Debye-series analysis of the transmission coefficient of a water-saturated porous plate obeying Biot’s theory

We derive the Debye-series expansion of the normal transmitted plane wave through a water-saturated porous plate. By using relations from Biot’s theory, the theoretical transmission coefficient of the plate is related to a limited number of unknown parameters (velocity, attenuation coefficient of the fast and slow wave, reflection coefficients at the interfaces of the plate). They are determined via a comparison with the experimental transmission coefficient. The measurements show that the attenuation of the dilatational waves scales as the second power of frequency.