Nonlinear joint PP-PS AVO inversion based on improved Bayesian inference and LSSVM

Abstract

Multiwave seismic technology promotes the application of joint PP-PS amplitude versus offset (AVO) inversion; however conventional joint PP-PS AVO inversioan is linear based on approximations of the Zoeppritz equations for multiple iterations. Therefore the inversion results of P-wave, S-wave velocity and density exhibit low precision in the faroffset; thus, the joint PP-PS AVO inversion is nonlinear. Herein, we propose a nonlinear joint inversion method based on exact Zoeppritz equations that combines improved Bayesian inference and a least squares support vector machine (LSSVM) to solve the nonlinear inversion problem. The initial parameters of Bayesian inference are optimized via particle swarm optimization (PSO). In improved Bayesian inference, the optimal parameter of the LSSVM is obtained by maximizing the posterior probability of the hyperparameters, thus improving the learning and generalization abilities of LSSVM. Then, an optimal nonlinear LSSVM model that defines the relationship between seismic reflection amplitude and elastic parameters is established to improve the precision of the joint PP-PS AVO inversion. Further, the nonlinear problem of joint inversion can be solved through a single training of the nonlinear inversion model. The results of the synthetic data suggest that the precision of the estimated parameters is higher than that obtained via Bayesian linear inversion with PP-wave data and via approximations of the Zoeppritz equations. In addition, results using synthetic data with added noise show that the proposed method has superior anti-noising properties. Real-world application shows the feasibility and superiority of the proposed method, as compared with Bayesian linear inversion.