Generally speaking, there are two classes of ADCIGs: those computed in the data space, which produce images with reflectivity described as a function of offset ray parameter ph Prucha et al. (1999); de Bruin et al. (1990) and those computed in the image space, which produce images with reflectivity function of scattering angle Sava and Fomel (2003); Weglein and Stolt (1999).
The mechanics of computing angle-gathers with either of these two methods are similar, since both involve slant-stacks or radial-trace transforms at various stages of the wavefield extrapolation migration, before or after imaging.
The main advantages and disadvantages of the two methods are discussed by Sava and Fomel (2003). The most important advantage of the image space method over the data space method is its versatility: the same transformation can be used for images produced by shot-geophone (S-G) migration Sava and Fomel (2003), shot-profile migration Rickett and Sava (2001), reverse-time migration Biondi and Shan (2002), and even for migrated images of converted waves Rosales and Rickett (2001). In all cases, we obtain at every point in the image a 1-D description of the reflection magnitude function of the scattering angle (), measured with respect to the normal to the reflector.
However useful, this ADCIG transformation is incomplete. There are situations when by observing how reflectivity changes with the scattering angle, we cannot distinguish among totally different geologic scenarios. A striking comparison is that between a reflector and a diffractor which are both kinematically represented by flat gathers.
This paper presents a simple extension to the angle-gather transformation. By employing similar techniques as the ones used for the more traditional approach, we can create ADCIGs where reflectivity is described by two parameters in 2-D, or by four parameters in 3-D. These angles represent the structural dip, acquisition azimuth and scattering angles. Using simple examples, I show that this more complex decomposition is capable of highlighting new and useful information. Possible applications of this decomposition include illumination compensation due to limited acquisition, or dip-dependent migration amplitude corrections Sava et al. (2001).