Anisotropic Nonlinear Inversion Based on a Novel PP Wave Reflection Coefficient for VTI Media

The hydrocarbon-bearing shale reservoirs can be approximately modeled as the transversely isotropic media with the vertical symmetry axis (VTI), usually exhibiting strong anisotropy and significant contrast among the reservoirs. Therefore, the effects of strong anisotropy should be considered when conducting the seismic interpretation for this type of reservoir through the amplitude variation with offset (AVO) technique. However, the existing approximately linear reflected P-wave generated by incident P-wave (PP) reflection coefficient equations derived based on the assumption of weak anisotropy and weak contrast in elastic parameters will create considerable errors in the case of strong anisotropy and contrast. Quadratic approximation has also been proposed in the case of strong contrast in elastic parameters. To overcome the problem of strong anisotropy and contrast in AVO inversion, we propose a novel PP-wave reflection coefficient equation (expressed by the Lame constants) in terms of five reflectivity parameters (i.e., the ratio of the difference to the mean value between the parameters of two half-spaces) based on the quasi-Zoeppritz equation for the VTI media. Combining the novel reflection coefficient equation and Bayesian inversion framework, we constructed the nonlinear inversion objective function. We chose the multivariate Gaussian distribution as the prior function to reduce the inversion multiplicity. The Markov chain Monte Carlo (MCMC) sampling algorithm was adopted to estimate the five reflectivity parameters for the nonlinear inversion problem.