Seismic responses of a hemispherical alluvial valley to SV waves: a three-dimensional analytical approximation

Abstract

An analytical solution to the three-dimensional scattering and diffraction of plane SV-waves by a saturated hemispherical alluvial valley in elastic halfspace is obtained by using Fourier-Bessel series expansion technique. The hemispherical alluvial valley with saturated soil deposits is simulated with Biot's dynamic theory for saturated porous media. The following conclusions based on numerical results can be drawn: (1) there are a significant differences in the seismic response simulation between the previous single-phase models and the present two-phase model; (2) the normalized displacements on the free surface of the alluvial valley depend mainly on the incident wave angles, the dimensionless frequency of the incident SV waves and the porosity of sediments; (3) with the increase of the incident angle, the displacement distributions become more complicated; and the displacements on the free

An Efficient Approach for Seismoacoustic Scattering Simulation Based on Boundary Element Method

“…The analytical solutions, however, only exist for a few special cases [5], such as the semi-cylindrical canyon and alluvial valleys, semi-elliptical canyon, and hemispherical canyon. The methods based on high-frequency approximation [6](such as asymptotic ray theory, Gaussian beam method, and so on) can give a proper solution by including the contribution from the neighboring rays but are only appropriate for handling body wave propagation under relatively high frequency.…”