In this article, we propose an inversion scheme to replace the adaptive subtraction approaches which are widely used in conventional two-step (prediction + subtraction) multiple elimination methods. This new method, named SIMP (simultaneous inversion for multiples and primaries), inverts seismic data using constraints (e.g., modeled multiples and/or geologic discriminants) for multiples and primaries simultaneously. SIMP incorporates pattern recognition and shaping filters into one concise and practically solvable formulation. Its main advantages are that no orthogonality between multiples and primaries is assumed and that wavelet information is not necessary for the inversion.
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Luo et al. (2003) studied this question.