Dynamic Green's functions for a poroelastic half-space

The dynamic responses of a poroelastic half-space to an internal point load and fluid source are investigated in the frequency domain in this paper. By virtue of a method of displacement potentials, the 3D general solutions of homogeneous wave equations and fundamental singular solutions of inhomogeneous wave equations are derived, respectively, in the frequency domain. The mirror-image technique is then applied to construct the dynamic Green's functions for a poroelastic half-space. Explicit analytical solutions for displacement fields and pore pressure are obtained in terms of semi-infinite Hankel-type integrals with respect to the horizontal wavenumber. In two limiting cases, the solutions presented in this study are shown to reduce to known counterparts of elastodynamics and those of Lamb's problem, thus ensuring the validity of our result.