Reflection and transmission of waves at a fluid/porous-medium interface

We study the wave properties at a fluid/porous-medium interface by using newly derived closed-form expressions for the reflection and transmission coefficients. We illustrate the usefulness of these relatively simple expressions by applying them to a water/porous-medium interface (with open-pore or sealed-pore boundary conditions), where the porous medium consists of (1) a water-saturated clay/silt layer, (2) a water-saturated sand layer, (3) an air-filled clay/silt layer, or (4) an air-filled sand layer. We observe in the frequency range 5 Hz-20 kHz that the fast P-wave and S-wave velocities in the four porous materials are indistinguishable from the corresponding frequency-independent ones calculated using Gassmann relations. Consequently, for these frequencies we would expect the reflection and transmission coefficients for the four water/porous-medium interfaces to be similar to the ones for corresponding interfaces between water and effective elastic media (described by Gassmann wave velocities). This expectation is not fulfilled in the case of an interface between water and an air-filled porous layer with open pores. A close examination of the expressions for the reflection and transmission coefficients shows that this unexpected result is because of the large density difference between water and air.