feb04 avo modeling
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42 CSEG RECORDER February 2004
Continued on Page 43
Introduction
AVO modeling plays an active role in three areas: new
technology development, QC data processing, and
assisting data interpretation. This paper attempts to
discuss these issues, with emphasis on the applications of
AVO modeling in data p rocessing and interpr etation. Data
modeling is introduced for its theoretical background and
its applications in isotropic and anisotropic situations. In
the data processing side, we will focus on calibrations.
Finally, some discussion is given on the applications of
AVO modeling in interpretation with additional case
studies.
AVO D ata Modeling
In the pre-stack processing stage, the cmp gathers that are
c on s id e red having app ropriate amp litude recovery or
having gone through true amplitude processing are
mod eled using AVO equations to solve AVO attr ibutes. This
can be called AVO data m odeling. Using the AVO equations
introduced in Part I of this article, data modeling is imple-
mented on the amp litud es at a given two-way time of a cmp
gather. This is often implemented using angles of incidence
for a linear fitting, or, a surface fitting for cases where two
variables, offset and azimu th for H TI media, are involved.
AVO data m odeling is usually cond ucted using least squares
method (L2 norm) or other robust m ethods such as L1 norm.
The difference between L2 and L1 norms is that L2 mini-
mizes squared deviation and L1 minimizes the absolute
deviation of the d ata from a m odel. L2 norm an d L1 norm
have the form of
Where is the single data point residu al and
d(xi) is the data and m(xi) represents an AVO equation fitted
at given offset or angle of incidence xi. Since number of d ata
points n or offsets is always greater than the n um ber of vari-
ables or AVO attributes to be solved, this is an over-deter-
mined problem. Minimization of the norms results in the
solution. For L2 norm, the m atrix form of the m inimization
is a = (ATA)-1ATd, where a is AVO attribute vector, A is
angle-dependent coefficient matrix formed by an AVO
equation corresponding to angles of incidence, and d is the
vector of d ata (amp litud es). For L1 norm , median of coeffi-
cient of an AVO equation may be used in minimization
(Press et a l., 1989). To stab ilize the solu tion, constra ints from
rock p hysical relationships m ay be brou ght in. The solution
often consists of two AVO attributes. Shueys equation, for
example, yields intercept and gradient, and Fattis equation
yields P- an d S- reflectivities.
In the amplitude fitting, L2 norm is particular appropriate
when the data contain random noise. L1 norm is consid-ered robust when a small number of data points have
deviant amplitudes, such as a multiple cutting across a
primary reflection. To demonstrate L1 norm and L2 norm
in AVO attribute extraction, a synthetic data set w ith strong
coherent interfering noise was u sed and is shown in Figure
1. Fattis equation was used for amplitude fitting in this
case. We can see that the L1 norm operation results in a
better solution wh ile the L2 norm solution is comprom ised
by the spurious data p oints.
To further demonstrate this, a synthetic gather with
primary reflections and mu ltiples was p rocessed through
L1 norm solution of Fattis equation. Figure 2a to 2d are
prim ary-only gather, inpu t cmp gather, re c o n s t ru c te dgather from th e extracted P- and S-reflectivities, and differ-
ence between Figur e 2b and Figure 2c. As expected, The L1
norm solution does a good job in rejecting the large
moveout multiples (the large moveout multiple is essen-
tially gone from the reconstru cted gather Figure 2c). Some
energy from th e small moveout m ultiples labeled 1 and 2 is
still present on the reconstru cted gather. Ideally, the recon-
structed gather should contain only primary signal (Figure
2c should look like 2a). Hence, mu ltiple attenuation m ay be
required before AVO attribute extraction.
A real data examp le of AVO data mod eling is shown in
Figure 3. We can see that the inpu t cmp gath er (Figure 3a)
contains random noise, linear coherent noise, and multi-ples. The input cmp gather (Figure 3a) is modeled by
Fattis equation with L1 norm operation. The P- and S-
reflectivities were solved and used in constructing Figure
3b. As ind icated, the Class III AVO is successfully m odeled.
