Dispersion in poroelastic systems

We address one key source of the known discrepancies between theory and experiment in poroelasticity, i.e., the fact that Gassmann's equations for the bulk and shear moduli predict that the shear modulus is independent of the saturating fluid properties, whereas it is observed on the contrary that at high enough frequencies the shear modulus can in fact depend on the fluid's elastic properties in many porous materials. One clue to understanding this behavior comes from effective medium theory, which shows that the shear modulus does depend on the fluid properties in many circumstances. In comparison to values predicted by effective medium theory, Gassmann's equations predict different, smaller values for both the effective bulk and shear moduli of porous media. Sorting through these apparent (but not actual) disagreements among theory and theory, and theory and experiment is the main thrust of the paper.