Temporal Dispersion Correction and Prediction by Using Spectral Mapping

Time-domain finite difference (FD) modeling for wave propagation has been widely used for illumination studies and advanced imaging techniques such as RTM and FWI in complex geology. Any finite-order approximation of the time and space derivatives using FD methods suffer from some degree of numerical dispersion. The temporal and spatial dispersion are independent of each other. Spatial dispersion can be reduced with higher-order finite difference operators and optimized coefficients. The time derivatives are usually approximated to 2nd order. Thus, FD-based simulations and imaging methods often suffer from numerical temporal dispersion error.

In this paper, we show that the numerical temporal dispersion from 2nd-order time FD can be corrected via a trace-by-trace spectral mapping operation. For RTM, this spectral mapping operation is to add the predicted temporal dispersion into each gather before backward propagation. This approach eliminates the temporal dispersion at only small cost. One clear benefit of the temporal dispersion correction is a significant speed up because a larger time step can be used.