Fast dual domain reduced rank algorithm for 3D deblending via randomized QR decomposition
ABSTRACTWe 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 o x y 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 o x y 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 select.