Reflection and transmission coefficients in fluid-saturated porous media

Abstract

Using Biot’s theory to describe the propagation of elastic waves in a fluid-saturated porous elastic solid (a Biot medium), the reflection and transmission coefficients were computed at a plane interface between a fluid and a Biot medium and at interfaces inside a Biot medium defined by either a change in saturant fluids or in the intrinsic rock permeability. The reflection and transmission coefficients were computed with and without the inclusion of a frequency correction factor that according to Biot has to be introduced in the equations above a certain critical frequency (‘‘frequency-dependent’’ versus ‘‘classic model’’). For a fluid–Biot medium interface and in the range 5 kHz–10 MHz for the example analyzed the two models show differences of the order of 11% for the reflection coefficients and between 11% and 31% for the type I, type II, and shear transmission coefficients. For the interfaces within a Biot medium, and for type II incident waves, in the same range of frequencies the cases examined showed differences in the reflection and transmission coefficients in the range 5%–80%. Because of the asymptotic properties of the frequency correction factor, the reflection and transmission coefficients coincide at very low and high frequencies. The analysis shows the importance of the inclusion of the frequency correction factor in analyzing wave propagation in Biot media for frequencies lying between the seismic and ultrasonic ranges.