A Simulation of Three-Dimensional Wave Field Based on Elastic Wave Optimization Quasi-Analytic Method

Pseudo-spectral method has low accuracy in the second order difference scheme in the time direction, and it is unstable for the large time sampling intervals. The seismic wave fields of the quasi-analytic method have large errors in both time and space in models with rapid velocity changes. In this paper, a three-dimensional wave field simulation based on the elastic wave optimization quasi-analytic method is realized. The normalized quasi-Laplace operator is applied to the wave field continuation of decoupled P-wave and S-wave, and the elastic wave optimization quasi-differential operator is used to represent the quasi-Laplace operator. The quasi-differential operator can accurately compensate the error caused by the second-order difference in the time direction of the wave equation in the wavenumber space domain, and the low rank decomposition is used to approximate the solution of the elastic wave optimization quasi-differential operator, and it can effectively improve computational efficiency. The numerical simulation results of the three-dimensional uniform model and the salt dome model indicate that compared to the conventional pseudo-spectral and quasi-analytical methods, the proposed method has high accuracy in both time and space.