The existing fracture-characterization techniques are based on assuming the unfractured host rock either to be isotropic or the magnitudes of both the back- ground and crack-induced anisotropy to be small. I relax both assumptions and examine the effec- tive media caused by fractures with realistic (not small) crack densities in moderately and strongly anisotropic, primarily transversely isotropic (TI), host rocks. The analysis of penny-shaped cracks in the non-interaction approximation (NIA) reveals the dependence of their excess fracture compliance ten- sors, Z, on the orientation of the background sym- metry axis. As a result, tensors Z generally become rotationally non-invariant even when the cracks are circular. One of the consequences of this complica- tion (compared to the background isotropy) is a re- duction of the effective symmetry from TI to mono- clinic due to the presence of a single oriented fracture set. Vertical cracks in a vertically transversely isotropic (VTI) host constitute an important exception from this general rule. The effective symmetry for this arrangement is approximately orthorhombic (or or- thotropic) 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 the effective symmetry to orthotropy and the accuracy of the NIA. Although an approximate effective orthotropy, which makes it possible to replace multiple fracture sets with two orthogonal ones, simplifies fracture char- acterization, the inverse problem of estimating the crack and background parameters from the effective elasticity is still nonunique. Its ambiguity can be overcome by combining wide-azimuth seismic reflec- tion data with sonic logs.
Overwhelming majority of fracture-characterization techniques assumes cracks to be embedded in an oth- erwise isotropic host. Yet, intrinsic anisotropy of many unfractured rocks, such as shales, makes it de- sirable to extend the existing fracture-characteriza- tion methods to anisotropic, at least vertically trans- versely isotropic (VTI) backgrounds. Such an exten- sion has to tackle two related problems: (i) devising accurate e®ective media schemes for anisotropic rocks with fractures and (ii) handling an inherent ambigu- ity of inversion of seismic data for the fractures and the host anisotropy. While some best-case inversion scenarios examined by Grechka and Tsvankin (2003) partially address the second class of problems, the effective proper- ties of intrinsically anisotropic formations containing cracks have not been treated adequately in geophys- ical literature. Many authors follow the slip theory of Schoenberg (1980) and describe the influence of cracks by adding the excess fracture compliance ten- sor, Z, calculated in a purely isotropic background to the compliance tensor, sb, of an anisotropic host. Such an approach is erroneous even for dilute crack concentrations because the dependence Z = Z(sb) can be ignored only when the background anisotropy is weak. Here I discuss a theoretically sound representation of Z(sb), which is valid for penny-shaped cracks em- bedded in arbitrarily anisotropic (triclinic) hosts, and use it to construct the non-interaction approximation (NIA) for the effective properties of fractured VTI media