Sand acoustics: The effective density fluid model, Pierce/Carey expressions, and inferences for porous media modeling

Recently, Pierce and Carey [J. Acoust. Soc. Am. 124, EL308-EL312 (2008)] presented a low frequency analysis of sound propagation in sand/silty sediments. Here, equivalent expressions are presented using a low frequency expansion of an unconsolidated version of Biot porous medium theory. The resulting expression for attenuation allows identification of the non-dimensional parameter beta in the Pierce/Carey result in terms of physical parameters. The agreement of these two derivations motivates further analyses. The results imply that porous media propagation models that treat the medium's inertia via a single component approximation disregard a fundamental physical effect resulting from the relative inertia of the grains and fluid and are thus incomplete.