On effective characteristics of wave propagation in a porous fluid-saturated medium containing entirely fluid inclusions

To investigate the behaviour of seismic wave propagation in natural rocks and soils, a model for the elastic properties of a heterogeneous porous medium containing uniform fluid inclusions is useful. The problem has already been addressed before, utilizing Biot's theory of poroelasticity, and there have been some analytical and numerical results obtained for the different types of cavities. However, as it is shown in this paper, immediate passage within heterogeneous porous media from spherical porous heterogeneities to continuous fluid or solid inclusions cannot be performed on the basis of previously developed models. In this paper, we extend the results for wave scattering in porous media due to a random ensemble of spherical porous inclusions to allow for continuous fluid inclusions instead. To consider this case, we first obtain the single scattering series. Then we utilize multiple scattering theory to find the effective wavenumber due to an ensemble of inclusions. Our results make it possible to analyse wave attenuation and velocity dispersion at low frequencies due to the presence of entirely fluid inclusion heterogeneities within a porous material. Explicit analytical expressions for solution of single scattering problem for a fluid cavity, and effective propagation velocity and attenuation factor in a porous medium with random ensemble of these cavities constitute main results of this work.