Multiple attenuation is crucial for improving the quality of seismic images. An adaptive multiple subtraction step is necessary for almost all the methods predicting seismic multiple reflected waves. The different adaptive multiple subtraction schemes mainly differ in the objective function to be optimized and the strategy to overcome the non-stationarity of the filter. In this work, we aim at giving a better understanding of matching filters based on Lq-norms and on statistical independence.

We show that the formulation of all these techniques can be gathered in a mutual framework by introducing a space-time operator, called primary enhancer, acting on the estimated primaries. The differences between the considered matching filters become more intuitive as this operator behaves as a simple amplitude compressor. In this perspective, all the methods tend to uncorrelate the predicted multiples and the enhanced estimated primaries.

Moreover, we aim at evaluating the importance of the objective function with respect to the windowing strategy. Our analysis shows that setting a good windowing strategy may be more important than changing the classical least-square adaptation criterion to other approaches based on Lq-norms minimization or independent component analysis.


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