Estimation of parameters of multiple fracture sets is often required for successful exploration and development of naturally fractured reservoirs. The goal of this paper is to determine the maximum number of fracture sets of a certain rheological type which, in principle, can be resolved from seismic data. The main underlying assumption is that an estimate of the complete effective stiffness tensor has been obtained, for example, from multiazimuth, multicomponent surface seismic and vertical seismic profiling (VSP) data. Although typically only a subset of the stiffness elements (or some of their combinations) may be available, this study helps to establish the limits of seismic fracture-detection algorithms.
The number of uniquely resolvable fracture systems depends on the anisotropy of the host rock and the rheology and orientation of the fractures. Somewhat surprisingly, it is possible to characterize fewer vertical fracture sets than dipping ones, even though in the latter case the fracture dip has to be found from the data. For the simplest, rotationally invariant fractures embedded in either isotropic or transversely isotropic with a vertical symmetry axis (VTI) host rock, the stiffness tensor can be inverted for up to two vertical or four dipping fracture sets. In contrast, only one fracture set of the most general (microcorrugated) type, regardless of its orientation, is constrained by the effective stiffnesses. These results can be used to guide the development of seismic fracture-characterization algorithms that should address important practical issues of data acquisition, processing, and inversion for particular fracture models.