Interpretation of shear wave birefringence in P to S converted waves data using the propagator matrix method

Abstract

We present an original method for estimating local shear wave birefringence properties for 3D surface P to S converted waves. To accomplish this we approach the problem using reverse VSP (RVSP). The method works in the pre-stack domain and uses the P waves converted to S as shear wave sources. We solve the transmission problem using the propagator matrix method. The importance of this method is that it does not require information about layering above the zone of interest and is accurate for estimating the anisotropy parameters. The method involves solving a non-linear problem in the frequency domain where Simulated Annealing is used as the global minimization technique. The procedure allows estimation of the propagator matrix related to the target zone, assuming plane wave propagation allows its diagonalization by pure rotations. This matrix diagonalization ends up with an estimation of the natural eigen directions of the medium when the range of offset angles does not exceed 35*. The proposed method is validated with synthetic RVSP data for two models with different densities of vertical fractures. Results show good accuracy in the estimation of the angle of the fractures for the whole range of offsets. The study also extends to show the dependence on the frequency and on the offset.