In a shallow water environment, mud-roll is often dominant and appears as prevailing coherent noise in OBC seismic data. It is dispersive, multi-modal, and spatially variable. Furthermore, it is usually aliased due to a too large spatial sampling interval. These complex properties make the noise removal notably challenging in seismic processing. To address these challenges, we propose a dispersive mud-roll noise removal method, which consists of three feedback loops: the first loop for establishing a mud-roll propagation operator using the co-called differential time-shift analysis in the focal domain; the second loop for removing most of mud-roll noise with a greedy sparse inversion of focal transformation; and the third loop for removing the remaining mud-roll noise with a greedy sparse inversion of cascaded Radon/focal transformations. In this paper, we illustrate the proposed method, and show some examples on synthetic seismic measurements for demonstrating its virtues.


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