Seismic response of three-dimensional alluvial valleys for incident P, S, and Rayleigh waves

A simplified indirect boundary-element method (BEM) is presented. It is used to compute the seismic response of three-dimensional alluvial valleys under incident P, S , and Rayleigh waves. The method is based on the integral representations for scattered elastic waves using single-layer boundary sources. This approach is called indirect BEM in the literature as the sources strengths should be obtained as an intermediate step. Scattered waves are constructed at the boundaries from which they radiate. Therefore, this method can be regarded as a numerical realization of Huygens' principle. Boundary conditions lead to a system of integral equations for boundary sources. A simplified discretization scheme is used. It is based on the approximate rectification of the surfaces involved using circles for the numerical and analytical integration of the exact Green's function for the unbounded elastic space. Various examples are given for three-dimensional problems of scattering and diffraction of elastic waves by soft elastic inclusion models of alluvial deposits in an elastic half-space. Results are displayed in both frequency and time domains. These results show the significant influence of locally generated surface waves in seismic response, and they evince three-dimensional effects.