Second-order approximate expressions of P- and SV-plane-wave reflection coefficients at the solid/solid media interface

Abstract

To completely use large incident angle seismic data and improve the accuracy of amplitude-variation-with-offset inversion, especially for density information, we have derived second-order approximate expressions of the P- and SV-wave reflection coefficients at the solid/solid media interface. Vectors and Hessian matrices are used to describe the first- and second-order terms of the approximate expressions. The second-order approximations are then rewritten in a simple form. Furthermore, different pseudosecond-order approximations with different power series of the ray parameter p are derived based on the Taylor expansion of the second-order approximation of the P-wave reflection coefficient for the incident P wave (PP-wave reflection coefficient) according to the ray parameter p. By establishing four different single-phase medium models, we have verified that the accuracies of the second-order approximate expressions were remarkably higher than those of the first-order approximations. Furthermore, the pseudo p2 second-order approximation of the PP-wave reflection coefficient is highly consistent with the exact analytical expression.