Accurate numerical methods for solving the elastic equation of motion for arbitrary source locations

In our previous studies we derived a general criterion for optimally accurate numerical operators for computing synthetic seismograms. In this paper we extend our results by deriving source representations that are ʹtunedʹ to match the errors of the numerical operators, so that optimally accurate synthetic seismograms are obtained. The same accuracy can be obtained whether the sources are at nodes of the numerical grid or between nodes. The accuracy of the synthetic seismograms is confirmed by numerical experiments. These results should facilitate inversion of seismic waveform data for 3-D Earth structure and earthquake source parameters.