Abstract of the review article ``Waves in partially saturated porous media''

Efforts to extend the theory of poroelasticity to semilinear and nonlinear elastic response, to partially saturated pores, to inhomogeneous solid frame materials, and to viscous losses due to localized flow effects are summarized. The prospects for a comprehensive theory of wave propagation in partially saturated porous media and the reasons for needing such a theory are also discussed. The main results are these:

(a) Using the physically reasonable assumption of negligible capillary pressure change during passage of an acoustic signal through the medium, equations of poroelasticity for partially saturated materials have been derived and boundary conditions assuring the uniqueness of the solutions have been found.

(b) Coefficients for scattering from a spherical inclusion in a poroelastic medium have been calculated. These coefficients may then be used to estimate effective constants in poroelastic wave equations when the medium is inhomogeneous; three common single-scattering approximations yield expressions that satisfy all known constraints on these constants and therefore provide generalized Gassmann's equations for inhomogeneous porous media.

(c) The observed anomalously high attenuation of sound in partially saturated porous media can be explained in part by accounting for the effects of inhomogeneous porosity and fluid permeability. Regions of high permeability allow more fluid motion than regions of low permeability and therefore may be expected to play the dominant role in sound attenuation.

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