Buried Point Source in a Poroelastic Half-Space

Abstract

The problem under consideration is to determine the motion of a poroelastic half-space produced by a buried point source with arbitrary time variation. The method followed is to generate the associated Green's functions as a superposition of the singular solution corresponding to the inhomogeneous problem for the whole space plus a contribution representing relevant effects due to the presence of the free surface. The mathematical approach is based on integral transform techniques: Fourier transform with respect to the time and Hankel transform with respect to the space. The Green's functions for the displacement fields (solid and pore fluid motion respectively) show additional integratable singularities arising from Rayleigh poles and by eight branch points resulting from combinations of three radicals containing the three fundamental wave numbers of poroelastic propagation. Recognizing that the branch points and poles are complex valued as a result of dissipation by the skeletal frame as well as viscous dissipation due to the relative motion of the pore fluid with respect to the frame material, integration in the ω-