Amplitude-variation-with-offset inversion based on group sparse regularization

Abstract

Seismic amplitude-variation-with-offset (AVO) inversion from prestack seismic data plays a significant role in estimating elastic parameters and characterizing reservoir properties. In general, sparse regularization is widely used to solve ill-posed inverse problems by reducing the solution space of subsurface parameters, which makes seismic AVO inversion more stable. However, the traditional sparse constraint inversion only focuses on the vector sparsity of reflectivity, instead of the structural sparse characteristics of the estimated parameters. Consequently, various elastic parameters demonstrate different formation structural features in the same location of stratum. In this study, we have developed a novel approach that combines the structural sparsity and the vector sparsity of the model reflectivity to establish the posterior probability density distribution and solve the objective function of the model parameters. Based on the relationship among multiple elastic parameters, we divide the model parameters to be inverted into several groups according to intrinsic structural sparse characteristics of elastic parameters. In this case, all of the model parameters at the same sampling point are classified into the identical group, which ensures that different estimated parameters indicate the same characteristic in terms of stratigraphic structure. From the perspective of Bayesian inference, we use the modified Cauchy probability density function (PDF) to characterize the group sparsity and describe the relationship among model parameters in the same group by Gaussian PDF. Furthermore, we estimate the optimum solution corresponding to the maximum a posteriori probability under Bayesian inference. Synthetic experiments on a Marmousi model prove that the estimated P-velocity, S-velocity, and density are consistent with those of the real models, and the application of field data confirms the availability and feasibility of group sparse inversion.