Kristek et al. (2002) developed a technique for simulating the planar free surface in the 3D fourth-order staggered-grid finite-difference (FD) modeling of seismic motion. The technique is based on (1) explicit application of zero values of the stress-tensor components at the free surface and (2) adjusted FD approximations (AFDAs) to vertical derivatives at and near the free surface. The technique was shown to be more accurate and efficient than the standard stress-imaging technique in 1D models.
In this study, we tested accuracy of the AFDA technique in media with lateral material discontinuities reaching the free surface. We compared the FD synthetics with synthetics calculated by the standard finite-element (FE) method because the FE method naturally and sufficiently accurately satisfies the boundary conditions at the free surface and the traction interface continuity conditions at internal material discontinuities. The comparison showed a very good level of accuracy of the AFDA technique. We also demonstrated the very good sensitivity of our FD modeling to different positions of the same physical model in the spatial FD grid.