The rand om noise, linear coherent noise, and mu ltiples are
rejected and shown in Figure 3c. In p ractice, the difference
gathers is used to examine if any reflections have been
rejected due to poor NMO or inappropriate processing.
AVO Modeling in Seismic Processingand InterpretationPart III. ApplicationsYongyi Li, Jonathan Downton, and Y ong X u, Core Laboratoires Reservoir Technologies Division,
Calgary, Canada
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Article Contd
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A second examp le is from a 3-D data set for stud ying AVO in a
fractured reservoir. The fractured reservoir is considered as
horizontal transverse isotropic (HTI) medium (Figure 4). For
this case, L2 norm data modeling was performed based on
Rgers equation (1996). To enh ance the r esolution and increasethe stability of the data modeling, a surface fitting approach
was taken to includ e all traces in the calculation. By examining
Figure 4c, we see th at the r eflection events have been success-
fully modeled since little primary energy leakage can be seen.
Figure 4d is a calculated theoretical amplitude surface that
illustra tes the amplitud e variation with offset and azimu th. The
resulting attr ibutes in this AVOZ analysis are zero-offset reflec-
tivity, fracture orientations, and gradients parallel and perpen-
dicular to the fracture orientations. The fracture density is
calculated based on the gra dients. Figur e 4e gives the estimates
of fracture orientation and fracture density at a carbonate
formation.
Data Calibrations
Calibration on cmp gathers and output AVO attributes can be
conducted for optimizing AVO processing. It helps to answer
the questions such as: whether the cmp gathers are properly
processed with an amplitude friendly processing flow andparameters; whether phase, tuning, signal-to-noise ratio and
other factors are influencing the solutions; and whether the
correct impedance background is used in elastic rock property
inversion. Calibration is often imp lemented by using w ell logs,
synthetic gathers, walkway VSP, and/ or know n relationships
between AVO attribu tes or between rock pro p e r t i e s .
Calibration can be perform ed locally at a cmp location, or glob-
ally on a data set.
Using synth etic cmp gather(s) to tie seismic often gives a quick
insight to the data. AVO type and its variation are often deter-
mined in this stage. Further, since AVO m odeling links seismic
responses directly to rock properties, it helps to confirm or
define reservoir condition. One may perturb the well logs torepresent the possible reservoir conditions. For example, gas
substitution m ay be perform ed on a w et well or vice verse. The
other parameters that are often changed are porosity, reservoir
thickness and lithology. Figure 5 shows an exam ple in which a
synthetic cmp gather ties to a re c o rded cmp gather.
In the zone of interest, the AVO expression has similar
c h a r a c t e r. We m ay there f o re consider that the dat a has
approp riate amp litude recovery.
Calibration at specific reflections may be performed. The
amplitudes for a given event from both the actual seismic and
the synthetic can be extracted and comp ared . Figure 6 shows an
example in which the seismic amplitudes from the top of a gas
reservoir are compared with the synthetic gather. The Class I
AVO anomaly with polarity reversal at the far offsets is
confirm ed as th e AVO expression for this reservoir.
AVO Mod eling in Seismic Pr ocessing an d Inter pr etat ionContinued from Page 42
Figure 1. Curve fitting using L1 and L2 norm.
Figure 2. Data modeling using L1 norm, a) primary-only gather, b) input gather for AV O extraction; c) reconstructedgather using P- and S-reflectivity; and d) difference between b) and c).
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Continued on Page 45
AVO Mod eling in Seismic Pr ocessing an d Inter pr etat ionContinued from Page 43
Figure 4. Data modeling using Rgers equation and L2 norm for a fractured reservoir: a) input cmp gather; b) reconstructed cmpgather using intercepts and gradients; c) difference between a) and b); d) a theoretical amplitude surface; and e) fracture orientationsand fracture density. N ote that these gathers are sorted by offset, not by azimuth. Vertical discontinuities of the amplitudes in b)occur where there is a jump in azimuth within the gather.
Figure 3. Data modeling using Fattis equation and L1 norm on a cmp gather: a) input gather; b) reconstructed gather using P- and
S-reflectivity; and c) difference between a) and b).
