Discussion

I presented a new approach for the joint imaging of primary and multiple reflections. My approach goes further than the separate imaging of multiples and primaries. I integrate information from the multiples and primaries in a least-squares inversion, via a new regularization term which exploits the kinematic similarity of primaries and pseudo-primaries, and the kinematic dissimilarity of crosstalk terms to obtain a noise-free image of the primaries.

The proposed algorithm demonstrates good noise suppression and signal preservation characteristics in the synthetic tests of Figure 4. Comparison of Figures 5 and 6 proves the validity of the new regularization term, equation (8), and more importantly, that the multiples provide valuable information in the inversion.

The results of testing a real data gather were mixed. I believe the single largest problem in this case is poor coherency of the water-bottom multiples. As the water bottom and most shallow reflectors on the Mobil AVO dataset are nearly perfectly flat, geologic complexity is surely not to blame. More likely, the solution(s) to the trouble is(are) more mundane; things like source/cable balancing and spherical divergence. An accurate RMS velocity function is important to success, but errors can be tolerated. Velocity errors lead to curvature in NMO'ed primaries and pseudo-primaries, but as I have dealt here only with water-layer multiples, the real danger, a large phase shift between primaries and pseudo-primaries, is somewhat unlikely.

In all tests, the removal of multiples at near offsets was incomplete. Since the near offsets contribute most to residual multiple energy in the stack, it is of crucial importance to improve performance.