** Next:** CONCLUSIONS
** Up:** Lin: Prestack migration
** Previous:** A FIELD DATA EXAMPLE

By sorting each constant *p* section into CMP gathers after prestack
slant stack migration, we can obtain unstacked migrated CMP gathers.
Consequently, we can perform AVO analysis on those gathers.
For AVO analysis, the most widely used approximation of the reflection
coefficient was derived by Shuey 1985 in the following equation:

| |
(4) |

where is the incidence angle, *R*_{0} the reflectivity for zero
incidence, and *G* a quantity related to elastic parameters. This
linearization defines a framework within which seismic amplitudes must fit.
Conventionally this formula can be directly applied to an NMO-corrected CMP
gather. For every sample point, amplitudes are used to compute *R*_{0}
and *G* through a linear regression. The series *R*_{0}(*t*)**G*(*t*)
provides a useful section for AVO analysis. In this section, positive
amplitude indicates amplitude increasing with offset, and negative amplitude
indicates amplitude decreasing with offset.

With data from the domain in each CMP gather, we can do
the AVO analysis directly according to equation (4), after some preprocessing for
amplitude correction. Because we already know the value of *p* for each trace
and the interval velocity in depth, we can calculate the
in equation (4)
directly from

| |
(5) |

This provides a more accurate measurement of . We also have to be very careful about the noise shown in the CMP gather
(Figure 4). Those low-frequency waves propagating nearly horizontally
should be avoided in the AVO analysis.
Owing to the prestack migration, the seismic events were moved to the
correct position, and more accurate amplitude was recovered. Figure 8 shows
the *R*_{0}**G* section after linear regression of the migrated CMP gathers. This
section displays bright spots (at 2.2 seconds and 1.8 Kilometers), which is similar to those in
Figure 13 of Lumley's
paper 1993. They indicate a known gas producing reservoir.

**avopg
**

Figure 8 An *R*_{0}**G* section

** Next:** CONCLUSIONS
** Up:** Lin: Prestack migration
** Previous:** A FIELD DATA EXAMPLE
Stanford Exploration Project

11/16/1997