OPTIMALLY ACCURATE 2ND-ORDER TIME-DOMAIN FINITE-DIFFERENCE SCHEME FORTHE ELASTIC EQUATION-OF-MOTION - ONE-DIMENSIONAL CASE

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.