A locally variable timestep scheme that matches with discontinuous grids in the finite-difference method is developed for the efficient simulation of seismic-wave propagation. The first-order velocity-stress formulations are used to obtain the spatial derivatives using finite-difference operators on a staggered grid. In the case of a media interface with high velocity contrast, the computational domain consists of two regions with different grid spacings. Each region roughly covers the medium of the lower or higher wave propagation velocity. There is a small overlap of the two regions, called the transitional zone, within the higher velocity medium. A grid three times coarser in the high-velocity region compared with the grid in the low-velocity region is used to avoid spatial oversampling. Temporal steps corresponding to the spatial sampling ratio between both regions are determined based on local stability criteria. The wave field in the margin of the region with the smaller timestep is linearly interpolated in time using the values calculated in the region with the larger one within the transitional zone. Since the temporal interpolation is a 1D operation performed separately from the spatial interpolation strategy employed to connect two regions with different grid spacings, the proposed scheme is not restricted to 2D or 3D problems with a specific order of accuracy of the spatial finite-difference approximation. The use of the locally variable timestep scheme with discontinuous grids results in remarkable savings of computation time and reductions in memory requirements, with the efficiency depending on the simulation model.

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