Multiple cracks in VTI rocks: Effective properties and fracture characterization

The existing fracture-characterization techniques are based on assuming the unfractured host rock either to be isotropic or the magnitudes of both the background and crack-induced anisotropies to be small. I relax both assumptions and examine the effective media caused by fractures with realistic (not small) crack densities in a strongly anisotropic, primarily transversely isotropic (TI) host rock. The analysis of penny-shaped cracks in the noninteraction approximation (NIA) reveals the dependence of their excess fracture compliance tensors on the orientation of the background symmetry axis. As a result of this dependence, the excess fracture compliance tensor generally becomes rotationally noninvariant even when the cracks are circular. One of the consequences of this complication (compared to the background isotropy) is a reduction of symmetry from TI to monoclinic resulting from the presence of a single oriented fracture set. Vertical dry cracks in a vertically transversely isotropic (VTI) host constitute an important exception to this general rule. The effective symmetry for this arrangement is approximately orthorhombic (or orthotropic) even in the presence of multiple fracture sets that have arbitrary azimuths. I perform finite-element simulations on the so-called digital rocks to verify both the proximity of effective symmetry to orthotropy and the accuracy of the NIA up to the crack density of 0.15. Multiple sets of dry vertical cracks in a VTI host not only result in nearly orthorhombic effective symmetry but also their cumulative influence is equivalent to that of just two orthogonal (or principal) fracture sets. The possibility of replacing multiple fracture sets with two orthogonal ones paves the way for their characterization. The inverse problem of estimating the parameters of two orthogonal crack systems in a VTI background from the effective elasticity, however, is known to be nonuique. I suggest overcoming its ambiguity by combining 31), wide-azimuth, multicomponent seismic data with sonic logs.