AVO inversion using the Zoeppritz equation for PP reflections

Abstract

In the past, various approximations to the Zoeppritz equations have been derived and used in conventional AVO inversion. These approximations have accuracy limited to small angles, and the number of invertible elastic parameters is limited to two or three (the so-called twoor three-term AVO). Although inapplicable near the critical angle, plane-wave reflection coefficients (RCs) given by Zoeppritz equations are closed form and accurate for models without critical angles. We propose using the “exact” elastic Zoeppritz equations to do AVO inversion for reflections without critical angles. We compare the PP RCs calculated by finite differencing (FD), the Zoeppritz equation, and some classical approximations. For inversion, the Frechet derivatives can be calculated analytically, and least-squares amplitude fitting is able to invert for the density ratio and three velocity ratios at the reflector. This algorithm is useful for inversion of long-offset PP reflections.