
"" "" "" "" "''' '"'' "" "00
0'
-0.5
.,
----.:::=-----&.4 ~n e(/4
Figure 11.15. Angle Stack Maps Generated from RO and G.
Using the idea of projections it is therefore possible to create maps (or indeed 3D cubes or 2D sections) at any desired projection. Figure 11.15 shows an example from Hendrickson (1999) of maps generated from intercept and gradient data in the Auger Field of the Gulf of Mexico. Notice that the coincidence of amplitude with structure holds for the lower angles. Between 18 and 30 degrees there is a significant change in the reflectivity. This is interpreted here as a change in the relative contribution of fluid and lithology. The map at 18 degrees is the optimum fluid angle. As the angle is increased lithology effects become more evident such that at 30 degrees the channelised nature of the reservoir is the evident feature rather than the association of an anomaly with the structure. Indeed it is characteristic that in the region of the fluid angle the maps can change quite rapidly with small increments of angle.
Mid angle for near and far stacks A practical consideration for the determined by offset/angle modelling interpreter is the relationship between
RO A(n) A(f)
______
j
~
,, ,, ,, ------~-------------------,, ,, ,, Sin 2 (n)
near and far partiai stacks and the intercept, gradient and projection angles. Figure 11.16 i1iustrates that Shuey's equation can be used to calculate the intercept and gradient from near and far angle data
Sin 2
Sin 2 (f) Figure 11.16. Partial
G = (A(f) - A(n)) / y where y = Sin 2 (f) -Sin 2 (n) RO = A(n)-GSin 2 (n) 10
Stacks and the AVO Attributes.
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AVO Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
Alternatively Shuey's equation can be re-written to derive a particular angle projection from near and far datasets.
Angle stack amplitude
projection
Amp1
P'Ol
2
[( {sin = Ampflo - Ampoew . B B
pwJ
2
SIn
G !H,-opdeel
Q.A/!~
2 -Sin . 2 BB,>ew'JJ + AmPoew'
1m - SIn
nem
\
Equation 11.1.. Angle projection using Shueys equation and near and far stacks
As a projection device Shuey's equation has limitations. It can only effectively be used to calculate up to incidence angles of 90 degrees (i.e. an AVO crossplot angle (X) of 45°) (figure 11.17). It would be useful to have a projection device that could give a value for any projection from +90 to -90 angle of X whilst preserving the sense of displacement (but not necessarily the magnitude). Whitcombe et ai (2002) has suggested that Shuey's equation might be modified to achieve this. The approach involves re-writing Shuey's equation in terms of the crossplot angle X (equation 11.2). .L A 1/. ~ 1:$
rJ4.eciL fJ0fM!C3
,! . 10 /,relet!; If..iU .vffl!V1
l7<212 ClR.e
d)./ 'l'U(
i'$u.,-e.
S'w;r-
Shuey projections are
limited to e=+90 -90
......----1-------...-/ " ,/' ". 8=90 -90 .
0.4
.•....
1i
0.2
G
X=45 -45
//\
1 .-//-+/01--1--0.2
..,/
•
-'}11o-J,.I~.J q0vvr's
---1.
Figure H.17. AVO crossplot
""" "
.//
showing the limits of Shueys
/"
-0.4
.'
""'"
",/
'
-0.4
4
(e p)
-0.2
o
0.2
.
equation for AVO projections
0.4
RO If the cosx term is dropped the result is an equation that gives a stable reflectivity attribute across the whole range of chi angles. This will be referred to as 'Modified Shuey' reflectivity.
'IX-" Shuey's Equation
Modified Shuey'S Equation
.:.R:..:O..:c.:.os,-,X"--+..:G:..:s,,,il.:.1X"'· 2 B =Rc= RO + G SIO
RO cos X + Gsin X
COSX
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Equation H.2. Reflectivity in terms of the crossplot angle (X) - Shuey and Modified Shuey
11
AVO Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
0.6
a.'
owe - Oil sand/brine sand
!
0.2 u
a:
a f--~~-=~='-f'''''''..,--~-
Shalel brine sand
.Q.2
Bold lines Shuey
.Q.4
Figure 11.18. AVO plot showing Shuey and Modified Shuey reflectivity for data shown in
Figure 11.7
=
.Q.6
·90
Figure 11.18 illustrates a comparison of Shuey and modified Shuey for the data shown in Figure 11.7. The main benefit of this approach to seismic projections is that sometimes the principal lithological projection falls beyond sin'8=90 or X=45. An example of this projection approach is shown in Figure 11.19. A projection of X=-51° appears to pick out the positions of the main turbidite channels in the oil field, whereas the fluid effect is picked out at angle of X=12°. Note that owing to a data quality problem in the Southwestern part of the field the fluid signature extends beyond the mapped oil water contact (light blue line).
x =-51.3°
X=12.4°
Figure 11.19. Map projections using coloured inversion data and modified shuey reflectivity (after Whitcombe et al 2002)
12
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AVO Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
"'had f,lA/d "
Mldtl/etr ''1'0(1 ~ ftc: SII,vds
Lithology Cube
Figure 11.20 shows an example of the data that was use to create the maps in Figure 11.19.
Fluid Cube
+
When using this type of dataset it must be remembered that tuning has not been addressed in the trace manipulation to band limited impedance. Figure 11.21 below shows an example where pay thickness tuning (principally on the far offsets) is evident on the fluid cube display. 40ms
Figure 11.20. Examples of fluid and lithology cubes generated from combining intercept and gradient bandlimited inversions (Courtesy
Apache Corp.)
Figure 11.21. Effect of far offset pay zone tuning on bandlimited
fluid projection
A simple 2D model justifies the tuning interpretation. Tuning of FI attribute -100ft column
.
r-······_~···..,..3GlI
,
."..--".J
~.oo
t
Effect of luning between Top Reservoir and owe
600
• ~ t.7(lD
Figure 11.22. Fluid
....
•
~
Projection Model
... .,#,. ;:-".
- .!--,o;-.-';,..-"".,----c!" dl"'Vl>oI~.&J.-
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AVO Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
Connolly (2005) describes an approach to net pay prediction using bandlimited impedance data. Figure 11.23 shows the bandlimited impedance of a soft wedge in which N:G=1. If the gross thickness (ie time difference between zero crossings) is crosspiotted against the average amplitude between zero crossings the effect of variable interference within the wedge is quite clear. Also, as expected, the 'thin-bed' part of the curve shows decreasing amplitude with thinning of the wedge but largely invariant gross thickness.
·6000
,\ ~.
·5000
, ••••
E ·4000
"
~ ·3000
~ -2000
1-.
.....
~
-1000
o
~
o
20
40
60
80
100
Gross thickness (ms)
Figure 11.23. Soft wedge model showing bandlimited impedance response
If the model were changed so that N:G was less than 1 then the amplitudes would plot below the curve shown on the crossplot. The first order assumption which often works well is that the relationship is linear. So for a N:G=0.5 case the curve falls about halfway between the x axis and the N:G=l curve (figure 11.24).
,• ..
-6000
-5000
E -4000 c(
~
-3000
E ~ -2000 -1000
oo
•• }- // / ! ••., .... It.... ~
~ -.......
A
=1
N:G=1
I
N:G=O.5 ~
/'
• 20
40
60
80
100
Gross thickness (ms) Figure 11.24. First order assumptrion of finear variation of N:G and average bandlimited impedance
14
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Thus to predict N:G from the average bandlimited impedance amplitude of real seismic involves (Figure 11.25): 1. For thick beds (ie greater than tuning thickness) a. create the N:G=l calibration curve from a soft wedge model (obviously the wavelet needs to be known) b. position the N:G=l curve on the gross thickness vs average impedance amplitude crossplot by using the available well control c. N:G is simply the ratio of the average impedance amplitude between zero crossings divided by the scaled calibration (N:G=l) curve. d. Net pay (ms) = N:G * gross 2. For thin beds (i.e. less than tuning) a. net pay thickness is directly predicted using the amplitude and an amplitude vs thickness relationship drawn from the origin to the highest tuned amplitudes
Calibrated curve
Q)
-
"'C :l
,oo!--f-"BiPf-+-l
Thick bed Net pay=N:G*G N:G=100/220=0.45 Net pay=0.45*40=18ms
C.
~
200I--f---:-l1i
Q)
Thin bed Net pay=2ms
Cl nl
... ~
nl
o
20
.
.0
.0
100
seismic gross interval (ms) , Figure 11.25. Principle of net pay prediction from bandlimited impedance data (modified after Connolly 2005)
1-/5 EAGLe
Issues: 1. Such net pay calculations assume that a. the encasing lithology is invariant b. fluid component is the same (eg wedge contains only hydrocarbon sands with single hydrocarbon phase) - if there is a contact within the wedge this could lead to error in the prediction 2. Relating N:G to the seismic signature is not always straightforward 3. It is only designed to work for 'soft' reservoir situations 4. If there are no wells then the calibration curve fit is an eyeball estimation. Despite this, the method can give a reasonable relative indication of net pay.
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AVO Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
t-,;;; GR SH
Phi AI
PR
is i--to.f /III0rfd
Wet (0-40) Res(0-40)
CC«1)
( wei)
,..".,...-;,.".....;".,-..."..,..,.,..;.-.,..".-T~
FF Wet
,{)ouaa-!J.:J.JL
FF Res
wJ
,lj'Jio.JJ'vt<.
2"1, If 0 Wet crossplot ~
..
... (
•
...
100ms
RO Thin gas sand
X=27.4° 8=46.1° FF=RO+Gsin 2 (460)
Figure 11.26. Adaptive fluid factor display (mo
(;II.t.-YI Sdt d (tWeU.
exfkW]:,1A..
/ling to ascertain the magnitude of the AVO effects)
~
In order to gauge the magnitude of AVO effects rated to fluid and lithology a useful modelling display to make is a fluid factor trace with and witho t hydrocarbons (Figure 11.26). Intercept and gradient parameters have been generated from model d gathers (in this case the gathers have been modelled as single trace solutions without traveltim (NMO) effects). A fluid factor angle has been generated by crossplotting the wet data. The fluid fa or has then been applied to wet and nds at the top of the section have hydrocarbon bearing model data. It can been seen that the strong AVO signatures even when they are wet. The presence of gas in the thin sand in the lower part of the section magnifies the fluid factor signature by a fa or of about 2. Thus the interpreter should be looking for down-dip up-dip differences rather than e magnitude of the fluid factor.
tz-I-----+----j-
rc.:---:.,.-.""'•. ----+-----f-.--f-""=-1:-=--+-----tP--
10 -:
I
.-,-
Z-f-~-ii!'
,-f---+ -Z-f-----=-~
-
-.-f----~
-,--
-.-
-10-
-12 -
•
~:;;;;::;;;;::;;;;::;;;;:;t:;;;;:;;:;:;;;;:;:;;~;;;
~~" ii, ,''.','' i" '~L~' "~ 11111 ... •~' ii,
Figure 11.27. Crossplot from Seismic Corresponding to to a wet zone in Figure 11.26.
An AVO crossplot from a portion of seismic at the well location but below the gas sand shows a different fluid factor angle. The modelled and seismic fluid factor angles are not the same owing to the effect of noise in the seismic. 16
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AVO Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
The role of noise on the AVO crossplot is illustrated by the model data in Figure 11.28. When noise is added to the model the optimum fluid discriminator steepens.
Modelled Class III/IV Shale/sand AVO responses
Simulated seismic crossplot incorporating seismic noise 0.' ~--------_ _,
0.12 0' 008 0." 0." 0.02
\
J-~30%
~
=2M~
..•."" HYdroca~n .., ·M2
-0.06
.30 brine 0.2
.(1.15
o
-M5
.27 brine .30 gas
.28.5 gas
•.2
••
..,
j
..,
.28.5 btjne
1, ol--_~_~
Wet sands
sands
-0.12
•.2
0'<
$=27%
0
0
06
., '0.05
-0.3
027 gas
.1---' ·0.25
-0.2
-Q.1S
"
-tI.l
-0.05
n05
Intercept
Figure 11.28. Model data illustrating the effect of seismic noise on AVO projections (data courtesy
Projections of the modelled seismic data show that the noise free 'theoretical' fluid factor angle is inappropriate to image the fluid changes (figure 11.29).
X=37
X=8.5
10
45
9
40
8
35
7
5
~
4
•
--\--1----
30
1;' 6
,•
i f\----
1--1
~
g
,•
25
-28.5 brine
I--hl--{I- - - -/++1-+--
- 3 0 brine
e20 "---1-1-1-+'11-\-1-1- -
27 9as -28.59as
~
15
3
1-)
10 5
o 0.3 Proj chi
r-J))
-0.25
-0.20
-
--
J~ (\.~~\~
-0.15
-0.10
-0.05
- 2 7 brine
0.00
30 9as
0.05
0.10
Proj chI
Figure 11.29. Gausssian fits to projections of the modelled seismic data shown in Figure 11.28.
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AVO Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
Fluid projection Raw data
Spatial smoothing
AVO intercept v. slope
·20
0.5,--------------,
."
Oil
·30
"~
0
•.,
·35
Wet
;;;
Inc porosity
• ·0.5 -0.2
-0.15
·0.1
·0.05
Lithology projection 0
Spatial smoothing
Raw data
intercept RO
Figure 11.30. Model illustrating the effect of seismic noise on AVO projection maps (courtesy R.E. White)
Figure 11.30 illustrates the fact that despite the noise the fluid and lithology projections show clear interpretable variations. Clearly the noisier the data the more ambiguous the lithology projection is Iikeiy to be. Equally, the smaller the hydrocarbon effect the more subtle the map variations related to fluid.
The role of noise on the crossplot signature is explained by the fact that the gradient is extremely sensitive to seismic noise. Figure 11.31 illustrates that including noisy far traces in the estimation of intercept and gradient results in a steepening of the gradient (i.e. its made more negative) whilst the positive intercept is increased (i.e. made more positive). It is a feature of the intercept and gradient that they are highly negatively correlated. Signal on near part of the gather (with correct gradient)
,,
/
,,
Noise on far
,,
..
/offsets
Linear regression
Figure 11.31. An Effect of Noise on the AVO Intercept and Gradient.
18
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AVO Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
Noise of course can affect all traces in the gather. The problem of fitting intercept and gradient can be envisaged in terms of the standard error statistic (figure 11.32). Successive fits from one cdp to the next will be made within the standard error bounds but will have a variability dependent on the noise level. Thus the gradient in particular will be highly sensitive to noise and a single horizon reflection on the crossplot will be an ellipse not a single point (Hendrickson 1999, Simm et al 2000). The slope of the noise is dependent generally on the average angle of traces used in the intercept and gradient determination (Hendrickson 1999). Figure 11.32. Explaining
The gradient and intercept fils vary (with high degree of anti-correlation) benveen the standard error bounds in the data
the noise ellipse (after Swan 1993, Hendrickson, 1999 and R.E.White pers.comm.)
., 01
0.2
OJ
o,~
.1o'~
Slope
G
approximately related to average
angle of traces used in RO and G determination
.+ 33
"00
1250
background
M>"~
anomaly
Color Key n~
123'1.2
1232.5 1230.9 1229.2
1221.6 1225.9 1224,3 '222.6
12210 1219.3 12\7 7
-5.0
-2.5
0 Inl&lcepl (P)
Figure 11.33. Horizon Crossplots Showing the Effects of Var
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A real data example of a noise ellipse effect is shown in Figure 11.33. The full stack seismic section shows a bright spot associated with the presence of gas and a dimming of the reflection downdip where the sand is brine bearing. Looking at the gather displays it is clear that the down dip brine sand response has low S: N as well as a clear elliptical response on the crossplot with a high angled slope. The bright spot has high S: N and a relatively low slope. In this instance the low angled slope is interpreted as an effect of decreasing pay thickness. Tuning effects will be discussed later in this section.
19
AVO Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
Variations in lithology can give rise to difficulties in crossplot interpretation. The example from Sams (1998), shown in Figure 11.34, shows two culminations from an area in which reservoir is varying in quality (figure 11.34 a). The crossplot interpretation (figure 11.34b) is complicated by the fact that clean brine sands in one part of the area coincide with oil bearing shaley sands in another part of the area. Although the crossplot interpretation is complicated (figure 11.34b) what is important is the AVO signature on map projections (figure 11.34c). Obviously the clean sands will show a strong correlative amplitude change (from hydrocarbon bearing to wet sands) coincident with structure but it is also likely that there will be a similar but more subtle effect associated with the shaley sands.
North
A
Figure 11.34. AVO signatures related to changing fluid and sand quality a) cross section b) AVO crossplots and
TWT
c) schematic fluid projection map (data redrawn from Sams 1998, interpretation by RPA Ltd)
Possible contact
&;;edaiUJtJJ d fWlI1d
'
..
vA-' .AVO
UtI/tit
1~,Le.~ IteAJ
r/d.;'''R-R .
-
".
Hydrocarbon sands Dispersed shale trend
"""'"
""
Clean
~
"-,
Sand
-"".'
Oil and gas
o
RO Fluid factor projection Shuey with Sin'8=0.18 High
Low
Southern hydrocarbon accumulation
20
North
Northern hydrocarbon accumulation
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J
AVO Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
Figure 11.35 illustrates the impact of noise on the simple AVO model previously described in Section 3 (figure 3.11). It can be appreciated how brine bearing good quality sands may yield strong AVO anomalies. In areas where there is a strong AVO anomaly on a slope with no obvious correlation to structural closure it may weli be difficult to confidently interpret the presence of hydrocarbon (figure 11.35).
G
Rock Physics Model
Seismic Crossplot with Noise + G
+
Figure 11.35. The
+
RO
RO+
-.....
j '" Lithological trend
problem of interpreting isolated AVO anomalies
/ ..., ... / \
.
AVO Anomaly
.... 'b c'
/'1
t
.f
·,,1. ••
~1.
,
~'\l ),'Ir.:' .~~!~)~r.fjr/...i~_;;::' .AVO projection . .. ""/.' 1", ... ·_""~IP':O.,.I
"'._"'! "'lor'" I,·"j;., ~~;w\,.'''' 'I~ ~''''l.;. -,. II' ",I - =- ~~~":.' . ~l :.1';'- ,I I~ I,,'J:' I,: j ....
~.,.,
r l 'J"toI:,. '~'" I I......
11I"oJ
,I
•
:'~IHI': ~
.•
~~ ~."
,Ill:
I
,I,
I
111
I ,;' ,~.I\\ \ I '\
. (1\
Offset dependent reflector interference is an added complication for AVO (figure 11.36). The problem arises from the fact that reflector hyperbolae are not parallel, giving rise to variable interference across the offsets. Added to this is the band with distortion associated with NMO stretch.
Offset--
Variation in bandwidth due to
Time thickness variation across the gather (non parallel
t~
Depends on velocity contrasts
1
I2.l...
~ae)
TWTI
Tuned gas sand
••
.. ..••
figure from Allen and Peddy 1993
When the nears are tuning the lower frequency on fars
rOf~fl
..
",
''''',
,,,.,
...-
- . '000-
.. ,,=..-
,
I
•
Peak Freq
_0.1
NMO stretch
NMO stretch - relationship between thickness and amplitude is not constant
39Hz
'. \
,
30Hz
Amplitudes are
related to different tuning curves high frequency (near) tuning curve '"
Low frequency (far) tuning curve
.,/ Amplitude
effectively reduces the relative amplitude of
the fars
thickness
Figure 11.36. AVO Tuning and NMO Stretch. •""')) GEOSCIENCE 0.,3TRAINING
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21
AVO Analysis 11.2 Conventional Intercept-Gradient AVO Analysis
The effect of varying offset interference on the AVO crossplot is to generate a looping pattern. The position of this pattern on the plot is dependent on the magnitude of the (untuned) AVO gradient. In Figure 11.37 a 'mild' Class III signature may change to a Class IV signature due to the effect of offset dependent tuning. + AVO Crossplot
G:i
Sin'O
,, ,
GI,
G:i
~@CD
Amp
, ,
,
3
0 CD
Sand geometry model
~
,, /
~
G
,,
,,
"'RO
~CD
':0
Effect of lun;rlg at near offsets· increase in RO butllecrease in G
Elfecl of tuning at Far offsets (non parallel NMO curves)· increase in G wh~e RO remains constant
Figure 11.37. One Possible Effect of offset dependent interference
With steep gradients there is no change of AVO class but there are variations in intercept and gradient depending on where the tuning is occurring along the offsets (figure 11.38). It is evident that AVO anomalies can be generated simply through these interference phenomonen. In the presence of multiple thin layers the AVO response is unpredictable. O,---..---~--~----,----~---r---,
5m
10~ JOm
·0,025
• 15m
·0,03
~
Isolated reflector
t".~
•
/
35~\'.--rI I
40m
~.~20m
'00~50LJ"'2--"'.0-',O"'J--"'.0"',OL28'----."'O,.L02"'6----'.0"',O"'24---.0"',OL2"2---.0-',O"2---.0-',018 AVO intercept
Figure 11.38. Tuning signature of sand with strong Class III response (courtesy R.E. White)
22
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AVO Analysis 11.3 Seismic Processing Issues
11.3 Seismic Processing Issues Whatever the approach to AVO analysis the key ingredient is good data quality (figure 11.39) and of course this is related to the application of an appropriate processing stream.
Consistent frequency content across the gather (no NMO stretch effects)
Zero phase data
Good multiple and noise attenuation Consistency of scaling of each trace (high source repeatability)
Correct relative amplitude across the gather Good fold (high no of traces) (adequate offseUangle sampling)
No critical angle energy
Offset
Flat gathers (correct moveout velocities)
Clear continuity of reflectors across the gather
Data points imaged properly (pre-stack migration)
Figure 11.39. Characteristics of a Good Quality Dataset for AVO
Seismic processing for imaging and AVO is a rapidly developing area and it is not possible to give an exhaustive account here. With regard to AVO processing it is worth quoting Cambois (2001). 'Although preserved amplitude processing is a clear requirement for AVO studies, such a processing sequence is not uniquely defined. In particular, "preserved amplitude" has a different meaning for land and marine data. ~possibie definition couid be: Any sequence that makes the data compatible with Shuey's equation if thiS is the model used for the AVO e simp icity of this definition should not hide the Herculean ana YS/s. nature of this task. ;
The interpreter needs to be aware that careful QC of the data after each processing step is vital to check on the effects of the processes on relative amplitudes. Where possible, maps need to be used as part of the QC. Spatial variations in amplitude, phase and timing need to be appreciated across the 3D seismic survey.
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~rtJ.(A/
I,
f:£ttlT
d.:la c.ef
/I,
A.! rl)~IJ'd
Se;It~,VC4 ua..llo
Jed.;
©Rock Physics Associates Ltd 2007
23
AVO Analysis 11.3 Seismic Processing Issues
Table 11.1. Seismic Processing for AVO - Issues
---; Issue
Process
Notes
Offset dependent SPherica/
- May be inadequate in the presence of Anisotropy - Avoid AGC
divergence correction - V2T or exponential - surface consistent corrections
Recover true amplitude
Near surface velocity variations
(land)
Statics Residual statics
General phase character
Zero phasing
Noise attenuation
FXY decon
Anti-multiple
High Resolution Radon transform
Deconvolution
- Tau-P Predictive deeon or whitening trace-by-trace - Surface consistent deeon
- Avoid FK - Care needed attenuating strong shot noise on land data Wave Equation Demultiple or SRME should be used in conlunction with Radon Avoid single trace deeon design
Pre-stack (Kirchoff) time
Reflector Alignment
t
("'0,<)
Velocity analysis
+ NMO
Tt.l.A- r.,1/~ (e,.f;~)
NMO stretch
- Stretch free stacking (Trickett et al 2005) - Partial stack spectral eoualization (White oers. comm.)
Phase distortion with depth
Q compensation
(
Final amplitude balancing of gathers
24
Curved ray anisotropic PSTM should be used where aoorooriate
migration
Trace positioning
- 4 th order NMO for long offset non-hyperbolic reflections - Residual velocity analysis using ~and(;(Swan, 2001) afterstretch correction - Avoid lo-fidelity interpolators and trim statics
- surface consistent scalars - long gate AGC (marine)
Model based offset balancing
Variable scalars across the offsets
Offset to angle conversion
- Check angle mutes - need slow varying velocity field. - Curved ray algorithm
Muting / signal recognition
Careful QC of gathers
Intercept/gradient estimation
Robust fitting (Walden 1990)
© Rock Physics Associates Ltd 2007
-
- May not totally remove the effect on AVO - Mute out excessive stretch (>2: 1) - Usually applied after stack - PreStack should be tested - model/well tie based is a good aooroach PreStack Time migration should balance the amplitudes. Best done on a target oriented basis Careful QC where changing velocity structure (eg water depth) Be aware of problems caused by shot point qaps in land data Supergathers are a useful diagnostic tool for enhancing siqnal - Analyse seismic for linearity of response with respect to sin 2e - use statistics of fits to evaluate data oualitv
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AVO Analysis 11.3 Seismic Processing Issues
The following illustrations focus on the interpreters requirement to appreciate various aspects and implications of data quality. From the interpreters point of view there are a number of key issues that need to be addressed prior to performing AVO analysis • Data Quality • S:N recognising bad data noise removal vs. signal enhancement identifying signal;: !OC4S ......aly""jo 0"the effect of noise on the AVO gradient • Alignment Effect of RNMO on the avo gradient Residuai moveout vs. Class IIp AVO Understanding the effect of NMO stretch • Amplitude Scaling Final Scaling and offset balancing for AVO calibration
s:/1!MJ/
It is surprising how many AVO projects are carried out on unsuitable data and unfortunately it is 'garbage in, garbage out'. The data example in Figure 11.40 proved to be unsuitable for AVO owing to the presence of interbed multiple energy contaminating the near traces, a strong frequency lowering with offset and increase in amplitude with offset that was related to the application of an inappropriate process.
.
~
[~
.
........................... ~...
... -...
_-
Figure 11.40 The Problem of
Multiple Energy
l!. i.. .......
..:
tJNO'
"""'7"'~p
:~I
=':-~:-:-:~~:.':~~..;.::: ..: . . '.'''.... J "i! ...~._ ..".... ."-.... v :.::.. :.:f.~"110 -"H.. .':'.'. -
~ ~
-
.-
1400
Recognising Bad Data.
After
Before
'~ ..;~.-:
• . ".
.....-... " ........
..• : -..; ;
I
51.&
•• ....!1
....
1500
The interpreter needs to work with the processor to ensure that not only is noise eliminated but that signal is enhanced. Figure 11.41 shows an instance where multiple removal was particularly successful. There are many instances, however, where noise is removed but the process also
removes signal. ~l~ GEOSCIENCE ~_TRAINING
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25
AVO Analysis 11.3 Seismic Processing Issues
440
10100 440
10100
440
10100 440
10100
1.4
1.4
1.6
1.6
1.8
1.8
,mmmt-2.0
2.0
2.2
"1II"1I,'11I
2.4
2.4
2.6
'!>IHlIHll- 2.6
Figure 11.42. Noise Reduction Through Supergather (after Allen & Peddy,
1993).