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AVO Mod eling in Seismic Pr ocessing an d Inter pr etat ionContinued from Page 44
Figure 5. Seismic cmp gather (left) ties to synthetic cmp gather (right).
Further, calibration can be conducted on AVO attributes or
inverted r ock prop erties. P- and S-reflectivity synthetic may tie
to stacked P- and S-reflectivity sections. It also can be
condu cted in cross-plotting spaces su ch as P-reflectivity against
S-reflectivity, and against . Figure 7 shows an example
using w ell logs to calibrate inverted elastic rock prop erties for a
gas charged dolomite reservoir. In Figures 7a and 7b, the
inverted elastic rock properties of the reservoir are high lighted
in black squares. The overlain empirical relations are shale
(solid black), water saturated sand (solid blue), limestone
(dashed black), dolomite (dashed gr een), and gas charged clean
sand (red ). We can see that the da ta points from the gas-charged
reservoir are shifted towards low values and low / ratio.
Figures 7c and 7d show the cross-plots of dipole sonic logs. The
data from a gas charged dolomite reservoir are highlighted
with red squares, and brine-saturated porous dolomite with
green squares. This comparison leads to an interpretation of a
gas-charged dolomite based on the seismically-derived elastic
rock prop erties (Figures 7a and 7b). In ad dition, the porosity of
the reservoir is similar to the porous dolomite that is high-
lighted by the green squares.
Global calibration implies a way to QC data on entire data set.
For example, the amplitude variation with offset within a time
window can be calculated and compared to that from synthetic
gathers. Consequ ently, offset-variant scaling corrections m ay be
applied to the data set. Calibration may also be conducted
based on relationships of AVO attributes such as P- and S-
reflectivities. Background constraints that are used in data
modeling and elastic rock property inversion may also be cali-
brated through this method.
Interpretation
AVO modeling assists interpretation on cmp gathers, AVO
attributes, and inverted elastic rock prop erties. It helps in vali-
dating AVO respon ses and linking seismic expression to know n
reservoir cond itions. AVO mod eling can increase confidence in
interpretation an d red uce risk in reservoir characterization as it
provides independent information. We can use synthetic to
identify AVO anomalies and determine AVO types on a cmp
gather. Also, we can use synthetic pre-stack data to determ ine
the S-wave information that often is ignored in conventional
data processing. For instance, a strong S-impedance contrast
may exist for a reservoir even though P-impedance contrast is
small. The derived AVO attributes such as fluid factor, and
inverted elastic rock prop erties such as Vp/ Vs ratio, Poissons
ratio, and / ratio can be used to infer the fluid type in a
reservoir.
Tuning may invoke or mask an AVO anomaly. The synthetics
with varied bandwidth or reservoir thickness may give
answ ers to tu ning q uestions. Special lithologies or lithological
contrasts may generate AVO anomalies and can be proved by
AVO modeling. Lithological complexity may also bring in diffi-
culties in interpretation. Tight streaks may m anifest themselvesFigure 6. Comparison of amplitudes from seismic and synthetic cmp gathers.
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as AVO anomalies and brighten in a stacked section. Coal,
carbonate, and the lithologies that do not follow water-
saturated trend of rock properties for clastics may complicate
fluid stack anomalies. The lack of understanding on some
seismic rock properties may prevent one to effectively explore
those types of reservoirs. Further, high clay content in sand
may result in low gas saturation. This type of partial gas satu-
ration may still have relative high Vp/ Vs ratio that contrad icts
traditional theories of partial gas saturation. Therefore, AVO
modeling may provide opportunities for distinguishing the
partial gas satu rated reservoirs based on the lithological effect
on rock properties.
AVO Mod eling in Seismic Pr ocessing an d Inter pr etat ionContinued from Page 47
Figure 7. a) and b): elastic rock properties from inverted seismic; and c) and d): from well logs.
Figure 8. Workflow using AV O modeling in assisting data processing and interpretation.
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AVO Mod eling in Seismic Pr ocessing an d Inter pr etat ionContinued from Page 46
Figure 9. Zoeppritz modeling and elastic modeling for a reservoir in the Wabamun Formation in the
WCSB: a) Zoeppritz modeling; b) elastic modeling with reservoir; c) elastic modeling with no reservoir;and d) difference between reservoir and non-reservoir cases.
