Frequency domain fundamental solutions for a poroelastic half-space

In frequency domain, the fundamental solutions for a poroelastic half-space are re-derived in the context of Biot’s theory. Based on Biot’s theory, the governing field equations for the dynamic poroelasicity are established in terms of solid displacement and pore pressure. A method of potentials in cylindrical coordinate system is proposed to decouple the homogeneous Biot’s wave equations into four scalar Helmholtz equations, and the general solutions to these scalar wave equations are obtained. After that, spectral Green’s functions for a poroelastic full-space are found through a decomposition of solid displacement, pore pressure, and body force fields. Mirror-image technique is then applied to construct the half-space fundamental solutions. Finally, transient responses of the half-space to buried point forces are examined.