For AVO analysis, the most widely used approximation of the reflection coefficient was derived by Shuey 1985 in the following equation:
where is the incidence angle, R0 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 R0 and G through a linear regression. The series R0(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
Owing to the prestack migration, the seismic events were moved to the correct position, and more accurate amplitude was recovered. Figure 8 shows the R0*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.