INTERPRETER’S
Principles of AVO crossplotting
JOHN P. CASTAGNA, University of Oklahoma, Norman, Oklahoma
HERBERT W. SWAN, ARCO Exploration and Production Technology, Plano, Texas
H
ydrocarbon related “AVO anomalies” may show
increasing or decreasing amplitude variation with offset. Conversely, brine-saturated “background” rocks may show
increasing or decreasing AVO.
Amplitude-versus-offset interpretation is facilitated by
crossplotting AVO intercept (A) and
gradient (B). Under a variety of reasonable geologic circumstances, As and Bs
for brine-saturated sandstones and
shales follow a well-defined “background” trend. “AVO anomalies” are properly viewed as
deviations from this background and may be related to
hydrocarbons or lithologic factors.
The common three-category classification developed
by Rutherford and Williams is incomplete. We propose
that an additional category (Class IV) be considered. These
are low impedance gas sands for which reflection coefficients decrease with increasing offset; they may occur, for
example, when the shear-wave velocity in the gas sand is
lower than in the overlying shale. Thus, many “classical”
bright spots exhibit decreasing AVO. If interpreted incorrectly, AVO analysis will often yield
“false negatives” for Class IV sands.
Clearly, the conventional association of the term “AVO anomaly” with
an amplitude increase with offset is
inappropriate in many instances and has led to much
abuse of the AVO method in practice. Similarly, interpretation of partial stacks is not as simple as looking for relatively strong amplitudes at far offsets. We recommend that
all AVO analysis be done in the context of looking for deviations
from an expected background response.
Summary
Figure 1. The two-term Shuey
approximation to the Zoeppritz
equations represents the angular dependence of P-wave
reflection coefficients with two
parameters: the AVO intercept
(A) and the AVO gradient (B).
In practice, the AVO intercept
is a band-limited measure of
the normal incidence amplitude, while the AVO gradient
is a measure of amplitude variation with offset. Assuming
appropriate amplitude calibration, A is the normal incidence
reflection coefficient and B is a
measure of offset-dependent
reflectivity.
Shuey’s Two-Term
Approximation
R( ) = A + B sin2( ) + ...
R = reflection coefficient
= angle of incidence
A = AVO intercept
B = AVO gradient
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Figure 2. For brine-saturated clastic rocks over a
limited depth range in a
particular locality, there
may be a well-defined
relationship between the
AVO intercept (A) and
the AVO gradient (B). A
variety of reasonable
petrophysical assumptions (such as the
mudrock trend and Gardner’s relationship) result
in linear A versus B
trends, all of which pass
through the origin (B = 0
when A = 0). Thus, in a
given time window, nonhydrocarbon-bearing
clastic rocks often exhibit
a well-defined background trend; deviations
from this background are
indicative of hydrocarbons or unusual lithologies.
Figure 3. This figure
shows A versus B
trends for various constant ratios of compressional (Vp) to
shear wave (Vs) velocity. Notice that the
AVO gradient (B) and
the AVO intercept (A)
are generally negatively correlated, and
that the A versus B
trends become more
positive as Vp/Vs
increases. Also, note
that the trend
becomes positive at
high Vp/Vs ratios.
Thus, the normal
response for (nonhydrocarbon-related)
reflections at very
high background Vp/Vs
(as we would expect
for very shallow
unconsolidated sediments) is an amplitude increase versus
offset. Large reflection coefficients associated with shale over porous brine-sand interfaces will exhibit “false positive” AVO anomalies in the sense that they will have larger AVO gradients than weaker reflections lying along the
same background trend. When interpreted in terms of deviation from the background A versus B trend, such
reflections are correctly interpreted as not being anomalous.
EDGEN ET
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Figure 4. Deviations from
the background petrophysical trends, as would
be caused by hydrocarbons or unusual lithologies, cause deviations
from the background A
versus B trend. This figure shows brine sand-gas
sand tie lines for shale
over brine-sand reflections falling along a
given background trend.
In general, the gas sands
exhibit more negative As
and Bs than the corresponding brine sands
(assuming the frame
properties of the gas
sands and the brine
sands are the same). Note
that the gas sands form
a distinct trend which
does not pass through the
origin.
Figure 5. We propose that
the classification of AVO
responses should be
based on position of the
reflection of interest on
an A versus B crossplot.
First, the background
trend within a given time
and space window must
be defined. This can be
done with well control if
the seismic data are correctly amplitude calibrated, or with the seismic
data itself if care is taken
to exclude prospective
hidden hydrocarbon-bearing zones. Top of gas sand
reflections then should
plot below the back ground trend and bottom
of gas sand reflections
should plot above the
trend. We can classify the
gas sand response accord ing to position in the A-B
plane of the top of gas
sand reflections. Our classification is identical to that of Rutherford and Williams (Geophysics, 1989) for Class I
(high impedance) and Class II (small impedance contrast) sands. However, we differ from Rutherford and
Williams in that we subdivide their Class III sands (low impedance) into two classes (III and IV). The Class IV
sands are highly significant in that they exhibit AVO behavior contrary to established rules of thumb and occur in
many basins throughout the world including the Gulf of Mexico.
