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The removal of multiple reflections remains a major challenge in seismic data processing. We develop<br>a new method, inspired by the wavefield decomposition approach developed by Nemeth3 and based on<br>a linearized waveform inversion to attenuate multiple reflections. Compared to Nemeth’s algorithm,<br>we reduce significantly the inversion CPU time by a judicious formulation of the inverse problem. The<br>computational cost for multiple elimination is then negligible compared to the standard linearized<br>inversion cost.