Estimation of fracture parameters from reflection seismic data - Part III: Fractured models with monoclinic symmetry

Geophysical and geological data acquired over naturally fractured reservoirs often reveal the presence of multiple vertical fracture sets. Here, we discuss modeling and inversion of the effective anisotropic parameters of two types of fractured media with monoclinic symmetry. The first model is formed by two different nonorthogonal sets of rotationally invariant vertical fractures in an isotropic host rock; the other contains a single set of fractures with microcorrugated faces. In monoclinic media with two fracture sets, the shear-wave polarizations at vertical incidence and the orientation of the NMO ellipses of pure modes in a horizontal layer are controlled by the fracture azimuths as well as by their compliances. While the S-wave polarization directions depend only on the tangential compliances, the axes of the P-wave NMO ellipse are also influenced by the normal compliances and therefore have a different orientation. This yields an apparent discrepancy between the principal anisotropy directions obtained using P and S data that does not exist in orthorhombic media. By first using the weak-anisotropy approximation for the effective anisotropic parameters and then inverting the exact equations, we devise a complete fracture characterization procedure based on the vertical velocities of the P- and two split S-waves (or converted PS-waves) and their NMO ellipses from a horizontal reflector. Our algorithm yields the azimuths and compliances of both fracture systems as well as the P- and S-wave velocities in the isotropic background medium. In the model with a single set of microcorrugated fractures, monoclinic symmetry stems from the coupling between the normal and tangential (to the fracture faces) slips, or jumps in displacement. We demonstrate that for this model the shear-wave splitting coefficient at vertical incidence varies with the fluid content of the fractures. Although conventional fracture models that ignore microcorrugation predict no such dependence, our conclusions are supported by experimental observations showing that shear-wave splitting for dry cracks may be substantially greater than that for fluid-filled ones.