General Definition of Reflection-point Coverage for P- and PS-wave COV Data

Common-offset vector (COV) data have served industry well for survey design, generating well-sampled datasets for noise suppression, offset and azimuth analyses and inversion, and image improvements. For P-waves acquired on a flat recording surface, the basic cross-spread theory assumes that reflection-points (RPs) occur below common mid-points (CMPs). This assumption is ray-based, for 3D propagation in isotropic laterally homogeneous media. However, converted P- to S-waves (PS-waves) and other geometries violate this theory because of their asymmetric ray paths. In this paper I apply a general ray-based theory to define COV illumination area for both P- and PS-waves of various geometries. This involves a first-order approximation in ray-parameter, <i>p</i>, of reflection-point (RP) position as a function of <i>t</i>₀<i>V</i>² terms: vertical traveltime and NMO velocity. This definition facilitates corrections to improve RP consistency within a COV gather or volume. I describe corrections applied to offset-vector tile (OVT) distortion for conventional land orthogonal cross-spread data, and for marine geometries of ocean-bottom cable and node (OBC and OBN) geometries where source and receiver have a different datum. Also, I show that this theory can be applied to illumination distortion from structure (plane dipping layers) and discuss corrections for COV data in the context of migration.