Bounds for seismic dispersion and attenuation in poroelastic rocks
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Recently, Hashin-Shtrikman bounds for bulk and shear moduli of elastic composites have been extended to the moduli of composite viscoelastic media. Since viscoelastic moduli are complex, the viscoelastic bounds form a closed curve on a complex plane. We apply these general viscoelastic bounds to a particular case of a porous solid saturated with a Newtonian fluid. Our analysis shows that for poroelastic media, the viscoelastic bounds for the bulk modulus are represented by a semi-circle and a segment of the real axis, connecting formal HS bounds (computed for an inviscid fluid). Furthermore, these bounds are independent of frequency and realizable. We also show that these viscoelastic bounds account for viscous shear relaxation and squirt-flow dispersion, but do not account for Biot's global flow dispersion.
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