Reflection and refraction of obliquely incident elastic waves upon the interface between two porous elastic half-spaces saturated by different fluid mixtures

A theoretical model for the analysis of the reflection and refraction of obliquely incident elastic waves upon the interface between two semi-infinite porous elastic half-spaces saturated by different fluid mixtures is developed in the present study based on the poroelasticity theory of and the normal coordinates derived by for describing the modes of dilatory motion. The amplitude and energy ratios of the reflected and refracted waves generated from either an incident P1 wave (the first dilatational wave) or an incident SV wave (the shear wave polarized in the vertical plane) are in turn theoretically determined for the first time with respect to the angle of incidence. As a representative example, a numerical simulation is conducted for Lincoln sand permeated by an air–water mixture in the lower half-space and Columbia fine sandy loam permeated by an air–water mixture in the upper half-space. Our numerical results indicate that regardless of the type of pore fluid mixtures and porous media, the sum of the energy ratio of the reflected and refracted waves is always equal to unity, a result that indeed can not be achieved if the normal coordinates for dilatory motional modes is not taken into account as to represent the Helmholtz potential of the reflected and refracted waves. In addition, their amplitude and energy ratios are shown to be significantly affected by the angle of incidence. It is also revealed that as a SV wave is incident upon the interface, a critical angle of 31° and 33° can be found for the reflected and refracted P1 waves respectively, while the occurrence of the critical angle is not observed for the case of an incident P1 wave.