Non-hyperbolic moveout inversion of wide-azimuth P-wave data for orthorhombic media

The azimuthally varying non-hyperbolic moveout of P-waves in orthorhombic media can provide valuable information for characterization of fractured reservoirs and seismic processing. Here, we present a technique to invert long-spread, wide-azimuth P-wave data for the orientation of the vertical symmetry planes and five key moveout parameters: the symmetry-plane NMO velocities, V-nmo((1)) and V-nmo((2)), and the anellipticity parameters, eta((1)), eta((2)) and eta((3)). The inversion algorithm is based on a coherence operator that computes the semblance for the full range of offsets and azimuths using a generalized version of the Alkhalifah-Tsvankin non-hyperbolic moveout equation. The moveout equation provides a close approximation to the reflection traveltimes in layered anisotropic media with a uniform orientation of the vertical symmetry planes. Numerical tests on noise-contaminated data for a single orthorhombic layer show that the best-constrained parameters are the azimuth phi of one of the symmetry planes and the velocities V-nmo((1)) and V-nmo((2)), while the resolution in eta((1)) and eta((2)) is somewhat compromised by the trade-off between the quadratic and quartic moveout terms. The largest uncertainty is observed in the parameter eta((3)), which influences only long-spread moveout in off-symmetry directions. For stratified orthorhombic models with depth-dependent symmetry-plane azimuths, the moveout equation has to be modified by allowing the orientation of the effective NMO ellipse to differ from the principal azimuthal direction of the effective quartic moveout term. The algorithm was successfully tested on wide-azimuth P-wave reflections recorded at the Weyburn Field in Canada. Taking azimuthal anisotropy into account increased the semblance values for most long-offset reflection events in the overburden, which indicates that fracturing is not limited to the reservoir level. The inverted symmetry-plane directions are close to the azimuths of the off-trend fracture sets determined from borehole data and shear-wave splitting analysis. The effective moveout parameters estimated by our algorithm provide input for P-wave time imaging and geometrical-spreading correction in layered orthorhombic media.