Current depth imaging technology works very well in areas that have slow velocity variations but may fail in more complex areas Claerbout (1985) for a variety of reasons, such as multiple reflections, bad velocities, and spatial aliasing. One potential cause of imaging failure is reflector location ambiguity due to multipathing of reflected energy: it is possible that a single event recorded in the data at one surface location could come from reflectors at two or more subsurface locations. Besides contributing to imaging artifacts, reflector ambiguity contributes non-flat events to common image gathers, thus rendering velocity analysis ambiguous Nolan and Symes (1996).
Several authors have suggested angle domain imaging as a solution for the reflector ambiguity Brandsberg-Dahl et al. (1999); Xu et al. (1998). Angle domain sections collect the energy in a data set which has scattered over a specific reflection (``opening'') angle .We will argue below that an event in an angle section uniquely determines a ray couple, which in turn uniquely locates the reflector. Thus imaging artifacts and velocity update ambiguity due to multipathing are eliminated in this domain.
Multipathing is better handled by wave-equation migration methods than Kirchhoff ones, therefore the former are a natural choice for producing angle-domain common image gathers (CIGs). We present a simple method for extracting CIGs from 3-D prestack data downward continued using the Double Square Root equation (DSR). The method is based on a slant-stack decomposition of the downward continued wavefield at each depth level. Our method is thus different from the method proposed by Ottolini and Claerbout 1984, that applies the DSR to downward continue prestack data slant-stacked at the surface. In layered media the two methods should produce equivalent results, but in presence of lateral velocity variations plane-wave downward continuation is not strictly valid and true angle-domain CIGs can only be produced by wavefield decomposition at depth.
Migration methods based on DSR operators have been applied to 2-D prestack migration for long time Claerbout (1985). However, the direct application of DSR migration methods to 3-D prestack data have been prevented by the tremendous computational cost. Only recently computationally efficient methods to continue 3-D prestack data have been presented Biondi and Palacharla (1996); Mosher et al. (1997). In particular, common-azimuth migration is an attractive alternative to Kirchhoff migration for sub-salt imaging because of its robustness with respect to the complex multipathing that is induced by salt bodies.
We will explain how some widely used common image gathers can contain reflector ambiguity due to multipathing and why angle-domain common image gathers will not. Then we will demonstrate the construction of angle-domain common image gathers from wave equation downward continued data for use in velocity analysis and amplitude-versus-reflection angle analysis. Finally, we apply this method to the Marmousi model.