Open AccessOptimally accurate second‐order time‐domain finite difference scheme for the elastic equation of motion: one‐dimensional case
Author(s) -
Geller Robert J.,
Takeuchi Nozomu
Publication year - 1998
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1046/j.1365-246x.1998.00596.x
Subject(s) - seismogram , mathematics , grid , domain (mathematical analysis) , equations of motion , motion (physics) , time domain , spacetime , finite difference , algorithm , mathematical analysis , computer science , geometry , physics , classical mechanics , computer vision , civil engineering , quantum mechanics , artificial intelligence , engineering
Summary 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.