Estimation Of Nonorthogonal Shear Wave Polarizations And Shear Wave Velocities From Four-Component Dipole Logs

Abstract

Polarizations of split shear waves and flexural borehole waves are most commonly estimated from four-component data using the rotation technique of Alford (1986). This method is limited to the case of the two polarizations being orthogonal to each other. We present a method that is able to handle the case of nonorthogonally polarized waves and, moreover, is computationally more efficient than Alford's technique. Our method is based on the eigenvalue decomposition of an asymmetric matrix and a least-squares minimization of its off-diagonal components. In the case of orthogonally polarized waves, our method will yield exactly the same results as the Alford rotation. We apply our method to a cross-dipole shear-wave logging data set from the Powder River Basin in Wyoming and find that independently rotated source-receiver sets are very consistent with each other in anisotropic sections. After the rotation we compare two methods for estimating the phase velocities of fast and slow waves-a semblance method and homomorphic processing (Ellefsen et al., 1993). We find homomorphic processing to be more reliable due to the dispersive nature of flexural waves.