Local Angle Domain in Seismic Imaging

Imaging systems involve interaction of two wave-fields at the image points (elements): incident and reflected/diffracted. Each wave-field can be decomposed into local plane-waves (or rays) indicating the direction of propagation. The direction of the incident and the reflected/diffracted rays can be conventionally described by two polar angles, respectively. Each polar angle includes two components: dip and azimuth. Therefore, a set of four scalar angles is required to define an angle domain imaging system at a given image point. Ray-based and wave-equation angle-domain migrations deal with systems in which at each image point both the incident and the reflected wave-field are composed of a wide range of directions. The imaging stage involves combination of ray pairs (or pairs of local plane waves) indicating the incident and reflected/diffracted rays. Each ray pair maps seismic data, recorded on the free surface, into the four-dimensional Local Angle Domain (LAD) space. In our notation, these angles are dip and azimuth of the ray-pair normal, opening angle and opening azimuth. We establish relationships between the directions of the ray pairs and the LAD angles. We consider a general case of transverse isotropy with tilted axis of symmetry (TTI) and waves or converted waves.