The problem with illumination in this case is clear. It may be possible to examine it further by finding traveltimes from the synthetic model with a more sophisticated raytracing algorithm that utilizes maximum amplitudes and/or multiple arrivals. This won't solve the problem but might be useful.
One of the most obvious solutions is to simply weight the appropriate offset range before stacking. It would be fairly easy to weight the offsets according to the amount of illumination they provide to the region in question. This would be a fast and easy way to increase the amplitudes along the missing part of the reflector. This is obviously not a perfect solution but it is a possibility.
In addition to the offset weighting, inversion is an option. Presently there is a substantial amount of noise and artifacts obscuring parts of the reflector. If this noise can be attenuated by the inversion process, the small amount of energy we receive from the shadow zone may be visible. Also, the inversion process will help correct for inconsistent ray coverage along the reflector.
Future investigations may also include the use of common angle gathers rather than common offset gathers. Common angle gathers provide a more equalized amplitude versus angle panel Xu et al. (1998). This may allow us to see the weak events that must exist in this shadow zone but are obscured by noise and/or migration artifacts.
Actual solutions to this problem are sensitive to our knowledge of the velocity field. Obviously with the synthetic model this is not a great concern but when we begin work on the real 3-D dataset it will be a factor. Further analysis and velocity refinement might be needed for any of the solutions implemented.