Fresnel volume and interface Fresnel zone for reflected and transmitted waves from a curved interface in anisotropic media

Abstract

The Fresnel volume and the interface Fresnel zone (IFZ) concepts play an important role in seismic exploration because the IFZ largely contributes to the formation of the reflection and transmission wavefields at an observation point. We derived analytic expressions based on traveltime approximations to evaluate the IFZ size for converted and nonconverted waves reflected (or transmitted) by a curved interface between two homogeneous general anisotropic media, and more specifically for dip-constrained transversely isotropic homogeneous media. The reflectors are of anticline, syncline, or saddle type, and their principal curvature axes may not lie in the incidence plane. As in an anisotropic medium the isochron in most cases assumes a nonelliptical shape, the size and the shape of the IFZ for reflected waves are predominantly dependent on the curvatures of the isochrons together with the curvatures of the interface. The IFZ shapes also exhibit large variation with interface curvature and incidence angle. In addition, the difference between the Thomsen anisotropy parameters [Formula: see text] and [Formula: see text] is found to control the size of the IFZ for P-P and P-S reflections. The IFZ for anisotropic media with curved interface can be much larger than that for equivalent isotropic media, and more specifically for positive values of [Formula: see text]. The spatial resolution of unmigrated seismic data in anisotropic media would consequently be different from that determined for the same configuration for isotropic models and a planar interface.