Adaptively Matching and Separation for Multiples Using Complex-valued Curvelet Transform

Surface-related multiple attenuation consists of predicting multiples and adaptively subtracting multiples model from original data with matching filters. Despite major advances made by surface-related multiple elimination (SRME), errors in the predicted multiples remain a problem.The matching filters are always got by minimizing the residual between the original data and the filtered multiples in a least-squares sense with the assumption that primaries have minimum energy and are orthogonal to multiples. In practice, the energy contrasts and orthogonality between primaries and multiples always vary as a function of offset, time and dip, which will pose a serious challenge for conventional least-squares(LS) matching. We propose an adaptive method that corrects those misfits, which vary smoothly as a function of scale (frequency band), angle and location. With this method, the predicted multiples can be adaptively macthed with the real ones in original data under LS sense by using an complex-valued curvelet transform. Instead of subtaction of the matched multiples, we estimate primaries by primary-multiple separation with curvelet-domain soft-thresholding. Synthetic data show great improvements over conventional least-squares matching with better attenuation of multiple energy and better preservation of estimated primaries.