Discussion and Conclusions

Surface-related multiple prediction works well for predicting the free-surface multiples, but, as shown through a series of tests and examples, it fails for certain ray paths where the subsurface geometry is complicated, and we have access to only small offsets. Though data-space and image-space SRMP are mathematically equivalent, image-space subtraction gives us a better chance of reconstructing the missing parts of the multiple model because of the redundancy associated with the image space. In the present analysis we used angle gathers as a preferred domain of reconstruction.

In the presence of complicated structures and salt bodies, multiples migrate to the image space in a fairly complicated fashion when we use the true migration velocity. The use of the multiple velocity for migration takes us to a domain where multiples are identifiable and appear flat in ADCIGs. We may carry out the process of reconstruction relatively easily in this domain. But the drawback is that this should be followed by the process of demigration and migration, making it computationally very expensive. As discussed earlier, we may also use Radon-style transforms for reconstruction, which should work even when the multiples are not absolutely flat in ADCIGs. This allows us to migrate with the true velocity in one step, avoiding the extra steps of migration and demigration. Although the performance of the Radon transform depends upon how many angles we actually have, in the case of a very narrow range of angles, the spectrum would be very smeared, and effective reconstruction would not be possible.

To illustrate these points, in the examples above I retain only very small offsets, which might appear unrealistic for the inline direction. However, there is a trade-off between the offsets and dip of the structure; for instance, if dip is very high, SRMP can fail even for large recording offsets. Furthermore, in 3D surveys, along with many limitations of SRMP, extremely limited crossline offsets might be a concern for even a gently dipping water bottom. The heuristic extension of the idea discussed here would be that in 3D, a multiple event might be perfectly modeled for some azimuths, but not all. In that case we may spread information across azimuths to reconstruct the multiple model, like we did across aperture angles in the 2D case.