Rj. Geller et N. Takeuchi, A NEW METHOD FOR COMPUTING HIGHLY ACCURATE DSM SYNTHETIC SEISMOGRAMS, Geophysical journal international, 123(2), 1995, pp. 449-470
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.