High-resolution three-term AVO inversion via a Trivariate Cauchy probability distribution
Wubshet Alemie, Mauricio D. Sacchi · 2010
Three-term AVO inversion can be used to estimate P-wave and S-wave velocities and, in addition, density. The density term, however, exhibits little sensitivity to amplitudes and therefore, its inversion is unstable. One way to stabilize the density term is by including a scale matrix that provides correlation information between the 3 unknown AVO parameters. In this article, we investigate a Bayesian procedure to include sparsity and a scale matrix in the three-term AVO inversion problem. To this end, we model the prior distribution of the AVO parameters via a Trivariate Cauchy distribution. We present an iterative algorithm to solve the Bayesian inversion and, in addition, we provide comparisons with the classical inversion approach that uses a Multivariate Gaussian prior. It is important to point out that the Multivariate Gaussian prior allows us to include the correlation of the AVO parameters in the solution of the inverse problem. The Trivariate Cauchy prior not only permits us to incorporate correlation but also leads to high resolution (broadband) P-wave, S-wave velocities and density perturbations.