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Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 1, Pages 42–55 (Mi timm778)  

This article is cited in 5 scientific papers (total in 5 papers)

Sparse optimization methods for seismic wavefields recovery

Y. F. Wang

Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, P. R. China

Abstract: Due to the influence of variations in landform, geophysical data acquisition is usually sub-sampled. Reconstruction of the seismic wavefield from sub-sampled data is an ill-posed inverse problem. It usually requires some regularization techniques to tackle the ill-posedness and provide a stable approximation to the true solution. In this paper, we consider the wavefield reconstruction problem as a compressive sensing problem. We solve the problem by constructing different kinds of regularization models and study sparse optimization methods for solving the regularization model. The $l_p$-$l_q$ model with $p=2$ and $q=0,1$ is fully studied. The projected gradient descent method, linear programming method and an $l_1$-norm constrained trust region method are developed to solve the compressive sensing problem. Numerical results demonstrate that the developed approaches are robust in solving the ill-posed compressive sensing problem and can greatly improve the quality of wavefield recovery.

Keywords: seismic inversion, optimization, sparsity, regularization.

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UDC: 517.983.54
Received: 10.05.2011
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Citation: Y. F. Wang, “Sparse optimization methods for seismic wavefields recovery”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 1, 2012, 42–55

Citation in format AMSBIB
\Bibitem{Wan12}
\by Y.~F.~Wang
\paper Sparse optimization methods for seismic wavefields recovery
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 1
\pages 42--55
\mathnet{http://mi.mathnet.ru/timm778}
\elib{http://elibrary.ru/item.asp?id=17358677}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Ya. Wang, P. Liu, Zh. Li, T. Sun, Ch. Yang, Q. Zheng, “Data regularization using Gaussian beams decomposition and sparse norms”, J. Inverse Ill-Posed Probl., 21:1 (2013), 1–23  crossref  mathscinet  zmath  isi  elib  scopus
    2. J. Cao, Ya. Wang, “Seismic data restoration with a fast $L_1$ norm trust region method”, J. Geophys. Eng., 11:4 (2014), 045010  crossref  isi  scopus
    3. Ya. Wang, Sh. Luo, L. Wang, J. Wang, Ch. Jin, “Synchrotron radiation-based $l_1$-norm regularization on micro-CT imaging in shale structure analysis”, J. Inverse Ill-Posed Probl., 25:4 (2017), 483–497  crossref  mathscinet  zmath  isi  scopus
    4. Z. Yan, Ya. Wang, “Full waveform inversion with sparse structure constrained regularization”, J. Inverse Ill-Posed Probl., 26:2 (2018), 243–257  crossref  mathscinet  zmath  isi  scopus
    5. Xu F., Wang Ya., “Recovery of Seismic Wavefields By An l(Q)-Norm Constrained Regularization Method”, Inverse Probl. Imaging, 12:5 (2018), 1157–1172  crossref  mathscinet  zmath  isi  scopus
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