Comparison of two independent methods for the solution of wave-scattering problems: Response of a sedimentary basin to vertically incidentSHwaves

Abstract

The transient solution to several problems that was obtained by numerical integration of equations of motion using a finite difference (FD) technique is compared with the complex-frequency solutions obtained by the approximate wave theoretical (AL) method of K. Aki and K. L. Lamer. The excellent agreement between the two solutions not only provides a comparative check on the accuracies of the two techniques, but also demonstrates that the interpretation of the AL solution is comparable to the Fourier transform of the transient solution premultiplied by an exponential window. Most of the paper is devoted to a discussion of two models that are relevant to the engineering-seismological study of earthquake motions in soft layers of varying thicknesses. The FD and AL solutions show that lateral reverberations of waves produced by the nonplanar structure form complex interference patterns that are not predicted by the usual flat-layer approximations. In one example, constructive interference enhances the peak amplitude of the transient motion over the center of the basin by a factor of 3 relative to the flat-layer solutions. The results indicate that a realistic appraisal of earthquake hazards in areas underlain by soft surficial layers should include the effect of nonuniformity in the structure.