Bayesian generalized linear AVA inversion for VTI media
Xin Fu, Kristopher A. Innanen
The research in this paper is to realize the simultaneous AVA (amplitude variation with 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 called ASI equation for isotropic elastic media. Then by replacing the isotropic part of Rger equation with this equation, we obtain a new PP-wave reflection coefficient approximation equation called ASI Rger equation for VTI media. In order to invert the VTI parameters based on ASI Rger equation, we develop the Bayesian generalized linear inversion (BGLI), in which the noise and model perturbation are assumed to conform to the zero mean Gaussian distribution. ASI Rger equation can express the PP-wave reflection coefficient in VTI media well. Compared with Rger equation, ASI Rger equation demonstrates less sensitivity to the bias in the intrinsic constant, lowers the relevance between the parameters, and reduces the ill-posedness of inversion problem. The synthetic data test shows that the proposed method can stably and reliably invert VTI parameters (the vertical P-wave impedance, the vertical S-wave impedance, Thomsen’s parameters and ) , and the inverted results are almost unaffected by the errors in the intrinsic constant.