EDGENET
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Class
Relative Impedance
Quadrant
A
B
Amplitude vs. Offset
I
Higher than overlying unit
IV
+
-
Decreases
II
About the same as the
overlying unit
II, III, or IV
+ or -
-
Increase or decrease;
may change sign
III
Lower than overlying unit
III
-
-
Increases
IV
Lower than overlying unit
II
-
+
Decreases
Figure 6. This chart summarizes the AVO behavior of the various gas sand classes. Note that when we say “amplitude versus offset” we are referring to the variation of the magnitude of the reflection coefficient. Thus, a negative
reflection coefficient that becomes more positive with increasing offset has a decreasing reflection magnitude versus offset. Note that Class IV gas sands are anomalous in that they have a positive AVO gradient and that amplitude decreases with increasing offset.
Plane-wave reflection coefficient
at top of gas sand
Figure 7. We have superimposed an example of a Class
IV gas sand on a figure taken from Rutherford and
Williams which shows their gas-sand classification
based on normal incidence reflection coefficient. The
vertical axis is reflection coefficient and the horizontal
axis is local angle of incidence. Note that Class III and
IV gas sands may have identical normal incidence
reflection coefficients, but the magnitude of Class IV
sand reflection coefficients decreases with increasing
angle of incidence while Class III reflection coefficient
magnitudes increase.
E DGENET
Figure 8. Here are examples of shale over gas-sand
and shale over brine-sand reflections. Both decrease
in amplitude versus offset and have about the same
AVO gradient, even though the gas sand is a bright
spot (it is Class IV). The model parameters are:
Lithology
Vp (km/sec)
Shale
3.24
Brine Sand
2.59
Gas Sand
1.65
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Vs (km/sec)
1.62
1.06
1.09
p (gm/cc)
2.34
2.21
2.07
DECEMBER 1997
Figure 9. This figure shows the difference in AVO
behavior for a gas sand when overlain by a shale or,
alternatively, by a high-velocity tight streak. In both
cases, the gas sand is a bright spot. When overlain
by a shale, the gas sand is Class III and amplitude
increases with increasing angle of incidence. However, when overlain by a tight streak, the gas sand is
Class IV and amplitude decreases with increasing
angle of incidence. The parameters are:
Lithology
Vp (km/sec)
Shale
2.90
Brine Sand
3.25
Gas Sand
2.54
Vs (km/sec)
1.33
1.78
1.62
p (gm/cc)
2.29
2.44
2.09
The model parameters for this example were
obtained from well log measurements and provided
by Jeremy Greene of ARCO Exploration and Production Technology.
Figure 10. Consider a
“bright” gas sand
reflection with an AVO
intercept (A) of -.4 and
an AVO gradient (B) of
.4. If the frame proper ties of the brine sand
are not identical to that
of the gas sand, the
reflection coefficient
for the shale over
brine-sand reflection
with an A of, say -.2,
could easily have the
same B of .4. This cir cumstance would con found most interpreters
in that the gas sand is a
bright spot (A = normal
incidence reflection
coefficient = -.4) but (1)
the reflection magnitude decreases with
offset (B is positive so
the negative reflection
becomes smaller!), and
(2) the AVO gradient is not anomalous with respect to the brine sand. Thus, the result would be a false negative for
most interpreters. (Commentary: So this perfectly good bright spot may not be drilled because it has not been “verified” by AVO analysis. Imagine management’s disgust when a competitor who (1) hasn’t bothered doing AVO, or
(2) has interpreted the AVO data correctly comes along and drills a discovery. Is it any wonder that AVO has a bad
name in some quarters? Of course, the problem here is not with AVO, it is with interpreters who cling to naive rules
of thumb; i.e., gas-sand amplitude increases with offset or use partial stacks rather than more sophisticated analysis
techniques even though they may have no idea what to look for on a partial stack until after the well has been
drilled and logged. Clearly, one should interpret anomalous AVO behavior in the context of deviation from background gradient AND intercept behavior.)
EDGENET
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Reasonable petrophysical assumptions for clastic
stratigraphic intervals result in linear background trends
for limited depth ranges on AVO intercept (A) versus gradient (B) crossplots. In general, background B/Abecomes
more positive with increasing Vp/Vs. Thus, if too large a
depth range is selected for A versus B crossplotting, and
background Vp/Vs varies significantly, a variety of background trends may be superimposed, resulting in a less
well-defined background relationship. For very high
Vp/Vs, as may occur in very soft, shallow, brine-saturated
sediments, the background trend B/A becomes positive;
n o n h y d ro c a r b o n related reflections
may exhibit increasing AVO and show
false positive anomalies (especially for
large reflection coefficients). Partial stacks, Atimes B product indicators, and improperly calibrated fluid-factor sections are all susceptible to such false positives.
