In this paper we assume that the multiple model has already been estimated by whatever method. We concentrate on the adaptive subtraction step to match and subtract the multiples from the data to get the estimated-matched primaries.
In the next section we present our adaptive-matching algorithm. It estimates non-stationary filters Rickett et al. (2001) that simultaneously match both the estimates of the primaries and the multiples to the data. These filters act on micro-patches Claerbout and Fomel (2002) and can handle inaccuracies in the estimated multiples in terms of both amplitudes and kinematics. The filters are estimated iteratively by re-estimating the multiple and primary models until the residual (the difference between the sum of the matched primaries and multiples and the data) is zero. Only a few iterations (three to five) seem to be necessary.
In the following section we apply the new method to two synthetic datasets
contaminated with multiples. In
the first test we match kinematically perfect estimates of primaries and
multiples contaminated with 40 of cross-talk and show that the method
produces a cross-talk-free result. Then we apply the method to a very
inaccurate estimate of both the primaries and the multiples obtained
via migration-demigration as described in a previous report
Alvarez (2006). Even with such a poor estimate of both
primaries and multiples, and the strong cross-talk on both, the matched
results are very good, with little cross-talk. To illustrate the method
with stacked data, we apply it to a migrated section of the Sigsbee model.
Here the multiples were estimated with an image space version of
SRME (). The results show that the method attenuated
most of the multiples and produced a largely multiple-free estimate
of the primaries.
In the last section we apply the method to an angle-domain common-image gather taken from a real 2D line in the Gulf of Mexico. The estimate of the multiples was obtained by Radon filtering in the image space Alvarez et al. (2004). In the final estimate of the primaries, most of the residual energy from the diffracted multiples was eliminated. Finally, we apply the method to a different problem, namely the separation of ground-roll and body-waves. We use a real land shot gather contaminated with strong ground-roll and show that most of the residual ground-roll can be attenuated in the final estimate of the body waves. This is a more challenging problem because the non-stationarity characteristics of the ground-roll and the body waves are different requiring different filter lengths and patch sizes to match them to the data.