Application of Optimal Transport to Exact Zoeppritz Equation AVA Inversion

Abstract

Since most information on S-wave velocity and density exists in the middle to large angle range of seismic data, traditional inversion methods based on the Zoeppritz approximation have difficulty in obtaining satisfactory results. Therefore, as a high-accuracy amplitude varied with angle (AVA) inversion, exact Zoeppritz (EZ) equation inversion has aroused a lot of attention in recent years. As for any other nonlinear inversion, iterative convergence and error are the important problems. In this letter, based on a Bayesian framework, we introduce optimal transport into EZ equation AVA inversion. Then, the limited-memory Broyden–Fletcher–Goldfarb–Shanno method is adopted to solve the regularization-constrained least-square argument function to obtain the inversion results, including P-wave velocity, S-wave velocity, and density. We compare this method with a conventional method, which is based on an L2 norm or weighted L2 norm as a residual method in the model test. The results show that the proposed method not only reduces the error of the results to be smaller than L2 norm, but it also improves the convergence rate.