Reflection and transmission of waves in composite porous media: A quantification of energy conversions involving slow waves

Abstract

This paper studies the reflection and transmission of plane elastic waves at interfaces in fluid-saturated poroviscoelastic media in which the solid matrix is composed of two weakly coupled solids. The analysis of this problem, not formally performed before, is based on a theory recently developed by some of the authors, which allows us to derive expressions for the reflection and transmission coefficients at a plane interface within this kind of media and their relationship with the energy flux (Umov-Poynting) vector. The results of the present derivation were applied to study the energy splitting that takes place when a plane fast compressional wave strikes obliquely an interface defined by a change in ice content within a sample of water saturated partially frozen sandstone. The numerical results show wave mode conversions from fast to slow compressional and shear waves, with maximum energy conversion on the order of 20% from fast to slow wave modes near the critical angle. This phenomenon was observed at frequencies lying from the seismic to the ultrasonic range, showing that the role of the slow waves must be taken into account when considering wave propagation in this type of media.