Finite‐difference modeling with variable length spatial operators and time steps

Abstract

We propose a finite‐difference modeling scheme that uses variable spatial operator lengths and variable time steps. This scheme adopts long spatial operators and large time steps for low velocity grids and short spatial operators and small time steps for high velocity grids respectively. Variable spatial operator lengths and time steps are determined by the modeling accuracy and stability condition. The time‐space domain dispersion‐relation‐based spatial finite‐difference methods are adopted to improve the modeling accuracy. The hybrid absorbing boundary conditions are used to reduce boundary reflections. 1D and 2D modeling examples demonstrate the validity and efficiency of our proposed method.