The perception of noise and signal can be critical in designing data workflows. The supergather technique, where a gather is constructed by stacking each offset from a range of CDPs', is a useful technique for the interpreter to visualise the signal content of the data (figure 11.42).
0.15 0.1
1'..:.:~15 ~
15
~ 0.05
~o
....
:E
a. E
«
0
~
0.05
CO _____ 1-- sample
~
y = -O,.4535X + 0;1304
-0.1
o
______________ 1-- reflection
~y = -0.0823x + 0i1~59
0.1
0.2
0.3
K
0.4
0.5
Figure 11.43. Effect of Residual Moveout on Gradient
Figure 11.43 shows that residual moveout has a similar effect to random noise on a Class I response, ie steepening the gradient (more negative) and increasing the intercept (more positive).
26
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AVO Analysis 11.3 Seismic Processing Issues
Far
Near
Figure 11.44. Red pick - Phase reversal or RNMO?
Deriving intercept and gradient from partial stack combinations is good so long as the data is good quality and there is no residual moveout. Figure 11.44 shows an example of the effect of RNMO on picking partial offset stacks. The pick from the near stack has been transferred to the far stack. The red pick appears to have a phase reversal but this is only an effect of localised variations in RNMO. When there is residual moveout separate picks need to be made on near and far stacks. If this is not done spurious anomalies may be generated from the combinations of near and far amplitude data. It is always advisable when working with partial stacks for understanding where the partial stacks have originated. A set of gathers will validate the correlation of events on the two stacks. Differentiating residual moveout from a Ciass IIp response on seismic gathers can be difficult (figure 11.45). In fact, you really need to know that a Class IIp response is expected in order to recognise it. The gather shown in figure 11.45 illustrates a Class IIp response. Note the flattened peak reflections above the reservoir.
Offset
~~! • ~ )
)
,) ')
H
....
)
()
)).
.~
~.~)
\~))).)
. .'C.<
~.
•<
,..
,)\ •• ,,\
.
!
(rr''''II-+--~:ervoir I
... ~
lie/OW
Figure 11.45. A Class IIp Response (after Simm et ai, ~)1.. GEOSCIENCE
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AVO Analysis 11.3 Seismic Processing Issues
Another Class IIp example is shown in Figure 11.46. There is slight residual moveout here but it is difficult to quantify without the model.
50ms
Zoeppritz synthetic
Seismic Gather
Figure 11.46. The problem of appreciating NMO in Class IIp situations
Acoustic Model
- -AI
~j
Single Interface Model
Poisson Ratio
+
--
Ref Coeff Series Zero Offset
The interpreter should always expect surprises in Class IIp environments. Figure 11.47 shows that near and far seismic data will look quite different in the presence of a Class IIp effect. Note that it would not be possible to use correlation statistics to match the two datasets, except above the target or within a large time window.
Seismic Trace
Zero Offset
*
~ + Noise =
*
~ + Noise
--
30 degrees
=
Figure 11.47. Class [III AVO Reflectivity.
28
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AVO Analysis 11.3 Seismic Processing Issues
1°~1~ ~I 5: ~=-\j
(>vif,...
'J
U
...
a\J'v"c;nCC)
=
.L Q
0-
2300-=
2400--:: .
-~
2700
II
-= ~
2800-=
t.
500ms AGe
No final scaling
<;bO,e f ~te
Figure 11.48. Final Scaling Problem
lv/A/Jo.,; w/
Toward the end of the processing sequence the processor may have to apM~al set of scalars. The left panel of figure 11.48 shows that the near traces have higher amplitudes than the rest of the gather. Scalars need to be applied to balance the data across the gather. There are a number of possible solutions to the probiem including surface consistent corrections (Taner and Koehler 1981) and long gate AGe. In land applications surface consistent corrections are required. For many marine applications a long gate AGC seems to be a good solution. Figure 11.48 shows how the long gate (~1500ms) AGC has brought out the Class III response at the target. It also shows how shortening the AGC flattens the gradient and changes the relative amplitudes. Whilst short gate AGC can be a necessary process to highlight structure in some areas of complex geology it is inappropriate for AVO applications. Please note that current implementations of pre stack time migration are likely to do a good job of balancing the amplitudes. Offset 5 dB
Model
o I-~~=-~L-=':::"
dB
Seismic background
Seismic background ·10
-5 After Ross & Beale, 1994
Figure 11.49. Offset Balancing using Model-Driven Scaiars. ~)&
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II
AVO Analysis 11.3 Seismic Processing Issues 11.4 Other Reflectivity Techniques
At some point the seismic amplitude response needs to be compared to a model based on well data. It is often the case that when comparing a modelled response to a seismic response (e.g. by normalising the near trace) the gradients are different. Ross and Beale (1994) suggested that offset dependent scalars might be derived to scale the seismic to the well response (figure 11.49). The problem with this approach is that the scalars tend to vary depending on where they are calculated (e.g. amplitude at the target reflector or RMS amplitude in a zone above the target)
If AVO is being used to locate anomalies rather than predict rock properties then the scaling issue is not very important. Notice in figure 11.49 that the relative difference between the background and target (DHI) responses stays the same irrespective of the scalars applied. When rock property calibration is the aim then offset balancing as shown in figure 11.15 is one option. Another option preferred by the author is a target specific calibration using AVO crossplots based on amplitude maps at the target horizon (see figure 11.57). Note that in elastic inversion (see section 11.5) the scaling issue is dealt with in the well tie process, effectively matching the seismic amplitudes to the elastic model. Given that amplitude scaling can be a critical aspect of the interpretation the interpreter needs to work closely with the processor to get a valid dataset for AVO analysis.
11.4 Other Reflectivity Techniques 11.4.1 Chiburis' Reference Method In the early days of AVO analysis Chiburis (1987) analysed Class III targets in terms of the ratios of target to background responses. This approach proved useful in land AVO where scaling across the offsets may not be perfect and the ratio becomes independent of absolute scaling. The rock physics basis to the technique has been described in Section 3. Figure 11.50 shows the measurement of the target and the background response from a supergather. In this instance the increase in the ratio with offset was taken as a gas indicator and the well was successful.
a)
'"
.2 4
,.., '. ,
~
......
'0
li '0
co'"
2
.
.!!!
E z" 0 0
b)
•
'0"./
•• .. ,..~ V ~d v
2 -,----,--,----,-------,
~" ",
'"
10
20
30
Trace Number
40
o+---j---+---+---j o 10 20 30 40 Trace Number
Figure 11.50. Chiburis' Reference Method (after Allen & Peddy, 1993).
30
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AVO Analysis 11.4 Other Reflectivity Techniques
The technique depends on recognising the appropriate background response. Figure 11.51 shows an example where there was an increase in the ratio with offset but the well found water. The problem appeared to be that owing to variable lithology, the reference reflector was not appropriate to the target reflector. Today, this approach is not usually used as the primary AVO anlaysis tool. Other techniques that use the data from all seismic gathers is preferred. 10 ,--,---,-----,--,~,
.~
f
.. ..
Reference
Target
II
Figure 11.51. The problem
5+--+--f"""'fI-¥--¥-'.o...J of identifying the appropriate
Jo+-_+-_+-_+"'R.""''-''''I'''''-----1 o
background reflector (after Allen
and Peddy, 1993).
510152025 Trace num!>er
All
A
"\ Positive AVO interpreted well found water
o
o
V\I
10
j"" 15
"
20
-y
25
Trace number
11.4.2 Partial Stack Techniques Partial stack techniques utilise the power of the stack in improving S:N whilst preserving the AVO effect. The simplest approach is to stack equal number of traces from parts of the gather, an example of which is shown in Figure 11.52. Note that the presence of oil gives a Class IIp AVO response.
Figure 11.52. Partial Offset Stacks highlighting a dramatic Class IIp AVO ~l& GEOSCIENCE ~""TRAINING
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AVO Analysis 11.4 Other Reflectivity Techniques
L
~
In the same way that was discussed in relation to the intercept and gradient analysis crossplots can be used to discriminate between different responses and derive combinations of near and far amplitudes to emphasise anomalies (figure 11.53).
+ Near
L
~
lip
L~
Figure 11.54 shows a practical application of this crossplot. In this case Class I responses are related to brine sands and shales but Class II responses are related to oil sands.
~ Figure 11.53. The Near vs. Far Crossplot.
r----.---,-------, Figure 11.54•
•
•
•
Class II Anomaly Identification using Near/Far Crossplots
r""L!.
'rn== u.
Nea,
Base Sand responses and contacts Top Sand responses with high gradients
"-:-;::--;---;0
AVO ~~OmaIY
[ r~r
Apply time shift
.'"
or pick separately (if necessary) Extract amplitudes
stacks(offset or angle) is that the ~ RNMO can be [;] taken account of by interpreting the two stacks
1
N,
I . determine
"
Far
The benefit of partial
ICrossp Iot I
I Amplitude Maps I
optium stack
separately and combining the maps to give the correct view on AVO relationships (figure 11.55).
Figure 11.55. AVO mapping using Near and Far Partial Stacks
32
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AVO Analysis 11.4 Other Reflectivity Techniques
Figure 11.56 gives an example of the relationship of the RO/G and near/far crossplots. ,0
..\l \
0.12
•
0.' 0.08
0.Q2
o
o.
Q,.J~fk c,
0.'
,( (" fc.
0
-0.02
<."
Porosity
••
-0.06 -0.08
and fluid fill .30 brine
<.6
<.,
<.•
-0.12
<.,
d v~ .f.v
/ Q
•
•
I
• /, eli.'" ( >J"O CI
0.8 . - - - .- - - - - - -.. , - - - ,
•
•
006
0."
, ~ II
{'!"J,(I)
<'
-0.15
-0.05
<.3
0.05
J _ _..J
L-
-0.25
<.,
.0
.{I.OS
.{l,IS
0.05
Intercept
" .28.5 brine .27 brine
.30 gas .28.5 gas
0.'
0.05 , - - - - - - - - - - - . , - - - - - ,
027 gas
0.06 006
0." 0,02
-G.DS
o .o.Q2
•• •
.. -0.04 ~ -0.06 <06
-0.16 ·0.18
••
<'
0
·(1.25
<.3
<' -0.2
-0,15
.{l.1
.{I.OS
0.05
0.1
RO G and Partial stack (near vs far) erossplots (near=10 degrees, far=30degrees)
+--_--.......---_1~
Ii I •
I
.Q.15
-0.1
-0.05
0.05
Model data with simulated seismic noise
Figure 11.56. Illustrating the relationship between
I
._----'
-0.2
near
Model data with no seismic noise
II '.
L-
·(1.25
near
I
/Iv/,J (A/d;c.do;e
-0,15
<., -0.12 -0.14
IC2.R - 4.C(e,r
--'.{l.1
I'
Il, . •
i
Figure 11.56 illustrates how the intercept/ gradient data shown previously in Figure 11.28 translates into near and far crossplot space. For this model 'near' has been calculated at 10 degrees and 'far' calculated at 30 degrees. Notice that the far stack is a good discriminator in the presence of noise. The far stack is close to the optimum fluid stack shown in Figure 11.28.
ERb (fjjV (~)
- fMl(I-iu.)) • [vv(rt2lC)
(1h~()C09 )
Figure 11.57. ERG Attribute (increasing AVO=red).
When performing reconnaisance AVO a useful attribute that is based on near and far stacks is the ERG (Enhanced Restricted Gradient) attribute (figure 11.57). Using the reflection strength attribute, it is defined as (Far-Near)*Far. Given that it uses the reflection strength (or amplitude envelope) attribute the ERG attribute is phase independent (and therefore less susceptible to RNMO effects). Positive ERG responses are associated with increasing amplitude with offset (i.e. Class III and Class VI responses). Class I responses will have negative ERG values and Class IIp responses will have weak positive values.
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AVO Analysis 11.4 Other Reflectivity Techniques
11.4.3 An Approach to AVO Calibration Calibration of the AVO crossplot is an offset balancing (scaling) procedure. Figure 11.58 illustrates one approach to the calibration issue in a region where the reservoir is relatively thick and regionally extensive.
Amplitude Maps It!) k
Near
Far
Data point from the AVO model at the
w
20 r-__."e,lIr-_ _-,--_
Background trend - data from around a well with water bearing formation
15
o f---;*''''''.....-+~-=--''\;----t----t----1 Of course applying this model to areas
f---~-~cl-t-''---<---''I---.),.-+---+------jaway from
the calibration assumes that the geology does not change significantiy.
·5
L -_ _...J...._+---J...3-~-' .....--''-..--'-
•10
-8
-6
-2
o
' -_ _..J 4 2
RO Expected anomaly related to oil sands >15
Calibrated AVO Anomaly (Fluid Stac
Map
·20 -10
.\ tJ 0
~
~eP~
~\
"J
- 0
\l'
. /"
Figure 11.58. An Approach to Calibrating AVO.
34
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AVO Analysis 11.5 Elastic Inversion
11.5 Elastic Inversion A recent and rapidly developing area of geophysics is the exploitation of AVO phenomena via inversion techniques. This discussion details the relationship between AVO and elastic inversion as well as discussing some of the practical approaches that are commonly used: • • •
Combined Angle stack inversions (Connolly Elastic Impedance approach) Rp and Rs from pre-stack Curve fitting (2 and 3 term, Fatti et al 1994 Approach) Model based Pre-Stack AVO Inversion Two step approach • Inversion for Rp Rs • Followed by model based inversion to AI and SI Pre-stack Simultaneous Inversion • Direct inversion for angle-dependent elastic parameters AI,SI,p
11.5.1 Combined Angle Stack Inversions (EI and EEl) Elastic Impedance It follows from the idea that the reflectivity at any point on a stacked seismic section represents reflectivity at an angle and that the inversion of seismic data to acoustic impedance can only be done (in a literal sense) on normal incidence (or intercept) stacks. It also follows that the impedance inversion of non-normal incidence data (e.g. such as far offset stacks) requires a reflectivity sequence based on the average angle of the stack. The parameter inverted from the far stack is not a real rock property but a function of both acoustic impedance and offset reflectivity. This parameter has been termed 'elastic impedance' (figure 11.59).
Invert using
AI,=AI,«1 +Rc)/(1-Rc))
Figure 11.59. Elastic
AVO plot
Impedance (or how to
_-
invert offset stacks). 2
.... ..../
term EI Equation after
EI is a derivative of offset reflectivity -
I-------L::-/''
Connolly (1999).
Amp
"
EI
""
£1 = Vp(I+Sin'O)Vs(-SKSin'O)p(I-4KSin'O)
(.P"'r,'vchA ..;s\)) GEOSCIENCE ~3TRAINING ALLIANCE
.1
I .~
z-.j-e,eu.d
stacks
~ d'v~
2 term EI equation Connolly (1999)
[
*,0 91.vu/r
r
(If);.J
~ "koUivt-J);
fFi" = eoft/slCl..of/i rJ>£ //vw iUett.?
'If:
j/=
i
~
Can be used to invert angle
©Rock Physics Associates Ltd 2007
35
:.
AVO Analysis 11.5 Elastic Inversion 2 ..fed[, v I, ~ ..;e,cU1 .
3/etuE vted' ~R F<1R pfad..
. (lA/!w.
d
2..;.e;u;;
(A
oifQ {IN~
t
r uvld I/W; Using the Aki-Richards simplification of the Zoeppritz equations as a starting point, Connolly (1999) has derived a formulation for calculating EI from log data, There is a 3 term (equation 11.3) and as well as the 2 term formulation shown in Figure 11,59, For any particular area K «Vp/ Vs)') is a single number and is usually set to the average for the log (Vp/Vs), Equation 11.3. EI from log data - 3 term, (-BKsin 28)
(1+tan"O)
(1-4Ksin 2S)
=Vp Vs P EI =Vp (Vp (lan'8)Vs(·8Ksin'8) p(1-4KSin'8) EI
.-
Figure 11.60. Comparison of acoustic
011 JO.
impedance and 2 term elastic impedance
calculated at 40 degrees 1M ,,,,
Of course an inversion of near and far angle stacks results in cubes of elastic impedance at two angles, These cubes then need to be combined to give desired angle independent elastic attributes, For example using Connollys (1999) equations and assuming that k=O,25 then an intercept and far angle stack can be used to create AI, SI and poisson ratio (equations 11.13 to 11,15):
JlloO l\U
1'00 I'M
-
n"
-,*
-71.
k~o,U
EI(B) ]1/ (-2sin'O) SI= [
Vp = Al
V,
AI(l+sin'O)
SI
Equation 11.4. Shear Impedance
Equation 11.5. Vp/
from Angle Stack Impedances
vs from AI and SI
Equation 11.6 Poisson Ratio from Vp/Vs
Lambda*rhob and Mu*rhob may be derived from the seismic impedances according to (equation 11.7):
Jop
= AI' - 2SI'
fJP = SI' Equation 11.7. Lame parameters from seismic impedances.
36
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AVO Analysis 11.5 Elastic Inversion
A relatively simple approach to absolute elastic inversion using separate inversions of near and far cubes is shown in figure 11.61. Key features of the workflow shown in figure 11.61 include deriving the appropriate EI logs Rock physics log conditioning -:~;; for the angle stacks to be inverted and performing if;~}--c.--"'r-:-; ~~: --: ~:::. well ties and wavelet extractions on both near and far angle stacks ~" ) ....--- and far angles (figures 11.62). Near and far well lies
'i":-
_
~I·j\
~rogsa,"e"
•
Figure 11.61. A partial stack Interpretation
,.-
ShoJo.,......
elastic inversion workflow.
",~t
~. ,;",i
Figure 11.62. Near and far well
ties (after Connolly, 1999).
The elastic inversion procedure effectively matches the seismic to the log data (i.e. via the wavelet scaling, figure 11.63) - thus accounting for the offset balancing problem discussed in the AVO section. Clearly an analysis of the match is a key QC of any elastic inversion product.
Figure 11.63. Example of the use of well ties to determine wavelet scaling for elastic
-100 -50
TWTms
---------------------
o
Blue=Near
ti.:.---~ ~CkWaYelel
I
~
100
inversion. ~)& GEOSCIENCE
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37
AVO Analysis 11.5 Elastic Inversion
One pragmatic approach to define a fluid sensitive elastic attribute is to effectively create a weighted stack of near and far impedance (Simm et ai, 2002). This has been termed AVOImpedance™. When plotting near impedance on the x-axis and far impedance on the y-axis there is usually a clear arrangement of shales, brine sands and hydrocarbon sands descending down the plot. AVOImpedance is basically a weighted stack (or projection) normalised to the brine sand data (see figure 11.64). It would also be possible for example to normalise to the porosity trend and derive a lithology discriminating attribute.
\)\<7\
"§' :5
1700 ,-----,-------,----,----'ll(".;
1
"00+--+-+-r----j,~___1
.•
1500+--+-;Il-~H-_I
~ ~
, !~
~
• KiJOOlclay
1400
• Oil sands
1300
• Brine sands
N
OJ
• Ettrick shale Projection
axis
1200
9000 +
/ (
/ I 1\\\ I I I \ ,\ II / /1 / .~\ ~ /---' /
I
I
,
- - - - .- .
.• ..
" /
.
11000
"
13000 •
AI (near impedance)
Shales Water sands
Il:~=oi="=,"=d'===~tt~~~===~
Figure 11.64. AI VS. EI crossplot and
1't------J~_+----v'rt-----,
deriVJtin of AVOImpedance.
. (/I£c-o ) Figure 11.65 illustrates the additional discrimination of AVOImpedance compared to near and far impedances. In fact AVOImpedance is very similar to poisson ratio In Its discriminating qualities.
It Vo h--'f:O (f!! ~ 111: c) - flU
.~
/ \
I
/
I .
\1
/
1\ .//0
/ / "
«
I / \ / II
"
.
\ \
1\
\
\
\
. .
\
'-...
!<ef US·ll D7J
'4000 , - - - , - - - - - - - - , - - - - - , - - - - , Oil trend Increasing Vsh • Klmmclay
13000
12000
-+-- ~ Brine trend
10%9
Figure 11.65. Histogram facies distributions - AI,
EI25 and AVOImpedance
• Oilsands • Brine sands • Eltrickshal
11000
"
To aid interpretation AVOImpedance is
10000
9000 8000
000 L-----l----J-:=::::::±c~J o Increasing SO ·100 ·50 '00 AVO Impedance
FIgure 11.66. AVOImpedance template.
38
sensitive attribute, see figure 11.66). If the Vp Vs trends follow the Greenberg Castagna relationships then shales usually plot to the left, brine sands in the middle and hydrocarbon sands to the right. Porosity increases down the plot. A framework derived from a generalised rock physics model can be drawn on the plot to indicate porosity and fluid lines.
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AVO Analysis 11.5 Elastic Inversion
Figure 11.67 shows an example where the problems of tuning and lateral property changes in the overburden are addressed by elastic inversion. Position of
Position of
GTe,
GTe,
Figure 11.67. Near and far
-.......,;;:---:-;;..~~rn-""=- stacks and gather display from ';"-::~P':"-"~-4r~
Seismic Gather
Near Stack
dry wei/location.
Far Stack
Similar features were potential targets. (figure 11.68.
Figure 11.68. Far offset stack from a prospect location.
Seismic Data Gradient (G) (gradient slack)
Color Key Time
12.5
3151
Figure 11.69 shows a crossplot from the dry well. AVO responses from layered models were scaled to the seismic values. Oil and gas sands would plot to the left of the red trend line on the plot (figure 11.69).
3141
3132
5.0
"
2.5
3123
3113
3104 -2.5
3095
Oil
c:r 0», 1----'!!
1hOv~
$(.I1J
fyVO
M
r
\1 (.
3085
-5.0
-.....,~Gas
-7.5
3076
3067
-10.0
-12.5
"
""-::":"'---i:-......._~... -2.5
0
1
3057
2.5
P-wave (P) (gradient slack)
Legend • Seismic Data -
y = -S.63171x -6.1192
Figure 11.69. Calibrated Horizon Crossplot. ~lb GEOSCIENCE ~""'TRAINING
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39
AVO Analysis 11.5 Elastic Inversion
AVO analysis at the prospect might be interpreted as oil bearing based on the calibrated crossplot (figure 11.70). However the gather (figure 11.71) shows that there is the possibility that the response is tuning on the far offsets. Thus the higher gradient may be related to far offset tuning rather than the presence of hydrocarbon. Tuning is a problem for the interpretation of the conventional AVO analysis. Seismic Data Grlldienl (G) (gradienl stack)
Color Key Time
•
Tuned brine sand or oil sand?
10
~
- Tuning on far offsets
51
... ,41
3132 3123
~
~
3113
0 3104
Oil
3095
-5 3095 3076 -10
3067
Figure J1..7:1. Gather from the prospect.
1
3057
-" -3
-2
-1
0
1
P-wave (P) (gradient slack)
I ,~,oo ~
Seismic Data
I
y =-4.8630Sx - 9.5955
-
Figure 11.70. Tuning or hydrocarbons? One approach to getting around the problems of tuning and lateral parameter changes in AVO is elastic inversion. Elastic inversion (i.e. inversion of near and far angle stacks, either simultaneously or separately) may: 1. account for tuning through the use of the wavelet - so long as the wavelet can be accurately defined and the correct low frequency component added to the seismic. 2. effectively address the probiem offset balancing (matches model to seismic through scaling of near and far wavelets - lets hope the scaling doesn't change laterally or with time 3. solve the problem of lateral impedance changes - if the low frequency component is correctly modelled.
Log based analysis shows that elastic attributes such as AVOImpedance will theoretically give better discrimination than acoustic impedance (figure 11.72).
EllS
-
i
I
Hard shales
Soh shales Brine sands Oil sands
Gas sands
I
f
\
-Figure 11.72. Facies distributions using near elastic
"impedance and AVOlmpedance. 40
© Rock Physics Associates Ltd 2007
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oil
ALLIANCE
AVO Analysis 11.5 Elastic Inversion
Near angle
Figure 11.73. Inversion results
of near and far angle stacks at the well location.
6000
Brine Oil
Gas
5500 5000
~ 4500
+
+ ++
12.5% 4J
w
4000
20% 4>
3500
Values are taken directly from the inverted stacks and the AVOImpedance attribute is calculated. The plot in figure 11.74 shows that the calibration is very good (owing to a very good well tie). Note that there is an elongation in the AVOI axis direction owing to the fact that this attribute is sensitive to noise.
30% $ 3000 -100
-50
0
100
50
AVO Impedance
Figure 11.74. Elastic inversion result at the weI/location.
The prospect that has tuning on far offsets (and from AVO analysis might be interpreted as an oil sand) shows a similar result to the dry well (figure 11.75). It thus appears to increase the risk on
<'I2!:te
the prospect.
OIl haLt'-'(/./-tu "j'-/!di..J-;J5.
<;,wed
6000 Brine Oil Gas 5500
5000 :; ~ 4500
'\- \
,,'
. tP~~~
<000
3000 -100
~l)
GEOSCIENCE
&3TRAINING
.1
ALLIANCE
12.5%¢
"-
~\ \1\ 'I '-\
3500
Figure 11.75. Prospect Inversion Results.
N
N
W
\
o
-50
50
20%¢
30%; 10(
AVO Impedance
©Rock Physics Associates Ltd 2007
41
AVO Analysis 11.5 Elastic Inversion
Extended Elastic Impedance 'Extended Elastic Impedance' (Whitcombe et al 2002) is the derivative of modified shuey reflectivity as defined previously.
Equation 11.8. Extended Elastic Impedance (after Whitcombe et al 2002)
Note that EEl is normalised to an average acoustic impedance. El can also be normalised in a similar way (Whitcombe, 2002). A key importance of these equations is that not only can they be used to invert seismic but also to perform AVO analysis on log data.
v pO = average Vp V sO = average Vs Po = average density p = (cos X + sin X)
q = -8Ksinx
r=(cosx-4Ksinx)- L-k=(vs/vpf Again foliowing Whitcombe et al (2002), it can be shown that certain theoretical projections of RO and G (ie EEl) provide optimum discrimination in terms of particular rock prjerties. Note that with real seismic data the chi angle is affected by noise. (cdfO /996
lJolf '
G
oc +
Figure 11.76.
VSp oc~
Relationship between EEl and Elastic
+
Parameters (after
K a EEl (X=12.4") '" EI ( 6=28') A a EEl (X=19.8°)", El ( 6=37') ~ a EEl (X=-51.3°)
RO
Whitcombe et al 2002)
oc
VpN S1.414
t oc
42
Vpp
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AVO Analysis 11.5 Elastic Inversion
From a rock physics analysis point of view, EEl can be used to determine the potential magnitude of AVO effects. A number of displays illustrate this (see below). A useful plot is the cross correlation of log curves with EEl logs calculated over a chi range from 90 to -90 degrees (figure 11.77). To determine the optimum discrimination of facies of interest the separation of facies distributions at different chi angles also needs to be considered (figures 11.79-80).
rrn eV cIh aNf
t!,
"
-Phi
o
-Sw
~
U
60
o
30
-60
-30
-GR
.2 ~
-Vsh
-mu -Lambda
Figure 11.77. Correlation of log curves
with EEl from 90 to -90 degrees
-90
Chi Angle
Figure 11.78.
