Effective-Medium Anisotropic models of Fractured Rocks of TI Symmetry: Analysis of Constraints and Limitations in Linear Slip model

Abstract

The simplest effective-medium model of fractured rocks known as the Linear Slip (LS) model of Schoenberg (1980) represents a single fracture set in an isotropic background rock. In the LS model, the stiffness C13 is not independent as in the overall transversely isotropic (TI) model, but it is related to other stiffnesses by the equation, C11C33 C 2 13 = 2C66(C33+C13). We have studied a physical sense of this constraint on the C13 and found out that in terms of the TI elastic compliance tensor S it leads to the equality 12 = 13, where 13 and 12 are the two different horizontal Poisson’s ratios. In contrast to the Linear Slip model, in the overall TI model, one of these Poisson’s ratios, 13, is always greater than the other one, 12, that is validated by numerous static and dynamic laboratory measurements of these Poisson’s ratios in VTI-type rocks. Thus we have revealed a contradiction and inconsistency in the constraint on the C13 for the LS model. Moreover, the restriction on C13 for the LS model doesn’t work for the overall TI medium in which there are physical constraints on the C13, namely, C13_min C13_min. The LS model is not a universal model for real rocks. It may work successfully only in several special cases, or under certain conditions, for example, when the normal fracture weakness ΔN =0 (fluid-saturated cracks), or in the case of ΔN = ΔT (dry cracks). Also we have revealed that the LS model may suit better for sandstones and carbonates than for shales.