Optimally accurate second order time-domain finite difference scheme for computing synthetic seismograms in 2-D and 3-D media

Abstract

We previously presented an optimally accurate time-domain finite difference method (FDM) scheme for computing synthetic seismograms for one-dimensional (1-D) problems [Geller, R.J., Takeuchi, N., 1998. Optimally accurate second-order time domain finite difference scheme for the elastic equation of motion: 1-D case. Geophys. J. Int. 135, 48–62]. This scheme was derived on the basis of a general criterion for optimally accurate numerical operators obtained by Geller and Takeuchi [Geller, R.J., Takeuchi, N., 1995. A new method for computing highly accurate DSM synthetic seismograms. Geophys. J. Int. 123, 449–470]. In this paper, we derive optimally accurate time-domain FDM operators for 2-D and 3-D problems following the same basic approach. A numerical example shows that synthetics for a 2-D P-SV problem computed using the modified scheme are 30 times more accurate than synthetics computed using a conventional FDM scheme, at a cost of only 3.5 times as much CPU time. This means that the CPU time required to compute synthetics of any specified accuracy using the modified scheme is only 1/47 that required to achieve the same accuracy using the conventional scheme; the memory required by the modified scheme is 1/18 that of the conventional scheme. We have not conducted computational experiments for the 3-D case, but we estimate that the CPU time advantage of the modified scheme will be a factor of over 100. The stability condition (maximum time step for a given spatial grid interval) for the various modified schemes is roughly equal to that for the corresponding conventional scheme.