**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 wave (S wave) velocities, and
Poisson's ratio. Using three-component seismic data and Zoeppritz

*, one can also analyze the S-wave amplitude changes with offset by*

**equations***for the P-wave velocity. Thus, with three-component seismic data, the amplitude vs. offset inversion (AVO) of the P-wave gathers (SAMPLE3*

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

*and can be used to check the predicted P- and S-wave velocities.*

**equations**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 wave 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.

Using AVO inversion (SAMPLE3) to tie the P-wave, S-wave, 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_{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-wave 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.

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