Efficient finite‐difference modelling of seismic waves using locally adjustable time steps[Link]

Conventional finite‐difference modelling algorithms for seismic forward modelling are based on a time‐stepping scheme with a constant (global) time step. Large contrasts in the velocity model or in the spatial sampling rate cause oversampling in time for some regions of the model. The use of locally adjustable time steps can save large amounts of computation time for certain modelling configurations.  The computation of spatial derivatives across the transition zone between regions of the model with different temporal sampling requires the definition of the wavefield at corresponding time levels on both sides of the transition zone. This condition can be obtained by extrapolation in time, which is inaccurate, or by multiple time integration in the transition zone. The error in the latter solution is of the same order as the conventional time‐stepping scheme because both methods are based on the same iteration formula. The technique of multiple time integration simply requires the use of different sizes of time step. It is applicable only for certain factors of variation of the time step.