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Under the assumption of small incident angle, there is a well-known linearized
Zoeppritz equation (). Because we only consider the
incident angle less than 35 degree, we have omitted the C term in the
original form. For the acoustic and elastic media, the expressions for the
reflection coefficients are different.
Acoustic AVO approximation
| |
(189) |
where
| |
(190) |
Elastic AVO approximation
| |
(191) |
where
| |
(192) |
Using the reflection coefficient R and specular incident angle ,
we find the solution for intercept and slope is a least-squares problem.
| |
(193) |
The resulting estimates of A and B are given by
| |
(194) |
Getting AVO intercept and slope is not our final goal. The purpose of AVO
analysis is to display the Vp/Vs anomaly in the subsurface. This
anomaly is a very important hydrocarbon indication, especially for
gas-charged reservoirs. Here we use the fluid-line technique to highlight
this anomaly. Assume there is a linear relation
between intercept A and slope B.
We specify a window with reasonable size and use least squares algorithm to
estimate the coefficient X. Similar to , we get an
expression for X
| |
(196) |
The A X + B section is called the fluid-line section, which highlights
the Vp/Vs anomaly.
Next: PARAMETER ANALYSIS
Up: Rickett, et al.: STANFORD
Previous: THEORY OF 2.5-D KIRCHHOFF
Stanford Exploration Project
7/5/1998