Discussion and conclusions

The issue of cross-talk is a very important one when separating signal from noise and in particular primaries from multiples. The standard approach is to match the estimated multiples directly to the data and obtain the primaries by subtraction of the matched multiples. This approach often leads to weakened primaries and/or contamination with residual multiples. By exploiting the estimates of both, multiples and primaries, we prevent the matching algorithm from attempting to match primaries into the multiples which is almost unavoidable otherwise. Furthermore, we obtain simultaneous estimates of both the primaries and the multiples that are guaranteed to be consistent with the original data.

It should be emphasized that the algorithm, as presented, is independent of the method employed to obtain the initial estimates of the multiples and the primaries. It should also be stressed that the algorithm does not rely on explicit knowledge of the moveouts of the primaries or the multiples. It only relies on the fact that the data is the sum of the multiples and the primaries.

The method presented in this paper can be used not only to match primaries and multiples but in general to match estimates of noise and signal to data containing both. We showed an example with the separation of ground-roll and body-waves with land data, but other applications may also be possible.