200
Correlation of GR log
150
with EEl-41
FGRl
ii: 100
«
~-EEI-41
50 0 2550
2600
2650
2750
2700
depth
9500 9000 8500 8000 7500 7000 6500 6000 5500 5000
r---,-----,---r---,----,----,
-sele iii
w ~
-good oii sands
-poor oil sands -brine sands -shales
Figure 11.79. Variation of average EEl of
various facies with chi
90
60
30
o
-30
-60
-90
angle
Chi Angle
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AVO Analysis 11.5 Elastic Inversion
Chi=26 _ 80
g 70 •& 60
!l:.
I
50
F
"
sele -good oil sands
\
A\
1 40
~ 30 E 20 o 10 z 0
-
~~ ~\
" ........""-" ""
.#,
poor oil sands
-brine sands
-shales
./
6000
8000
10000
EEl
Chi=-40 G'
30,--------:;:-----, -j---------cf--\-------I
~ 25
if
.t
a:
-1-------1 15 -t-------J'-:=:::-+---j
20
~ 10·1-----
E
~
5
sale
-good oil sands -poor oil sands -btinesands
1----/'-/
-shales
o .J-~-4L....#._-""'O""':""___j o 2000 4000 6000 8000 10000 12000 EEl
Figure 11.80. EEl histograms showing optimum fluid (chi=26) and lithoiogy discrimination (chi=-40)
Neves et ai, 2004 have utilised the EEl technique to derive a pseudogamma ray volume which has then been inverted using a model based inversion technique. The EEl cube has enabled differentiation of good vs poor quality reservoir sands in the Umayzah sandstones of Central Saudi Arabia (figure 11.81).
Slice through high EEl unit Figure 11.81. Ampiitude siice through high EEl unit within inverted pseudo-gamma ray (EEl) volume (after Neves et al 2004)
C/V~tj 44
I
'W'O;j) © Rock Physics Associates Ltd 2007
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AVO Analysis 11.5 Elastic Inversion
When using projections the rock physics should always be kept in mind. In particular when there is a large variation in porosity a single projection will not work equally well say to define fluid efffects across the whole porosity range (Figure 11.82). In these instances two parameters may be the
0eJ 00/1 \? r
best way to provide discriminatis~11
W011
No 5.ingle projection will provide good discrimination across al porosities 20000 16000 16000
-" --
Figure 11.82.
vs GI and AI vs PR
0.5
-
-.
.•
crossplot - note
~-
0,4
-
a-t. '. ......•
12000
LL
Comparison of AI
\
14000
f
JL. t'J.J,A.-P ~. U
eF.: 1-
"
iii 10000 !!! 6000 8
-
6000
0.3
•• 0.2
..-!
"-
<000
..
.
the difference • gas slinds
011." ~
••." ..,
• weI sal'lds
..r.>
~
shales
acarb
in the ability to discriminate across
the porosity range.
0.1
2000
o 5000
o 7000
9000
11000
13000
15000
5000
AI
7000
9000
11000
13000
15000
AI
As discussed in the AVO section data quality and correct scaling are key factors in the combining of angle cubes. While the theory may suggest that combining cubes is a good idea, in practice it may not be. If the process is compromised for example through misalignment issues then map combinations may be the best approach. The reader should be aware that detailed quantitative use of these attributes may be compromised not only by the effects of tuning (as previously discussed) but also by data quality (figure 11.83). An appreciation of amplitude, phase and s',=c::a~lin=",a"-cr,-,o",s,,,s the 3D survey is required.
&P
Low amplitude - ovt )t,}s kN< I,av~ R£l20WN'''- m'l
FarSta:~
to'; Mo.
/
Low amplitude shadow effect
Far dataWindowed RMS above target
Fluid projection map
Figure 11.83. Example of an amplitude shadow on far offsets having a detrimental effect on a fluid projection ~ll.! GEOSCIENCE
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45
,
AVO Analysis 11.5 Elastic Inversion
C00 (2(fJ {vI U-f4/
R = Rp(l + tan
2fJ)_s(~;)2 sin 2fJRs -( ~ tan 2fJ- {~;)2 sin 2fJJ11;
where
_.!.(tlVP
Rp(O) -
+
2 Vp
tl
P)_MI -
P
2A!
3 rd term only important at large angles
R= Pwave reflection coefficient Vp=average of Vp1 and Vp2 Vs= average of Vs1 and Vs2 p= average of p1 and p2
. _.!.(.6.VS I1P)_ !lSJ
Rs(O) -
2
Vs
+
P
-
2S1
!t.;V€a"e /JO.Rfk/V ILe d/e~ ;!VO /:
O=avEfage of
Ci./K,vdv
Equation 11.9. Aki-Richards (1980) 3 term equatiomlwritten in
e incident and 0 transmitted
rms of Rp and Rs
The application of this equation in AVO inversion is not without its difficulties. As noted by (Gidlow et aI1992): 'A single major problem posed in extracting rock property information from the shape of reflection coefficient curves is that there are more unknowns than there are equations'..
Thus, constraints have to be applied to stabilise the estimations of reflectivity components. For a 2 term inversion for Rp and Rs a smoothed interval velocity background model is required to generate angles from offsets and, via Castagna's equations, values for background Vs/Vp (Goodway 2002, Fatti 1994, Gidlow et al 1992). White (2000) has shown, however, that in the presence of noise there is no additional benefit with regards to fluid discrimination of inverting for Rp and Rs compared to Intercept/Gradient analysis (figure 11.84). RO·G Fluid Factor
Oil
Wet
.,
RO-G Fluid Factor with Spatial Smoothing
. . •" • •
Figure 11.84. Maps
1·111
generated from noisy model
. ..•.r. ~ III. - •
I
~
,
data similar to those shown
";.;'
.
"
-,_.
::-.',. "
-.
in Figure 11.30. High
I
Inc porosity AI 51 Fluid Factor
AI SI Fluid Factor with Spatial Smoothing Low
Figure 11.85 illustrates the role of noise on the elastic parameter crossplots after AVO inversion.
46
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AVO Analysis 11.5 Elastic Inversion
Model data - No Seismic Noise
..'"
Model Data with Seismic Noise
0.'
0.'
0.45
0."'5
0.'
0.'
0.35
0.35
•••
0.3 0.25
000
0.3 :. 0.25
0.'
0.'
0.15
0.15
"
0.'
.
0.05 0
•
0.05 0 6
AI
•
... in
f
3.'
0
o
•
..•
JIQ(C
in
.....
3.
, '
,.• ,
.,
•
•••
•
:I'lt ,I
• ••
0
?>
,.. ,
7.!
6.'
7.'
6.'
0" 0 0
:/' •
•••
AI
6.'
AI
"
Figure 11.85. Effect of noise in AVO Inversion
11.4.2 Pre-Stack Model Based Inversion In order to produce inversions with the promise of better discriminating power, some workers are using model based inversion techniques. In early approaches the reflectivities derived from model based AVO inversion were subsequently inverted for the parameters AI and SI (figure 11.86).
I
Wavelet
Angle stacks at various angles
Figure 11.86. Schematic
I
~
workflow for pre-stack model Inversion/Model Constraints
based inversion for rock elastic properties
Error small enough?
I Optimisation procedure I
Yes AI, 51, p
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.1
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AVO Analysis 11.5 Elastic Inversion
The latest approach simultaneously inverts pre-stack data (gathers or angle stack cubes) in one step for angle independent rock properties, It is claimed that Simultaneous Inversion provides a means for improved handling of noise (eg Haskey et al 2000) (figure 11.87), Whilst such sophisticated techniques always derive an answer within the expected range, the interpreter needs to be aware that the constraints used in the inversion may well mask problems with data quality,
'EJ
11/0 !I/VUsUr;v
VI' h'Jl.,V..t!Q4d,Ot/J
Separate AVO Inversion
Simultaneous AVO Inversion
PR 2.2
High
2,3 TWT 2.4
Low
2.s L ==", 0,2
0,5
PR
0,2 ~
I
red·=weillog PR
1» t ,( .
blue=inversion
I
'~.
(/;)/('0 1#
/
-,(...c-l r(l~'( ~ c.~
..
at.!c-
PR
0.5
red-=weillog PR
blue=inversion
Figure 11.87. Improvement in poisson ratio inversion using simultaneous avo inversion compared to the combination of angle stack inversions. (after Maver et aI, 2004)
The advent of elastic inversion as a realistic proposition has firmly connected the rock physics and the seismic world, Given a good (exceptional?) inversion appropriately scaled numbers that come out of rock physics analysis can be directly compared to the results of elastic inversion, Some workers are applying probabilistic models based on rock physics data to infer the probability of a particular facies occurring (figure 11.88), Clearly there is an implicit assumption here that the wells have adequately sampled the facies population and that seismic noise does not have an adverse effect.
8e+06
Figure 11.88. Facies models based on Al and Poisson Ratio well data (lines show contours
of individual facies distributions) (Courtesy
7e+06
Heterolithic Odegaard),
AI
6e+06
undetermined
5e+06.f---.....---.-----.----' 0,20
0,25
0,30
0,35
0.40
0.45
Poisson Ratio
48
© Rock Physics Associates Ltd 2007
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AVO Analysis 11.5 Elastic Inversion
Figure 11.89. Probability of oil sand occurrence (based on applying statistical rock physics model in elastic inversion interpretation) (Courtesy
Odegaard).
Density Inversion Emerald Geoscience have shown that if sufficient angles are available (greater than 40') density might be inverted from the seismic. It is possible that with exceptional data the density reflectivity can provide a useful discriminator for low vs. high gas saturations (figure 11.90). I
_~-
-A.
. ;-. -. -~'. a ~._ ~~.'
--
..- - --'~ ~ ...
~;
- ..--
-..:.:-==
-~
..-
::'~-
~
A
-
~..:-
.-
c
:-
inversion - presents possible
.,..- -»
P Reflectivity -
'I:'
Reflectivity
~ _'- ~-:~~~~-
-=--...
Figure 11.90. Density
_-
Density reflectivity
AVO anomaiy
'-
advantages in discriminating low gas saturation from
Density
commercial gas saturations (Courtesy Emerald Geoscience and PGS).
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AVO Analysis 11.5 Elastic Inversion
Another example of density inversion for detection of commercial vs low gas saturation is shown in Figure 11.91
West
East Abll!Sir2X
•
I
200ms
--+i.. •
===::::::,
Figure 11.91. Discrimination of sands with high and low gas saturation (after Roberts et al 2005)
)1r1Mu..
£1Y (}1IrJ,o~ I
! Fiu r-;
? )
Encouraging developments in AVO • AVO before NMO (Downton 2002) address NMO and AVO problems simultaneously • More accurate velocities through Neural Net Imaging
Conclusions • AVO inversion is a rapidly developing area. • The interpreter needs to keep the basic geophysics in mind and understand the potential and limitations of reflectivity based techniques. • Pre-Stack Simultaneous Inversion is an improvement on combining EI inversions. • Make sure that nothing is lost in the gap between the experts and the interpreters - it isn't magic and data quality is key.
50
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Professional Level Rock Physics for Seismic Amplitude Interpretation 12. Rock Physics and Probability
12.1 Introduction 12.2A Workflow
Rock Physics Associates
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Rock Phys;cs and P,obabmty
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Rock Physics and Probability ~ 12.1 Introduction
~
12.1 Introduction The use of correlations that exist between seismic attributes and rock properties that have a relevance to field description and development is an old art and there are a whole range of techniques that can be used to translate correlations into predictions. They include single and multivariate, linear and non-linear regression techniques. In such approaches care must be taken to identify spurious correlations (Kalkomey, 1997). Spatial mapping of rock properties using geostatistical techniques such as co-located kriging is an approach that gives an understanding of probability to the mapped attribute (e.g. Doyen, 1988, Hirsche et ai, 1997) and another technique that has been successfully used to transform seismic data to rock properties is neural networks (e.g. Trappe and Hellmich,2000). In the last two years, driven by the developments in elastic inversion, there has been a growing trend of linking seismic lithofacies probability models generated from the rock physics data, directly to the seismic (usually inverted impedances) (e.g. Mukerji et ai, 2001, Avseth et ai, 2001). For any value (eg of inverted impedance) the method defines the most likely facies interpretation and its associated probability. Mukerji et al (2001) have described the use of Bayesian classification and neurai network techniques. What is documented here is intended as an introduction to this relatively new area and the probability descriptionjpredicition technique that will be described is 'Fuzzy Logic'. For a detailed description of Fuzzy Logic the reader is referred to Cuddy (1998). A workflow associated with statistical rock physics interpretations of seismic is: a) Dry rock modelling, correction for invasion and fluid substitution on logs b) Upscaling of log data to the seismic scale c) Classifying seismic lithofacies from logs d) Defining probability density functions of elastic attributes (or indeed reflectivity attributes) e) Invert seismic for elastic parameters f) Apply the pdf's in some modelling scheme to interpret likely facies (on section, volume or map data).
~~
e.. . . . GEOSCIENCE ...., ALLIANCE TRAINING
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Rock Physics and Probability 12.2 A Workflow
12.2 A Workflow 12.2.1 Rock Physics Analysis The various components of rock physics analysis on log data has been dealt with previously in the course.
For the purposes of prediction from seismic, the initial log sample, on which the probability models are based, needs to be representative. If certain facies are missing then it may be possible to model them. For example Mukerji et al (2001) document an example where they use fluid substitution to extend the data set to include oil sands as well as water sands. This type of data set extension is fine so long as there is a good geological basis. If the water sands actually have lower porosity than the oil sands, for example due to diagenesis in the water zone, then the substitution technique may not be appropriate.
12.2.2 Upscaling Log Data to the Seismic Scale In order to relate well based analyses of rock properties to seismically derived attributes the scales of measurement have to be reconciled. Although vertical resolution may vary between various logs they are traditionally measured at 1Scm sample rate. The vertical resolution of seismic, however, is related to seismic frequency and compressional velocity. Typically seismic frequency is in the range of around 1O-80Hz, giving vertical resolutions between about Sand SOm for a rock velocity of 3000m/s (the higher the frequency the higher the resolution). One of the effects of differences in resolution is for example that the acoustic impedance distribution of a seismic inversion result is much narrower than that derived from log data (see figure 12.1 and 12.2).
Solid line - wells Dashed line - seismic
100 Q)
1>' c
Cl
l!l c
Q)
::>
Q)
f:'
f
Q)
0-
'0
Q)
Q)
> ~ "5 E
.'!l
c;; E (;
z
::>
o AI
o ~_-----..:--~:::::=-
Acoustic Impedance
Figure 12.1. Acoustic impedance Distributions - Log Sampling vs. Inverted Seismic.
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Rock Physics and Probability
m
12.2 A Workflow ~
Distribution of AI . Sands «50%Vsh)
DEPTH m
o
VSH (dec)
AIO
1 4000 - - 10000
"'~--~-----~--~
1:2000
-+- Log sample ___ 2ms sample __ 4mssample
2500
;-tttttl ~;:=:*";;;;; •
'" ..00
.000
'2000
• 2550+f-H+l
DiSlribution of AI . Sands «50%Vsh)
-+- Log sample ...... 2ms sample __ 4ms sample
L_---.J
o >-_=t~e-L
'000
.000
.000
2000
0000
'0000
" Figure 12.2. Real Data Example of AI Distributions - lop vs. Seismic.
Another important aspect of seismic to well scale differences is the magnitude of velocity. Velocity is dependant on the scale of measurement (i.e. seismic frequency) relative to the scale of the geology (Marion et ai, 1994). Where the wavelength (A) to layer spacing (d) is <1 (as in sonic logging) the velocity basically follows a time average function (i.e. ray theory sum of travel times through each layer). For evenly sampled data this would be equivalent to the arithmetic average. In the case where Aid >1 (as in seismic) the velocity is calculated using an effective medium theory called the 'Backus Average' (Backus, 1962). Long wavelength velocities are generally slower than short wavelength velocities. Differences in veiocity due to dispersion are not particularly great for relatively thick-bedded and isolated thin bed cases. However in thin layered rock units (for example with alternating shale and dolomite) velocity dispersion can be up to 20% (Marion et ai, 1994, figure 12.3).
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Rock Physics and Probability 12.2 A Workflow
Ray theory (time average)
----..:...
Effective medium theory (Backus average)
1
An example of velocity dispersion is the difference between log and checkshot velocities. The drift curve estimated during log calibration is a measure of the amount of dispersion.
/
vp
o
10
100
IJd
Figure 12.3. Velocity dispersion due to the relationship between
layering and frequency (after Marion et ai, 1994).
Vsh Applying the Backus Average to log data in the depth domain involves: 1. Determine
~
, "00
Vp
and Ksat from Vp Vs and p
~=Vs'p
Ksat= p(Vp'-4/3Vs') 2600
2. For selected sample range (i.e. operator length) Calculate the arithmetic Average of p and the harmonic average of ~ and Ksat e.g. ~bf= 1/(sum of (frac/~» Original log
3. Reconstitute velocities
Arithmetic average Backus average
Vp' =(Ksatb,., +«(4/3)~b'.'»/p,.,) Vs'= (~".,1p,.,)
Figure 12.4. Velocity Logs - Backus averaging V5.
arithmetic averaging.
Commonly the Backus average is applied in the depth domain prior to log calibration with an operator length of around 1/4 A - 1/5th A. (A. Francis pers.comm.)
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12.2 A Workflow ~
12.2.3 Classification of Seismic Lithofacies Once the logs have been upscaled to the seismic scale, 'Seismic lithofacies' need to be classified from the data. At this point there needs to be a discussion with the petrophysicist and geologist to address the definition of significantly different facies. Clearly this process is geared to the aim of the project (e.g. in some cases a discrimination of sand and shale is the basic aim, rather than trying to categorize different fluids). . D • t.W" "he< 1'1 S7 t~ IV' ," 2.9 .------,---=J-,!---'i7-----, /
2.5
E
• shales
2.3
~
1__ -
2.1
I I
1.9
1.1
• water sands • gas sands
1.5 ~------'---------'--------- 2000 3000 4000 5000 6000 Vp (mls)
Figure 12.5. Lithofacies Analysis Using Crossplots.
As an example, Figure 12.5 is a Vp/Rhob crossplot from 3 zones in a well. Whilst the gas sands and shales appear to form single distributions, it is clear that the water sands comprise clean and shaley sands as well as low porosity cemented sands.
12.2.4 Defining the Probability Model The simplest probability model is the single attribute histogram, describing the numbers of values falling within particular class ranges for a defined number of populations (facies). The extent to which different facies can be discriminated can be qualitatively assessed by the degree of overlap of the different distributions. For the purpose of seismic lithofacies interpretation it is common now for acoustic impedance and derivatives of the elastic parameters (e.g. EI and LMR attributes) to constitute the data that is plotted on the histogram. Other attributes such as linear discriminants of two variables can also be used. Figure 12.6 shows a variety of methods for simple facies discrimination.
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Rock Physics and Probability 12.2 A Workflow
1. Single attribute
/ / o
./ o
4000
6000
8000
j_ .::-=t'r 1"00
,----,-----,--.,-,.-.::'~=;;. •
"00
.,,\.
/
2000
2. Linear Discriminant (weighted stack)
...
f\ J \ '/.. \ J \ \.
1400
'. 10000
-'-" 12000
1.000
16000
1100
•
I
I
1_\
l000~
1
"'"
3. Spatial probability (2 variables)
m ..... _
.....m A~ WI slack = O.0667A1" 483.33-EI
Bet06
7e+06 AI
6e+06
set06 +--~--~--~ 0.20
0.25
0.30
0.35
0.'10
0.45
Poisson Ralio
Figure 12.6. Simple approaches to facies discrimination.
Using the histogram as a predictive model is the basis of Fuzzy Logic (Cuddy, 1998, see figure 12.7). Fuzzy logic takes the distribution (often described in terms of a Gaussian model (i.e. mean and variance define the distribution)) and recognises that for a given value of the attribute any facies interpretation is possible but some are more probable than others.
frequency
Figure 12.7. The basis of
For a Gaussian (normal) distribution - area under the curve represents the probability of a value between xl and x2
Fuzzy Logic (after Cuddy, Standard deviation
1998).
occuring
Probability of a value x occuring:
P (x) = x
e
-(X-Il )2/ 2 120
Mean
LX
11=-n
crA2rr
Probability (fuzzy possibility) of x belonging to a particular facies (ie distribution):
F (X r) = An r *e
-(X-Il )2/ r /20(2
Combined fuzzy possibilities from different variables
1 I I I -=--+---+--+ Cr
F (xr)
F (Yr)
F (zr)
.
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12.2 A Workflow ~
The histogram in figure 12.8 shows an example of normal distributions fitted to data from 4 facies. 14
12
Categories:
f\
I---- 1 oilsand
"/ '\
2 shale
I - 3 walersand
/\./.
4 sandyshale
h .,/~ . 17.1'\<· \
o
o
/IJ/\~'·~ 2000
4000
6000
8000
10000
12000
AI
Figure 1.2.8. Gaussian fits to acoustic impedance data from various facies.
12.2.5 Inversion of Seismic for Elastic Parameters The issues involved in inverting seismic data for elastic parameters have been described at a basic level in the Essentials notes (sections 9 and 11.5).
12.2.6 Applying the Probability Model Once a probability model has been established it is a relatively simple matter to apply it to any type of attribute data (e.g. logs, sections, maps). A common statistical procedure to check the prediction accuracy is cross-validation. For example in geostatistical kriging the spatial correlation model is tested by leaving out individual wells and evaluating the accuracy of the prediction by using all other wells in the kriging process. In fuzzy logic a similar approach can be done whereby the fuzzy logic model is applied to the input dataset. This gives an idea of the accuracy of predicting facies for a given attribute (see figure 12.9).
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,',
Rock Physics and Probability 12.2 A Workflow
Original categories
Predicted winning C3t'ies
Coofidence in categories Categories: loilsand 2 shale 3walersand <1 sarnlysh!lle
5 6 7
'"
1
150
Variables' 1 AI
2
3 4
1'--+---1---
'"
CROSS VALIDATION RESULTS: No. spol-on: 159 64.9% No. runner-up: 64 26.1% No. mis-hit: 22 9.0% No. irrelevant: 0 TOTAL: 245 100.0%
Figure 12.9. Testing the Fuzzy Logic model on the 'training' dataset.
Figure 12.9 shows a graphical and numerical summary of the 'cross-validation' exercise as implemented in RokDoc-Fuzzy Logic. The winning facies for each sample is documented as well as an indication of classification success, with the percentages of correct predictions as well as those predictions where the correct facies is either runner-up or completely mis-classified. The relative confidence of each facies for each sample is also shown. This type of display can help in qualitatively evaluating the possible success on real seismic data. In practice 'spot-on' percentages need to be of the order of 80-90% for the model to be confidently used to predict facies on real seismic data. Any number of variables or attributes might be used in a probability prediction technique such as fuzzy logic. It is usual to limit the number to less than four and commonly two. Figures 12.10 and 12.11 give an example of a test data set where there is overlap of three facies distributions with two variables, yet distinct separation of the facies in crossplot space.
l
_I
0.35 0.3
'1
Figure 12.10. A test dataset.
I
0.25
• facies 1
0.2
a: Q.
• facies 2 0.15
facies 3
0.1 I
--+-
0.05
~
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i
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Rock Physics and Probability
m
12.2 A Workflow ~
,,
Original categories
GR(API) 50
100
150
O;----,'i----"'------"'-----i~
Predicted winning cal'ies
0
1
Confidence in categories
4
0
10
Categories: 1 fades 1
2 faCies 2 3 faCies 3
'"
, '00
'00
Variables:
'AJ 2 PR 3
, CROSS VALIDATION RESULTS: No. spot-on: 513 100% No. runner-up: 0 0.0% No. mis-hit: 0 0.0% No. irrelevant: 0 TOTAL; 513 100.0'1'.
Figure 12.11. Fuzzy logic discrimination of the three facies using the two variables.
Fuzzy logic has been used to predict the facies on the basis of the pdf's for both variables. The 'cross-validation' results show a 100% hit rate. Figure 12.12 is an example where a probability model, based on a crossplot of acoustic impedance and poisson ratio, has been used to predict the probability of encountering oil sands.
Figure 12.12. Map and section showing probability of oil sand occurrence (after applying a probability model based on acoustic impedance and Poisson ratio) (courtesy Odegaard).
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Rock Physics and Probability 12.2 A Workflow
The example in figure 12.13 shows a facies prediction using map data and a model based on a single variable (EI).
I
3.31.85~:---:3.':.'---:3.~~5:--..":----,'4.0·5 Easlirog
~ 10~
Oil Sand Facies Confidence Map
Map showing Facies 'Winners' 3.375
r',,'0__,.-__,--__,-_---, '
3.375
2
x 10i
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3.37
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1.3 1.2
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Oil sands 3 3;.a!o5:---::3':.'---:3::95:---;';---,J4.0'5 Easling
3.35 '--_ _"--_ _.L.._ _-'-_----' 3.85 3.9 3.95 4.05
x 10'
Easting
x 10'
Figure 12.13. Facies Prediction Based on E1.
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12.2 A Workflow ~
12.2.7 Addressing Uncertainty 1. Uncertainty in the low frequency component. As discussed in the Inversion section a key eiement in the uncertainty of absolute acoustic impedance inversions is the low frequency component. One way of addressing this problem is to use geostatistics to model numerous realisations of the starting model (all of which tie the well data) and which are then input to inversion software. A key challenge is to automate the procedure such that the run times of inverting a large number of cubes of data are acceptable (see figure 12.14).
---r=:-=--~~~;---D .
-
•
-
..... ....-.-
t------'-~-I'-"""~
....."""-t---_\~
Figure 12.14. Stochastic Inversion. A-C: 3 separate inversions performed using different stochastic realisations of
the broadband starting model, 0; Probabifity of sand occurrence based on the results of 50 inversions (High=red, low = blue). (After Francis, 2002. Courtesy Earthworks.).
2. The relevance of the rock physics model Applying a pdf based on upscaled well data to interpret facies is fine if the probability model is stable from well to well. The geological context of the model should not be overiooked (e.g. differences in rock properties (e.g. cemented vs. uncemented sands or variations in shale properties) due to sedimentology and stratigraphy).
