We previously derived a general criterion For optimally accurate numer
ical operators for the calculation of synthetic seismograms in the fre
quency domain (Geller & Takeuchi 1995), We then derived modified opera
tors for the Direct Solution Method (DSM) (Geller & Ohminato 1994) whi
ch satisfy this general criterion, thereby yielding significantly more
accurate synthetics (for any given numerical grid spacing) without in
creasing the computational requirements (Cummins et al, 1994; Takcuchi
, Geller Sr Cummins 1996. Cummins, Takeuchi Sc Geller 1997. In this pa
per, we derive optimally accurate time-domain finite difference (FD) o
perators which are second order in space and time using a similar appr
oach, As our FD operators are local, our algorithm is well suited to m
assively parallel computers, Our approach can be extended to other met
hods (e,g, pseudo-spectral) for solving the elastic equation of motion
, Tt might also be possible to extend this approach to equations other
than the elastic equation of motion, including non-linear equations.