An Analytic Solution for the Three-Dimensional Diffraction of Plane SV-Waves by Hemispherical Canyon in a Fluid-Saturated Porous Medium Half Space

Abstract

On the basis of the Biot dynamic theory, an analytic solution of three-dimensional scattering of incident plane SV waves by hemispherical canyons in a fluid saturated porous media half space is derived. The Fourier-Bessel series expansion technique is used to get the analytic solution for the first time. The results of surface displacement amplitudes are presented, the effects of frequency and angle of incident waves on the surface displacement amplitudes are discussed. These results are compared with those from the same situation but with an elastic one-phase medium. We conclude that (1) there is a significant difference between the previous single-phase model and the present two-phase model; (2) the normalized displacements on the free surface of alluvial valley are mainly dependent on the incident wave angles, the dimensionless frequency of the incident SV-waves; (3) with the increases of the incident angle, frequency, the displacements become more complicated; and the amplification of the displacement on the free surface of alluvial valley is more prominent than that modeled by single-phase.