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Professional Level Rock Physics for Seismic Amplitude Interpretation 13. Rock Physics and Time Lapse Seismic
13.1 13.2 13.3
Introduction Which Reservoirs are Candidates for Time-lapse? Two Important Rock Physics Issues
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Rock Physics and Time Lapse Seismic 13.1 Introduction
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13.1 Introduction In the past few years time-lapse techniques (i.e. the use of repeat seismic surveys to map rock and fluid changes in a reservoir) have become accepted, certainly among the major oil companies, as an integral part of reservoir management strategy (see figure 13.1). Integrated with traditional field development methodologies time-lapse seismic can help to: • Locate bypassed oil • Optimise infill driliing • Monitor fluid flow (e.g. identify barriers) and sweep efficiency, thereby helping to reduce operating costs and maximise profitability by enhancing recovery. Enhanced recovery is iikely to be a significant component of hydrocarbon supply for the foreseeable future. In deep water fieid development, where wei! interventions are very expensive, timelapse seismic is set to become a major tool for both the geophysicist and reservoir engineer. Reservoir Model Reservoir
Base
Simulation
Predicted Floodmap Monitor
Seismic-Derived Floodmap Difference
Production Optimization
Interpretation
Figure 1.3.1. Time-lapse seismic: a tool for reservoir management (after King,
1996).
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Rock Physics and Time Lapse Seismic 13.1 Introduction . 13.2 Which Reservoirs are Candidates for Time-lapse?
Of course the basis for interpreting differences between seismic surveys acquired at different times during field life is an understanding of rock physics. However time lapse studies involve: • Seismic acquisition and processing issues - seismic and processing repeatability - equalisation and matching techniques • Field management issues - timing of production and injection strategies as well as rock physics, and there is a formidable literature for the interested reader to get to grips with. The reader is referred to Jack (1997) and Wang (1997) as useful introductions to the subject. The aim of this section in the course is to focus on some of the rock physics issues in time-lapse modelling: • Which reservoirs are candidates for time-lapse? • When should time-lapse be undertaken? • Other issues: - fluid properties (theory vs. PVT) - the use of lab data in modelling frame sensitivity to pressure.
13.2 Which Reservoirs are Candidates for Time-lapse? Rock physics modelling for time-lapse interpretation can give information on • the response of fluid properties to varying saturation, temperature and pressure • changes in rock frame with changes in effective pressure. Certainly time-lapse techniques are more likely to work in areas where the reservoir has: • Large changes in fluid compressibility with production • Low frame elastic moduli (bulk and shear moduli) - unconsolidated/poorly consolidated rocks - rocks with open fractures - or low aspect ratios. One famous example illustrates this very well. Between 1992 and 1995 a pilot study was undertaken to monitor steam injection in the Duri Field on Sumatra (Jenkins et ai, 1997, and Waite et ai, 1997). The acoustic response of the reservoir was found to be very sensitive to changes in fluid saturation owing to the fact that the rock is unconsoiidated (high porosity) and there is a huge difference in the fluid compressibility related to the thermal heating of the oil. Time lapse effects include significant amplitude and time distortions (figure 13.2 and 13.3).
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Rock Physics and Time Lapse Seismic 13.2 Which Reservoirs are Candidates for Time-lapse?
m ~
In summary (after Jenkins et ai, 1997, and Waite et ai, 1997): • • • • • • • •
High viscosity oil Primary recovery - 8% Shallow (600ft depth) Deltaic unconsolidated sands 30-38% 1500md High degree of heterogeneity Initial temp lODe, steam temp 250e Steam injection increases recovery to 60% + 2 Months
+ 5 Months
+ 9 Months
+ 13 Months + 19 Months
+ 31 Months
No change above injection
100
_ Top Injection interval
200
300
o 100 c=-
m
Figure 13.2. Travel time effects related to steam injection.
Observation well shows high temperature in Upper Pertama
~~~~::::::
Timec. . (mS)j'" N,g
Top (red) and base (blue) of steam zone
'Snapshot' seismic section showing spots associated with the presence steam (after Waite et a/lg97)
Figure 13.3. 'Snapshot' seismic section showing bright spots associated
with the presence of steam (after Waite et ai, 1997).
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Rock Physics and Time Lapse Seismic 13.2 Which Reservoirs are Candidates for Time-lapse?
In contrast to the Duri Fieid is the case of Nelson Field in the North Sea, an oil field under waterflood (see figure 13.4). The porosity is relatively constant at around 23% and the oil is medium grade 38API with about 500scf/stb GaR. The dominant effects are pressure drawdown and saturation change. The combined fluid and pressure change is around 14% on acoustic impedance over a seven year time-lapse period (Hansen et al 2001, Boyd-Gorst et al 2001). Changes to rock fabric (owing to pressure depletion) are considered to be minimal. 8.5
Pressure
8
1 ~
Combined Change
g,"!;,\ 7.5 AI
7
6.5
Fluid Change Only
6 0.2
0.25
0.3
0.35
0.4
Poisson Ratio
Figure 13.4. Nelson Field: Modelled time-lapse change.
After Hansen et ai, 2001.
At the time the first Nelson Field time-lapse seismic survey (figure 13.5) was undertaken it was not known whether the change in impedance would be great enough to be measured. A stringent approach to the processing was undertaken, re-processing the baseline survey together with the processing of the repeat surveys (Harris 1997, EAGE abs). In addition, the AVO component (which serves to enhance the difference in reflectiVity) was utilised by differencing far stacks.
749
799
849
•
899
•949
999
1049
2170
2240
2310
2380
2450
Figure 13.5. Far offset difference section showing a
clear signal in the area of the oil water contact.
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13.2 Which Reservoirs are Candidates for Time-lapse?
Subsequent studies utilised inversions of near and far angle stacks, together with a probability model, to create time-lapse maps that showed oil sand probability.
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Figure 13.6. Oil sand probability maps - Nelson Field (after Hansen et ai, 2001).
Whilst it is true that certain reservoirs are more amenable to time-lapse techniques the criteria for where time-lapse is appropriate are as yet ill-defined. Two useful approaches have been published by Lumley (1997) and Marsh et al (2003) Figure 13.7 The time lapse feasibility (scorecard) approach of
Ideal
Reservoir dry rock bulk modulus fluid compress. contrast fluid saturation change porosity predicted impedance change reservoir lolal
Lumley (1997)
Reservoir scorecard 5 5 5 5 5 25
Seismic image quality resolution fluid contacts repeatabitity Seismic total
5 5 5 20
Total Score
45
5
Score
5
4
3
2
1
0
Dry rock bulk modulus
GPa
<3
3·5
5·10
10·20
20·30
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% change
250+
150·250
100·150
50·100
25·50
0·25
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% change
50-
40·50
3040
20·30
10·20
0·10
Porosity
%
35-
25·35
15·25
10-15
5-10
0·5
Impedance change '% change
12-
8·12
4·8
2·4
1·2
0
# samples
10'
6·10
4·6
2·4
1·2
0
Traveltime change
The approach of Lumley (1997) uses a scorecard appioach which-is based on both rock physics criteria (the 'reservoir' scorecard ) and seismic criteria ('seismic' scorecard). If the 'reservoir' scorecard passes a 60% mark th en it is possible that time lapse may work and the seismic scorcard is evaluated again witha 60 0Va pass mark.
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Rock Physics and Time Lapse Seismic 13.2 Which Reservoirs are Candidates for Time-lapse 13.3 Two Important Rock Physics Issues
BP have published a simpler gUide based on modelled single interface reflectivity of the oil water contact and some empirical thersholds based on the experience of processing dfferent types of time lapse data.
RO (OWC)
o
0.01
0.02
M:lchar Hardimg
Foinawn
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•
I I I
scheme based on modelled
owe reflectivity and empirical processing/acquisition t hresholds
(re-drawn after Marsh e ta12003)
The Lumley and BP approaches are a useful guide and should not be used as a definitive analysis of the likelihood of whether time lapse will work or not.
13.3 Two Important Rock Physics Issues One of the critical factors to understand in any time lapse feasibility project is the response of the dry rock frame to changes in effective pressure. This presents the rock physicist with a number of difficulties. Without laboratory measurements (of core velocities at different effective pressures) it is very difficult to be sure how the rock will respond. Macbeth (2004) has shown that the variation of dry rock properties with effective pressure is not dependent on porosity and that different fields show widely different characteristics (figure 13.9)
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Rock Physics and Time Lapse Seismic ~ 13.3 Two Important Rock Physics Issues
35
30 25
/
20
15 10
5
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60
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Figure 13.9 Variation of dry rock properties with effective pressure (data from Macbeth 2004)
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Rock factors s'ifch as pore distritfutlon are important in the variations between the fields. For example sands with framework shales are likely to show greater rate of change of dry rock frame parameters than clean sands owing to the greater compressibility of the shale related pores (figure 13.10).
27
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.
25
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Figure 13.10. Differences in the
-
"3
1'i
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=5
.----
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-
rate of change of dry bulk moduli
-
with increasing effective pressure
related to clay content (using data
16% porosity
from Han et ai, 1986).
15
o
10
20
30
40
50
Effective Pressure (MPa)
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Rock Physics and Time Lapse Seismic 13.3 Two important Rock Physics issues
Even when there is laboratory data available there is always some doubt as to the relevance of high frequency measurements on small samples (micro-fabric measurement) to a field wide response under the influence of subsurface stress regimes. In general it appears that rocks which are over-pressured and are relaxed through pressure drawdown will show (relatively large) dry rock changes consistent with laboratory measurements. However if a normally pressured reservoir is drawndown then the effect may well be less than that shown by laboratory measurements (pers. Comm .. C. Macbeth). Drawdown in the overpressured situation results in the dry rock frame taking more of the weight of the overburden and thus the frame stiffens. In a normally pressured situation the effect is minimised as the rock frame already supports the overburden. The second issue in assessing the time lapse response of reservoirs is related to fluid mixing. Recent work at Stanford University has shown that the scale factor is important in timelapse modelling. Figure 13.11 is a flow simulation of a waterflood of an oil reservoir. The injected waters have preferentially moved along high permeability layers within the model and created a 'patchy' mixture of oil and water. These patches are relevant at the seismic scale. injector
producer
Figure 13.11. Flow simulation of water injection into an oil-wet
reservoir (after Sengupta and Mavko, 1998). 60
In the case of oil (in which the gas saturation properties are unchanging, figure 13.12) the effect of the patchiness is not large (in this case of the order of 0.2% difference in Vp from that predicted using Reuss mixing). However in the case of gas injection (figure 13.13) the effect is up to 6% (the biggest differences being at low oil saturations).
Figure 13.12. Measured velocities from flow
'''' ''''
simulation of waterflooding and oil wet reservoir
(drainage). After Sengupta and Mavko, 1998).
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Rock Physics and Time Lapse Seismic 13.3 Two Important Rock Physics Issues
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!
!
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saturated reservoir. After Sengupta and
Mavko, 1998. .!
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Obviously if time-lapse modelling is undertaken using homogenous models, yet at the seismic scale saturation it patchy, the actual change in fluid compressibility with production might be significantly underestimated.
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An Approach to Time Lapse Interpretation Rock PhysIcs Associates
It is common for time lapse interpretation to be geared to sophisticated inverted solutions for saturation and pressure. Such inversions can take significant time and may not be easily changed (for example if the top reservoir pick is subsequently modified).
Analysing bandlimited impedance differences can be a useful approach for the interpreter to rapidly estimate moved hydrocarbons and remaining oil. The technique has been suggested by Gouveia et ai, 2004. Reference: Gouveia, W.P., Johnston, D.H., Soiberg, A., and L. Morten, 2004. Jotun 40: Characterisation of fluid contact movement from time-lapse seismic and production logging tool data. November, The Leading Edge. 14101,'(,
;:y_
Modelled bandlimited impedance difference
Top reservoir Present contact
!
~--....-..
I Modelled oil saturation change
Modified from Gouveia. et al 2004.
If the coloured inversion time lapse surveys are differenced then to first order the current contact is identified as the upper boundary of the difference signature whereas the lower boundary defines the initial contact. So, if there is a good top reservoir pick (based on other seismic displays) then the first order change in the position of the contact can be appreciated relatively quickly.
Of course the difference signature is actually an interference effect so there is the potential to overestimate movement where the difference is below tuning. The zero crossings on the difference section are relatively stable in the presence of small timing errors whilst the amplitudes are not. So at the very least the difference signature is a good QC of the data and at best provides a data set to interpret time lapse effects which is relatively independent of amplitude (this can be important where the time lapse processing is not very good quality). Experience has shown that integrating the interpretation of band limited impedance difference data with simulation and reservoir characterisation studies provides a robust and flexible approach to time lapse interpretation.
© Rock Physics Associates 2006
An Approach to Time Lapse Interpretation Rock Physics Associates
Original saturation
The illustration to the left illustrates how the difference is derived. Variable contact model (fluid only change)
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The model below illustrates a side-sweep scenario. Whilst most of the zero crossings are incorrectly positioned with respect to the contacts the difference is symmetrical with respect to the new and original contact. If the amplitudes in the difference are reliable then the difference signature might be de-tuned (following Connolly 2005) to estimate the amount of moved hydrocarbon. Remaining oil underestimated on lop reservoir 10 upper zero crossing thickness
Zero crossing above Top Reservoir where swept zone is thin
Amplitude difference may be de-tuned to estimate the thickness of moved hydrocarbons
© Rock Physics Associates 2006
Professional Level Rock Physics for Seismic Amplitude Interpretation 14. Anisotropy
14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9
Types of Anisotropy - What is Anisotropy? Modelling AVO in Rocks with Vertical Transverse Isotropy VTI in Real Rocks Effect of VTI on Seismic Imaging Effect of VTI on Seismic Amplitude Another Complication - Attenuation Azimuthal Anisotropy Azimuthal Anisotropy and the Phenomonen of Shear Wave Splitting P Wave Exploitation of Azimuthal Anisotropy (AVZ, AVOA, AVAZ, AVO)
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Anisotropy
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14.1 Types of Anisotropy - What is Anisotropy? ~
So far the discussion has proceeded on the basis that rocks can be modelled using elastic and isotropic assumptions (i.e. that the rock properties are the same irrespective of direction or axis). However rocks generally do not behave like this (see figure 14.1) and they have different properties in different directions (i.e. they are anisotropic). This is especially true over the scales of measurement characteristic of seismic data. In addition they may not be elastic but more of that later. Instrument
Superimposed Noise
Geophone
Response
Sensitivity
Source Strength and Coupling
Absorption
Spherical Divergence
Reflector interterence
Reflection
Coefficient
Small scale horizontal layering
O
Transverse Isotropy
Elasti~ Isotropy
Figure 14.1. Factors affecting seismic amplitudes (modified after Sheriff, 1975).
It is becoming clear that we need to incorporate anisotropy into our interpretation of seismic. Anisotropy affects the imaging of seismic data as well as the amplitude of reflections.
14.1 Types of Anisotropy - What is Anisotropy? Types of anisotropy relevant to seismic interpretation can be divided into: 1. Transverse isotropy with vertical symmetry (VTI or verticai polar anisotropy (Thomsen, 2002» (e.g. shale units with aligned particles and horizontally organized beds or layers on a scale much smaller than the seismic wavelength). Rock properties vary depending on angle of incidence but do not vary with direction. 2. Azimuthal anisotropy - related to dipping zones of thin beds or more usually to fractured rock. The simplest form of azimuthal anisotropy is transverse isotropy with horizontal symmetry.
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m ~
Anisotropy 14.1 Types of Anisotropy - What is Anisotropy?
Whilst isotropic materials require only two moduli to describe them (e.g. k (bulk modulus) and ~ (shear modulus)) a VTI material requires 5 moduli to describe it (figure 14.2 and equation 14.1).
c"
c" Figure 14.2. Stiffness moduii describing
a transversely isotropic material (redrawn after Sondergeld, 2001).
C33 Cll C" C" C13
determines the vertical compressional velocity. determines the horizontal compressional velocity. controls the vertically travelling horizontally polarized Sv (Vs) and Sh wave (Vs) velocities. controls the horizontally travelling horizontally polarized Sh wave velocity. controls propagation in oblique directions for P and Sv waves (but not for Sh waves).
C33 = K + 4/31-t = V p2p = M modulus C44 = I.l = Vs 2 p
Equation 14.1. Stiffness Moduii.
Thomsen (1986) defined 5 parameters that are required in order to practically characterise TI (equation 14.2): VpO - vertical P-wave velocity Vso - verticalS-wave velocity Equation 14.2. Characterisation of TI.
e, (C l1 ' C,,) I 2C" y' (C,,' C,,) 12C"
I> -[(C 13 + C,,)', (C,,' C,,)'
Jt [2C
33 (C",
C"U
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Anisotropy 14.2 Modelling AVO in Rocks with Vertical Transverse Isotropy 14.3 VTI in Real Rocks
I .
14.2 Modelling AVO in Rocks with Vertical Transverse Isotropy A useful approximation published by Ruger (1997) can give a useful insight into the effects of VTI on the AVO response. This is an anisotropic equivalent of the Aki-Richards approximation (equation 14.3):
Equation 14.3. Vertical equivalent of the Aki-Richards approximation.
Where:
e = angle of incidence = av P wave (vertical) velocity 13 0 = av 5 wave (vertical) velocity Zo = poD vertical P impedance Go = p13D2 vertical shear modulus i5 and £ - Thomsen parameters For the isotropic case i5 and £ = D General observations on the data: 00
14.3 VTI in Real Rocks Published measurements of VTI have been derived in the laboratory and from the analysis of multi-offset VSPs. Figures 14.3 to 14.6 show some of the published data on epsilon and delta. OO'--~--'---~-'----~-71
"
,.•
:
0.4 .
B
'2
"''--~--'---~-'----~-71
."
"'-:'
..
.........
'.
: t.
".. '." ""lIo:" .",,1 " ..
.,
,.,
.
. "':
',...' .. .. ..
E 0.2
..
.., .o.~~
.0.2
02
0."
0'
0.1
.o.~."'.-----:.,:-.,----C!---:,.:-,- ----:,.,,---.,.,,,-----",.• y
t
Figure 14.3. Crossplo
of VTl anisotropy parameters listed by Thomset86), Vermk and Liu
(1997) and Ryan-G 19, r (1997) (pers.comm C. Macbeth).
(f- WCl/lle
a,1/!fO
Ix.
~
5' -kAWe ilJ!f)
I CW/roq.
~l&
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Anisotropy 14.3 VTI in Real Rocks
0,25
r----,----,----,------,
0.15
A..
0.1
00
...
0:: -=-
•
0
,0." -0.2 '---
o
•
l
r
Ryan-Grigor (1997).
roO
•
- •
0.05
Figure 14.4. Crossplot based on data selected by
..1
0.2·
:~
0
t,r-
0
0
'I
-'----
-'----
0.2
~1
+
.Ims • sh
-1 , --
55
-'----_ _----.J
0.4
~3
E
O'r-----------------;~-___, • Intrinsic Crack induced Dry 04 C' Crack induced Wet
Figure 14.5. E vs. i5 for black shales at high confining
o
pressure of 70MPa (intrinsic) and low confining pressure (crack-induced) redrawn (after Vernik and Lui, 1997).
03
~
~
, ,
0
0
•
0.2
0
0.'
•
•
0
C'
e'l
~.,
••
•
'-0": •
•
•
0
. ••
• • •
••
-0.2 0
0.'
02
03
0.4
0.'
0.'
Epsilon c
•
Pierre shale
'\
• Easllex sand+chalJ
Figure 14.6. VTI data derived from multi-offset VSPs (Macbeth, 2002).
East texas shale • East texas mart
t::. S china sea shale • North sea shale D North sea chalk
x Java sea shale
+
W africa unatlrib
E
General observations on the data: 1. The data for VSP determined values fall in the same range as the lab sub-set described by Ryan-Grigor (1997) 2. £ is always positive 3. Shales generally have higher £ values than sands 4. In general £ is twice <5 5. <5 values are generally positive for sands but can be negative as well as positive for shales.
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I
14.3 VTI in Real Rocks 14.4 Effect of VTI on Seismic Imaging.
.
Ryan-Grigor (1997) has suggested that the type of shale overlying the sand may be important and that organic-rich shales (with relatively low values of Vp/Vs and low <5-E will make the gradient more negative, but that 'lean' shales (with relatively high Vp/Vs) will make the gradient more positive.
C 13 / C44 = 3.61Vp / Vs - 5.06 (V = km/s) Equation 14.4. Empirical relationship between Vp, Vs and
o.
<5 is then simply a function of Vp/Vs through the equation that relates <5, C13/C 44 and Vp/Vs (equation 14.5):
Equation 14.5. Thomsen parameter 0.4
0.3 0.2 01
o -0.1 -0.2 -0.3 -0.4 1.4
t..
Figure 14.7. Broad relationship between Vp/Vs and
I
I
~
I
I
I
"
~-..
L I I
-t -{ 1.6
o.
I
II •
-L.• I
I • I
t
1.8
2.0
o for rocks with weak VTI (i.e. •
I
t
•
•
E
and 0 <0.2) data
from Ryan-Grigor, 1997).
.Ims ",h
ss • Pred delta
-
I
2.2
2.4
VpNs
14.4 Effect of VTI on Seismic Imaging Figure 14.8. Effect of VTI on NMO - reflector cannot be flattened using standard NMO equations, even with higher order terms.
The gather in figure 14.8 shows non-hyperbolic moveout that is probably related to VTI. Not all non-hyperbolic moveout is related to anisotropy, it can result simply from rapid lateral variations in isotropic velocity. ~l.l
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Anisotropy 14.4 Effect of VTI on Seismic Imaging
An effect of transverse isotropy is to make it impossibie to flatten reflectors beneath the transversely isotropic layer (even using higher order terms on the NMO equation). To illustrate the effect of VTI on NMO a simple model has been constructed (figures 14.9 to 14.12). The variation of 'effective' velocity due transverse isotropy has been estimated through the phase velocity equation (Thomsen, 2002, equation 14.6).
Equation 14.6. Phase velocity.
Where: Vp=P wave velocity VpO = vertical P-wave velocity. Single layer model
I
vp =2200 ml,
To =1sec
8 = 0.25, E = 0.4
5O,--,--~---,-----,-----,
40
2.45
d
'"
30
2.35
g-
2.3 2.25
j -+-
ilol!opie
~"
2' 0.5
1
2
1.5
2.15
2.5
0
0.'
offset (km)
..
"'
'.5
'"
Figure 14.9. Offset vs. angle
Figure 14.10. VTI model - Vp
relationship for model.
varying with offset.
09 , - - , - - - - , - - - - - - - . - - - - - - . - - - - - ,
0.9
I
J
"
!
0." -+-
" " "
iSolrop;e
-
! , I lOS
"
I I
"o
offset
I
0.'
L.
1-++ ..
"
"'
Figure 14.11. Reflector 'hyperbolae' for
Figure 14.12. NMO 'corrected'
isotropic and TI model.
reflectors using NMO equation assuming
T1 : :
fKCWSI/.(.RU
(\'-f)fpor'c.
isotropy.
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m
14.4 Effect of VTI on Seismic Imaging ~
Figure 14.13. Modelled artifacts on a full stack section related to (laterally variable) TI induced non-hyperbolic moveout (after Chen and Castagna, 2000).
Clearly if a hyperbolic assumption is made in the presence of transverse isotropy there is the possibility of creating artifacts in the various stacks (e.g. Chen and Castagna, 2000, figure 14.13). Pseudofaults, anticlines, channels, amplitude anomalies and flat spots can all be produced in this way. Something to check out. The effect of varying velocity with direction in a VTI medium is to change the shape of the propagating wavefront (i.e. it becomes non-sphericai). Performing velocity analysis and migration in the presence of VTI can only be done by incorporating an approximation to the change in the wavefront. This is done by estimating the anellipticity parameter (~, equation 14.7), dependent on epsilon and delta.
Hyperbolic moveout using V.....(O)
Elliptical wavefront
c=o Vp(90)
Vp(O)
Isotropic wavefront (velocities are same in all directions ,and 0=0)
Wavefronts are generally not elliptical - they travel at intermediate angles - velocity through VTI media will be between Vp(O) and Vp(90)
£-0 1)=1+20
Figure 14.13a. Effect of VTI on
Equation 14.7.
seismic wavefronts .
Anellipticity parameter.
Hyperbolic moveotll
Non-hyperbolic moveoul using
using v......
V.....(Oj.l1
-
t----"'-.,j-- - - - - - " ' - .
I
!
In seismic processing travel times are inverted for a combination of Vnmo(O) (moveout velocity at zero offset) and ~ (the anellipticity parameter that describes the nonhyperbolic component of the moveout). The example in figure 14.14 shows that incorporating VTI into the moveout helps dramatically in flattening the gathers.
Figure 14.14. An example of moveout analysis (after Toldi et ai,
1999). ~~ GEOSCIENCE e.~TRAIN1NG
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Anisotropy
~
14.5 Effect of VTI on Seismic Amplitude
Applying anisotropic velocities in migration can greatly improve imaging. The example in figure 14.15 shows improved imaging and spatial positioning. Figure 14.15. An example of anisotropic migration from the Southern North Sea (after Hawkins et ai, 2001). Courtesy Veritas DGC and GDF Production Nederland
av.
14.5 Effect of VTI on Seismic Amplitude It is the difference in 1> (i.e. 61> = upper layer 1> - lower layer 1» that is the controlling factor in the effect of VTI on the AVO response. When 61> (i.e. upper layer 1> - lower layer 1» is negative it tends to increase the gradient (i.e. making Class III responses more negative with offset). If 61> is positive then the gradient is made more positive (figure 14.16).
.
Figure 14.16. Shale on oil sand model - effect on AVO
if;=::~n; is;O;Z ~ok . ~/f-41 /;rC4V~
0.05
·0.05
..... Isolroplc
~
...-T'
·0.1 -0.15
-,
·0.2
I
t
20
"
+
/f(J!t.:;I! ~
MIi'/«;7l1 ¥'hole;
-0.25
0
layer1 layer 2
"
Angle 0( Incidence
"
"
vp
vs
Rho
delta
2.438 2.953
1.006 1.774
2.250 2.036
0.150 0.000
epsilon 0.2 0
Ryan-Grigor (1997) has suggested that the type of shale overlying the sand may be important and that organic-rich shales (with relatively low values of Vp/Vs and low 1>-£ will make the gradient more negative, but that 'lean' shales (with relatively high VP/Vs) will make the gradient more positive. It is possible that some AVO anomalies within shale sections might be explained by the effects of variable TI. For example if a shale with high VP/Vs overlies a shale with low Vp/Vs the 61> will be positive.
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I
14.5 Effect of VTI on Seismic Amplitude 14.6 Another Complication - Attenuation.
-¢-
.
Figure 14.17. A bright spot on full stack data related to shale on shale (from Dey-Sarker & Svatek, 1992).
There is much speculation about the role of anisotropy in positive AVO from shale on shale contacts (figure 14.17). Unfortunately there are no published case studies (that I could find) that illustrate categorically a link between measured VTI (in the lab or using VSP) an AVO modei and pre-stack data observations. Other possible false negative and false positive scenarios discussed by Ryan-Grigor (1998): 1. False bearing 2. False overlies
negative AVO scenario: If 5 is -ve (e.g. where Vp/Vs is >2) and a shale overlies a gassand positive AVO scenarios: If an organic rich or overpressured shale (with Vp/Vs <1.8) a water-bearing sand.
