Optimally accurate second-order time-domain finite difference scheme for the elastic equation of motion: one-dimensional case

Abstract

We previously derived a greater criterion for optimally accurate numerical operators for the calculation of synthetic seismograms in the frequency domain (Geller and Takeuchi 1995). We then derived modified operators for the Direct Solution Method (DSM)(Geller and Ohminato 1994) which satisfy this general criterion, thereby yielding signifiantly more accurate synthetics (for any given numerical grid spacing) without increasing the computatitonal requirements (Cummins et al. 1994; Takeuchi, Geller and Cummins 1996; Cummins, Takeuchi and Geller 1997). In this paper, we derived optimally accurate time-domain infite different (FD) operators which are second order in space and time using a similar approach. As our FD operators are local, our algorithms is well suited to massively parallel computers. Our approach can be extended to other methods (et pseudospectral) for solving the elastic equation of motion. It might also be possible to extend this approach to equations other than the elastic equation of motion, including non-linear equations.