Separation of split S-waves in two nonorthogonal sets of vertical fractures

Abstract

The phenomenon of S-wave splitting indicates the development of fractures in the shallow crust. Therefore, methods based on S-wave splitting have been established to predict the development of one set of parallel fractures. However, for rocks containing two nonorthogonal sets of vertical fractures, the mechanism of S-wave splitting is more complex, and the available methods cannot be applied. To resolve this inadequacy, we have developed a two-way rotation method to separate split S-waves with the aim of restoring the split S-wave polarizations and predicting the fracture azimuths. First, we calculate the stiffness matrix of fractured media based on the linear slip theory and derive the phase velocities and polarizations of split S-waves induced by fractures using the Christoffel equation. Second, we clarify the S-wave splitting mechanism in this media by using velocity analysis and deconstruct the S-wave polarizations on the horizontal components. Third, we deduce a two-way rotation matrix obtained by the S-wave splitting modes to separate the split S-waves. To solve for the angle parameters related to the fracture azimuths in the two-way rotation matrix, we superpose the subspace polarizations in two dimensions to determine the polarization azimuths of the split S-waves. Numerical model tests demonstrate that our method is stable under noisy conditions. Finally, we apply our method to real near offset and walkaround vertical seismic profiling data, and the predicted fracture results are verified by imaging logs and prior knowledge.