Seismic finite-difference modeling with spatially varying time steps

Numerical seismic modeling by finite-difference methods usually works with a global time-step size. Because of stability considerations, the time-step size is determined essentially by the highest seismic velocity, i.e., the higher the highest velocity, the smaller the time step needs to be. Therefore, if large velocity contrasts exist within the numerical grid, domains of low velocity are oversampled temporally. Using different time-step sizes in different parts of the numerical grid can reduce computational costs considerably.