Optimally accurate second-order time-domain finite difference scheme for the elastic equation of motion: one-dimensional case

Details Optimally accurate second-order time-domain finite difference scheme for the elastic equation of motion: one-dimensional case Optimally accurate second-order time-domain finite difference scheme for the elastic equation of motion: one-dimensional case

Oct 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998geoji.135...48g&link_type=abstract

Geophysical Journal International, Volume 135, Issue 1, pp. 48-62.

Astronomy and Astrophysics

Astronomy

10

Finite Difference Method, Synthetic Seismograms

Scientific paper

We previously derived a general criterion for optimally accurate νmerical operators for the calculation of synthetic seismograms in the frequency domain (Geller & Takeuchi 1995). We then derived modified operators for the Direct Solution Method (DSM) (Geller & Ohminato 1994) which satisfy this general criterion, thereby yielding significantly more accurate synthetics (for any given numerical grid spacing) without increasing the computational requirements (Cummins et al. 1994; Takeuchi, Geller & Cummins 1996; Cummins, Takeuchi & Geller 1997). In this paper, we derive optimally accurate time-domain finite difference (FD) operators which are second order in space and time using a similar approach. As our FD operators are local, our algorithm is well suited to massively parallel computers. Our approach can be extended to other methods (e.g. pseudo-spectral) for solving the elastic equation of motion. It might also be possible to extend this approach to equations other than the elastic equation of motion, including non-linear equations.

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