Topographic effects for incident P, SV and Rayleigh waves

Abstract

The topographical effects for incident P, SV and Rayleigh waves in an elastic half-space were studied using an integral representation of the diffracted elastic waves in terms of single-layer boundary sources. The free-boundary condition leads to a Fredholm integral equation of the second kind for boundary sources. We used a discretization scheme based on the numerical and analytical integration of exact Green's functions. This approach is called indirect BEM in the literature. However, it provides far more insight on the physics of diffraction problems than the direct approaches. This is because diffracted waves are constructed at the boundaries from which they are radiated. Therefore, this method can be regarded as a numerical realization of Huygens' principle. Various examples that cover extreme cases are presented. It is found that topography may cause significant effects both of amplification and of deamplification at the irregular feature itself and its neighborhood but the absolute level of amplification is generally lower than about 4 times the amplitude of incoming waves. These facts must be taken into account when the spectral ratio technique is used to study topographical response.