Quartic reflection moveout in a weakly anisotropic dipping layer

Abstract

Deviations of P-wave reflection traveltimes from a hyperbola, called the nonhyperbolic or quartic moveout, need to be handled properly while processing long-spread seismic data. As observed nonhyperbolic moveout is usually attributed to the presence of anisotropy, we devote our paper to deriving and analyzing a general formula that describes an azimuthally varying quartic moveout coefficient in a homogeneous, weakly anisotropic medium above a dipping, mildly curved reflector. To obtain the desired expression, we consistently linearize all quantities in small stiffness perturbations from a given isotropic solid. Our result incorporates all known weak-anisotropy approximations of the quartic moveout coefficient and extends them further to triclinic media. By comparing our approximation with nonhyperbolic moveout obtained from the ray-traced reflection traveltimes, we find that the former predicts azimuthal variations of the quartic moveout when its magnitude is less than 20% of the corresponding hyperbolic moveout term. We also study the influence of reflector curvature on nonhyperbolic moveout. It turns out that the curvature produces no quartic moveout in the reflector strike direction, where the anisotropy-induced moveout nonhyperbolicity is usually nonnegligible. Thus, the presence of nonhyperbolic moveout along the reflector strike might indicate effective anisotropy.