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Seismic data reconstruction via complex shearlet transform and block coordinate relaxation

JICHENG LIU,  YA GU,  YONGXIN CHOU
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School of Electrical & Automatic Engineering, Changshu Institute of Technology. Changshu 215500, P.R. China,
JSE 2019, 28(4), 307–332;
Submitted: 1 May 2018 | Accepted: 12 February 2019 | Published: 1 August 2019
© 2019 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

Liu, J., Gu, Y. and Chou, Y.X., 2019. Seismic data reconstruction via complex shearlet transform and block coordinate relaxation. Journal of Seismic Exploration, 28: 307-332. Due to practical and economic limitations, real seismic data is not densely sampled in all coordinates, which will affect the subsequent seismic data processing steps, such as migration, surface-related multiple elimination and inversion. Therefore, it is necessary to reconstruct the incomplete seismic data. This paper explains the application of the complex shearlet transform to seismic data reconstruction. With a Z; constraint and the Block Coordinate Relaxation (BCR) method, performance of the complex shearlet-based, real shearlet-based and well-accepted curvelet-based reconstruction are compared in terms of recovered f-k spectrum and signal to noise ratio (SNR). We also discuss the shift invariance of the complex shearlet transform and compare the performances of the BCR and the widely used Projection Onto Convex Sets (POCS) method. The numerical experiments on synthetic and real data with different under-sampling rates demonstrate the validity of the proposed method, especially for the case of large amounts of traces missing.

Keywords
seismic data reconstruction
complex shearlet transform
curvelet transform
block coordinate relaxation
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Journal of Seismic Exploration, Print ISSN: 0963-0651, Published by AccScience Publishing
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