Full-azimuth subsurface angle domain wavefield decomposition and imaging: Part 2 — Local angle domain

Abstract

We have developed an angle-based system, which defines the interaction between incident and reflected waves at a specific image point. We provide details about the technique used for angle-domain decomposition and imaging; in particular, the creation of two types of 3D subsurface angle gathers, as discussed in Part 1. The system, referred to as local angle domain (LAD) consists of two subsystems: directional and reflection. In the directional subsystem, the orientation of the ray-pair normal is represented by dip and azimuth. The reflection angle system is defined by the opening angle between the phase velocities of the incident and reflected rays, and by the opening azimuth, which describes the orientation of the ray-pair incidence plane measured in the ray-pair reflection plane. The directional angles are defined in a rotated local frame, and the opening azimuth is defined in the ray-pair reflection plane. The vertical axis of the local frame is collinear with a preset background normal to the physical reflection surface at the image point. We derive the forward transform between the directions of the phase velocities of the incident and reflected rays and the LAD angles (used in the imaging process) and its inversion, which is required for modeling and analysis. We derive the transformation of the opening azimuth from the subsurface tilted reflection plane to the global horizontal plane and vice versa. Isotropic and general anisotropic media, pressure waves and converted waves were considered. The relationship between the surface acquisition geometry parameters and the LAD angles at subsurface points below salt is demonstrated using the SEG/EAGE salt model. Rich information about full-azimuth angle-domain illumination can be obtained, taking into consideration the complexity of the overburden model and the limitations of acquisition geometry.