Elastic waves at the plane interface of swelling porous half-space and viscoelastic half-space with voids

Reflection/ refraction phenomena of inhomogeneous plane waves at a plane interface with a swelling porous elastic solid consisting of three constituents - an elastic solid, viscous liquid, inviscid gas on one side and a viscoelastic solid with voids on the other side have been studied. This model has been considered in the spirit of a gas and oil/ water reservoir containing the porous solid skeleton that swells up due to the shear response of the viscous liquid present in the pores and natural gas; trapped beneath the Earth's crust containing minerals rocks. We have considered two problems: (i) Incident wave strikes the interface from the swelling porous half-space; (ii) Incident wave strikes the interface from the viscoelastic solid half-space with voids. Assuming the pores of the swelling porous medium at the interface to be sealed, appropriate boundary conditions have been formulated and the amplitude ratios corresponding to various reflected/ refracted waves have been presented. While conducing the numerical simulation for the specific model, the variations of energy ratios against the angle of incidence and frequency parameter have been thoroughly studied and are illustrated graphically. Attention has been paid to analyze the effects of voids of the viscoelastic half-space and swelling of the porous half-space on the energy ratios corresponding to various propagating waves in the two media. It is concluded that during reflection/ refraction phenomena, the sum of the energy ratios carried along various reflected and refracted waves is equal to unity at each angle of incidence only if the interactional energy ratios are included.