Introduction

Most methods to attenuate multiples perform, in one way or another, two complementary but clearly distinguishable steps: first, estimate a model for the multiples and second, adaptively match and subtract the estimate of the multiples from the data to get the estimate of the primaries. Surface Related Multiple Elimination Berhout and Verschuur (1997); Dragoset and Jericevic (1998); Dragoset (1999); Verschuur and Berkhout (1997); Weglein et al. (1997) uses the auto-convolution of the data to estimate the multiples whereas moveout-based methods use filtering in either frequency-wavenumber or Radon domain Alvarez et al. (2004); Hampson (1986); Sava and Guitton (2003) to estimate the multiple model. Whatever the method, the estimate of the multiples is likely to be contaminated with residual primary energy and have errors in amplitude and phase. After adaptive subtraction, the estimated primaries are likely to suffer from undesired residual multiple energy, or weakened primaries, or both Guitton and Verschuur (2004).

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.