Prestack Seismic Inversion Based on Anisotropic Markov Random Field

Abstract

Prestack seismic inversion is an ill-posed problem and must be regularized to stabilize the inverted results. In particular, edge-preserving regularization with prior constraints based on Markov random field (MRF) has proved to be an effective technique for reconstructing subsurface models. However, regularized seismic inversion, based on the standard MRF scheme, typically makes use of isotropic MRF neighborhoods, in which the weighting coefficients of the model gradients are equivalent in all directions. Considering real geological conditions, subsurface formations are expected to be laterally continuous and vertically stratified. Therefore, the anisotropic effects caused by model gradients which vary along different directions should not be ignored. In this paper, we proposed a new prestack seismic inversion method based on anisotropic MRF (AMRF). In this method, AMRF coefficients are incorporated into the standard MRF scheme. These coefficients demonstrate directional variations and gradient dependencies, intended to directly correct the errors caused by the anisotropic model gradients on the prior constraints. In particular, we introduced the anisotropic diffusion method to calculate the AMRF coefficients. The proposed inversion method can effectively remove the anisotropic features of the model gradients and significantly improve the inversion results, especially for geologically layered formations. We demonstrated the effectiveness of the inversion method by both 2-D synthetic test and field data example, which presented encouraging results.