A very common noise attenuation problem is the subtraction of multiples. It is well known that the subtraction of multiples becomes very challenging when they interfere strongly with primaries Spitz (1999). Some solutions have been proposed by various authors to cope with correlated noise and signal. For instance, the so-called pattern-based methods have proved to be particularly efficient at attenuating multiples in the most complex areas Guitton et al. (2001); Spitz (1998).
In this paper, I investigate an improved adaptive subtraction scheme that can separate interfering multiples and primaries. With this method, I do not assume that the signal has minimum energy. Building on Guitton (2002), I estimate a signal covariance operator with time domain (t, x) prediction-error filters (pef). This covariance operator is then utilized within an inversion scheme to remove the signal spectrum in the data leading to an unbiased estimation of the matched-filters.
In the first section, I review theoretical issues about adaptive subtraction and I present the new hybrid scheme. In the second section, I illustrate the advantages of the proposed method with synthetic and field data examples.