De‐aliased and de‐noise Cadzow filtering for seismic data reconstruction

Abstract

ABSTRACTCadzow filtering is currently considered as one of the most effective approaches for seismic data reconstruction. The basic version of Cadzow filtering first reorders each frequency slice of the seismic data (to be reconstructed) to a block Hankel/Toeplitz matrix, and then implements a rank‐reduction operator, that is truncated singular value decomposition, to the Hankel/Toeplitz matrix. However, basic Cadzow filtering cannot deal with the problem of recovering regularly missing data (up‐sampling) in the case of strongly aliased energy, because the regularly missing data will mix with signals in the singular spectrum. To solve this problem, it has been proposed to precondition the reconstruction of high‐frequency components using information from the low‐frequency components which are less aliased. In this paper, we further extend the de‐aliased Cadzow filtering approach to reconstruct regularly sampled seismic traces from the noisy observed data by modifying the reinserting operation, in which the high‐frequency components are projected onto the sub‐space spanned by several singular vectors of the low‐frequency components. At each iteration, the filtered data are weighted to the original data as a feedback. The weighting factor is related to the background noise level and changes with iteration. The feasibility of the proposed technique is validated via two‐dimensional, three‐dimensional and five‐dimensional synthetic data examples, as well as two‐dimensional post‐stack and three‐dimensional pre‐stack field data examples. The results demonstrate that the proposed technique can effectively interpolate regularly sampled data and is robust in noisy environments.