Features of Markov Random Field about Simultaneous Inversion of Pre-stack Seismic Data in Transversely Isotropic Media

Simultaneous inversion of multi-parameters for pre-stack seismic data has inherently supremacy. However, its result is non-unique and the process is unstable since the inversion is ill-posed and band-limited. To alleviate these problems, we developed a new inversion method by constructing a new objective function with edge-preserving regularization (EPR) and soft constraint based on transversely isotropic Markov random field (TIMRF). The method gains reflectivity RPP by the full Zoeppritz equation instead of its approximations and controls the inversion stability by two additional assumptions (i.e., sectional constant VS/VP and the generalized Gardner equation). We replace VS with LS (fitting deviation of VS) in the inversion and apply fast simulated annealing to solve nonlinear optimization problem. Test results indicated that the inversion stability for VP, LS and density are better than that for VP, VS and density. Additionally, for transverse isotropy media, a large weighting coefficient value in horizontal direction for MRF can preserve lateral continuity; a small value in vertical direction is helpful to large longitudinal gradients of inter-layers. Moreover, the inverted results could be improved by utilizing high-order TIMRF at early stages but low-order TIMRF at late iterations. Final test of field data demonstrates our methods with encouraging results.