Green’s functions in an infinite transversely isotropic saturated poroelastic medium

The purpose of this article is to study Green’s functions for an infinite transversely isotropic saturated poroelastic medium. In the first part, equations of motions of such a medium are recalled according to Biot’s theory and completed by homogenization techniques, for harmonic displacements. The second part gives Green’s functions for such an infinite medium in the 3-D Fourier-transformed geometrical space. In the third part, a 1-D inverse analytical Fourier transformation, followed by an inverse Hankel transformation, leads to an analytical expression of Green’s functions for harmonic motions. Some numerical methods to compute final Green’s functions in time space are listed.