Fast dual-domain reduced-rank algorithm for 3D deblending via randomized QR decomposition

Abstract

We have developed a fast dual-domain algorithm based on matrix rank reduction for separating simultaneous-source seismic data. Our algorithm operates on 3D common receiver gathers or offset-midpoint gathers. At a given monochromatic frequency slice in the [Formula: see text]-[Formula: see text]-[Formula: see text] domain, the spatial data of the ideal unblended common receiver or offset-midpoint gather could be represented via a low-rank matrix. The interferences from the randomly and closely fired shots increased the rank of the aforementioned matrix. Therefore, we could minimize the misfit between the blended observation and the predicted blended data subject to a low-rank constraint that was applied to the data in the [Formula: see text]-[Formula: see text]-[Formula: see text] domain. The low-rank constraint could be implemented via the classic truncated singular value decomposition (SVD) or via a randomized QR decomposition (rQRd). The rQRd yielded nearly one order of processing time improvement with respect to the truncated SVD. We have also discovered that the rQRd was less stringent on the selection of the rank of the data. The latter was important because we often had no precise knowledge of the optimal rank that was required to represent the data. We adopted a synthetic 3D vertical seismic profile and a real seismic data set acquired at the North Viking Graben to test the performance of the proposed source separation algorithm. The proposed algorithm effectively eliminated the interferences while preserving the desired unblended signal. Especially for the synthetic vertical seismic profile example, experiments were evaluated under different survey time ratios. Our tests indicated that the proposed method could save up to 90% of acquisition time under a self-simultaneous source acquisition scenario.