Effective medium theory for partially saturated porous solids

In the theory of elastic composites, one may construct an effective medium theory by choosing the effective moduli so the forward scattering from isolated elastic inclusions vanishes on average. In the theory of partially saturated porous media, the analogous problem requires knowledge of the multipole scattering coefficients for elastic scattering from isolated inhomogeneities in a fluid-saturated porous medium. Using Biot's equations of poroelasticity, these coefficients for single-scattering from spherical inhomogeneities have been calculated. When these coefficients are used to construct an effective medium theory, the resulting formulas for the effective density and bulk modulus of the composite (liquid/gas) fluid recover Wood's well-known results. Equations for wave propagation through partially saturated porous media with the coefficients deterimined by the effective medium results predict wave speeds agreeing with experiment in the seismological frequency range.