In practice the confident parameterisation of VTI models is hampered by: 1. Lack of local measurements 2. Uncertainties over scale effects (for example relating VTI parameters from the lab to the seismic scale).
14.6 Another Complication - Attenuation The variable attenuation characteristics of rocks can also affect AVO (e.g. Samec and Blangy (1992», Blangy (1994) and Carcione et al (1998». If the modelling is to be believed it appears that attenuation might be more important in AVO than the relative differences between VTI and isotropic elastic effects (see figure 14.18). There are significant problems parameterising these models owing to the requirement to have 10 model parameters per model layer (Vp, Vs and the three Thomsen parameters, together with five values of Q).
"'
1----=::::::::::-_
Figure 14.18. AVO models of shale over gas sand Isotropic response Elastic VTI shale
effect of changing shale parameters (isotropic, elastic VTI and viscoelastic VTI). Blangy, 1994.
ID
~
0.
~
Viscoelastic VTI shale
1--__A--'n9'--le_o_f_in_ci_de_n_ce
--.
~
j t-----"'==:::::::--_
Isotropic response Elastic VTI shale
VIscoelastic VII shale ~'\ GEOSCIENCE ~.GiITRA'NING
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Anisotropy 14.7 Azimuthal Anisotropy 14.8 Azimuthal Anisotropy and the Phenomonen of Shear Wave Splitting
14.7 Azimuthal Anisotropy Most rocks have (sub) vertical fracture systems that relate to the stress history of the crust (figure 14.19). Fractures that relate to the extensional parts of current stress regime are likely to be open and fluid filled. It Is these fractures that effectively contribute to the azimuthal anisotropy. Closed fractures do not contribute significantly to the anisotropy because of a lack of impedance contrast across the fracture.
cr, Figure 14.19. Fracture
orientations related to shear and
extension (after Neison, 1985) .
Some oil and gas fields rely almost entirely on fractures for their production. It follows that if we can exploit the azimuthal anisotropy using seismic data we can get direct information on permeability and other related to production (e.g. permeability).
14.8 Azimuthal Anisotropy and the Phenomonen of Shear Wave Splitting The investigation of azimuthal anisotropy has to a large extent been focussed on the effects of fractures on shear waves. A shear wave entering an azimuthally anlosotropic rock unit at an angle oblique to the fractures splits into two waves with polarization of the faster wave (51) parallel to the fractures (figure 14.20). Figure 14.20. Shear wave splitting in aZimuthally
,oW
Shear source
r
l~~~~~~~
anisotropic media (redrawn after Martin and Davis,
/Oriented Fractures
~
N45W
1987 and Crampin, 1990).
Shear wave splilling
·time delay
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14.8 Azimuthal Anisotropy and the Phenomonen of Shear Wave Splitting·
.
The slower shear wave (52) is polarized perpendicular to the fractures and travels vertically at a lower velocity than the Sl wave. Fracture Trend NE·SW
Figure 14.21 below shows Sl and 52 sections from the Austin chalk (Mueller, 1992) with the fracture swarm evident as a dimming of amplitudes on the 52 section.
N
Poo< Produd.kln
A "",
, Good ...... Production
,It
""'"'} Middle
Information on the intensity of fracturing is contained in the delay between the two shear waves (figure 14.22). The average azimuthal anisotropy (p) is described by LlT/TS2 (where LlT = T51- T52). By referencing the measurements to marker horizons variations in azimuthal anisotropy in different units can be determined.
~:~n
lower
Figure 14.21. Fast (51) and slow (52) shear wave sections in the
Austin Chalk (after Mueller, 1992).
1.5 Fracture Onenlallon from core
1.5 T/GR
Traveltime change 2.0 between Sl(fast) ___ allCl S2(slow) indicates
z TN1
presence 01 Seismic
20
fraclures in Z unil
1I~
Max hQ(lzonlal stress from caliper data aocl dyke ()(ienlatioos
Bluebell-Altamont Field NE Ulah
All'" Lyon et aI 1995
Figure 14.22. Time delays between 51 and 52 shear sections
highlight presence of fractures (after Lynn et ai, 1995).
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Anisotropy
14.9 P Wave Exploitation of Azimuthal Anisotropy (AVZ, . AVOA, AVAZ, AVO)
14.9 P Wave Exploitation of Azimuthal Anisotropy (AVZ, AVOA, AVAZ, AVO) It is also possible to exploit azimuthal anisotropy using P wave seismic, and very often this is a
cost-effective option. In areas with significant azimuthal anisotropy (such as fractured fields) the P-wave AVO response is dependent on the azimuth of the seismic.
Transverse Isotropy with a horizontal axis (HTI) is the simplest form of azimuthal anisotropy and it generally applies to those rocks in which the fractures can be modelled as penny cracks. Ruger (1996) defined an equation for modelling isotropic overburden on an HTI layer. This is similar to a Shuey type approximation. Taken from Jenner (2002, equation 14.8):
Equation 14.8. Isotropic overburden on an HTI layer.
This applies for up to 35° incidence angle where: R(8,
Equation 14.9. Anisotropic gradient.
Where: G = Vp!Vs (av P wave vel / av S wave velocity) 11<5(0) = the difference in the Thomsen style parameter <5 for HTI media lIy = change in the shear wave splitting parameter y. y is directly related to the crack density.
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Anisotropy 4.9 P Wave Exploitation of Azimuthal Anisotropy (AVZ,
I
AVOA,AVAZ,AVD).
Figure 14.23. AVO Model of VTI shale overlying
0.5
TI Shale over Vertically Fractured Granite
0,45
fractured granite (after Leaney et ai, 1995).
j-
0.'
~
I
'0
~ 0.35
~
i
I
In the example in figure 14.23 there is a more negative gradient where the P wave energy is perpendicular to fractures. The AVO response where the energy is parallel to the fractures is not too dissimilar to the isotropic case (i.e. no fractures) .
i
!
,
I %I
i
03
~
~
.
0,25 1
-,
0.2
1
Perpendicular to fractures
0.15
0
15
10
25
20
35
30
Angle of incideoce (degrees)
Initial work that showed the practicality of using multi azimuth p wave data to interpret fracture related azimuthal anisotropy was performed on 2D lines with different shooting directions (e.g. Macbeth and Li, 1999). The Fife Field exam pie (figure 14.24) shows that the greatest attenuation on gathers at base chalk level is where the 2D line Is perpendicular to the fracture strike, offset(m)
....................
(a)
121
871
1621 2371 121
871
1621 2371 121
~
871
INSIDE
Top Chalk -
region of interest
Bottom Chalk -
A1 Fracture Direction
A3 A2
offset(m)
.......................
(b) OUTSIDE
'" '"
'!i21 2371 121
~71
1621
'I
~31l
.121
."
1621 2311
20
22
region of interest
TopChalk -
.~
Bollom Chalk -
'"
2.' 0.135 "
A,
A,
A2
Figure 14.24. Gathers acquired from inside and outside the Chalk fracture zone - Fife Field UK North Sea, (Note map with colour coded 20 lines relates to colour bar on the gathers.) Also shown is the azimuthal AVO model (Macbeth and Li, 1999).
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Anisotropy 14.9 P Wave Exploitation of Azimuthal Anisotropy (AVZ, . AVOA, AVAZ, AVO)
The AVO response through fractured zones is a complicated function of fracture density, azimuth, porosity, aspect ratio, and target impedance contrast. Modelling by Hall et al (2002, figure 14.25) has shown that azimuthal AVO behaviour can also be dependent on the fluid fill of the fractures. I
a)
0.2
~ C •E • u m
0.•
0
brine
~ 0.18
0.4
E 0.16 •~ 0.14
-.l
a. 00
0
brine
II
a. 00
is 0.2 0
-.l
C
0.6
is 20
0"0
60
40
0.12
Incidence angle
20
40
60
Incidence angle 1
0.2 0
~
0.•
't:
gas
C 0.6
•E
•mu
0.4
.~
0
0
0.18
E 0.16
a. 00
0.14
is
0.12
0.2 0
~
C
\\ -.l •~ - --I
• I)
a.
g
20
40
0"0
60
Incidence angle
b)
gas
20
Angle 20"
Angle 30"
60
Angle 30"
0.25
0.25
0.25
C
0.2
02
0.2
•mu
0.15
0.15
0.15
is
0.1
0
40
Incidence angle
~
~
•E
a. 00
0.1 0
100 150 50 Azimuth (degrees)
0.1 0
100 ISO 50 Azimuth (degrees)
0
50 100 150 Azimuth (degrees)
Figure 14.25. Valha/l Field: Mode/led Pop AVO for top chalk
reflection (II para/lel and perpendicular I to fractures. AVO Responses vary in quasi linear fashion with azimuth between
extremes shown. Fracture density=O.l and fracture aspect ratio
=
0.001. (redrawn after Ha/l et ai, 2002).
The possibility of performing analysis of azimuthal AVO has been enhanced by recent developments in acquiring multi azimuth, multi-offset data using 3D ocean bottom cables (e.g. Hall et ai, 2002).
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15. Issues in Applying Rock Physics in Prospect Evaluation
Rock Physics Associates
15.1 Introduction 15.2 Amplitude (DHI) Interpretation 15.3 Amplitudes in the Risking Context 15.4 Comments on DHI Risking 15.5 A Risking Dilemma Geology vs. Geophysics
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Issues in Applying Rock Physics in Prospect Evaluation
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Issues in Applying Rock Physics in Prospect Evaluation 15.1 Introduction 15.2 Amplitude (DHI) Interpretation 15.1 Introduction Using amplitude information in prospect evaluation requires that a significance is assigned to seismic amplitude observations. In order to do this requires: • An understanding of the limitations of the seismic analysis techniques • Evaluating the consistency of the observations with a geological and geophysical model • Attempting to estimate uncertainty. There have been a large number of dramatic 'failures' of amplitude interpretation models in exploration (probably more than notable successes) and it is necessary to put the role of amplitudes into context. We must attempt to guard against making unrealistic claims for the significance of amplitude information.
15.2 Amplitude (DHI) Interpretation The term 'amplitudes' is used here in a general sense to cover all interpretation based on reflection seismic and its derivatives (so it includes full and partial stack interpretation, AVO analysis and (elastic) inversion) and attribute derivatives. In reflection seismic the acronym DHI (Direct Hydrocarbon Indicator) is generally used within the industry to denote a seismic effect related to the presence of hydrocarbon (Figure 15.1). DHI's as has been discussed previously commonly comprise (but are not limited to) • Single or associations of reflection signatures (pre and post stack, bright spots dim spots, phase reversals) or impedance characteristics linked to the effects of hydrocarbon via rock physics models • down dip limit/termination or structural conformance of amplitude • flat spots. The criteria for the use of the term DHI for a recognised seismic effect are in fact quite stringent but are often applied recklessly or foolishly. A clear consistency has to be shown between the observed attributes and a rock physics model that illustrates a likely hydrocarbon interpretation. In addition consistency between the signature and other expected effects predicted by the model needs to be evaluated but very often are not. It is too easy to neglect other plausible causes for the effects as they may not lead to a viable prospect - the human mind appears to be constantly engaged in a creative search of corroborative evidence for its favoured hypothesis.
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Issues in Applying Rock Physics in Prospect Evaluation 15.2 Amplitude (DHI) Interpretation
Common DHl's Amplitude confomance High amplitudes
Bright spots Frequency and timing effects with gas
Low amplitudes
~
I
eN,?
'. Oilfield
Dim spot Reflector terminations
.
.
7j;/'e-o-l
Flat spots
1x'<.< '>( of o/.ft..f I rJ)
~'dd
Rock physics model
~
+fE:+O;lwalecconlact
: ._
Shale/brine sand ,.".
Shale/oil sand
Figure 15.1. Examples of Direct Hydrocarbon Indicators,
15.2.1 DHIs - Reasons for Getting it Wrong There are a whole host of reasons why we can get the interpretation wrong. These include: • non·uniqueness of the effects - (i.e, other geological scenarios are responsible, e.g. high porosity or low gas saturation) • seismic polarity is misinterpreted • there are Interpretive problems with seismic data acquisition and/or processing • the model fails (i.e. the assumption that seismic can be approximated as the convolution of a wavelet with a reflection series determined from elastic/isotropic rock properties is wrong), Of all the reasons for 'failure' the least is known about when the assumptions of elastic and isotropic rock properties fall down (figure 15.2).
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Issues in Applying Rock Physics in Prospect Evaluation 15.2 Amplitude (DHI) Interpretation
Instrument
Superimposed Noise
Response
Geophone Sensitivity
Source Strength
and Coupling Array
Directivity
Absorption
Spherical
Scattering
Reflector interference
Divergence
Reflection
Coefficient
Small scale horizontal layering
Figure 15.2. Factors affecting
Transverse
O
seismic amplitude
Isotropy
ElaSli~
(after Sheriff,
Fractures
1975).
Isotropy
We should not forget that the reality of sound propagation in the earth is complex and that sometimes the elastic/isotropic assumption can be invalid. There is no doubt that anisotropy can playa role in giving 'false positive' DHI indicators. In terms of AVO models there are basically two situations that might prove pitfalls in the elastic/isotropic assumption. 0-,---,---,---,---,-------, -0.02 +---+--+---+--+----1 -0.04 +---+--+---+--+----1 -0.06 -0.08
ri.
-0.1
-0.12 -0.14 -0.16 -0.18 -0.2
!~~t:!'~~~t:=t=~
-... ...
'. +---+--+-----=.,,---.,........---1 '.~ +---+--+---+-"l.,--+----1
____ isotropic
···liI---VTI
-\--+--1--+--1,---1
+---+--+---+--h,,-,---I +---+--+---+--+--h---1
The first (the more usual?) is where the AVO gradient of a shale/ sand reflector is increased owing to a positive contrast across the boundary in the anisotropic parameter 'delta'. Thus a brine sand reflection could take on the gradient characteristics that with isotropic modelling would be associated with a pay sand (figure 15.3).
+---+---+---1--1------< 0.00
10.00
20.00
30.00
40.00
50.00
Angle of Incidence
Figure 15.3. Modelled anisotropic modification of AVO response of Top brine sand.
The other scenario is where the contrast in delta is negative. In this instance it is possible to turn a negative gradient into a positive one. There are very few case studies in the literature that show conclusively an anisotropic effect with AVO. Margesson and Sondergeld (1986) seemed convinced that a positive AVO effect that appeared after drilling to be related to the boundary between a tuff and a shale was related to anisotropy (figure 15.4). While they didn't show a definitive link it is not difficult to generate a model that might fit the observations. ~lb
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Issues in Applying Rock Physics in Prospect Evaluation 15.2 Amplitude (DHI) Interpretation AMOCO
wd!, fltdl".;,;J
4700m
Anisotropic (VTI)
"-
0." 0.03
'\
,
V--
0.02 0.01
r--.
o .(1.01
./
~.02
isotropic
~.03 ~
...
I
~.05
o
10
""-
I 20
30
50
Angle of Incidence
Figure 15.4. Positive AVO resulting from anisotropy? Seismic picture from Margesson and
Sondergeld (1986) Speculative model based on work by RPA Ltd.
Given the practical problems of parameterising anisotropic models we currently don't know enough about how often AVO gradient estimation is adverseiy affected by contrasts in anisotropy. It may be that in those situations where a drilled AVO response has revealed no sand (for example where shales with different anisotropic parameters are juxtaposed), anisotropy may be contributing to false positive AVO signatures. At present the effects of anisotropy is part of the uncertainty to be taken account of in the risking process.
15.3 Amplitudes in the Risking Context Clearly if a verifiable DHI is present on a prospect then it is possible that the risk on the prospect may be considerably reduced relative to a standard geological risk either by utilising the DHI evidence within a probabilistic risking scheme or, possibly more dangerously, by using it to override the risking scheme. There are pitfalls, however, at almost every level of the process, One pitfall is that the DHI interpretation tends to be invoked too readily, for example when there has been no play specific corroboration through modelling or direct analogy of the effect(s) under question. What is more, in these situations the term DHI implies more certainty of hydrocarbon presence and a much narrower range of outcomes than is warranted (Citron and Rose, 2001). Loose thinking combined with big promises can be a fatal combination! Equally fatal is the confidence trick where we are blinded by the elegance of the positive model, how can it possibly fail?
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Issues in Applying Rock Physics in Prospect Evaluation 15.3 Amplitudes in a Risking Context
15.3.1 The Classic Risking Example - the Yegua of Onshore Texas The relationship between DHls and exploration risk is neatly illustrated by the classic example of the Yegua trend in the Gulf of Mexico (figures 15.5, 15.6, 15.7 and 15.8). This is a mature gas play comprising shallow high porosity sands that give bright spots on stacked sections and increasing amplitude with offset on prestack gathers (shale/brine sand reflections generally show opposite polarity and decreasing amplitude with offset). 84 wells that were drilled on 'AVO anomalies' were documented in a study by Allen et al (1993). The commercial success rates improved dramatically, from around 5 -10% to 50%, when AVO techniques were employed (using 2D seismic data). Clearly the DHls and associated risks described above are specific to the Yegua play and it would be foolhardy to take these particular DHls and expect them to work in a similar way in different types of plays for example West of Shetlands. However you could argue that on plays less mature than the Yegua the likely chance of success associated with DHls must be considerably less than 50%.
500 Fluvial
Offset (ft)
10000
Watersand-
-----:6"-:
v~l
Gas sand-
o/aIS
Gulf of Mexico
ii
Re-drawn after Alen and Peddy 1993
Figure J5.5. The Yegua trend of Onshore Texas.
Figure J5.6 The first order AVO model for the Yegua trend (after AI/en and Peddy, 1993).
• commercial success
D gas shows at objective
.no shows
Figure J5.7 AVO Results Yegua Trend-Gulf Coast (84 Anomalies). Data from AI/en et ai, 1993.
50%
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Issues in Applying Rock Physics in Prospect Evaluation 15.3 Amplitudes in the Risking Context
2%
10%
Figure 15.8 Yegua Trend .thick clean 55 shows
-Gulf Coast AVO Results
Dthick clean 55 no shows
23%
.thin clean sands no shows
- Reasons for Failure. Data
o tight sands shows
from Allen et ai, 1993.
• tight sands no shows
III no sand • hard streak (polarity issue)
• lignite
15.3.2 Other Examples In the North Sea, most of the oil and gas fields have been found without exploration being driven by amplitude information (e.g. the Nelson Field, figure 15.9). In part this has to be due to the timing of exploration relative to improvements in seismic fidelity and the development of applied rock physics approaches. There are numerous exampies of interpreters spotting the critical seismic DHI but misinterpreting it. Later field studies bring to light the real interpretation.
l:~m~~mm~ geometry ~II - 0Wedge We. -;: ha,fJ Fluid interpretation
Lithological interpretation
-=~ I
--~ I
owc
Base Upper Forties Shale
Figure 15.9. The Nelson Field Signature: An example of physical understanding after the discovery.
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Issues in Applying Rock Physics in Prospect Evaluation 15.3 Amplitudes in the Risking Context
On some fields seismic amplitudes can be used to define the limits of oil and gas fields. Seismic and rock physics modelling can help in significantly constraining volumetric calculations, not only in terms of area but also in terms of the range of N:G and porosity values input to the calculation (figure 15.10).
High HCPT
Figure 15.10. Hydrocarbon Pore Thickness from a Coloured Inversion Fluid Cube
What is certain is that amplitude technologies are now adding considerable value in field development, owing to the high degree of calibration available. On the basis of bottom line benefit Time-Lapse Seismic techniques, underpinned by thorough rock physics, have become established practice in many of the larger oil and gas companies within the last 5-6 years (figure 15.11).
..
1049
- ..
, Difference response to )II ~
change in level of contact
Figure 15.11. Time-lapse difference section illustrating
the effect of the change in the level of the oil-water
24
15.3.3 Amplitudes in Partially Explored Basins Whilst the challenge is always there to use the lessons from the fields to drive the exploration models in partially explored basins, in these situations it is easy to convince ourselves that we know more than we actually do. Very often if a well is available there is a tendency to believe that it contains all that is necessary for calibration (including all likely variability). Our problem then is to ask ourselves 'what is the likelihood that the model will hold over the prospect area?'. In some cases significant changes can occur to invalidate the conclusions drawn from modelling close well control whilst in other situations a well 50km from the prospect may be entirely relevant. Experience has shown that there are 'optimum' and 'non-optimum' situations for applying rock physics in near field appraisal and exploration in partially explored basins. ~):!. GEOSCIENCE
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'.' i·
Issues in Applying Rock Physics in Prospect Evaluation 15.3 Amplitudes in the Risking Context
15.3.4 Optimum Scenarios An 'optimum' scenario is where there is a high degree of confidence in the connection between the seismic observations and seismic models. The confidence is high because: • This is a moderately explored area with good analogues and extensive 3D coverage • Relatively simple deep sea sedimentary environment with a low degree of stratigraphic variability of the units overlying the target • Thick sands that have a narrow porosity range and shales that are laterally quite invariant • There is a predictable variation in the response of hydrocarbon vs brine filled sands • There is a large amount of high quality well data to - Determine phase and polarity of the seismic - Model the effects of fluid fill and lithological variation - Understand the seismic signature of the 'play'. In such areas rock physics applied in interpretation can have a direct impact on the perception of risk on production drilling locations and new prospects.
15.3.5 Non-Optimum Scenarios There are non-optimum situations where for good reasons the mapping of fluids and lithologies with p-wave seismic data is almost impossible. Obviously structurally complex areas that require complex processing are one such area. However, non-optimal situations can also be found in areas of relatively flat lying geology. The example in figure 15.12 from a basin margin location is characterised by:
"-.
-
;:l.'.~;=~~~:::;,:,;;,:;;,;;::;;,;p.~':';;;Ilii'!~~,*
..
:~;~~~ 4 ...
Figure 15.12. A Non-Optimum Rock Physics Scenario: seismic line shows
sediment structuration (gives rise to lithological and stratigraphic uncertainty).
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Issues in Applying Rock Physics in Prospect Evaluation 15.3 Amplitudes in the Risking Context
,")~
A1-'VI
2D:I'N;.....,....-\----;'"\----r-\_-----,
..
Increasing AI / '
2.7
l<
2.4
1><.
\
Jl'""
" IC"~
>l"'" "
2.1
~x
Shales
l<"
IC
*" ;IIi:!
,.
"
. IC
><"~ "" "II ><~,,~I<
.
r:.,..~.' """,
~.: ~'
~
Brine Sand
Oil Sand (30%Sw) ,/ Gils Sand (40%Sw)
I
\
\
\
15 ':---=---:-="'--=~~=_-__:' 190. 160. 130/ 100. 70. 40.
/DT24
,
Figure 15.13. DTjRHOB Crossplot showing significant overlap of sand and shaie impedances.
15.3.6 Virgin Basins Calibration is clearly the key to the application of DHIs in risk. Our models are only as good as the data on which they are based. In virgin basins where there is stratigraphic uncertainty and no calibration it may be completely unrealistic to try and apply DHIs in the risking process. In such areas conventional AVO analysis can give us an idea of the degree to which different responses are anomalous but it cant tell us how likely a particular seismic effect will be related to hydrocarbon rather than for example a high porosity brine sand (or any other as yet undefined lithology combination for that matter). At best (and if you are lucky enough to have a number of potential prospects) it can be used as a ranking tool. Figure 15.14 is an example where a flat spot high-graded a virgin exploration area. At least two papers were written pre-drill where the flat spot was interpreted as good evidence for the pres-
27)
enceofhydrocarbons.
/;/G.ee.eN/o-M:!. S'fti1n'(tPh,'/I,r (- nil! ~f"(ieIU
_.
- If we
."
l' ' -
claiDil1;1.e<; : 'ua pdw //<90£ ~;L,'~s eS2~
-,;., .
"-.
.--.
~ '....,. ~ .~
~
...." - ...-.. 1 km
Figure 15.14. An example of an unsuccessful exploration fiat-spot (after Aram, 1999). ~l& GEOSCIENCE &_TRAINING
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Issues in Applying Rock Physics in Prospect Evaluation 15.3 Amplitudes in the Risking Context 15.4 Comments on DHI Risking Of course similar (more believable?) flat spots in pre-rift settings are associated with some large oil and gas fields (e.g. the Troll Field, figure 15.15). Unfortunately, it is difficult without calibration to assign a high confidence to a hydrocarbon interpretation of a flat spot.
Figure 15.15. Troll Field Flat
Spot.
15.4 Comments on DHI Risking There is always a risk in DHI interpretation in exploration (as some of us know from bitter experience) and we must get away from the idea that if DHls really worked there would be no need for risking. Many companies and individuals follow this 'silver bullet' idea and it is no surprise that the DHI approach moves rapidiy in and out of fashion. It is better to think of the Casino owners analogy (Rose, 1999), in which we hope to stack the odds in our favour over a certain period of time with a portfolio that is risked appropriately. We will not know necessarily which particular wells will come in but over the life of the portfolio we believe that an appropriate use of use of amplitude information will put us ahead. Companies that cannot afford another dry hole should hope for lady luck. ,.
~
(/ _
~" 'J)."
C •
~:I
=
qIV>
o
L..--
~~
;""""!.
~ r:
~
• -n:~
.-~-..:---=-
-'-
Figure 15.16. Two brights - one was a discovery - is it possible to tell which one?
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Issues in Applying Rock Physics in Prospect Evaluation 15.4 Comments on DHI Risking
Very often we don't have the statistics to support the risks applied to DHIs, usually because we are trying to apply the techniques in non-mature areas. And when it comes down to it, whichever way you assign a risk significance to DHIs it is highly subjective. Fundamentally it depends on the level of knowledge of the play and an understanding of the particular DHI characteristics of the target. With greater knowledge of the play the vagaries of the DHI signature (and its relationship to factors such as data quality) are likely to be more completely understood. Two companies may recognise the same seismic effects but place different significance on them simply because of differences in the understanding of the play. In the Yegua example noted above 10 out of 84 prospects had a questionable interpretation (Allen et ai, 1993).
15.4.1 Amplitude in the Context of Rule Sets Every exploration team has to incorporate amplitude information into their ranking/risking schemes. Understandably there are few published cases. However, an interesting example has been given by Lamers and Carmichael (1999). They outline a rule set for the West of Shetland. High grade criteria/success factors are: 1. reliable trap model based on structure and seismic geometries (not based on amplitude
alone!) 2. presence of an amplitude anomaly that is consistent with a relevant rock physics model 3. amplitude conformance with structure. Thus in this case amplitude indicators are secondary to trap definition elements. The main geological criteria for success are: 1. presence of intra-basin pre-tertiary high for focussing charge 2. depocentre for tertiary sands 3. Post-rift focus for re-migration and/or late charge. In this area there is a lack of flat spots due to limited sand thickness. Amplitude conformance (a commonly cited attribute to high-grade a prospect) alone gave mixed results in terms of exploration success (figure 15.17). Variation in boundary conditions at the top reservoir interface such as gradational contacts and the presence of soft and hard shales.were cited as reasons for the poor performance of this attribute. In this area, amplitude conformance has been used to best effect in an appraisal context. 2O.f1f9
.'
