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

We develop a method for the simultaneous amplitudevariation -with -offset or -angle inversion of anisotropic parameters for 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 R & uuml;ger ' s equation with this equation, we obtain a new PP -wave reflection coefficient approximation equation called the ASI R & uuml;ger equation for VTI media. To invert the parameters for VTI media based on the ASI R & uuml;ger equation, we adopt the Bayesian generalized linear inversion (GLI) method, a combination of GLI and Bayesian linear inversion, in which the noise and model perturbation are assumed to conform to the zero -mean Gaussian distribution. Compared with R & uuml;ger ' s equation, the ASI R & uuml;ger equation decreases 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 our method for inverting VTI media parameters (the vertical P -wave impedance, the vertical S -wave impedance, and Thomsen ' s parameters delta and & varepsilon; ).