Hybrid Seismic Inversion Based on Multi-Order Anisotropic Markov Random Field

The prestack seismic inversion effectively transforms reflection data into elastic parameters attributed to rock properties, which has enabled us to explore subsurface in detail. Because the forwarding operator is nonlinear and the observed data are usually insufficient, the inverse problem suffers from ill-posedness. Regularization has proven to be an effective technique making the problem well-posed by adding extra constraints to the estimated model. In particular, the anisotropic Markov random field (AMRF) approach can formulate the prior constraints stabilizing inversion procedure and taking special care of the geological boundaries. However, the standard AMRF only deals with the first-order neighborhood and its capability of revealing geological details is thereby limited. In addition, the auxiliary model, which significantly affects the performance of the AMRFs on correcting anisotropic gradients, is difficult to determine because reliable prior information is usually absent. This articlepresents a hybrid seismic inversion method for estimating the elastic parameters, which is featured by the multi-order AMRF (MAMRF) neighborhoods. In specific, the poststack inverted acoustic impedance result is used as the auxiliary model for the subsequent prestack seismic inversion; the MAMRF-based prior constraint incorporates low- and high-order AMRF neighborhoods during the inversion procedure, whose capability of correcting anisotropic gradients is achieved by the MAMRF coefficients and is enhanced by order-depended and statistically estimated diffusion coefficients. The proposed inversion method is verified by a synthetic test followed by application to inverting field data. Compared with the standard MRF and (first-order) AMRF approaches, the proposed inversion method is applicable for revealing detailed subsurface models, especially under complex geological conditions.