Adaptive Multiple Subtraction Based on Sparse Coding

Multiple removal is one of the key steps in seismic data processing. In the surface-related multiple elimination method, the adaptive multiple subtraction technique is of great importance. In this paper, we propose a new pattern-based adaptive multiple subtraction method using the sparse coding technique (AMS-SC). By assuming that the multiples consist of different patterns from those of the primaries in the time-space domain, the proposed method first obtains some basis vectors, which represent the patterns of the multiples compactly, from the predicted multiples by sparse coding, and then estimates the multiples contained in the recorded seismic data using these basis vectors obtained in the previous step. Different from the traditional matching filter methods, which estimate the multiples by fitting the predicted multiples to the recorded seismic data directly, AMS-SC obtains the multiple estimations by reconstructing the recorded seismic data with the basis vectors obtained from the predicted multiples. Benefitting from sparse coding, AMS-SC is robust to the differences between the predicted and the true multiples, and preserves the primaries well. Applications on several data sets give some promising results of AMS-SC.