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Three-dimensional sparse hyperbolic Radon transform and its application to demultiple

JSE 2018, 27(2), 137–150;
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

Gong, X.B., Wang, S.C. and Zhang, P., 2018. Three-dimensional sparse hyperbolic Radon transform and its application to demultiple. Journal of Seismic Exploration, 27: 137-150. Radon transform (RT) has been widely used in seismic data processing. In this paper, we propose a fast version of three-dimensional (3D) sparse hyperbolic RT (HRT) to eliminate multiples. The adjoint operator transforms the hyperboloids of 3D gather into the points of 3D Radon space, which is used for separation of signal and noise. The forward operator transforms the points of 3D Radon space into the hyperboloids of 3D gather. By using a stretching time axis and the mixed frequency-time domain inversion, we perform the forward and adjoint 3D HRT operators as matrix-matrix multiplications in the frequency domain, which can result in high-resolution Radon panel with high computational efficiency. In addition, a monotone version of fast iterative shrinkage thresholding algorithm (MFISTA) is implemented to accelerate the convergence of the sparse RT-based inversion. Synthetic and field examples of off-shore data demonstrate that our new method can be successfully applied in this context.

Keywords
Radon transform
three-dimensional
sparse
demultiple
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
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