Figure 10. AV O modeling and interpretation for a gas charged dolomite reservoir, a) synthetic cmp gather, and b) stack section and cmp gathers at well locations.
Figure 8 shows an ideal workflow in using AVO modeling to
assist data p rocessing an d inter pretation. We can see that AVO
modeling workflow is the same as that of data processing.
Therefore, seismic data and synthetics can be compared in the
stages of cmp gath ers, AVO attributes and inverted elastic rock
properties. In interpretation, the information from all three
branches can be integrated. The risk in reservoir characteriza-
tion may thus be reduced since the interpretation is broadly
based, involving und erstand ing of seismic, rock physical prop-
erties and geology.
Several AVO modeling examples for AVO interpretation have
been given in Part 1 and Part 2 of this article (Li et al., 2003;
Li et al. 2004). Figure 9 shows an example using AVO modeling
to understand interference of multiples and converted energy
at the Wabamu n dolomite poro s i t y. The mod eling was
conducted using both 1) Zoeppritz modeling with ray-tracing,
and 2) full wave elastic wave equation. For the elastic
modeling, two cases were modeled: reservoir case (with
porosity) and n on-reservoir case (withou t porosity). The obser-
vations that can be m ade for this typical study includ e: a) Class
a) b) c) d)
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III AVO anom aly (a trough brightens w ith offset) at the top of
the reservoir presents in the Zoeppritz mod eling but it does not
show in th e elastic modeling; b) the elastic mod eling show s that
mu ltiples and converted energy (w hich are not accounted for in
a Zoeppritz model) interfere with the reflections from both the
top and the base of the reservoir; and c) the difference between
the reservoir case (Figur e 9b) and the n on-reservoir case (Figure
9c) indicates that it could be enough for differentiating the
porosity case from non-porosity case. Further, we may notice
the inter-bedded mu ltiples and converted energy generated by
the reservoir (Figure 9d). This study provides the information
of wave prop agation and interference. We ma y use it as a guide
for attenuating the coherent noise and performing amp litude
recovery.
The second example is from a study on carbonate reservoirs
(Li et al., 2003). In Figure 10a, AVO modeling shows that a gas
charged dolom ite reservoir prod uces a Class III AVO anomaly.
This is consistent with the AVO response in the cmp gather at
the location of the p rodu cing w ell. We can see that at the tight
well locations, a completely different AVO response presents.
The information provided by AVO modeling validates the
information from seism ic.
Conclusions
This paper, the third part of AVO modeling in seismic
processing and interpretation, demonstrates some applications
of AVO mod eling involving da ta processing and interpr etation.
The discussion of data modeling provides an insight in AVO
attribute extraction. Calibration using AVO modeling in data
processing sheds som e light on how to optimize AVO solution.
Combined with rock physical property analysis, petrophysical
analysis, and geological information, AVO modeling provides
useful information in interpretation and thus incre a s e s
certainty in reservoir characterization.
AcknowledgementsThe authors thank Core Laboratories Reservoir Technologies Division for
supporting this work.
ReferencesLi, Y., Down ton , J., and G ood wa y, B., 2003, Recent ap plication of AVO to
carbonate reservoirs in the Western Canadian Sedimentary Basin, The Leading
Edge, 22, 671-674.
Li, Y., Down ton , J., and Xu, Y., 2003, AVO modelin g in seism ic processing and
interpretation, P art 1: fund amentals, Recorder, 28 December, 43-52.
Li, Y., Down ton , J., and Xu, Y., 2004, AVO modelin g in seism ic processing and
interpretation, P art 2: method ologies, Recorder, 29 January, 36-42.
Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W .T., 1989, Num ericalRecipes, The Art of Scientific Comp uting, Cam bridge U niversity Press.
R g e r, A ., 1996, Reflection Coefficients and Azimu thal AVO Ana lysis in
Anisotrop ic Media, Ph.D. Thesis, Colorado School of Mines.
This is the third and final part of the series.
Article ContdAVO Mod eling in Seismic Pr ocessing an d Inter pr etat ionContinued from Page 47
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