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A fast uncoiled randomized QR decomposition method for 5D seismic data reconstruction

SHENGHOU WANG1 ,  JIANJUN GAO1,2 ,  JINGYE LI2
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1 School of Geophysics and Information Technology, China University of Geosciences (Beijing), 29 Xueyuan Road, Haidian District, Beijing 100083, P.R. China.,
2 State Key Laboratory of Petroleum Resources and Prospecting (China University of Petroleum, Beijing), Beijing 102249, P.R. China.,
JSE 2018, 27(3), 255–276;
Submitted: 9 June 2025 | Revised: 9 June 2025 | Accepted: 9 June 2025 | Published: 9 June 2025
© 2025 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

Wang, S., Gao, J. and Li, J., 2018. A fast uncoiled randomized QR decomposition method for 5D seismic data reconstruction. Journal of Seismic Exploration, 27: 255-276. The low rank matrix completion methods have been widely applied to reconstruct multidimensional irregular seismic data. The existing literature shows that well sampled seismic data can be represented by a low rank block Hankel or block Toeplitz matrix. However, incomplete data and random noise can destroy the low rank property of the block matrix. Hence, the recovery of missing seismic traces can be treated as a rank reduction problem. This paper presents a fast rank reduction algorithm named randomized QR decomposition to interpolate the pre-stack 5D irregular missing seismic traces. Compared with the popular matrix rank reduction algorithms, such as the Singular Value Decomposition (SVD) and the Lanczos bidiagonalization decomposition method, this method has higher computational efficiency and faster reconstruction speed. Moreover, for the computationally low efficient problem of the diagonal averaging operation of the rank-reduced level-4 block Toeplitz matrix, a fast uncoiled diagonal averaging strategy is designed. The new diagonal averaging algorithm can greatly reduce the amount of data storage and decrease the computational cost. In the end, the validity of the proposed method is verified by synthetic data experiments and a field data test.

Keywords
rank reduction
randomized QR decomposition
multilevel Toeplitz structures
5D seismic data reconstruction
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
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