A New Time-space Domain Dispersion-Relation-Based Implicit Staggered-grid Finite Difference Scheme for Scalar Wave Equation Modeling

摘要

Recently implicit staggered-grid finite difference (ISFD) scheme is widely investigated. Most ISFD stencils for spatial derivatives are usually designed in the space domain. In this paper, we discuss a new optimal way to determine the first-order implicit finite difference coefficients for the staggered-grid and their application for the numerical simulation of the acoustic wave propagation. The proposed method is based on the time-space domain dispersion relation and plane wave theory, which is made to satisfy the exact dispersion relation. The dispersion analysis and the numerical simulation examples demonstrate that the constructed operator using the new optimal coefficients have greater accuracy and more effective ability to attenuate the numerical dispersion, with the same stencil as the conventional finite different method.