A new method for computing highly accurate DSM synthetic seismograms

Abstract

We derive modified matrix operators that minimize the numerical error of solutions of the discretized elastic equation of motion. The criterion for obtaining the modified matrix operators is that the net error of the discretized equation of motion must be approximately equal to zero whenever the operand is an eigenfunction and the frequency is equal to the corresponding eigenfrequency. As it is not necessary to know the explicit values of the eigensolutions, our approach can be applied to arbitrarily heterogeneous media. In this paper we primarily consider frequency domain solutions calculated using the direct solution method (DSM) (Geller et al. 1990; Hara, Tsuboi & Geller 1991; Geller & Ohminato 1994). We present explicit formulations of the modified operators and numerical examples for P‐SV and SH wave propagation in laterally homogeneous, isotropic media. The numerical solutions obtained using the modified operators are about 30 times more accurate than those obtained using the unmodified operators for the same CPU time. Our methods are readily applicable to problems in spherical coordinates or involving laterally heterogeneous media, as well as to time‐domain solutions. It should also be possible to apply the methods of this paper to numerical methods other than the DSM. Copyright © 1995, Wiley Blackwell. All rights reserved