A NEW METHOD FOR COMPUTING HIGHLY ACCURATE DSM SYNTHETIC SEISMOGRAMS

We derive modified matrix operators that minimize the numerical error of solutions of the discretized elastic equation of motion. The criter ion for obtaining the modified matrix operators is that the net error of the discretized equation of motion must be approximately equal to z ero whenever the operand is an eigenfunction and the frequency is equa l 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 consid er frequency domain solutions calculated using the direct solution met hod (DSM) (Geller et al. 1990; Hara, Tsuboi & Geller 1991; Geller & Oh minato 1994). We present explicit formulations of the modified operato rs and numerical examples for P-SV and SH wave propagation in laterall y homogeneous, isotropic media. The numerical solutions obtained using the modified operators are about 30 times more accurate than those ob tained using the unmodified operators for the same CPU time. Our metho ds are readily applicable to problems in spherical coordinates or invo lving laterally heterogeneous media, as well as to time-domain solutio ns. It should also be possible to apply the methods of this paper to n umerical methods other than the DSM.