Finite Difference Method for Solving Acoustic Wave Equation Using Locally Adjustable Time-steps

Explicit finite difference method has been widely used for seismic modeling in heterogeneous media with strong discontinuities in physical properties. In such cases, due to stability considerations, the time step size is primarily determined by the medium with higher wave speed propagation, resulting that the higher the speed, the lower the time step needs to be to ensure stability throughout the whole domain. Therefore, the use of different temporal discretizations can greatly reduce the computational cost involved when solving this kind of problem. In this paper we propose an algorithm for the local temporal discretization setting named Region Triangular Transition (RTT), which allows the local temporal discretizations to be related by any integer value that enables these discretizations to operate at the stability limit of the finite difference approximations used.