Determination of the principal directions of azimuthal anisotropy from P-wave seismic data

In an azimuthally anisotropic medium, the principal directions of azimuthal anisotropy are the directions along which the quasi-P-and the quasi-S-waves propagate as pure P and S modes. When azimuthal anisotropy is induced by oriented vertical fractures imposed on an azimuthally isotropic background, two of these principal directions correspond to the directions parallel and perpendicular to the fractures. S-waves propagating through an azimuthally anisotropic medium are sensitive to the direction of their propagation with respect to the principal directions. As a result, primary or mode-converted multicomponent S-wave data are used to obtain the principal directions. Apart from high acquisition cost, processing and interpretation of multicomponent data require a technology that the seismic industry has not fully developed. Anisotropy detection from conventional P-wave data, on the other hand, has been limited to a few qualitative studies of the amplitude variation with offset (AVO) for different azimuthal directions. To quantify the azimuthal AVO, we studied the amplitude variation with azimuth for P-wave data at fixed offsets. Our results show that such amplitude variation with azimuth is periodic in 2 phi, phi being the orientation of the shooting direction with respect to one of the principal directions. For fracture-induced anisotropy, this principal direction corresponds to the direction parallel or perpendicular to the fractures. We use this periodic azimuthal dependence of P-wave reflection amplitudes to identify two distinct cases of anisotropy detection. The first case is an exactly determined one, where we have observations from three azimuthal lines for every common-midpoint (CMP) location. We derive equations to compute the orientation of the principal directions for such a case. The second case is an overdetermined one where we have observations from more than three azimuthal lines. Orientation of the principal direction from such an overdetermined case can be obtained from a least-squares fit to the reflection amplitudes over all the azimuthal directions or by solving many exactly determined problems. In addition to the orientation angle, a qualitative measure of the degree of azimuthal anisotropy can also be obtained from tither of the above two cases. When azimuthal anisotropy is induced by oriented vertical fractures, this qualitative measure of anisotropy is proportional to fracture density. Using synthetic seismograms, we demonstrate the robustness of our method in evaluating the principal directions from conventional P-wave seismic data. We also apply our technique to real P-wave data, collected over a wide source-to-receiver azimuth distribution. Computations using our method gave an orientation of the principal direction consistent with the general fracture orientation in the area as inferred from other geological and geophysical evidence.