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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.

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Stanford Exploration Project

1/16/2007