Joint P-P and P-S seismic inversion

Gary F. Margrave, Robert R. Stewart, Jeffrey A. Larsen

A methodology is presented using P-P and P-S seismic reflection data in a joint least-squares inversion to estimate lithologic parameters. The method uses the linearized Aki-Richards approximations to the P-P and P-S plane-wave reflection coefficients and inverts for the fractional contrasts in compressional and shear impedance. An extended case study uses the Blackfoot 3C-3D survey over the subtle stratigraphic target of a buried sand channel. Input data was processed conventionally into suites of migrated volumes of limited offset range. Five offset ranges were used for both P-P and P-S modes. The approximate background amplitude variation with offset was imposed on these volumes by applying a constant scalar to each volume that is determined to match the RMS amplitudes to those calculated for realistic elastic synthetics. These migrated volumes were flattened on a picked marker just above the target and converted into depth relative to that marker. The inversion methodology stacks (sums) horizon slices from each of the ten migrated volumes, using stacking weights that are known analytically from our theory. The weights depend upon the particular lithologic parameter being estimated, upon the background lithology, and upon the raypath incidence angles at the target. Raytracing through a background velocity model was used for this purpose. Inversions using P-P data alone are compared to those using P-P and P-S data jointly and the latter are found to be superior in all cases. The main reason for the improved performance is the effectively doubled fold of the joint estimates. A numerical comparison with well control shows the joint inversion results are up to 800% improved over the P-P inversion alone.