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Spectral decomposition with sparsity constraint and its application

HAN XU1 ,  XINWEN WANG1 ,  LI GAO2
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1 School of Earth Sciences and Recourses, China University of Geosciences, Beijing 100083, P.R. China,
2 Institute of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, P.R. China,
JSE 2018, 27(1), 89–103;
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

Xu, H., Wang, X. And Gao, L., 2018. Spectral decomposition with sparsity constraint and its application. Journal of Seismic Exploration, 27: 89-101. Spectral decomposition has been widely used in seismic signal processing and interpretation at present because it can reveal lots of valuable information hidden in the broadband seismic response. Unlike the conventional frequency-based methods, spectral decomposition is able to estimate the frequency contents of the signal at the specific time. How to seek an optimal solution is the most significant aspect for Spectral Decomposition with Sparsity Constraints (SDSC). In this paper, the Li regularized L2-norm is employed as the objective function, the Ricker wavelet is chosen to construct a wavelet library and the optimal solution is obtained by the Iterative Soft Thresholding Algorithm (ISTA). We apply SDSC to the synthetic and field examples. The former show that the SDSC method does a better job in both time and frequency resolution than the traditional spectral decomposition technique, namely the continuous wavelet transform (CWT) method, which always suffers from the conflict between time resolution and frequency resolution. Applications to field data further indicate the potential of the SDSC method in identifying the strong anomalies related to hydrocarbon, and detecting the variations in amplitude associated with faulting.

Keywords
spectral decomposition
sparsity constraint
continuous wavelet transform
hydrocarbon detection
fault identification
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  71. JOURNAL OF
  72. SEISMIC EXPLORATION
  73. Volume 27, 2018
  74. EDITORS-IN-CHIEF :
  75. M. Nafi Tokséz (Cambridge, MA, U.S.A.)
  76. Arthur B. Weglein (Houston, TX, U.S.A.)
  77. EDITORIAL BOARD
  78. L. Amundsen (Trondheim, Norway) E. Liu (Houston, TX, U.S.A.)
  79. J.M. Carcione (Trieste, Italy) R. Marschall (Hannover, Germany)
  80. P. Cary (Calgary, AB, Canada) G.A. McMechan (Richardson, TX, U.S.A.)
  81. Y.K. Chen (Oak Ridge, TN, U.S.A.) M. Meier (Houston, TX, U.S.A.)
  82. W.K. Chung (Busan, South Korea) F. Poletto (Trieste, Italy)
  83. V. Cheverda (Novosibirsk, Russia) M. Sacchi (Edmonton, AB, Canada)
  84. P.F. Daley (Calgary, AB, Canada) M. Sen (Austin, TX, U.S.A.)
  85. E. Filpo (Rio de Janeiro, Brazil) G. Rubino (London, ON, Canada)
  86. D. Foster (Houston, TX, U.S.A.) S. Shapiro (Berlin, Germany)
  87. B. Gurevich (Perth, Australia) J. Sheiman (Houston, TX, U.S.A.)
  88. W. Ha (Busan, South Korea) C.S. Shin (Seoul, South Korea)
  89. M. Hall (Calgary, AB, Canada) W. Séllner (Oslo, Norway)
  90. B.A. Hardage (Austin, TX, U.S.A.) P.L. Stoffa (Austin, TX, U.S.A.)
  91. T. Hertweck (Karlsruhe, Germany) L. Thomsen (Houston, TX, U.S.A.)
  92. L.T. Ikelle (Bryan, TX, U.S.A.) I. Tsvankin (Golden, CO, U.S.A.)
  93. M. Jacobsen (Bergen, Norway) C. Vanelle (Hamburg, Germany)
  94. G. Lambaré (Paris, France) A.R. Verdel (Utrecht, Netherlands)
  95. E. Landa (Tel Aviv, Israel) D.J. Verschuur (Delft, Netherlands)
  96. L. Lines (Calgary, AB, Canada) D.H. Yang (Beijing, P.R. China)
  97. J.E. Lira (Rio de Janeiro, Brazil) J. Zhang (Houston, TX, U.S.A.)
  98. Scope
  99. The Journal of Seismic Exploration is an international medium for the publication of research in
  100. seiusmic modeling, processing, inversion, interpretation, field techniques , borehole techniques,
  101. tomography, instrumentation and software.
  102. Policy
  103. Short publication time, high scientific level, easily readable and concise papers are the main
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  106. Subscriptions
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  113. GUIDE FOR AUTHORS
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  152. JOURNAL OF
  153. SEISMIC EXPLORATION
  154. Volume 27, Number 1
  155. O. Giireli and T. Kayiran
  156. M. Bai, J. Wu, J. Xie and
  157. D. Zhang
  158. A. Dahroug, S. Mahmoud,
  159. E. Morsy, H. Nada and
  160. H. Karsli
  161. G. Li, Y. Li and X. Lu
  162. Y.T. Zhou and W.X. Han
  163. H. Xu, X.W. Wang and
  164. L. Gao
  165. February 2018
  166. CONTENTS
  167. On the non-uniqueness of the
  168. refraction solution.............
  169. Least-squares reverse time
  170. migration of blended data with
  171. low-rank constraint along
  172. structural direction.............
  173. Contribution of inverted seismic
  174. data in extracting attributes to
  175. characterize Pliocene aged
  176. channel located off-shore the
  177. Nile Delta, Egypt.............
  178. Seismic events detection in strong
  179. low-frequency background
  180. noise by complex shock filter. . . .
  181. Multiples attenuation in the
  182. presence of blending noise. .... .
  183. Spectral decomposition with
  184. sparsity constraint and its
  185. application ...................
  186. 40 TVNXNnOT
  187. x
  188. a
  189. 回
  190. 圖
  191. 區
  192. x
  193. >
  194. S
  195. 之
  196. (8I0Z) ZOI-T ‘LZ TOA
  197. Volume 27, Number 1, February 2018
  198. ISSN 0963-0651
  199. JOURNAL OF
  200. SEISMIC EXPLORATION
  201. IMAGING TECHNOLOGY IN APPLIED GEOSCIENCES
  202. EDITORS-IN-CHIEF : M. NAFI TOKSOZ and ARTHUR B. WEGLEIN
  203. GEOPHYSICAL PRESS
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