The transformation to angle domain performed by slant-stacking the prestack image along the subsurface-offset axis generates angle gathers that are approximately function of the phase aperture angle. When the accuracy of this approximation is not sufficient, the computation of the true aperture angles requires the measurement from the image of the geological dips of the reflections.
The differences between the true phase angle and the subsurface-offset slopes measured by slant stacks are caused by the difference in propagation velocity between the incident and the reflected waves. In a general TTI medium, the differences vanish for events normal to the isotropic axis of symmetry. In a VTI medium the differences vanish for flat reflectors and they are small unless the anisotropy is strong, the dips steep, and the aperture angle wide. This conclusion is supported by the detailed analysis of the ADCIGs generated my migrating a real data set in the presence of fairly strong anisotropy and steep salt flanks.
I would like to thank the ExxonMobil Exploration Company for making the Gulf of Mexico data set used in this paper data available to SEP through the generous efforts of Ruth Gonzalez and Joe Reilly. The anisotropic parameters cube were kindly shared with us by Laura Bear and Jerry Krebs, also at ExxonMobil.