Seismic amplitude inversion based on a new PP-wave reflection coefficient approximation equation for VTI media

The research in this paper is to realize the simultaneous AVO/AVA (amplitude variation with offset or angle) inversion of anisotropic parameters for the transversely isotropic media with vertical axis of symmetry (VTI media). First, we introduce a nonlinear PP-wave reflection coefficient approximation equation in terms of only P- and S-wave impedances for isotropic elastic media. Then by replacing the isotropic part of Rüger’s equation with this equation, we obtain a new PP-wave reflection coefficient approximation equation called the ASI Rüger equation for VTI media. To invert parameters for VTI media based on the ASI Rüger equation, we adopt the Bayesian generalized linear inversion method, a combination of generalized linear inversion and Bayesian linear inversion, in which the noise and model perturbation are assumed to conform to the zero mean Gaussian distribution. Compared with Rüger’s equation, the ASI Rüger equation lowers the trade-off between the parameters, and reduces the ill-posedness of the inverse problem. The synthetic and field data tests demonstrate the feasibility of the proposed method for inverting VTI media parameters (the vertical P-wave impedance, the vertical S-wave impedance, Thomsen’s parameters δ and ϵ).