~
Unfortunately most prospects currently being identified West of Shetlands are predominantly stratigraphic in which seismic amplitude may be the only indicator of prospectivity.
Figure 15.17. Amplitude Map from
Foinaven Field (after Cooper et ai,
1999) .
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Issues in Applying Rock Physics in Prospect Evaluation 15.4. Comments on DHI Risking
15.4.2 A Suggestion for Risking using Amplitudes The issue of incorporating the significance of amplitude observations into a perception of the chance of success is one that companies constantly have to deal with. The following are some observations on requirements for a risking scheme that incorporates amplitudes: • Owing to the fact that DHI interpretation effectively includes all the petroleum risking elements it is worth attempting at least initially to gauge a chance of success (if possible) from the amplitude observations in their context as a counterpoint to the traditional risking approach . • The scheme or approach needs to be: - generic because uniformity of approach is desirable-ensures consistency - but easily adaptable to different situations - straightforward so that - non-specialists can be comfortable with using it - it addresses the key issues while recognising the element of subjectivity - it cuts through potentially confusing pseudo-science and helps guard against unrealistic claims for seismic effects that may be at best ill-defined. A generic (and non-specialist) approach (that follow the criterion above) is to use the chance of success matrix idea of Citron and Rose (2001) but in which the axes are related to the knowledge of the play (in terms of the seismic responses of lithology and fluid, calibration if you like) and the confidence in the recognition of the DHI(s). A questionnaire for each component (see figure 15.18) would help arrive at the appropriate position on the matrix. Chance of success values will be specific to a particular play for a given range of analytical techniques.
flJu:
/!.o~
-----
N/A
20% 50%
N/A
10% 25%
N/A N/A
12%
;A:
Good
::::l
0 ~ CD
a.
to
Poor
CD 0
"U
Ql
Low
High
'<
Confidence in DHI Figure 15.18. Amplitude vs. Play Chance of
Success Matrix.
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Issues in Applying Rock Physics in Prospect Evaluation 15.4 Comments on DHI Risking
A high, moderate or low confidence can be assigned to the following statements in terms of the extent to which they are believed to be true. These are a simplification of the checklists given in Appendix 2. Data quality • The data is good enough to interpret relative amplitudes (good level of S:N and continuity • Processing parameters have been checked (ie there has been no compromise on relative amplitude) • Migration errors and other imaging artefacts (including anisotropy in the overburden) are not a problem • Good quality well ties provide confidence in the phase and polarity of the data • If AVO is a critical element of the play: - reflectors can be tracked from near to far traces - there are no major problems with residual moveout - the approach to AVO analysis is appropriate for the given data quality. Trap definition • The trap is adequately defined and fits with the expected style of trap for this play. Well control/analogue information • There is enough well data of good quality to calibrate the seismic data • Appropriate reflection/impedance models have been generated - both pay and non-pay scenarios
• There is good reason to believe that the assumptions in the modelling (including low frequency component in seismic inversions) hold over the prospect area. Amplitude Relationships • Event recognition is not a problem • There are clear relative/absolute differences in amplitude across the prospect area that fit with the hydrocarbon rock physics model. Conformance of amplitude to structure • The amplitudes show a high degree of conformance with a particular depth contour.
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Issues in Applying Rock Physics in Prospect Evaluation 15.4 Comments on DHI Risking
Flat spot • There is a flat spot that shows discordance to stratigraphy • The flat spot can be used to confidently map the gross pay interval. Other Issues • The DHI interpretation is not being exaggerated due to the well drilled).
non~technical issues
(i.e. desire to get
Confidence in the play • Confidence in the seismic stratigraphy is high • The target has been drilled before in this type of situation • Reliable statistics are available for the target of interest • The effects of variability of lithologies, fluids, bed thicknesses in conjunction with reflection angle is well understood. The Problem of False Negative Scenarios As well as evaluating the value of a DHI in the possible lowering of risk we also need to address the significance of a lack of a DHI in a situation where one would be expected (i.e. where we might use the lack of a DHI to increase the risk). Obviously the matrix chances of success could be modified to account for this situation (figure 15.19). Interestingly, examples of 'faise negatives' (i.e. discoveries where there is no DHI but with the given data quality one would be expected) are thin on the ground.
Prospect
ljHH
!1!lllli Iii i II
I
li!~
Ij
Ili!!l! Iii I ,Ii!
Field
I
II
,I
/
False negatives could be included here
/'. I N/A ) 20%
-N/A
50%
10%
25%
N/A
N/A
12%
\
A
Good
::l
0 ~ <1l
Cl.
co Poor
<1l 0
-"U
Low
High
OJ
'<
Confidence in DHI Figure 15.19. Risking False Negative Scenarios.
15.4.3
DHI
Database - Successes and Failures
In order to implement any amplitude based risking system geologists and geophysicists there is a requirement for a database of previous examples to help achieve understanding and consistency of approach. 16
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Issues in Applying Rock Physics in Prospect Evaluation 15.5 A Risking Dilemma
15.5 A Risking Dilemma - Geology vs. Geophysics There are some situations where the geologists and geophysicists perception of risk is quite different. Figure 15.20 is a schematic illustration of a frontier exploration scenario. The notion of long distance hydrocarbon migration is considered unlikely by the geologist but the geophysicist, using analogues from other basins, is quite confident in recognising seismic effects which are consistent with the presence of oil. In some ways this may be an unusual situation as perceptions of risk are not usually this polarised. In the authors view, positive rock physics information can change the risk from high to medium or from medium to low but seldom from high to low. However, the example does highlight the potential dilemma that can face explorationists when attempting to weigh different data interpretations.
Problem of long distance migration = high risk prospect Turbidite channel environment
_prospect 50km
\
.-------'----r--------, apparent thickening a isochore
h'ivL(v I; "co'-{. /V~ uo :
I
~
'"
1~ "te,dIt-W Id-el!r;/, /oR 07/ h
--'.
Basin generating hydrocarbon
~
'- ----- ..
')D 1<.'"'
'Yf l/,/7b ILl',
\
herr
terminations flat spot lowe high amplitude brine sands
-'.
Recognition of features associated with hydrocarbon reduces perceived risk
Figure 15.20. Figure Risking: Geology vs. Geophysics.
_ VO JrP! CI<.-vde
Would you drill the prospect?
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17
Professional Level Rock Physics for Seismic Amplitude Interpretation 16. Exercises
Rock Physics Associates
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Contents 16.1 Quick-look workflow 16.2 Log conditioning and modelling workflow 16.3 Forward modelling using Xu-White 16.4 20 AVO modelling lithology and fluid 16.5 Elastic inversion interpretation exercise 16.6 Rock physics and probability 16.7 Time lapse exercise 16.8 Anisotropy scenarios
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Exercises
2
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Exercises 16.1 Quick-look Workflow
16.1 Quick-look workflow (Well H) This exercise reviews the Quicklook workflow that was the focus of the 'Essential Level' course. n is the simplest form of rock physics interpretation workflow and it can have great value in revealing the expected first order AVO response for various lithology and fluid scenarios (particularly where the reservoir and cap are 'seismically thick'). The workflow covers many aspects of practical rock physics (such as fluid substitution and shear prediction) and is based on 'average' values obtained from logs.
Well with water bearing reservoir
! Vp rhob
<j>
Reservoir and fluid parameters
~
----
/'
Gassmann
~s,
Vp, p Water, oil, gas bearing reservoir
!
Vs Prediction
~ Real rock QC Pre d'ICted Eftects
Reflectivity Model
--,j:....-+~~
Single interrace AVO
.
/ Angles and offsets
41
...........'_,
I'Ogh emp!ilude brin& _
_.
!
Seismic Interpretation
The QUick-look Workflow
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Exercises 16.1 Quick-look workflow
Below is a log plot of a well in which there are several units of shaley sands. The aim of the exercise is to describe the differences in the AVO response of sands A and B with brine and oil. It highlights the importance of understanding the stratigraphy when interpreting AVO responses.
Stratigraphy
... UNIT IV
UNIT III
UNIT II 2.100 1,399 1,BOO
2,~66
1,900
2.533
3,000
1,598
3,100
'-'"
3,200
2,727
Sand C
UNITI
3.300 2,791 3,'00 2,859 3,500 2,930
Well H Log Display
Data Pressure (psi) Temperature ("C) Salinity (ppm) Oil API GOR (v/v) Gas oravilv Mineral Parameters rho Quartz
Shale
2.65 2.32
3630 74 50000 29 30 0.7 K
U
36.6 13
45 3.9
-
0.7
0.' ~ 0.5 0.' 0.3 0.2 0.1
o
Shale A Sand A brine Sand A oil Shale B Sand B brine Sand Boil 4
, 0.' 0.'
\
\._ Sw=1.7*EXP(-8*phie)
Water based mud assume that the log is reading formation brine (ie SW=l)
"
I-
o
=
0.1
0.2
0.3
0.'
Also assume brine is gas free
0.5
Porosity
Vp 2650 2900
Vs
2800 2820 2624
1288 1387 1397
Rhob 2.22 2.18 2.3 2.23 2.2
© Rock Physics Associates Ltd 2005
Vsh
Phie
0.17
I
0.26
I
0.22
I
0.22
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Exercises 16.1 Quick-look Workflow
The aim of the exercise is to 1. complete the table on the previous page (ie Predicts Vs and perform fluid substitution for Sand A) 2. enter the data into an AVA modeller 3. predict the relative reflectivity amplitudes of various fluid and lithology scenarios at a particular seismic offset. Workflow To begin click on the RokDoc icon on the desktop select project management and select exercise 1 1. Calculate fluid parameters a. Click on the well H in the map view b. Select Project data, then 'Fluids' c. Click 'create new fluid set' d. click on 'new' fluid e. click 'calculate fluids' f. input temp, pressure, salinity g. select 'gas free' for brine h. input GOR, dead oil gravity and gas gravity i. press 'calculate' j. (note to convert (eg from psi to MPa) double click on the input cell) k. click on the 'active' button to make this set the active fluid parameter set 2. Vs prediction for Shale A a. Select 'blocky ops' b. Click on 'fluid sub'(gassmann) c. Input Vp of shale d. Press 'Vs prediction' e. Click on Greenberg Castagna f. Mineral proportions - Enter 1 for shale and 0 for sandstone g. Click 'calculate' h. Note the Vs in the table on the previous page i. Click 'close' 3. Vs prediction for Sand A a. In the 'Fluid sub' (Gassmann) tab click on the 'multi-mineral' option under minerals b. Select quartz in the drop down menu in the mineral column c. Do the same in the cell below for shale d. Assign the mineral proportions for Sand A (shale=0.17 quartz=0.83) e. Enter Vp and rho into the 'inputs' box at the top f. Click on Vs prediction g. Select Greenberg Castagna Hit 'calculate' and close h. i. Note the Vs in the table 4. Fluid substitution in Sand A In the 'Fluid sub' (Gassmann) tab the brine Vp, Vs and density should now be a. visible in the 'inputs' b. In the 'Fluids' section set 'final fluids' to So=80 c. Click on 'calculate' d. Note down the Vp Vs and density values (from the 'porosity' row) in the table at the front of the exercise
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Exercises 16.1 Quick-look workflow
5. Single a. b. c.
Interface AVO Modelling The table at the front of the exercise should be complete In' Blocky ops' select 'AVO' Input the data from the table to the AVO sheet - to save time click on the 'get averages' button (the data have previously been stored to save your sanity) d. Enter the upper and lower lithology combinations to model (ie 'shale A' as upper lithology and 'Sand A brine' as lower lithology will model the AVO response from the shale/brine sand interface (click on the cell and a drop down menu will appear) I. Shale on brine sand il.Shale on oil sand iil.Oil sand on brine sand .... For both units A and B e. Click on the AVO plots tab to view the AVA curves f. Note set the x scale to sin2theta from 0-0.5 (to do this right click on the axis) - set the y scale from -0.2 to 0.2 g. Describe the AVA responses in terms of the Rutherford and Williams (1989) scheme
Question: A far stack is available with a mid-offset of 1500m What reflectivity would you expect for the two sands? To answer the question requires a model for the relationship of angle and offset 6. Modelling angle vs offset a. In 'blocky ops selcts 'angle to incidence' b. Select checkshots c. Select 'new set' checkshot data d. Click OK e. Top of sand A at 2330m to calculate the angle for an offset of 1500m I. input the interface no (ie checkshot no) at the top of the offset to incidence sheet (it is interface 8) il. read the angle off the plot or input the offset at the bottom of the sheet to give the angle iiI. (the way the software calculates the relationship will be discussed) f.
go back to the AVO modeller and input the angle using the far angle slider (this puts a marker on the AVA plot) g. describe the relative reflectivity of the different interfaces
6
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Exercises 16.2 Log Workflow
16.2 Log Conditioning and Modelling Workflow (Well R) The well is an oil discovery and the interpreter is trying to make sense of near (10) and far (30) angle stack observations. This exercise will be an interactive class session in which the following steps in the log conditioning process and modelling will be discussed.
....
"fWl' (ms)
1Il0(m)
tim.
~~~ss
OR_Track OR W'~
0.0 -
Volumes
POf_and_Sal
..
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VS Track
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-
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2,830 2,8Si
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2,121
2.n0 2,728
2,76tl 2,151
2,770 2,156 2,180 2,162
Porosity QC from density log Porosity has been calculated using the density log. Fluid density has been calculated from a crossplot of rhob vs overburden corrected core porosities (see over) VS QC and Vs prediction A shear log has been acquired and this will be QC'd through the use of crossplots, forward modelling and also through gassmann inversion Gassmann moduli inversion and fluid substitution Gassmann modelling is used to invert the data to the dry moduli - which are then checked (this can give a gUide as to the consistency of the various inputs). Once the Gassmann inputs have been established then fluid substitution can be performed to generate logs with different fluid fill for modelling AVA synthetic generation Zoeppritz synthetics for various fluid fill will be created 20 Model creation A 2D model will be created in two way time illustrating reflector relationships, sensitivity of seismic signature to angle, frequency etc ~l~ GEOSCIENCE
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©Rock Physics Associates Ltd 2005
7
Exercises 16.2 Log workflow
Well R Workflow 1.
2.
3.
4.
5. 6. 7. 8. 9.
10.
8
Data available a. GR, Vp, Vs, PO' Core Porosify b. Interpretation Phi, Vel and Sw c. Shale parameters from logs d. Water based mud in this scenario has similar properties to formation water e. Virgin fluid parameters (P. p.. K. K..) calculated from Batzle and Wang equations Vp Vs evaluation a. Create Poisson ratio log and zone the well b. Vs prediction using linear fits to Vp Vs zones c. Comparison of PR trend to PR log d. Editing of selected zones - replacement with Vs trend (Vs_ed) Correction of density for invasion a. use of SCAl (core porosity and matrix density) to determine fluid density in clean sands (see core porosity vs density crossplot) b. calculation of effective porosity (mix of quartz and shale for mineral) - compare to petrophysicists value for porosity c. calculate fluid density of virgin formation fluids (Pfl') d. using continuum of water and oil properties determine average Sx for the clean sands e. derive function that gives a continuous log of Sx in terms of Sw L Sx=((1-Sw)'0.57)+Sw f. Calculate invaded zone fluid density (P.,) g. Correct the density log - Pb oo,,=Pb-(W Po,)-W Po,) (rhob_corr) Evaluation of dry rock inversions a. Using Sw, Vp, Vs_ed, Rhob_corr b. Using Sx, Vp, Vs_ed, Rhob c. Use Reuss fluid mix d. Crossplot of phi vs moduli K. ~ and cr,,, e. Similar results if sonic assumed to be invaded or not Fluid substitution to wet a. run with corrected density and assume sonic is not invaded Sonic calibration a. First order polynomial works well here - (good match of calibrated and 'raw' sonic) AVA synthetics (30Hz Ricker) a. Oil and wet (well ties) Approaches to analysing discrimination at different angles a. Intercept gradient crossplot using wet data - Sin'9=0.355 X=19.5° 9=36.6° b. EEl analysis from Sw correlation X=23° 9=41 ° c. AI GI crossplot avg oil and brine sand data - X=36° 9=58° 20 modelling a. Model creation b. Reflectivity vs angle, apparent terminations, role of frequency c. Coloured inversion i. fluid (note tuning effects) iLlithology -52 degrees (near 10 far 30) Li=(near'6.959)-(far'5.959) d. Elastic projection eg ((0.6393'AI)-880.9)-Si
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Exercises 16.2 Log Workflow
Shale parameters from logs
Virgin Fluid Properties
Rhoshale 2.48g/cc K 12.6GPa ~ 4.8GPa
Pressure Temp Salinity GOR Oilapi Gas gravity
Brine Oil
Rhofl 1.04 0.661
3940psi 220F 104500ppm 960 scf/stb 39.3 0942 Kfl 2.917 0.437
Fluid density from comparing core porosity (depth corrected) and density log
',-------------, matrix density from core analysis = 2.666g/cc fiuid density derived from regression of core porosity and density log
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2700
Difference between deep and shallow resistivity curves illustrates that there is invasion
2720
27,(0
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©Rock Physics Associates Ltd 2005
9
Exercises 16.2 Log workflow
Deriving relation between Sx and Sw (WBM)
1.2
0.8 0:
~ 0.6
,
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-+- Virgin curve --lI-
Av Sw=O.58 . Sx=O.818
0.4 0.2
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Sx=( (1-Sw)*O.57)+Sw
Dry rock inversion results
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10
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T R A I N I N G
ALLIANCE
Exercises 16.2 Log Workflow
Transitional zone
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backdrop picture - Ex_2_modeLsection.jpg
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©Rock Physics Associates Ltd 2005
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11
Exercises 16.3 Forward modelling using the Xu-White model
16.3 Forward modelling using the Xu_White Model The exercise again will be interactive focussing on the parameterisation of forward models for predicting Vp Vs and density.
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Volumes
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2,200 2,250 2,300 2,350 2,400
2,450 2,500
2,550 2,600
2,650 2,100 2,750
1,800
12
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Exercises 16.4 20 AVA modelling - lithology and fluid
16.4 20 AVA modelling - lithology and fluid Open exercise 4 1. click on Ex 4 Well H Vs prediction 1. click on 'well ops' 2. click on 'Log Vs prediction' 3. click on 'Empirical' methods 4. click 'Greenberg Castagna' 5. click on 'select volume set' 6. select Vsh from the list 7. click on 'calculate', 8. click on 'Save Vs' - call the curve Vs_GC Model Setup 1. On the project viewer - in 'Project Management' select 'debug mode' 2. make sure the well is highlighted and select 'modelling ops' 3. Select 'Scenario'
4. Create 'new' 5. DeAne the model parameters as below: Input Scenario Session Name
session Nom.
I'M-Od-e-11---
Input Mod.l Extents
No Traces No 1WT Samples start 1WT (ms) 1WT Increment (ms) Input wei OlI'sets
Trace No
Well Name ex(WeliH
Vertical Shin
10
0
5. Click on 'Select logs' 6. The following should appear _
fx4_H
"'Lag
GRLog
I
I
vp
VOLog
II
VS_GC
_Log
,I
~Lag
Rho~1
VShOl.
II
Par Lag Por,E1f
Sol Lag
I
Brine
7. Markers - select the 'a' and 'c' markers in the list and transfer to the events column using the '>' button 8. Click on 'select wavelet' and deAne a 25Hz ricker wavelet (SEG polarity) - call the wavelet '25R' 9. Click 'launch' ~l~
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Exercises 16.4 20 AVA Modelling - lithology and fluid
Making the Model 1. Assign colours to the horizons 2. Hit '1. make synthetic at well' button 3. To change scaling of synthetic click on 'quantity l' button and set wiggle overlap to 1 4. Note also that in the 'quantity l' menu you can select any elastic attribute to display 5. To change the polarity click on the 'switches' menu on the top bar-the 'switches' menu also enables you to turn on the colour bar for the display 6. On the 'modelling' menu click on 'operations' button on top menu 7. select 'open a jpg' and find the 'ex 4 model section.jpg' file
;--~~
L--~/
_.-.
-
.~
----
;
8. To view it select 'overlays' then 'backdrop' 9. In the horizon 'type' boxes type a 'U' for the 'a' horizon and a 'C' for the 'c' horizon (these define stratigraphic relationships for data interpolation) 10. To make the horizon picks-click on the edit button for 'a'-c1ick on the first and last trace in accordance with the backdrop picture, then press the 'i' (interpolate) button-press 'X' key to finish and press 'Yes' to save 11. Repeat this for the 'c' pick (make sure the 'c' event doesnt cross the 'a' event) 12. Note that the basal bar gives a message read out in red advising on possible options 13. Turn off the backdrop in the 'overlays' menu 14. Hit the '3.Fix events/Detect bodies' button 15. For each body click '4.set body fill parameters' followed by OK 18. When all the bodies have been filled click on '5.fill bodies along events' - (note that the model section you have created is for the brine saturated case) 19. On the 'quantity l' menu select 'convolve with wavelet'
Performing Gassmann fluid substitution in a model body 1. Open the backdrop from the 'overlays' menu 2. Type 'contact' in Event 3 on the event list 3. Select a colour for the contact 4. Type a 'C' in the 'type' box for the 'contact horizon 5. Click on the edit button and digitise the contact (note that using the shift key and the < and> keys picks the event straight across the model - make sure that the event doesnt cross the others) 6. In the 'modelling' menu - Hit the 'Fix events/detect bodies' button 7. Click on the 'Gassmann on model 2' button 8. Hit the 'Copy model 1 to model 2' button 9. Click on the wedge shaped body 10. Define the fluid parameters using the following inputs 14
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ALLIANCE
Exercises 16.4 20 AVA modelling - lithology and fluid
Miwal-1:
Name: lQuartz
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11. Click the OK button 12. Turn off the backdrop in the 'overlays' menu To view the fluid substituted model go to the 'quantity l' menu and deselect the 'show 13. modell' button To show a particular angle stack move the slider of the 'Far stack' to the required number 14. 15. To reveal a synthetic gather-set 'Nstack' to 9, then under the 'operations' menu select 'popup a gather' - amplitude can be measured from the gather by moving the dashed green line to the selected reflection 16. Select an angle of 20' . 17. Find areas where there is brightening and dimming related to non-hydrocarbon and hydrocarbon effects
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15
Exercises 16.5 Elastic inversion interpretation exercise
16.5 Elastic inversion interpretation exercise AI Map
.. ' .. ,
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".
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Separate Inversions have been derived from an intercept stack and far stack. Note red dashed lines show depth structure.
.
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© Rock Physics Associates Ltd 2005
Sand prone
3200
~l~ GEOSCIENCE
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ALLIANCE
Exercises 16.5 Elastic inversion interpretation exercise
Do the impedance values on the maps appear to be calibrated? (ie calculate AVOI or poisson ratio at the well and both possible drilling locations) Think of reasons why the inversions may not be calibrated. Can you predict porosity accurately? Would you drill the structure? If so at location A or B?
12000
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EI25
AVOI
PR
well Location 1 Location 2
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17
Exercises 16.6a Introducing Fuzzy Logic
16.6a Facies discrimination using two variables - using fuzzy logic with a test data set This exercise illustrates the power of fuzzy logic for facies discrimination using two variables. It performs the same function as contouring probability points on a crossplot of the two variables. Below is a crossplot of AI and poisson ratio, Neither variable completely differentiates each facies.
No. of Points 0
-
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Follow the workftow on the next page.
18
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.,
ALLIANCE
Exercises 16.6a Introducing fuzzy logic
Workflow
1. Open Ex_6_Fuzzy_exercise 2. Double click on well Fuzzy A 3. Select 'well ops' then 'log fuzzy logic' 4. You will notice that the well view shows the collated data by facies 5. In the pre-processor click the training logs 'add' button 6. Select the PR and AI logs (use shift select to select the logs) 7. In the 'facies categories' click the 'add' button 8. Select Facies_l,_2 and _3 9. Click on the 'copy to fitting' button 10. Give the training set a name - eg Fuzzy A 11. Click on the 'fitting' tab (note that Gaussian fits have been made to the data for each of the facies) (data shown is mean, std dev and no. of samples) 12. To view histograms of the facies by attribute select the cells oin the PR column for example then click on the 'facies histogram' button 13. To perform cross-validation (ie testing the model on the training dataset select the crossvalidation option under 'prediction', then hit the 'calculate' button 14. Select the case 'Fuzzy A' then OK 15. Select both PR and AI (the probabilities from the two sets of distributions will be combined in the fuzzy logic engine) , then press OK 16. Notice that the winner column shows an exact prediction of the facies
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19
Exercises 16.6b Acoustic facies discrimination using fuzzy logic
16.6b Acoustic facies discrimination using fuzzy logic The aim of this exercise is to determine the best attributes to discriminate between various acoustic facies. A typical well log below illustrates the various facies (oil sands, water sands, shales and tight sands «10% porosity)). Time data has been collated from several wells and is presented in Ex_6_Fuzzy_exercise.rok On the following page are examples of some common types of elastic parameter displays.
Type well DEPTH
M
I
I
VSH (dec)
O.
SW (dec)
1. 1.
-------_. Sh I :::.-:.-:.-, --------
I' --------m::m:::_ I :j:::-:-:-:-:::.:.
PHIE (dec)
O. 0.5
VP (m/s)
RHOB (glee)
O. 2000.----5000. 1.95--2.95
ae
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Follow the workflow outlines in the previous exercise and evaluate the relative success of various parameters at discriminating the different facies
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© Rock Physics Associates Ltd 2005
~l/.! GEOSCIENCE
& ..... TRAINING .,
ALLIANCE
Exercises 16.6b Acoustic facies discrimination using fuzzy logic
Q
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~
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~
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©Rock Physics Associates Ltd 2005
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Exercises 16.6c Effect of low gas saturations on elastic attributes
16.6c Effect of low gas saturations on elastic attributes To what extent is density a better discriminator of low gas saturation in sands? Data is presented in EX_6_Fuzzy-exercise (well Fuzzy C) Use RokDoc-Fuzzy Logic to investigate and possibly answer the question. Note: creating the facies histograms for AVO! and Rhob will be sufficient In answering the question think not only in terms of impedances but also reflectivities g g g
g g
... ... ~
g g g
g g
ri
ri
. .
g g g
~
g g
g g g
~
.
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g g g
~
,.;
,.;
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g g
g g
g g
g g
g g
g g
;}
;}
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~
~
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~
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g g
10,000
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g ~
g g
g
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g
g ~
g
g
~
~
g g N
'0.000 9,000
8,000
8,000
.-:.
1,000
j
~ 6,000
..
