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We present a new pattern-based method that separates multiples from primaries. This method finds its mathematical foundation in the work conducted by Nemeth (1996) on coherent noise attenuation by least-squares migration. We show that a similar inverse problem can be formulated to attenuate coherent noise in seismic data. In this paper, we use deconvolution with prediction error filters to model the signal and noise vectors in a least-squares sense. This new formulation of the noise separation problem has been tested on 2-D real data and achieves similar results to the Wiener approach. However, we show that the main strength of this new method is its ability to incorporate regularization in the inverse problem in order to decrease the correlation effects between noise and signal.

Multiple attenuation using at − xpattern‐based subtraction method