Measurements of Shear-wave Azimuthal Anisotropy with Cross-dipole Logs

Three methods for analyzing azimuthal anisotropy from cross-dipole logs are applied to data from the Powder River Basin in Wyoming. These techniques are based on the phenomena of flexural wave splitting in anisotropic materials and are analogous to the techniques used for VSP data processing. The four-component cross-dipole logging data obtained with a Schumberger tool from a vertically-fractured section of 56 m at a depth of 3550 m are processed with three different techniques. The results demonstrate that the non-orthogonal rotation method works best for the data. The results from the linear transform and polar energy spectrum methods are acceptable. The linear transform processing takes much less computing time, while the polar energy spectrum method is computationally-intensive. INTRODUCTION Laboratory and field observations have demonstrated that, if a formation exhibits shearwave anisotropy, i.e., there is a directional crack system or ambient stress field, the flexural mode will propagate anisotropically with respect to their polarization direction. Intuitively, one might expect that a flexural mode polarized along the fast or slow direction will propagate at zero frequency with fast or slow formation shear velocities, respectively. This phenomenon could be used to characterize the formation anisotropy in principle. A simple mode calculation made by Leveille and Seriff (1989) proved that this is most likely the case. Further calculations carried out by Ellefsen (1990) and Cheng (1994) show that in the presence of azimuthal anisotropy, two (quasi-) flexural modes exist-a slow flexural wave for which the particle displacements are aligned with the 10-1 Tao et al. polarization of the slow shear wave, and a fast flexural wave for which the particle displacements are aligned with the polarization of the fast shear wave. Sinha (1991) also calculated the flexural mode excitation amplitudes in the presence of transverse isotropy. Ellefsen (1990) showed that for normal modes propagating along a borehole that is parallel to the symmetry axis of a transversely isotropic earth model, the shapes of the phase and group velocity curves are like those for an isotropic model. The phase velocities of these modes do not exceed the phase velocities of the two S-waves propagating parallel to the symmetry axis. Furthermore, the characteristics of the displacements and pressures are identical to those for an isotropic mode. The orientations of the two flexural waves and the two screw waves are arbitrary, just as the polarizations of the two S-waves propagating parallel to the symmetry axis are arbitrary. For the case of an orthorhombic model with an intersection of two symmetry planes being parallel to borehole, the phase and group velocities do not exceed the phase velocity of the slow qS-wave whose wavenumber vector is parallel to the borehole. The two quasi-flexural waves have different phase and group velocities, and the differences are large at low frequencies but small at high frequencies. Using the perturbation model, Sinha (1991) calculated the flexural wave propagation characteristics in a liquid-filled borehole in an anisotropic formation. His results for a slow formation (Austin chalk) that exhibits the symmetry of a TI medium confirmed that the low-frequency asymptote of the flexural wave velocity merges with the quasi-S wave velocity for the selected propagation direction and the flexure direction parallel to the shear polarization directions. The high frequency asymptote of the flexural wave velocity turns out to be the Scholte wave velocity appropriate for the propagation and polarization directions. However, his results demonstrated that the difference in phase velocity between the two orthogonally polarized quasi-flexural waves is essentially independent of frequency under this condition. This phase velocity difference is a maximum when the TI symmetry axis inclines 90 with respect to the direction of wave propagation, and diminishes when the inclining angle becomes less than 45 0 • The frequency dependence of the amplitude difference for the two orthogonally polarized quasi-flexural waves is significant in this case. The synthetic waveforms he calculated for dipole sources directed along the SH" and Sv-wave polarization directions show that, the early arrivals are dominated by the less dispersive, low-frequency components. His models also show that waveform amplitudes are significantly larger for the fast flexural wave than for the slow flexural wave for the same source amplitudes. Finally, the dispersive features of the flexural arrivals are shown to be quite similar to those calculated for the case of a liquid-filled borehole of the same radius surrounded by an isotropic, slow formation. Hatchell and Cowles (1992) described a spectral method for determining the magnitude and direction of shear wave anisotropy in a weakly anisotropic (6Vs IVs « 1) formation, using full waveform dipole logging data. Esmersoy et al. (1994) employed the technique of data matrix rotation, which resembles a method for VSP data processing, to measure the sonic-scale shear anisotropy of a formation with dipole logging 10-2 (