SEISMIC WAVE PROPAGATION IN INHOMOGENEOUS AND ANISOTROPIC POROUS MEDIA

Abstract

A set of macroscopic equations of motion for inhomogeneous and anisotropic porous media is constructed. The porous medium considered consists of an elastic solid with interconnected void spaces filled with a chemically inert viscous fluid. The constituents are assumed homogeneous in their material properties, but the unperturbed porosity is spatially varying and the distributions of pores and interfaces are uneven. The physics at the pore scale, which underpins the approach, is never lost sight of. Although very different in approach from that taken by Biot, a close correspondence to the Biot (1962) theory is established in this paper. The dynamic perturbation in porosity accompanying deformation is treated as kinematically independent of the macroscopic solid displacement field and the macroscopic fluid velocity field. The viscous loss within the pore fluid, which is absent in the Biot approach, is not excluded here. For the most general case, 27 independent macroscopic parameters enter into the macroscopic constitutive equations, not counting the spatial gradient of unperturbed porosity itself, which appears explicitly at various places. Whereas the elastic constants of the constituents are contained within Biot's parameters, here they are factored out. Thus, the parameters are directly linked to the manner in which distributed pores and interfaces control the deformation.