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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: 2 December 2016 | Accepted: 10 November 2017 | Published: 1 February 2018
© 2018 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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  32. Wigner-Wille distribution for sandstone reservoir characterization- a case studyfrom West Sichuan Depression, China. J. Seismic Explor., 19: 69-85.JOURNAL OFSEISMIC EXPLORATIONVolume 27, 2018EDITORS-IN-CHIEF :M. Nafi Tokséz (Cambridge, MA, U.S.A.)Arthur B. Weglein (Houston, TX, U.S.A.)EDITORIAL BOARD
  33. L. Amundsen (Trondheim, Norway) E. Liu (Houston, TX, U.S.A.)
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  35. P. Cary (Calgary, AB, Canada) G.A. McMechan (Richardson, TX, U.S.A.)
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  37. W.K. Chung (Busan, South Korea) F. Poletto (Trieste, Italy)
  38. V. Cheverda (Novosibirsk, Russia) M. Sacchi (Edmonton, AB, Canada)
  39. P.F. Daley (Calgary, AB, Canada) M. Sen (Austin, TX, U.S.A.)
  40. E. Filpo (Rio de Janeiro, Brazil) G. Rubino (London, ON, Canada)
  41. D. Foster (Houston, TX, U.S.A.) S. Shapiro (Berlin, Germany)
  42. B. Gurevich (Perth, Australia) J. Sheiman (Houston, TX, U.S.A.)
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  44. M. Hall (Calgary, AB, Canada) W. Séllner (Oslo, Norway)
  45. B.A. Hardage (Austin, TX, U.S.A.) P.L. Stoffa (Austin, TX, U.S.A.)
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  47. L.T. Ikelle (Bryan, TX, U.S.A.) I. Tsvankin (Golden, CO, U.S.A.)
  48. M. Jacobsen (Bergen, Norway) C. Vanelle (Hamburg, Germany)
  49. G. Lambaré (Paris, France) A.R. Verdel (Utrecht, Netherlands)
  50. E. Landa (Tel Aviv, Israel) D.J. Verschuur (Delft, Netherlands)
  51. L. Lines (Calgary, AB, Canada) D.H. Yang (Beijing, P.R. China)
  52. J.E. Lira (Rio de Janeiro, Brazil) J. Zhang (Houston, TX, U.S.A.)Scope
  53. The Journal of Seismic Exploration is an international medium for the publication of research inseiusmic modeling, processing, inversion, interpretation, field techniques , borehole techniques,tomography, instrumentation and software.Policy
  54. Short publication time, high scientific level, easily readable and concise papers are the mainobjectives. This will be achieved by fast review (4 months) and fast publication (4 months).
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  57. Subscription orders should be sent to: Geophysical Press Ltd., Urb. Los Flamingos — Tee 6,29679 Benahavis, Spain. E-mail: jse@geophysical-press.com ‧ www.geophysical-press.comGUIDE FOR AUTHORS
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  65. Submission of an article is understood to imply that the article is original and unpublished andis not being considered for publication elsewhere.THERE IS NO PAGE CHARGEJOURNAL OFSEISMIC EXPLORATIONVolume 27, Number 1O. Giireli and T. KayiranM. Bai, J. Wu, J. Xie andD. ZhangA. Dahroug, S. Mahmoud,E. Morsy, H. Nada andH. KarsliG. Li, Y. Li and X. LuY.T. Zhou and W.X. HanH. Xu, X.W. Wang andL. GaoFebruary 2018CONTENTSOn the non-uniqueness of therefraction solution.............Least-squares reverse timemigration of blended data withlow-rank constraint alongstructural direction.............Contribution of inverted seismicdata in extracting attributes tocharacterize Pliocene agedchannel located off-shore theNile Delta, Egypt.............Seismic events detection in stronglow-frequency backgroundnoise by complex shock filter. . . .Multiples attenuation in thepresence of blending noise. .... .Spectral decomposition withsparsity constraint and itsapplication ...................40 TVNXNnOTxa回圖區x>S之(8I0Z) ZOI-T ‘LZ TOAVolume 27, Number 1, February 2018ISSN 0963-0651JOURNAL OFSEISMIC EXPLORATIONIMAGING TECHNOLOGY IN APPLIED GEOSCIENCES
  66. EDITORS-IN-CHIEF : M. NAFI TOKSOZ and ARTHUR B. WEGLEINGEOPHYSICAL PRESS
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
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