Testing four elastic finite-difference schemes for behavior at discontinuities

Three second-order and one fourth-order finite-difference schemes are theoretically and numerically investigated for their behavior at elastic discontinuities. One of them is extended with new formulas for a flat free surface. Two of the schemes are consistent with the stress-continuity condition for P-SV waves at discontinuities coinciding with horizontal (or vertical) grid lines; none of them is consistent at diagonal discontinuities. Despite these significant theoretical differences, the numerical results from all four schemes are very similar. Moreover, the results compare well with semianalytic solutions for three different models. A practical conclusion is that the recent finite-difference schemes are by no means free from the accuracy problems at elastic discontinuities. Nevertheless, the schemes provide synthetic seismograms whose differences are well below the level normally introduced by structural and focal uncertainties.