Pushing AVO inversion beyond linearized approximation

Most AVO inversions for rock properties estimation are based on a linearized approximation of the PP reflection coefficient. One of the main reasons for not using the full Knott-Zoeppritz equation is its complex nature, which does not give an insight into the separate contributions made by P-velocity, S-velocity and density. Also a stable inversion of the nonlinear problem is not a trivial task. In this paper, we rewrite the Knott-Zoeppritz equation in terms of a background and three contrast parameters allowing a better handle on the parameters to be estimated. No limitations need be imposed on the magnitude of these contrast parameters. The use of an adjoint state technique made the nonlinear inversion possible. Analysis of the singular values and the singular vectors in terms of the new parameters show that a full Knott-Zoeppritz equation is necessary in order to correctly estimate the contrast parameters. We find that crucial information resides near the critical angle, which cannot be taken into account by the linearized approximation. We also show that addition of the PS AVO information improves the inversion results.