Deviations from the background trend may be indicative of hydrocarbons. This is the basis for the “fluid factor” of Smith and Gidlow (1987), the “NI versus Poisson
reflectivity” of Verm and Hilterman (1995), and related
indicators.
Inspection of the A versus B plane reveals that gas
sands may exhibit AVO behavior which differs dramatically from conventional rules of thumb. Surely, the idea that
“gas-sand amplitude increases versus offset” should finally be
put to rest for all time.
We suggest that hydrocarbon-bearing sands should be
classified according to their location in the A-B plane,
rather than by their normal-incidence reflection coefficient
alone. Class I sands are higher impedance than the overlying unit. They occur in quadrant IV of the A-B plane. The
normal incidence reflection coefficient is positive while the
AVO gradient is negative. The result is that the reflection
coefficient decreases with increasing offset. Class II sands
have about the same impedance as the overlying unit.
They exhibit highly variable AVO behavior and may occur
in quadrants II, III, or IV of the A-B plane. The normal incidence reflection coefficient (A) may be
positive or negative
and B is negative.
The reflection coefficient becomes increasingly negative versus offset, but the reflection amplitude may increase or decrease depending on the sign of
the reflection coefficient. When the reflection coefficient is
positive at near offset, amplitude will initially decrease
and may reverse polarity and then increase with offset (the
Class IIp of Ross and Kinman, where “p” indicates phase
reversal). Class II sands often exhibit poor ties between
conventional synthetic seismograms and the stacked seismic data. Our Class III sands differ from Rutherford and
Williams Class III sands in that we include only those
reflections which occur in quadrant III. These sands are
lower impedance than the overlying unit and are frequently “bright.” They have negative A and B and the
reflection coefficient becomes increasingly negative with
offset. These are the quintessential gas sands for which
amplitude increases versus offset. Our Class IV sands are
those low impedance sands which occur in quadrant II.
These sands have negative A but a positive B. The reflec tion coefficient becomes less negative with increasing offset and
amplitude decreases versus offset, even though these sands may
be bright spots.
Bear in mind that the two-term Shuey approximation
may not be appropriate for AVO analysis of long-offset
data. Analysis of such data should include (1) corrections
for various effects of anisotropy and (2) utilization of the
full Zoeppritz equations.
AVO analysis techniques that rely on AVO product indicators (such as Atimes B) or inspection of partial stacks (for
weak amplitude at near offsets associated with strong amplitudes at far offsets) are designed for Class III sands. Clearly, these approaches can easily lead to misinterpretation for
other gas-sand classes. Alternatively, the fluid factor and
related indicators will theoretically work for any gas-sand
class. Unfortunately, some algorithms for extraction of As
and Bs are not robust, particularly in the presence of small
NMO errors, so partial stacks are often resorted to. Sometimes, for logistical or economic reasons, the interpreter only
has access to partial stack data. In these situations, the data
should still be interpreted in the context of the A-B plane and
deviation from some “background” behavior should still be
the means of defining anomalies. LE
Conclusions and Discussion
Suggestions for further study.
The
Shuey approximation is described in his 1985 paper in
GEOPHYSICS. The “fluid factor” was introduced by
Smith and Gidlow in a 1987 article in Geophysical
Prospecting. This paper should be required reading for
anyone doing AVO analysis. The Rutherford and
Williams classification can be found in their classic 1989
paper in GEOPHYSICS. This paper gives real world examples of Class I, Class II, and Class III reservoirs. The
Rutherford and Williams classification is further discussed in GEOPHYSICS by Castagna and Smith (1994)
and Ross and Kinman (1995). AVO crossplotting is
described in some versions of Hilterman’s SEG Contin uing Education Course Notes, beginning in the mid-tolate 1980s. Some superb examples were shown by Foster, Smith, Dey-Sarkar, and Swan at SEG’s 1993 Annual
Meeting. TLE readers were introduced to the subject by
Castagna in 1993 and Verm and Hilterman in 1995.
Notably, two papers co-authored by Herb Swan are still
awaiting publication in GEOPHYSICS. One of these was
submitted in 1993. Jim DiSiena received a best presentation award at AAPG’s 1996 convention for application
of AVO crossplotting techniques to 3-D seismic data.
Would you like to learn more? John
Castagna is currently performing and compiling case
studies on datasets with Class IV sands and studying
AVO responses at long offsets. He can be reached at
405-3256697 or castagna@ou.edu for the digitally
inclined, if you are interested in collaborating, cofunding, or otherwise participating.
EDGEN ET
Acknowledgments: This tutorial is based on a more extensive paper
(complete with mathematics) co-authored by Doug Foster and Carolyn
Peddy which was submitted to GEOPHYSICS some months ago and may
be published some day in the distant future. This work was partially
supported by GRI under contract 5090-212-2050, by ARCO Explo ration and Production Technology, and by The University of Oklahoma
Institute for Exploration and Production Geosciences.
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