Comparison of Accuracy and Efficiency of Time-domain Schemes for Calculating Synthetic Seismograms

Abstract

We conduct numerical experiments for several simple models to illustrate the advantages and disadvantages of various schemes for computing synthetic seismograms in the time domain. We consider both schemes that use the pseudo-spectral method (PSM) to compute spatial derivatives and schemes that use the finite difference method (FDM) to compute spatial derivatives. We show that schemes satisfying the criterion for optimal accuracy of Geller and Takeuchi (1995) are significantly more cost-effective than non-optimally accurate schemes of the same type. We then compare optimally accurate PSM schemes to optimally accurate FDM schemes. For homogeneous or smoothly varying heterogeneous media, PSM schemes require significantly fewer grid points per wavelength than FDM schemes, and are thus more cost-effective. In contrast, we show that FDM schemes are more cost-effective for media with sharp boundaries or steep velocity gradients. Thus FDM schemes appear preferable to PSM schemes for practical seismological applications. We analyze the solution error of various schemes and show that widely cited Lax-Wendroff PSM or FDM schemes that are frequently referred to as higher order schemes are in fact equivalent to second-order optimally accurate PSM or FDM schemes implemented as two-step (predictor-corrector) schemes. The error of solutions obtained using such schemes is thus second-order, rather than fourth-order.