Slow wave propagation in air-filled permeable solids

The propagation of slow compressional waves in air-saturated permeable solids was studied by experimental means between 10 and 500 kHz. The velocity and attenuation coefficient were measured as functions of frequency from the insertion delay and loss of airborne ultrasonic waves transmitted through thin slabs of 1–5 mm in thickness. Porous ceramics of 2–70 Darcy and natural rocks of 200–700 mDarcy permeability were tested. In the low-frequency (diffuse) regime, the experimental results are consistent with theoretical predictions; the phase velocity and attenuation coefficient are essentially determined by the permeability of the specimen and both increase proportionally to the square root of frequency. In the high-frequency (propagating) regime, the experimental results are consistent with the theoretical predictions for the phase velocity but not for the attenuation coefficient. The phase velocity asymptotically approaches a maximum value determined by the tortuosity of the specimen while the attenuation coefficient becomes linearly proportional to frequency instead of the expected square-root relationship. It is suggested that the observed discrepancy is due to the irregular pore geometry that significantly reduces the high-frequency dynamic permeability of the specimens.