Variation of effective elastic moduli of a solid with transverse isotropy due to aligned inhomogeneities

In this paper the effective or overall moduli of a solid containing aligned ellipsoidal inhomogeneties, are derived by making the scattered displacement field equal to that scattered by a spherical-shaped effective medium in the same matrix. It is shown that the obtained formulae of effective elastic moduli are of second-order accuracy at least. The effective moduli decrease monotonically with porosity, thus excluding the unphysical behavior in Hudson's model in which there is an increase of moduli with porosity when the porosity goes beyond a certain threshold. By integration of inhomegeneity orientation angle, the effective moduli can be obtained for a solid with randomly orientated inhomogeneities, which are the same as those in the Kuster-Toksöz model. Numerical calculations show that a rock with fluid-saturated inhomegeneities has a higher longitudinal wave modulus in the direction of TI symmetric axis than the modulus for a rock with empty inhomegeneities.