Theoretical analysis of observed second bulk compressional wave in a fluid-saturated porous solid at ultrasonic frequencies

Abstract

We show that the second bulk compressional wave observed recently in an experiment by Plona is consistent with the ’’slow’’ compressional wave as predicted by Biot’s theory. We present dispersion and attenuation curves for all of the body waves for Plona’s samples computed as a function of frequency and Biot’s structure factor S. At high frequencies the velocity of the slow compressional wave is approximately equal to Vf/ S1/2, where Vf is the normal compressional-wave velocity in the pore fluid. Thus, from the measured velocities of slow compressional waves one can obtain S. For Plona’s three samples, the predicted structure factors are 2.1, 2.2, and 3.3.