SPECTRAL GREENS DYADIC FOR POINT SOURCES IN POROELASTIC MEDIA

A fairly detailed derivation of the spectral Green's dyadic for point sources in unbounded poroelastic media is presented. It is assumed tha t the motion of the poroelastic medium is governed by Blot's theory of poroelasticity; thus in a source-free unbounded space the wave field consists of two (fast and slow) longitudinal waves and a transverse wa ve. Considering a three-dimensional source-receiver system and then th rough a decomposition of the displacement and body force fields, the d ilatational and rotational components of motion are separated. Separat ion yields two sets of systems of two partial differential equations r epresenting scalar wave equations of poroelasticity, which unlike the case of elastic propagation are still coupled in terms of the motion o f the pore fluid and that of the frame material, respectively. General solutions are derived from the fundamental eigenvalue problems of por oelasticity, which are associated with the systems of the homogeneous wave equations. Singular solutions for point sources are then obtained by superimposing the latter with particular solutions of the inhomoge neous wave equations. Consistent with previous studies, the spectral G reen's dyadic shows that the body force singularity generates three di stinct waves. These waves are radiating from the source with wave spee ds, attenuations, and amplitudes, which depend on frequency and conseq uently on the level and type of dissipation in the two-phase medium.