Acoustic wave propagation through porous media with arbitrary pore‐size distributions

Abstract

In the Biot theory, the effect of frequency on the oscillatory viscous forces within a porous medium is treated by replacing the kinematic viscosity ν by an oscillatory viscosity νF. Here, F is a function of angular frequency ω, the kinematic viscosity ν, and the single pore size a. In this paper, a mathematical expression of F is presented for arbitrary distribution of pore sizes that can be used in the Biot theory without modification. It is shown that porous media with a given permeability and porosity may be represented by an infinite number of pore‐size distributions. The dispersion and attenuation of acoustic waves through such porous media are independent of the pore‐size distribution at the low‐ and high‐frequency limits, while they are strongly dependent on the pore‐size distribution in the intermediate frequency range. For porous media with φ‐normal pore size distributions having a given value of permeability, the maximum specific attenuation decreases and the bandwith of dispersion increases with an increasing standard deviation of the pore‐size distribution. Finally, the generalized Biot theory for arbitrary distribution of pore sizes is compared with the entire data of compressional wave attenuation through surficial marine sediments given by E. Hamilton. Comparison between his data and the predictions from this theory show good agreement. [Work supported by ONR.]