DISCUSSION and CONCLUSIONS

We have showed that the Abelian group attributes domain (g1'=T, g2'=T.V_nmo² - T.V_water²) is a good domain for waterbottom multiples and peglegs attenuation. We have achieved the correct timing in the mapping between the space-time domain and the Abelian group attributes domain. However, the amplitude remains a problem owing to the different velocity sensitivity between shallow and deep parts in the velocity transform. The geometrical progression of amplitude between primary and multiples in the Abelian group domain is not strictly satisfied. One remedy to the second problem might be to mute the far offset data along a slanted straight line, so that the data of near/far offset have the same recording angular aperture with respect to the source.

Beside the periodicity as discussed above, the other idea is sparsity. By implementation of more Abelian group attributes, events will be increasingly sparse, and primaries and multiples will be more easily differentiated. This helps us to avoid identifying multiples and peglegs as primaries. The next Abelian group attribute candidate to be implemented is anelliptic factor. This would better model non-hyperbolic effects that might be either extrinsic and due to layering, or intrinsic, if the layered material was anisotropic. As m=g3/(T.V_nmo⁴), there is still the problem of different sensitivity between small and large T. It seems to me that this different sensitivity does not offset the first one. Since the use of the two weighting functions in the paper is not satisfactory enough, we need a better strategy to handle the different velocity sensitivity between shallow and deep parts in the velocity transform.