0
~ 5,000
g
OJ 4,000 3,000
~
6,000
X..
4,000 3,000 2,000 1,000
g
g
g
~
~
"i
g
share_c_W1
5,000
2,000
~
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7,000
1,000 g
~ Mn. sand_'_W1
g
g
g
g
~
~
~
~
AVOI(None)
22
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Exercises 16.7 Time-lapse exercise
16.7 Time-Lapse Exercise An overpressured oil reservoir is produced through pressure depletion and natural water drive over a period of 10 years. Using data derived from the lab together with the field data the aim of this practicai is to calculate the change in AI due to fluid, pressure, fluid and pressure, and investigate the possible effects of patchy saturation
Field Data Original Pressure 6699psi Peff Drawndown pressure 3500psi
2438psi Peff 5637psi
Temperature
116C (assume no change with depletion)
Brine salinity (assume gas free brine) Oil GOR G=0.71 Gas gravity Sw (original) Sw (swept zone)
20000ppm 39API 1341/ 0.65 0.15 0.8
Fluid and mineral sets have already been calculated in EX_7_time_lapse.rok
Rock Parameters Vsh Phie Minerals Quartz Shale
0.2 0.252
K 36.6 U 45 K 13.89
Rho 2.65 U 4.34 Rho
2.38
Dry rock parameters RhodryKd Original pressure 1.943 Drawdown pressure 1.942
U
8.86 9.26
7.2 8.44
Follow the workflow on the next page
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Exercises 16.7 Time-lapse exercise
The aim of the execise is to calcualte the Vp Rho for each of the time lapse scenarios (a-g) in the table below and to compare the AI change
Workflow 1. Open Ex_7_time_lapse.rok 2. Select 'blocky ops' 3. Then 'Fluid sub (gassmann)' 4. Click on dry model input and input the relevant dry model values 5. For minerals - select Ex 7 minerals set 6. Set proportions to quartz=0.8 shale=0.2 7. For Fluids - click on the 'advanced' button 8. Input relevant saturation 9. Select mixing mode (woods for all sceanrios except 'g') select final fluids set (original or drawdiown) 10. Hit the calculate button 11. Document the Vp and rhob in the tale below Repeat this for each of the scenarios (note that for scenario g - a Brie mixing of 2 should be used) Calculate the percentage change in AI for the fluid and pressure only cases as well as the f1uid+pressure cases. (The formulae for calculating the AI change are shown on the far right column of the table).
a b
c
w B=2
24
de
~g
original pressure Sw Vp rhob 1., /1 1 ~Z% 0.15 :>0'1( V~ 0.8 y.l.(:I 'Z .1 ~ drawdown
""'-----""11
• 0
0 ·1'.8~
.
AI
%AI change
only 1-ITIPonIf '+-0'10
6123
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0C-b)/b}100
~
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+O~IY ~~~~:'~~000
. .
© Rock Physics Associates Ltd 2005
f+P
(d-a)/a*100
(g-b )/b*1 00
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Exercises 16.7 Anisotropy exercise
16.8 Anisotropy (VTI) exercise The aim of the execise is to calculate the Vp Rho for each of the time lapse scenarios (a-g) in the table below and to compare the AI change
A A False Negative Effect of VTI ?
B
A False Positive
C
West of Shetland false positive - Margeson et al1999
o Emphasising a positive AVO signature shale oil sand
2.438 2.953
1.006 1.774
RokDoc average sets Name Shale A Gas sandA Shale B Brine sand B TutrC Shale C Shale D Oil sand D
V~Mean
2.35 1.81 2.499 2.393 3.495 3.141 2.438 2953
VsMean 0.97 1.13 0.982 1.097 1.663 1.561 1006 1.774
RhoMean 22 1.71 2.24 2.083 2.1
24 2.25 2.038
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Exercises 16.8 Anistropy exercise
Workflow 1. Open Ex_8_anisotropy 2. Go into 'Blocky Ops' , 'AVO' 3. Select 'Get Averages' 4. Highlight the averages for a particular scenario and click 'OK 5. Click on the 'show advanced' toggle 6. Use the scroll buttons at the top to scroll to the right to the 'Anisotropy' tab 7. Input the anisotropic parameters delta (is) and epsilon (E) (gamma =0) 8. Specify the interfaces (eg shale on gas sand) 9. Specify interfaces 10. Click on update model 12. Draw out the responses on the crossplots below 13. Repeat this workflow for each of the scenarios
False negative? Shale on gas sand
B
A
False positive shale on brine sand
0-r----+--~--'---~-___t
O,+-----..--~-____<>__-~-_____+
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False positive tuff on shale
Enhanced positive shaie on oil sand
o
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.... ...'±.--".---,:-----,c----r--±
26
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© Rock Physics Associates Ltd 2005
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GEOSCIENCE e.. . . .., ALLIANCE TRAINING
Professional Level Rock Physics for Seismic Amplitude Interpretation
~l,
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17. Exercises - Answers
Rock Physics Associates
Contents 16.1 Quick look workflow 16.2 Log conditioning and modelling workflow 16.3 Forward modelling using Xu-White 16.4 20 AVO modelling lithology and fluid 16.5 Elastic inversion interpretation exercise 16.6 Rock physics and probability 16.7 Time lapse exercise 16.8 Anisotropy scenarios
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Exercises - Answers
26
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Exercises - Answers 16.1 Quick-look Workflow
16.1 Quick-look workflow (Well H) Calculated Fluids
Final Vp Vs and Rho Table
Vp Shale A Sand A brine Sand A oil Shale B Sand B brine Sand Boil
Rho
Vs
2650 2900 2730 2800 2820 2624
1172 1457 1471 1288 1387 1397
2.22 2.18 2.14 2.30 2.23 2.20
AVA Plot 02+--~--~-~~-~-----t
-
8hale Aon SandA brine
-ShaleAon Sand A 011 -
0-15
0.1
SandA 011 on SandA brine
-
Shale Bon Sand Bbrine
-
Sllale B on Sand B011
SaM B 011 on 8.M B brine
Near
'0<
-0.15
-O.2±o--"-----",-----.,,-----,,.------± ;;
Sln(lhela)2
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©Rock Physics Associates Ltd 2005
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Exercises - Answers 16.1 Quick-look workflow
Offset Angle Data
Incidence Plot
0 0
0 0
o.
'"
0 0
"'.
0 0 0
N
0 0
'"
N
0 0 0
M
0;-
'"~
'" '"
~
'" '"'" '" '<:;
C. c
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Angle Otl'sel (m) 0° 0.0
30
10" 20" 30" 40" 50"
20
u
C
"C
S
10
604.0 1224.0 1880.0 2594.0 3398.0
0
QC ray tracing Otl'sel:
b500 J
m
Incidence angle: 24.5
Responses at 25 degrees
Top Top Top Top
of Sand A brine filled - Class I Sand A oil filled - Class II Sand B brine filled - Class II Sand B oil filled - Class III
On far stack (25') would expect Top Sand A phase reversal from brine to oil fill Top Sand B - bright spots associated with presence
28
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AI
N I N G
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Exercises - Answers 16.2 Log workflow
16.2 Log conditioning and modelling workflow
VsQC
Poisson ratio logs and crossplots of Vp an Vs show that in general the data are good, although a section at the top of the log is clearly in error. In this instance straight line Vp vs Vs transforms were calculated for the various sections down the log giving the Vs_pred log.
Estimation of Invaded Zone Saturation
On the basis of the resistivity logs and the fiuid density calculated from the regression of core porosity and density there appears to be an invasion effect on the density logs. A correction ees to be applied to the density log. Gassmann inversion to dry rock parameters
Inverting the log data for the dry rock properties gives good result - therefore there is no issue with inconsistencies betwen the various logs. Similar results are obtained whether the sonic is assumed to be invaded or not. AVO signature
The 2D model is a powerful tool for the interpreter. It illustrates interference effects, shows how the AVA response can be highly sensitive to incidence angle and frequency and it can be used to evaluate the effects of various band limited impedance and elastic parameter projections.
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Exercises - Answers 16.3 Forward modelling using Xu-White
16.3 Forward modelling using Xu-White There is a reasonable fit to the data using the ellipsoid pore geometry with aspect ratio of 0.1 for both clays and quartz. Notice that the shear velocity predicted is significantly higher than the Greenberg-Castagna prediction (an appropriate approach in this area) - the reason for this is that the dry rock moduli in Xu-White always tend to be slightly low. Forward modelling is a highly unconstrained problem - many assumptions have to be made about moduli and other inputs. Whilst model parameters may have aphysical sugnificance they are really just tools for matching the data. Models with increased complexity are unlikely to be any more accurate.
MD(m)
OR_Track Volumes Por and Sat Vp_Track Vs_Track Rho_Track GR (APQ UTHOLOGY PHIT (fracQ V. )IJN (mI,) VU(W (mI,) R~flI (gIC 3) : M().lVDss 0.0 - - '50.0 0.0 - - - 1.0 0.0 - - - 0.' 2000.U - 6000.0500.0-- 2500.0 1.' - - .g5 V~ (mI,) V'-GC (mI') hO (glcm3 :1VOss· 2000.0 - 0000.0 500.0-- 2500.0 1.45 - - .95
1
2.200 2.250 2.300 2,350 2,400
2.'50 2.500 2,550 2,600 2,650 2,700 2,750 2.800
30
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Exercises - Answers 16.4 2D AVO modelling - lithology and fluid
16.4 20 AVA modelling - lithology and fluid Responses at 25 degrees The exercise illustrates the value in performing 2D modelling to help inform the interpreter about amplitude variations related to different causes
T,~
1900
1950 2000 2
2100 ~
E
?
2200 2250
2300 2350 2400
10
T,~
20
JO
60
1900
Dimming due to hydrocarbons 1950
_: . ::rlJ :
-lTlflHlllTl
2000 2050 2100
2200 2250 2300 2350
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Exercises - Answers 16.5 Elastic inversion interpretation exercise
16.5 Elastic inversion interpretation exercise The data in the prospect are clearly uncalibrated. The inversion cannot be used as a quantitative predictor of fluid and porosity. The main reason is the effect of an amplitude shadow above the prospect (noise on near offsets) - other potential reasons why these types of inversions may be uncalibrated include misalignment between nears and fars and scaling problems with well ties.
AI
EI25
well Location 1 Location 2
10000 9500 9000
PR
AVOI
0.21 0.23 -0.4
4.8
2310 2229 1915
-0.01 224
AVOI Map
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·20
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.... . ...
.... . "
..... ",
+ . --"
..'.... Dry well
....
32
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© Rock Physics Associates Ltd 2005
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Exercises - Answers 16.6a Introducing fuzzy logic
16.6a Facies discrimination with two variables - using fuzzy logic with a test data set If the facies have discrete clusters on the crossplot then fuzzy logic will be able to predict the facies using the two variables even though each variable has overlap in the facies distributions. Notice in the diagram below how the winner category mirrors the actual facies category.
~ RokDoc Well Viewer lStIdt
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©Rock Physics Associates Ltd 2005
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Exercises - Answers 16.6b Acoustic facies discrimination using fuzzy logic
16.6b Acoustic facies discrimination using fuzzy logic Below are some documented results using particular attributes and combinations of attributes.
AVOI and AI
AI only
Cross VaHdatlon ResuKs
Cross VaUdatlon Results Exact: Second: Mls·hK:
TOTAL:
477 173 83 733
Cross VaUdatlon Results 65.08% 23.6% 11.32% 100.0%
Poisson Ratio
TOTAL:
691 41 1 733
Second:
MIs-hil :
TOTAL:
34
Exact: 97.54% 2.46%
Exact :
Secood:
100.0%
TOTAL:
IoIls-hK:
0.0'/0
701 29 3 733
TOTAl:
0
3.41% 0.0'10
733
100.0'10
cross VaHdatlon Results
95.63% 3.08'10 0.41'10 100.0'10
MR only
Exact : Second: M1s·hK :
96.59'10
LIM only
381 272 80 733
I
Exact: Second:
688 38
Mls·hll:
7
TOTAL:
733
93.86'10 5.18'10 0.95'10 100.0'10
LIM and LR Cross Validation ResuKs
Cross Validation Results 95.36'10 4.5'10 0.14% 100.0'10
708 25
Second: Mls·hll: TOTAL:
100.0%
cross Validation Results
Cross Validation Results 699 33 1 733
715 18 0 733
TOTAL:
94.27% 5.59% 0.14%
AI and Poisson Ratio Exact :
Exact : Second: Mls·hK:
LR only
Cross Validation Results Exact: Second: Mls·hK:
LR and MR
51.98'10
37.11°,4 10.91'10 100.0'10
© Rock Physics Associates Ltd 2005
Exact : Second : M1s·hK:
721 10 2 733
TOTAl:
98.36% 1.36'10 0.27% 100.0'10
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Exercises - Answers 16.6b Effect of low gas saturation on elastic attributes
16.6c Effect of low gas saturation on elastic attributes There is no difference in discrimination of gas sands and low saturation gas sands on basis of density vs AVOImpedance. However in terms of density reflectivity there will be important differences - there will be no difference between density reflectivity of brine sands and fizz sands but there will be a significant difference between fizz sands and gas sands.
:!
:l
"'00
•N
::l
N
1,400
Brine sand
1,200
1,200
Gas sand Fizz sand
1.000
I
Shale
t,OOO
BOO
\
600
// '" -------
'00 200
.
0
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200 ~.
::l
~
rhob
~
!!
~
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~
!!
t,400
1,400
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Shale
1,200
Bri e sand
1.000
I
BOO 600
I 200
~
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~
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-600
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~
AVOI
©Rock Physics Associates Ltd 2005
35
., I
Exercises - Answers 16.7 Time lapse exercise
16.7 Time-lapse exercise
Sw a b c
1 0.15 0.8
d e f g
1 0.15 0.8 0.8
original pressure Vp rhob AI 3236 2.191 3064 2.129 3147 2.176 drawdown 3354 2.187 3179 2.124 2.172 3241 2.172 3290
%AI change 7090 6523 6848
5.01 f only
(c-b )/b*1 00
7335 6752 7039 7146
3.5 3.5 7.9 9.5
p only p only f+P f+P
(d-a)/a*100 (e-b )/b*1 00 (f-b)/b*100 (g-b )/b*1 00
Note that a combination of 'patchy' fluid mixing and stiffening of the rock frame during drawdown gives an effect (~10% difference in AI) which is nearly double that if only the fluid parameters are changed.
36
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Exercises - Answers 16.8 Anisotropy exercise
16.8 Anistotropy (VTI) exercise
False negative? Shale on gas sand
-
.,
__..c. ....,, _ _
.-,.
a _ _ AOIlGoo_A
__
.
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-
. --.
I _.
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Enhanced positive shale on oil sand
o - ,..c.. _c _ _ --,..e.. _c _ _
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~
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,,+--~-~-~-~-...,
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B
A
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©Rock Physics Associates Ltd 2005
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37
Professional Level Rock Physics for Seismic Amplitude Interpretation 18. References
Rock Physics Associates
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© Rock Physics Associates Ltd 2006
References Sections 1 and 2
Section 1 Luchford, J., 2001. A view of amplitude fit to structure as a hydrocarbon-indicating attribute. First break, 19 (7) 411-417
Section 2 Aki, K. and Richards, P.G., 1980. Quantitative Seismology. W.H.Freeman and Co. AI-Chalabi, M., 1974. An analysis of stacking, rms, average and interval velocitiesover a horizontally layered ground. Geophysical Prospecting, 22, 458-475. Bortfeld, R., 1961. Approximation to the reflection and transmission coefficients of plane longitudinal and transverse waves. Geophysical Prospecting, 9, 485-503. Connolly, P., 1998. Calibration and inversion of non-zero offset seismic. SEG abstracts. Dix, C.H., 1955. Seimsic velocities from surface measurements. Geophysics, 20, 68-86 Dobrin, M.B., 1976. Introduction to Geophysical Prospecting. McGraw-Hili 3rd Edition 630pp Hilterman, F., 2001. Seismic amplitude interpretation. SEG/EAGE Distinguished instructor short course No 4. Philipps, O.M., 1968. Heart of the earth, Freeman & Co. Sheriff, R.E., 1975. Factors affecting seismic amplitudes. Geophysical Prospecting 23, 125-138. Shuey R T 1985. A simplification of the Zoeppritz eqautions. Geophysics 50, 609-614 Yilmaz, 0., 1987. Seismic data processing. Soc Exp Geoph, Investigations in Geophysics series Zoeppritz, K., 1919. Erdbebenwellen VIIIB. On the reflection and propogation of seismic waves. Gottinger Nachrichten, I, 66-84.
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References Section 3
Section 3 Avseth, P. 2000. Combining rock physics and sedimentology for seismic reservoir characterisation of north sea turbidite systems. Stanford Univ. PhD thesis. Avseth, P, Mukerji, T and G. Mavko, 2005. Quantitative seismic interpretation. Cambridge University Press 3S9pp.
Castagna, J.P. & Swan, H.W., 1997. Principles of AVO crossplotting. The Leading Edge, April, 337-342.
Castagna, J.P. et al ,1993. AVO analysis - tutorial and review, & Rock Physics - The link between rock properties and AVO response. In l.P.Castagna and M.M.Backus (Eds), Offset Dependent Reflectivity - Theory and Practice of AVO Analysis. Investigations in Geophysics No.8, Society of Exploration Geophysicists, p135-174. Chiburis, E.F., 1992. Anaiysis of amplitude versus offset to detect gas/oil contacts in the Arabian Gulf: Presented at the 54th Ann. Intnl. Mtg. Soc. Exp. Geophys., Atlanta Dvorkin, J., Mavko, G., and Nur, A., 1999. Overpressure detection from compressional- and shear-wave data, Geophysical Research Letters, 26, 3417-3420.
Dvorkin, J. Gutierrez, M.A., and Nur, A., 2002. On the universality of diagenetic trends. Leading Edge 21, 40.
Eberli, G.P., Baechle, G.P., Anselmetti, F.S. and Incze, M.L., 2003. Factors controlling elastic properties in carbonate sediments and rocks. The Leading Edge 22, 654. Foster, D.J, Smith, S.W., Dey-Sarkar, S., and Swan, H.W., 1993. A closer look at hydrocarbon indicators. 63rd SEG meeting
Minear, J.W. 1982. Clay models and acoustic velocities: Soc Pet Eng of AIME 57th Ann Tech Conf and Exhib
Li, Y., Downton, J. and Goodway, W., 2003. Recent applications of AVO to carbonate reservoirs in the Western Canadian Sedimentary Basin. The Leading Edge 22, 670. Marion, D, Nur, A., Yin, H., & Han, D. 1992. Compressional velocity and porosity of sand-clay mixtures. Geophysics, 57, 554-563.
Ross, C.P. & Kinman, D.L., 1995. Nonbright-spot AVO: Two examples. Geophysics, 60, 13981408
Rutherford, S.R. & Williams, R.H., 1989. Amplitude versus offset variations in gas sands. Geophysics, 54, 680-688 .
.:$")/o! GEOSCIENCE T R A I N I N G ~_
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References Sections 3, 4 and 5
Sams, M and Andrea, M., 2001. The effect of clay distribution on the elastic properties of sandstones. Geophysical Prospecting, 49, 128-150. Yongi Li, Downton, J. & Goodway, B., 2003. Recent applications of AVO to carbonate reservoirs in the Western Canadian Sedimentary Basin. The Leading Edge 22, 670
Section 4 Campbell, S.J. & Gravdal, N., 1995. The prediction of high porosity chalks in the East Hod field. Petroleum Geoscience, 1, 57-70. Cowan, G., Swallow, J., Charalambides, P., Lynch, 5. , Dearlove, M. , Sobhani, K. , Nashaat, M., Loudon, E. , Maddox, S. , Coolen, P. , & Houston,R . 1998: The Rosetta Pi Field: a fast track development case study, Nile Delta, Egypt. 14th Egyptian General Petroleum Company Conference, Cairo, Egypt. Gregory, A.R., 1977. Aspects of rock physics from laboratory and log data are important to seismic interpretation. In Seismic Stratigraphy - applications to hydrocarbon exploration. AAPG memoir 26, Ed C.E.Payton. Luchford, J., 2001. A view of amplitude fit to structure as a hydrocarbon-indicating attribute. First break, 19 (7) 411-417 Newton, S.K. and Flanagan, K.P., 1993. The Alba Field: evolution of the depositional model. In: Petroleum Geology of Northwest Europe, Proceedings of the 4th Conference (ed. J.R. Parker), Geological Society of London, p.161-171. Ozdemir, H., Jensen,L. and Strudley, 1992. Porosity and lithology mapping from seismic data, EAGE Paris. Pearce, C.H.J. & Ozdemir, H. The Hod Field: chalk reservoir delineation from 3D seismic data using amplitude mapping and seismic inversion.
Section 5 Blache-Fraser, G. and J. Neep, 2004. Increasing seismic resolution using spectral blueing and colored inversion: Cannonball Field, Trinidad. SEG abstracts Walden, A.T and Hosken, J.W.J., 1985. An investigation of the spectral properties of primary reflection coefficients. Geophysical Prospecting, 33, 400-435.
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References Sections 6 and 7
Section 6 Archer, S.H., King, G.A., Seymour, R.H. & Uden, R.C., 1993. Seismic reservoir monitoring
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1035-104 Koefoed, 0., 1981. Aspects of vertical seismic resolution. Geophysical Prospecting, 29, 21-20 Lindsey J P 1989. The fresnel zone and its interpretational significance. The Leading Edge
October Sheriff, R. E. 1977. Limitations on resolution of seismic reflections and geologic detail derivable from them. In Seismic Stratigraphy - applications to hydrocarbon exploration. AAPG memoir 26,
C.E.Payton Ed, p3-14 Widnes, M.B., 1973. How thin is a thin bed? Geophysics, 38, 1176-1180.
Section 7 Neidell, N.S. & Poggliagliolmi, E. 1977. Stratigraphic modelling and interpretation geophysical principles and techniques. In Seismic Stratigraphy - applications to hydrocarbon
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lines for phase analysis. The Leading Edge July 774-777. Simm, R.W. & White, R., 2002. Phase, polarity and the interpreters wavelet (tutorial). First
Break, 20, 277-281. Simm, R.W., Xu, S. & White, R.E, 1999. Rock physics and quantitative wavelet estimation for seismic interpretation: Tertiary North Sea. In 'Petroleum Geology of Northwest Europe: Proceedings of the 5th Conference'. Eds A.J.Fleet and S.A.R.Boldy. Geological Society of London, p1265-1270. White R.E. 1980. Partial coherence matching of synthetic seismograms with seismic traces.
Geophysical Prospecting, 28, 333-358 White, R. E. and Simm, R.W., 2003. Tutorial - good practice in well ties. First Break 21, 75-83.
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Section 8 Alberty, M. 1989. The influence of the borehole environment upon compressional sonic logs. SPWLA 35th Ann. Logging Symp., June 19-22, 1994 Avseth, P., Mukerji, T. And Mavko, G., 2005. Quantitative seismic interpretation, by. (Cambridge University Press 2005). Batzle, M.L. & Z.Wang, 1992. Seismic properties of pore fluids. Geophysics, 57, 1396-1408. Baker, L.J., 1984. The effect of the invaded zone on full wavetrain acoustic logging. Geophysics, 49, 796-809. Biot, M.A., 1962. Mechanics of deformation and acoustic propogation in porous media. J.AppI.Phys., 33, 1482-1498. Blakeman, E.R., 1982. A case study of the effect of shale alteration on sonic transit times. SPWLA 23" Ann. Symp. Trans. Paper II, 1-14. 8ox., R. and Lowrey, P., 2003. Reconciling sonic logs with checks hot surveys: Stretching synthetic seismograms. TLE, June p51O-517 8ox, R., Maxwell, L., Loren, D., 2004. Excellent synthetic seismograms through the use of edited logs: Lake Borgne Area, Louisiana, U.S. The Leading Edge, March, 218-224. 8rie, A., Pampuri, F., Marsala, A.F. & Meazza, 0., 1995. Shear sonic interpretation in gas bearing sands. SPE 30595 Burch, D., 2002. Seismic to well ties with problematic sonic logs. AAPG Explorer, Part 1 February, Part 2 March. Castagna, J.P., 8atzle, M.L. & Eastwood, R.L., 1985. Relationships between compressionalwave and shear-wave velocities in clastic silicate rocks. Geophysics, 50, 571-581. Castagna, J.P. et al ,1993. AVO analysis - tutorial and review, & Rock Physics - The link between rock properties and AVO response. In J.P.Castagna and M.M.Backus (Eds), Offset Dependent ReflectiVity - Theory and Practice of AVO Analysis. Investigations in Geophysics No.8, Society of Exploration Geophysicists, p135-174. Clark, V.A., 1992. The effect of oil under in-situ conditions on the seismic properties of rocks. Geophysics, 57, p894-901. Cuddy,S., 1998. The application of the mathematics of fuzzy logic to the geosciences. SPE 49470. Dewan, J.T., 1983. Essentials of modern open-hole log interpretation. Pennwell publishing, 361pp
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Domenico, S.N., 1974. Effect of water saturation on seismic reflectivity of sand reservoirs encased in shale. Geophysics, 39, 759-769. Domenico, S.N., 1976. Effect of brine-gas mixture on velocity in an unconsolidated sand reservoir. Geophysics, 41, 882-894 Domenico, S.N.,1977. Elastic properties of unconsolidated porous sand reservoirs. Geophysics, 42, 1339-1368 Dvorkin, J Gutierrez and Nur, A., 2002. On the universality of diagenetic trends. The Leading Edge. January 40-43 Dvorkin and Nur, 1996. Elasticity of high porosity sandstones: Theory for two North Sea datasets. Geophysics, 61, 1363-1370. Dvorkin, J., Wall, J., Uden, R., Carr, M., Smith, M. and Derzhi, N., 2004. Lithology substitution in fluvial sand. The Leading Edge 23, 108-112. Faust, L.Y. 1951. Seismic velocity as a function of depth and geologic time. Geophysics, 16, 192206. Gardner, G.H.F, Gardner, L.W. and Gregory, A.R., 1974. Formation velocity and density: the diagnostic for stratigraphic traps. Geophysics, 39, 770-780. Gassmann, F., 1951. Elastic waves through a packing of spheres. Geophysics, 16, 673-685. Geertsma, J and Smit, D.C., 1961. Some aspects of elastic wave propogation in fluid saturated porous solids. Geophysics, 26, 169-181. Gist, G.A., 1994. Interpreting laboratory velocity measurements in partially gas-saturated rocks. Geophysics, 59, 1100-1109. Greenberg M L and Castagna J P 1992 Shear wave velocity estimation in porous rocks: Theoretical formulation, preliminary verification and applications. Geophysical Prospecting 40 195209 Gregory, A.R., 1977. Aspects of rock physics from laboratory and log data are important to seismic interpretation. In Seismic Stratigraphy - applications to hydrocarbon exploration. AAPG memoir 26, Ed C.E.Payton Guttierez, M.A., 2002. Stratigraphy guided rock physics. TLE January, 98-103. Hampson-Russell, AVO software documentation Han, D-H., and Batzle, M., 2002. Fizz water and low gas saturated reservoirs. TLE 395-398. Han, D-H., & Batzle, M., 1999. Fluid invasion effects on sonic interpretation. SEG abstracts. ~l!J. GEOSCIENCE
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Han, D-H., & Batzle, M., 2000. Velocity, density and modulus of hydrocarbon fluids - data
measurement. SEG abstracts. Han, D-H, Nur, A. & Morgan, D. ,1986. Effect of porosity and clay content on wave velocity in sandstones. Geophysics, 51, 2093-2107. Hashin, z. and Shtrikman, 5., 1963. A variational approach to the elastic behaviour of multiphase minerals. J. Mech. Phys. Solids, 11, 127-140
Hill, R. 1952. The elastic behaviour of a crystalline aggregate. Proc Phys Soc London A65 349-354 Hilterman, F., 1990. Is AVO the seismic signature of lithology? A case history of Ship Shoal South
Addition. The Leading Edge, June, 15-22. Knight, R., & Nolen-Hoeksema, R. 1990. A laboratory study of the dependence of elastic wave velocities on pore scale fluid distribution. Geophys. Res. Lett, 17, 1529-1532. Knight, R., Dvorkin, l & Nur, A. 1998. Acoustic signatures of partial saturation. Geophysics 63,
132-138. Kozak, M., Kozak, M. and Williams, l., 2006. Identification of mixed acoustic modes in the dipole full waveform data using instantaneous frequency-slowness method. SPWLA 47 th Ann. Logging Symp., June. Krief, M., Garat, l., Stelingwerf, l. & Ventre, l., 1990. A petrophysical interpretation using the
velocities of P- and S-waves (full waveform sonic). The Log Analyst, 31, 355-369. Kuster, G.T., and Toksoz, M.N., 1974. Velocity and attenuation of seismic waves in two-phase media: Part 1. Theoretical formulation. Geophysics, 39, 587-606. Leiphart, D.l., & Hart, B.S., 2001. Comparison of linear regression and a probabilistic neural
network to predict porosity from 3D seismic attributes in Lower Brushy Canyon channelised sandstones, southeast New Mexico. Geophysics, 66, 1349-1358. Marion, D and lizba, D. 1997 Acoustic Properties of Carbonate Rocks: use in quantitative interpretation of sonic and seismic measurements. in 'Carbonate Seismology', Geophys. Dev. Series
No6 Ed I.Palaz & K.J.Markurt, SEG Mavko, G. and Mukerji, T., 1995. Seismic pore space compressibility and Gassman's relation.
