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.
Applied Physics Laboratory, College of Ocean and Fishery Sciences, University of Washington, Seattle, Washington 98105, USA. williams@apl.washington.edu
Kevin L
KL
Williams