Seismic Response of Three-Dimensional Topographies

Three-dimensional topographic effects for incident P and S waves in an elastic half-space are studied using a simplified indirect boundary element method. It is based on the integral representation for diffracted elastic fields in terms of single layer boundary sources. It can be seen as a numerical realization of Huygens' principle because diffracted waves are constructed at the boundaries from which they are radiated. The free-boundary condition leads a Fredholm integral equation of the second kind for boundary sources. A simplified discretization scheme that uses circles of various sizes, that approximately cover the boundary surfaces, is used for the numerical and analytical integration of the exact Green's functions for displacements and tractions. The incidence of elastic waves upon a semi-spherical is used for testing the method. Results are also obtained for an irregular mountain. We analyze the surface motion along two perpendicular profiles in both frequency and time domains. Results show a great variability of the surface ground motion. These spatial variations are mainly due to locally generated surface waves. This can be seen by means of frequency-space descriptions and synthetic seismograms as well.