Characterization of dipping fractures in a transversely isotropic background

Although it is believed that natural fracture sets predominantly have near-vertical orientation, oblique stresses and some other mechanisms may tilt fractures away from the vertical. Here, we examine an effective medium produced by a single system of obliquely dipping rotationally invariant fractures embedded in a transversely isotropic with a vertical symmetry axis(VTI) background rock. This model is monoclinic with a vertical symmetry plane that coincides with the dip plane of the fractures. Multicomponent seismic data acquired over such a medium possess several distinct features that make it possible to estimate the fracture orientation. For example, the vertically propagating fast shear wave (and the fast converted PS-wave) is typically polarized in the direction of the fracture strike. The normal-moveout(NMO) ellipses of horizontal reflection events are co-orientated with the dip and strike directions of the fractures, which provides an independent estimate of the fracture azimuth. However, the polarization vector of the slow shear wave at vertical incidence does not lie in the horizontal plane - an unusual phenomenon that can be used to evaluate fracture dip. Also, for oblique fractures the shear-wave splitting coefficient at vertical incidence becomes dependent on fracture infill (saturation). A complete medium-characterization procedure includes estimating the fracture compliances and orientation (dip and azimuth), as well as the Thomsen parameters of the VTI background. We demonstrate that both the fracture and background parameters can be obtained from multicomponent wide-azimuth data using the vertical velocities and NMO ellipses of PP-waves and two split SS-waves (or the traveltimes of PS-waves) reflected from horizontal interfaces. Numerical tests corroborate the accuracy and stability of the inversion algorithm based on the exact expressions for the vertical and NMO velocities.