**Three-Component Amplitude vs. Offset Analysis**

**Deborah Miles, Gary Gassaway, Laurie Bennett, Richard Brown**

Amplitude changes in compressional waves (P waves) from a specific reflector
are a function of their angle of incidence and the elastic constant contrast at
the boundary. Zoeppritz, in 1909, quantified this relationship in his
simplification of Knott's 1899 equations. Beginning about 1976, P-* wave* amplitude
changes with angle of incidence on single-component seismic data were analyzed
through modeling or inversion to obtain shear

*(S*

**wave***) velocities, and Poisson's ratio. Using three-component seismic data and Zoeppritz equations, one can also analyze the S-*

**wave***amplitude changes with offset by solving for the P-*

**wave***velocity. Thus, with three-component seismic data, the amplitude vs. offset inversion (AVO) of the P-*

**wave***gathers (SAMPLE3*

**wave**^{TM}) provides an S-wav velocity and Poisson's ratio, and the AVO inversion of the S-

*gather yields P-*

**wave***velocities. Since they are done at the same CDP, the two solutions must agree and thereby tie the P-*

**wave***reflectors to the S-*

**wave***reflectors. The amplitude changes with offset of the converted waves are also predicted by Zoeppritz equations and can be used to check the predicted P- and S-*

**wave***velocities.*

**wave**Processing three-component seismic data for AVO analysis generally follows a
processing flow similar to the processing flow for single-component data. Just
as in single component AVO, the processor must be sure to preserve the amplitude
relative to the other traces. However, the processing must also preserve the
relative amplitudes between components. After processing to a P-* wave*, common
offset gather, corrections for the free surface effects, source arrays, receiver
arrays, and spherical divergence are applied to the amplitudes. When doing AVO
inversions (SAMPLE

^{TM}) on single-component seismic data, the corrections are calculated for z only with the assumption that there is no energy in the transverse direction. However, with three-component data, the corrections for spheri al divergence and the source and receiver arrays must be calculated in terms of

*fronts, not just ray paths, and for all three components. Geophone arrays are generally unnecessary for three-component seismic since the OMNIPHONE polarization filter removes much of the groundroll from three-component seismic data either in a processing center or in the field using a single OMNIPHONE.*

**wave**Using AVO inversion (SAMPLE3) to tie the P-* wave*, S-

*, and converted-*

**wave***data together gives the interpreter expanded interpretation capabilities. First, by identifying the top and bottom of a specific zone, one can use P-*

**wave***and S-*

**wave***time isochrons to calculate Poisson's ratio. Changes in Poisson's ratio or V*

**wave**_{p}/V

_{s}ratios are indicative of changes in pore fluids and lithologies. Second, geologic features such as reefs may be stronger events on the S-

*or converted-*

**wave***data than on the P-*

**wave***data, or vice versa. Therefore, by comparing the P, shear, and converted*

**wave***data, one may locate previously unknown responses.*

**wave**AAPG Search and Discovery Article #91024©1989 AAPG Pacific Section, May 10-12, 1989, Palm Springs, California.