Geophysics, 60,1743-1749 Mavko, G., Mukerji, T. & Dvorkin, l. 1998. The Handbook of Rock Physics. Cambridge University Press. Mavko, G., Chan, C. & Mukerji, T., 1995. Fluid substitution: estimating changes in Vp without
knowing Vs. Geophysics, 60, 1750-1755.
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Mavko, G. & Jizba, D. 1991. Estimating grain scale fluid effects on velocity dispersion in rocks.
Geophysics, 56, 1750-1755. Mukerji, T., Jorstad, A., Avseth, P, Mavko, G., & Granli, J.R., 2001. Mapping lithofacies and
pore-fluid probabilities in a North Sea resrevoir: seismic inversions and statistical rock physics. Geophysics, 66, 988-1001. Mukerji, T., Avseth, P. & Mavko, G. 2001. Statistical rock physics: combining rock physics,
information theory, and geostatistics to reduce uncertainty in seismic reservoir characterisation. Leading Edge March, p 313-319. Murphy, W., Reischer, A. & Hsu, K., 1993. Modulus decomposition of compressional and shear velocities in sand bodies. Geophysics, 58, 227-239. Nur, A., 1992. Critical porosity and the seismic velocities in rocks. EOS, Transactions of the American Geophysical Union, 73, 43-66. Nur, A., 1992. Critical porosity and the seismic velocities in rocks. EOS, Transactions of the American Geophysical Union, 73, 43-66. Nur A., Mavko G Dvorkin J & Galmudi 0 1998 Criticai porosity: a key to relating physical properties to porosity in rocks. The leading edge March Rafavich, F, Kendall, C.H. St. C. and T P Todd. 1984. The relationship between acoustic properties and the petrographic character of carbonate rocks. Geophysics, 1622-1636 Raymer, L.L., Hunt, E.R. & Gardner, J.S., 1980. An improved sonic transit time-to-porosity transform. 21st Ann Log Symp, SPWLA. Sams, M.S and Andrea, M., 2001. The effect of clay distribution on the elastic properties of sandstones. Geophys. Prosp., 49, 128-150. Schlumberger, 1994. DSI Dipole Shear Sonic Imager. Simm, R.W., Xu, S. & White, R.W., 1997. Rock Physics and Quantitative Wavelet Estimation for Seismic Interpretation: Tertiary North Sea. Petroleum Geology of Northwest Europe Conference. Simmons, G. & Wang, H., 1971. Single crystal elastic constants and calculated aggregate properties: Kichigan Inst of Tech. Press Cambs. Mass. Skelt C 2004a The influence of shale distribution on the sensitivity of compressional slowness to reservoir fluid changes. SPWLA 45 th Annual Logging Symposium June 6-9 Skelt, C 2004b Fluid substitution in laminated sands. TLE 485-493. Smith T M Sondergeld CHand Rai C S, 2003. Gassmann fluid substitution: A tutorial. Geophysics 68 430-440
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Spencer, J.W., Cates, M.E., & Thompson, D.O., 1994. Frame moduli of unconsolidated sands and sandstones. Geophysics, 59, 1352-1361. Tutuncu, A.N. and Sharma, M.M.,1992. Relating static and ultrasonic laboratory measurements
to acoustic log measurements in tight gas sands. SPE 24689 Vasquez, G.F., Dillon, L.D., Varela, C.L., Neto, G.S., Velloso, R.Q. and Nunes, C.F., 2004. Elastic log editing and alternative invasion correction methods. The Leading Edge, January, 20-25. Vernik, L. & Nur, A., 1992. Petrophysicai classification of siliclastics for lithology and porosity
prediction from seismic velocities. AAPG Bull, 76, 1295-1309 Vernik, L., 1998. Acoustic velocity and porosity systematics in siliclastics. The Log Analyst, JulyAugust, 27-35 Wan9 Z, Wang H and Cates M E 2001 Effective elastic properties of solid clays. Geophysics 66
428-440. Wang, Z. & Nur, A., 1992. Elastic wave velocities in porous media: A theoretical recipe. In Seismic and Acoustic Velocities in Reservoir Rocks, vol 2, SEG Geophysics Reprint series no. 10. Wang, Z., 2001. Fundamentals of seismic rock physics. Geophysics, 66, 398-412. Walls, J.D. and Carr, M B 2001. The use of fluid substitution modelling for correction of mud filtrate invasion in sandstone reservoirs. SEG abstracts. Wang, Z. & Nur, A., 1992. Elastic wave velocities in porous media: A theoretical recipe. In
Seismic and Acoustic Velocities in Reservoir Rocks, vol 2, SEG Geophysics Reprint series no. 10 Williams, D.M., 1990. The Acoustic Log Hydrocarbon Indicator. SPWLA, 31st Ann. Logg. Symp.,
June 24-27 Winkler, K.W. 1986. Estimates of velocity dispersion between seismic and ultrasonic frequencies. Geophysics, 51, 183-189. Wyllie, M.R.J., Gregory, A.R., & Gardner, G.H.F., 1958. An experimental investigation of factors affecting elastic wave velocities in porous media. Geophysics, 28, 459-493. Xu, S. & White, R., 1996. A physical model for shear-wave prediction. Geophysical Prospecting, 44,687-717 Xu, S. & White, R.E., 1995. A new velocity model for clay-sand mixtures. Geophysical
Prospecting, 43, 91-118. Zimmer M, Prasad M and G Mavko, 2002. Pressure and porosity influences on VpVs ratio of
unconsolidated sands. TLE. 21, 178 10
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Section 9 Gratwick, D and Finn, C., 2005. What's important in making far-stack well-to-seismic ties in West Africa. TLE, July, 739-745
Hall, D.l., Adamick, l.A., Skoyles, D., DeWoldt, l, & Erickson, l., 1995. AVO as an exploration tool: Gulf of Mexico case studies and examples. The Leading Edge, 14, 863-870. Simmons, l.L. & Backus, M.M., 1994. AVO modelling and the locally converted shear wave. Geophysics, 59, 1237-1248.
Section 10 Kleyn, A.H .. 1983. Reflection Seismic Interpretation. Applied Science Publishers Lancaster, S. and Whitcombe, D., 2000. Fast-track 'coloured' inversion. SEG Calgary. Ozdemir, H., lensen,L. and 5trudley, 1992. Porosity and Iithoiogy mapping from seismic data, EAGE Paris.
Simm, R.W., Batten, A., Dhanani, S. & Kantorowicz, l. 1986. Fluid effects on seismic: Forties sandstone member - Arbroath and Montrose Fields, Central North Sea, UKCS. NPF Biennial Geophysical Seminar - Geophysics for Lithology - 8, Kristiansand, Norway, 11-13 March.
Veeken, P.C.H and M. Da Silva, 2004. Seismic Inversion methods and some of their constraints. First Break, 47-70.
Waters, K., 1978. Reflection Seismology. J.Wiley & Sons, pp. 218-233.
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Section 11 Aki, K. and Richards, P.G., 1980. Quantitative Seismology. W.H.Freeman and Co. Allen, J.L. & Peddy, C.P., 1993. Amplitude variation with offset: Gulf Coast case studies. SEG Geophysical Developments Series, vol 4, Ed Franklyn K Levin. Cambois, G. 2001 AVO Processing: myths and reality SEG Expanded Abstracts 20, 189 (2001) Castagna, J.P. and Smith, S.W. 1994. Comparison of AVO Indicators: A modelling study. Geophysics, 59, 1849-1855 Castagna, J.P. and H.W.Swan, 1997. Principles of AVO crossplotting. TLE. 337 Castoro, A. 1998. Mapping reservoir properties through pre-stack seismic attribute analysis. PhD Univ of London. Chiburis, E.F., 1987. Studies of Amplitude Versus Offset in Saudi Arabia, SEG abstracts. Chiburis E, Franck C, Leaney 5, McHugo 5 and. Skidmore C 1993: "Hydrocarbon Detection With AVO:'. Oilfield Review 5, January: 42-50. Connolly, P., 1999. Elastic impedance. The Leading Edge, April, 438-452. Connolly, P. 2005, Net pay estimation from seismic attributes. Paper T-15 EAGE conference 2005 Downton, J.E and Lines, L.R., 2002 AVO before NMO. SEG abstract Fatti, J.L., Smith, G.C., Vail, P.J., Strauss, P.J. and Levitt, P.R., 1994. Detection of gas in sandstone reservoirs using AVO analysis: A 3D seismic case history using the Geostack technique. Geophysics, 59, 1362-1376. Gidlow, P.M., Smith, G.C. and Vail, P.J., 1992. Hydrocarbon detection using fluid factor traces: A case history. Expanded abstracts Joint SEG/EAEG Summer Workshop on 'How useful is Amplitude vsersus Offset (AVO) analysis?' 78-89. Goodway, B., 2002. Elastic-wave AVO methods. CSEG abs Goodway, W., Chen, T., Downton, J. 1997. Improved AVO fluid detection and lithology discrimination using Lame petrophysical parameters; Ir, mr and 11m fluid stack from P and S inversions. SEG conference Haskey, P., Pelham, A., Ma, X-Q., Schulte, T., 2000. Optimising the results of pre-stack seismic inversion for discrimination between fluids and lithologies. Petex abstract and ScottPickford Tech note 020. Hendrickson, J., 1999. Stacked. Geophysical Prospecting, 47, 663-706 12
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Hilterman, F.l. 2001 Soc. Expl. Geoph., Distinguished Lecturer Short Coure Monograph Keho, T., 2001. The AVO hodogram: Using polarization to identify anomalies. The Leading Edge, November, 1214-1224. Kelly, M., Skidmore, C., & Ford, D., 2001. AVO inversion, :Isolating rock property contrasts. TLE march and april
Ma, X-Q., 2002. Simultaneous inversion of prestack seisic data for rock peopoerties using simulated annealing. Geophysics, 1877-1885 Maver, K.G, and Rasmussen, K.M., 2004. Simultaneous AVO Inversion for accurate prediction of rock properties. OTC 16925
Mahob, P.N. and Castagna, l.P., 2002. AVO hodograms and polarization attributes. The Leading Edge, January, 18-27.
Mahob, P.N. and Castagna, l.P., 2003. AVO polarization and hodograms: AVO strength and polarization product. Geophysics, 68 (3), 849-862. Margrave, G.F., Stewart, R.R. and Larsen, l.A., 2001. Joint PP and PS seismic inversion. TLE 1048-1052.
Neves, F.A, Mustafa, H.M., and Rutty, P.M., 2004. Pseudo-gamma ray volume from extended elastic impedance inversion for gas exploration. The Leading edge, June 536-540.
Odegaard, E. and P. Avseth, 2004. Well log and seismic data analysis usng rock physics templates. First Break, 37-43
Ross, C.P. & Beale, P.L., 1994. Offset Balancing. Geophysics, 59, 93-101 Roberts, R., Bedingfield, l., Phelps, D., Lau, A.,Godfrey, B., Volterrani, S., Engelmark, F., and Hughes, K., 2005. Hybrid inversion techniques used to derive key elastic parameters: A case study from the Nile Data. The Leading Edge, January, 86-92
Ross, C.P., 1995. Improved mature field development with 3D/AVO technology. First Break, 13, 139-145.
Sams, M., 1998. Yet another perspective on AVO crossplotting. TLE, July. 911-917. Simm, R.W., Xu, S. & White, R.E, 1999. Rock physics and quantitative wavelet estimation for seismic interpretation: Tertiary North Sea. In 'Petroleum Geology of Northwest Europe: Proceedings of the 5th Conference'. Eds A.J.Fleet and S.A.R.Boldy. Geological Society of London, p1265-1270.
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Simm, R.W., White, R.E. & Uden, R., 2000. The Anatomy of AVO Crossplots. The Leading Edge,
February, 150-155 Simm, R.W, Kemper, M., Deo, J. 2002. AVOImpedance: A new attribute for Fluid and Lithology
Discrimination, Petex Conference, London 2002 Smith, G.C. and Gidlow, P.M. 1987. Weighted stacking for rock property estimation and
detection of gas. Geophys. Prosp., 39, 915-942 Smith, G.C. 2003. The fluid factor angle and the crossplot angle. SEG abstracts. Swan, H.W., 1993 Properties of Direct Hydrocarbon Indicators In 'Offset-dependent reflectivity
- Theory and Practice of AVO Analysis', Eds J.P. Castagna and M.M. Backus, SEF Investigations in Geophysics No 8, pp78-92. Swan, H.W., 2001. velocities from amplitude variations with offset Taner, M.T, and Khoehler, F., 1981. Surface consistent corrections, Geophysics, 46,17-22 Verm, R. & Hilterman, F., 1995. Lithology color-coded seismic sections: The Calibration of AVO crossplotting to rock properties. The Leading Edge, August. 847-853. Walden, A.T., 1990. Making AVO sections more robust. EAGE 52nd meeting, Copenghagen Whitcombe, D., 2002 Elastic impedance normalization. Geophysics, 67, 60-62 Whitcombe, D.N, Connolly, P.A., Reagan, R.L. and Redshaw, T.C., 2002. Extended elastic impedance for fluid and lithology prediction. Geophysics, 67, 63-67. Whitcombe, D.N. and Fletcher, J.G., 2001. The AlGI crossplot as an aid to AVO analysis and
calibration. SEG abstracts. White, R.E., 2000. Fluid detection from AVO Inversion: the effects of noise and choice of
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Section 12 Allen, J.L. & Peddy, C.P., 1993. Amplitude variation with offset: Gulf Coast case studies. SEG Geophysical Developments Series, vol 4, Ed Franklyn K Levin Allen, J.L., Peddy, C.P. and Fasnacht, T.L., 1993. Some AVO failures and what (we think) we have learned. TLE 162 Aram, R.B. 1999. West Greenland versus Voring Basin: Comparison of two deepwater frontier exploration plays. In 'Petroleum Geology of Northwest Europe: Proceedings of the 5th Conference'. Eds A.J.Fleet and S.A.R.Boldy. Geological Society of London, p313-324. Birtles, R. 1986. The seismic flats pot and the discovery and delineation of the Troll Field. In
'Habitat of Hydrocarbons on the Norwegian Continental Shelf'. Norwegian Petroleum Society, Graham & Trotman p 207-215. Citron, G. P. and Rose, P. R., 2001. Challenges associated with amplitude-bearing, multiple-zone
prospects. The Leading Edge, 20, 830. Cooper, M. M., Evans, A. C., Lynch, D. J., Neville, G. and Newley, 1999. The Foinaven Field; managing reservoir development uncertainty prior to start up. Petroleum Geology of Northwest Europe. Poc of 5th Conference. The Geological Society. p 675-682. Lamers, E and Carmichael, S.M.M, 1999. The Palaeocene deepwater sandstone play, West of Shetland. In 'Petroleum Geology of Northwest Europe: Proceedings of the 5th Conference'. Eds
A.J.Fleet and S.A.R.Boldy. Geological Society of London, p645-660 Margesson, R. W. and Sondergeld, C. H., 1999. Anisotropy and amplitude versus offset: A case history from the west of Shetlands. Petroleum Geology of Northwest Europe. Poc of 5th Conference. The Geological Society. p 635-644. Rose, P. R., 1999. Taking the risk out of petroleum exploration; the adoption of systematic risk analysis by international corporations during the 1990's. The Leading Edge, 18, 192. Sheriff, R.E., 1975. Factors affecting seismic amplitudes. Geophysical Prospecting 23, 125-138.
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Section 12 Avseth, P., Mukerji, T., & Mavko, G., 2001. Rock physics and avo analysis for lithofacies and pore fluid prediction in a North Sea oil field. The Leading Edge April, p429-434. Backus, G.E., 1962. Long wave elastic anisotopy produced by horizontal layering. J. Geophys. Res. 67, 3327-4440. Cuddy, S., 1998. The application of the mathematics of fuzzy logic to the geosciences. SPE 49470. Doyen, P.M., 1988. Porosity from seismic data: a geostatistical approach. Geophysics, 53, 12631275. Hirsche, K, Porter-Hirsche, J., Mewhort, L.,and Davis, R., 1997. The use and abuse of geostatistics. The Leading Edge, March. p253-360 Kalkomey, C.T., 1997. Potential risks when using seismic attributes as predictorsof reservoir properties. The Leading Edge March, 247-256. Marion, D., Mukerji, T. and Mavko, G., 1994. Scale effects on velocity dispersion: From ray to effective medium theories in stratified media. Geophysics 59, 1613. Francis, A., 1997. Acoustic impedance inversion pitfalls and some fuzzy analysis. The Leading Edge, March. Francis, A" 2002. Deterministic Inversion - Overdue for retirement? Petex Conference, London
Francis, A., 2003 Coloured, deterministic and stochastic inversion. Earthworks Environment and Resources Ltd Technical Note. See http://www.sorviodvnvm.co.uk/pdf/stochasticinversiontechnical note.pdf Trappe, H. & Hellmich, 2000. Using neural networks to predict porosity thickness from 3D seismic. First Break, p 377-384
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Section 13 Boyd-Gorst, J., Fail, P., & Pointing, L., 2001. 4-D time lapse reservoir monitoring of Nelson Field, Central North Sea: Successful use of an integrated rock physics model to predict and track reservoir production. The Leading Edge, December, 1336-1350.
Hansen, L., Davies, D., Garnham, J., McInally, A., & Boyd-Gorst, J. 2001 Time lapse lithology prediction in the Nelson Field. First Break 19.1 Jack, 1.,1997. Time-lapse seismic in reservoir management. 1998 Distinguished Instructor Short Course, Society of Exploration Geophysicists.
Jenkins, S.D., Waite, M.W., and Bee, M.F.,1997. Time lapse monitoring of the Duri steamflood: A pilot and case study. The Leading Edge, September, 1267-1274. Koster, K, Gabriels, P.,Hartung, M, Verbeek, J., Deinum, G., and Staples, R., 2000. Timelapse seismic surveys in the North Sea and their business impact. The Leading Edge, March, 286293
Lumley, D. 1997. Assessing the risk of a 4D seismic project. Leading Edge 16, 1287 MacBeth, C. A classification for the pressure-sensitivity properties of a sandstone rock frame. Geophysics, 69, 497-510.
Marsh, J.M., Whitcombe, D.N., Raikes, S.A., Parr, R.S and T.Nash, 2003. BP's increasing use of time lapse seismic technology. Petroleum Geoscience, 9, 7-13
Sengupta" M. & Mavko, G., 1998. Reducing uncertainties in saturation scales using fluid flow models. SEG abstracts
Wang, Z. 1997. Feasibility of time-lapse seismic reservoir monitoring: The physicsal basis. The Leading Edge, September, 1327-1329
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Section 14 Blangy, J.P., 1994. AVO in transversely isotropic media - an overview. Geophysics 59 (5) 775-781 Chen, H and Castagna, J. 2000. Anisotropic effects on full and partial stacks. Geophysics, 65 (4), 1028-1031
Crampin, S. 1990. The potential of shear wave VSP's for monitoring recovery: a letter to management. TLE SO-52 Dey-Sarker, S.K., and Svatek, S.A., 1992. Amplitude vs offset analysis: some basic concepts. Jnt SEG/EAGE summer research workshop Big Sky Montana (How useful is amplitude versus offset (AVO) analysis). 292-303. Hall, S., Kendall., J-M., and Barved, O.L., 2002. Fractured reservoir characterisation using P wave AVOA analysis of 3D aBC data. TLE 777-782
Hawkins, K., Leggott, R., Williams, G, Kat, H., 2001. Addressing anisotropy in 3-D prestack depth migration: a case study from the Southern North Sea. TLE, 528-535.
Jenner, E. 2002. Azimuthal AVO: methodology and data examples. TLE 782-786 Leaney, W.S., Miller, D.E.,and Sayers, C., 1995. Fracture induced anisotropy and muitiazimuthal walkaways. 3rd SEGJ/SEG Intnl Symp Nov 8-10 1995. Lynn., H.B., Simon, K.M., Bates., C.R., Layman., M., Schnieder., R., Jones., M. 1995. Use of anisotropy in P-wave and S-wave data for fracture characterization ina naturally fractured reservoir. TLE August 887-893 Macbeth, C. 2002. Multi-component VSP analysis for applied seismic anisotropy. Seismic exploration vol 26. Pergamon
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References Section 14 Rock Physics Associates
Macbeth., C., and Li., X., 1999. AVO - an emerging new marine technology for reservoir characterisation: acquisition and application. Geophysics 64 (4) 1153-1159 Martin., M.A., and Davis., T.L., 1987. Shear wave birefringence: a new tool for evaluating fractured reservoirs. TLE (6) 22-28 Mueller, M., 1992. Using shear waves to predict lateral variability in vertical fracture intensity. TLE 12 39-35 Rowbotham, P., Marion, D., Eden, R., Williamson, P.,Lamy, P., Swaby., P., 2003. The implications of anisotropy for seismic impedance inversion. First Break, 21, 53-57. Ruger, A. 1998. Variation of P-wave reflectivity with offset and azimuth in anisotropic media. Geophysics, 63 (3), 935-947. Ruger A. 1997. P-wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry. Gephysics, 62 (3), 713-722. Ryan-Grigor, 5., 1998. Empirical relationships between anellipticity and Vp/Vs in shales: Potential applications to AVO studies and anisotropic seismic processing. SEG abstracts Ryan-Grigor, 5., 1997. Empirical relationships between transverse isotropy parameters and Vp/ Vs: Implications for AVO. Geophysics, 62 (5) 1359-1364 Samec., P. and Blangy, J.P., 1992. Viscoelastic attenuation, anisotropy and AVO. Geophysics 57 (3) 441-450 Sheriff, R.E., 1975. Factors affecting seismic amplitudes. Geophysical Prospecting 23, 125-138. Sondergeld, C. and Rae, C., 2001. Fundamental seismic rock physics. Course notes. Thomsen, L., 2002. Understanding seismic anisotropy in exploration and exploitation. DISC no 5. SEG/EAGE Thomsen, L., 1986. Weak elastic anisotropy. Geophysics, 51 (10) 1954-1966 Toldi, J, Alkhalifah, T., Aziz, A.,Berthet, P., Arnaud., J., Williamson, P., and Conche., B. 1999. Case study of estimation of anisotropy. TLE may 588-593
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Section 15 Allen, J.L. & Peddy, C.P., 1993. Amplitude variation with offset: Gulf Coast case studies. SEG Geophysical Developments Series, vol 4, Ed Franklyn K Levin Allen, J.L., Peddy, C.P. and Fasnacht, T.L., 1993. Some AVO failures and what (we think) we have learned. TLE 162 Aram, R.B. 1999. West Greenland versus Voring Basin: Comparison of two deepwater frontier exploration plays. In 'Petroleum Geology of Northwest Europe: Proceedings of the 5th Conference'. Eds AJ.Fleet and S.A.R.Boldy. Geological Society of London, p313-324. Birtles, R. 1986. The seismic flatspot and the discovery and delineation of the Troll Fieid. In 'Habitat of Hydrocarbons on the Norwegian Continental Sheif'. Norwegian Petroleum Society, Graham & Trotman p 207-215. Citron, G. P. and Rose, P. R., 2001. Challenges associated with amplitude-bearing, multiple-zone prospects. The Leading Edge, 20, 830. Cooper, M. M., Evans, A. C., Lynch, D. J., Neville, G. and Newley, 1999. The Foinaven Field; managing reservoir development uncertainty prior to start up. Petroleum Geology of Northwest Europe. Poe of 5th Conference. The Geological Society. p 675-682. Lamers, E and Carmichael, S.M.M, 1999. The Palaeocene deepwater sandstone play, West of Shetland. In 'Petroleum Geology of Northwest Europe: Proceedings of the 5th Conference'. Eds A.J.Fleet and S.A.R.Boldy. Geological Society of London, p645-660 Margesson, R. W. and Sondergeld, C. H., 1999. Anisotropy and amplitude versus offset: A case history from the west of Shetlands. Petroleum Geology of Northwest Europe. Poe of 5th Conference. The Geological Society. p 635-644. Rose, P. R., 1999. Taking the risk out of petroleum exploration; the adoption of systematic risk analysis by international corporations during the 1990's. The Leading Edge, 18, 192. Sheriff, R.E., 1975. Factors affecting seismic amplitudes. Geophysical Prospecting 23, 125-138.
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