Abstract of the paper ``Single-scattering approximations for coefficients in
Biot's equations of poroelasticity''
Three single-scattering approximations for coefficients in Biot's
equations of poroelasticity are considered: the average T-matrix
approximation (ATA), the coherent potential approximation (CPA),
and the differential effective medium (DEM).
The scattering coefficients used here are exact results obtained
previously for scattering from a spherical inclusion of one Biot
material imbedded in another otherwise homogeneous Biot material.
The CPA has been shown previously to guarantee that, if the
coefficients for the scattering materials satisfy Gassmann's
equation, then the effective coefficients for the composite
medium satisfy Brown and Korringa's generalization of Gassmann's
equation.
A collection of similar results is obtained here showing that
the coefficients derived from ATA, CPA, or DEM all satisfy the
required conditions for consistency.
It is also shown that Gassmann's equation will result from
any of these single-scattering approximations
if the collection of scatterers includes only spheres of fluid
and of a single type of elastic solid.
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