A Global Optimized Implicit Staggered‐Grid Finite‐Difference Scheme for Elastic Wave Modeling

Abstract

The implicit finite-difference schemes make the process of numerical simulation possess higher accuracy and stability. However, most of the conventional implicit schemes have the limitation of lower computational efficiency because of the requirement of solving large scale matrix equation. In this paper, we first propose an optimized implicit staggered-grid finite-difference scheme based on first order velocity-stress elastic wave equation. Then we transform the new scheme from the time-space domain into the time-wavenumber domain, and construct the objective function by means of the two norm theory. Different from traditional global optimized schemes, we select the simulated annealing algorithm to get optimized coefficients. According to the shot records and wavefield snapshots acquired by homogeneous medium model and complex medium model numerical simulations, the optimized implicit staggered-grid finite-difference scheme not only reduces the calculating amount, but also suppresses the numerical dispersion, thus improves the precision of numerical simulation remarkably.