Acoustic wave propagation through porous media with arbitrary pore size distributions

Abstract

In the Biot [J. Acoust. Soc. Am. 28, 168–178 (1956); 28, 179–191 (1956)] theory, the effect of frequency on the viscous forces within a porous medium is treated by replacing the kinematic viscosity ν by an oscillatory viscosity νF, in which F is a function of angular frequency ω, the kinematic viscosity ν, and the single pore size a. The mathematical expression of F for arbitrary distribution of pore sizes that can be used in the Biot theory without modification is presented. It is shown that porous media with a given permeability and porosity may be represented by an infinite number of pore size distributions. The velocities and attenuation of acoustic waves through such porous media are independent of the pore size distribution at the low-frequency limit and at the high-frequency limit, while they are strongly dependent on the pore size distribution in the intermediate frequency range. Comparisons between Hamilton’s [Geophysics 37, 620–646 (1972)] data of attenuation coefficient of compressional waves through marine sediments and the prediction by our theory show good agreement.