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Figure shows a simple 2-D acoustic model based on one
used by Dong and Keys , as shown in Figure
. The only difference is that all the layers here have
a 10 degree dipping angle.
For the first interface, there is no velocity change and only density change.
According to equation r_coeff, the reflection coefficient is constant,
0.05.
Similarly, we can reach the same result from the acoustic AVO approximation.
The second layer has changes in velocity and density, but in opposite
signs. Therefore, these two changes cancel each other out and give a
zero-valued
intercept. Slope B is equal to 0.05. Reflection coefficient R increases
from zero to nonzero value with the increase of the incident angle.
The third interface has only a velocity change and no density change. The
velocity drops across the interface and results in a negative intercept
and slope.
model
Figure 4 Dipping acoustic velocity model used in
generating the synthetic dataset.
We use an acoustic modeling program developed by Dong, which is based on the
reflectivity method (). For such kind of layer model, the
modeling result is not only kinematically, but also dynamically exact.
As shown in the following result, such an accurate modeling program is
very helpful for verifying the performance of our inversion program.
Figure is a common-shot gather. The first two events have
a similar pattern, except that the second one goes to a zero-valued amplitude
in the near offset. However, the third event shows an opposite pattern.
shot
Figure 5 Common-shot gather generated from the
dipping velocity model using the reflectivity method.
Figure shows an image gather from the inversion result.
Since the correct velocity model has been used in calculating the WKBJ
Green's function, the three events have been flattened in the image gather.
However, due to the NMO stretching effect, the events broaden from near to
far offset.
dip-cig
Figure 6 Common-image gather of the inversion
result. (L) R as a function of offset. (R) as
a function of offset.
One way to check the accuracy of our inversion result is to pick the peak
amplitude along the three events and then compare it with the theoretical
solution. Figure shows that the numerical results match
the theoretical ones very accurately.
compare
Figure 7 Comparison of numerical result and
theoretical result. (TL) Numerical R. (TR) Theoretical R.
(BL) Numerical . (BR) Theoretical .
Figure and shows the intercept A
and slope B estimated from the inversion result. Compared with the
theoretical results under acoustic approximation, our solution matches
the theoretical one very well. These two figures also show the stretching
effect very clearly. How to remove this stretch effect efficiently is our
next research topic.
dip-avo
Figure 8 AVO coefficients A and B. (Top)
Intercept A. (Bottom) Slope B. The stretch effect is very obvious in the
first wavelet of slope B. Since the transmission effect has not been taken
into account, the absolute values for the second and third events are less
accurate.
crossplot
Figure 9 Crossplot of intercept A and slope
B. The solid curve represents the first event, the dashed-line curve
corresponds to the second one, and the dashed-dotted curve is linked with the
third event. The swirly nature of the curves is due to NMO stretch
(). The extent of stretching effect can be evaluated by the
distance between the curves and the original point.
Next: THE MOBIL AVO DATA
Up: Rickett, et al.: STANFORD
Previous: PARAMETER ANALYSIS
Stanford Exploration Project
7/5/1998