A detailed analysis of the relationship between elastic waves in inhomogeneous, porous media and the effect of wave-induced fluid flow is presented. Based on the results of the poroelastic first-order statistical smoothing approximation applied to Biot's equations of poroelasticity, a model for elastic wave attenuation and dispersion due to wave-induced fluid flow in 3-D randomly inhomogeneous poroelastic media is developed. Attenuation and dispersion depend on linear combinations of the spatial correlations of the fluctuating poroelastic parameters. The observed frequency dependence is typical for a relaxation phenomenon. Further, the analytic properties of attenuation and dispersion are analyzed. It is shown that the low-frequency asymptote of the attenuation coefficient of a plane compressional wave is proportional to the square of frequency. At high frequencies the attenuation coefficient becomes proportional to the square root of frequency. A comparison with the 1-D theory shows that attenuation is of the same order but slightly larger in 3-D random media. Several modeling choices of the approach including the effect of cross correlations between fluid and solid phase properties are demonstrated. The potential application of the results to real porous materials is discussed.
Elasticity Models, Theoretical