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# Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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# Full waveform inversion with sparse structure constrained regularization

Zichao Yan
• Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, P. O. Box 9825, Beijing 100029, P. R. China; and University of Chinese Academy of Sciences, Beijing 100049, P. R. China
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/ Yanfei Wang
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• Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, P. O. Box 9825, Beijing 100029, P. R. China; and University of Chinese Academy of Sciences, Beijing 100049, P. R. China
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Published Online: 2017-10-17 | DOI: https://doi.org/10.1515/jiip-2016-0076

## Abstract

Full waveform inversion is a large-scale nonlinear and ill-posed problem. We consider applying the regularization technique for full waveform inversion with structure constraints. The structure information was extracted with difference operators with respect to model parameters. And then we establish an ${l}_{p}$-${l}_{q}$-norm constrained minimization model for different choices of parameters p and q. To solve this large-scale optimization problem, a fast gradient method with projection onto convex set and a multiscale inversion strategy are addressed. The regularization parameter is estimated adaptively with respect to the frequency range of the data. Numerical experiments on a layered model and a benchmark SEG/EAGE overthrust model are performed to testify the validity of this proposed regularization scheme.

MSC 2010: 65J22; 86-08; 86A22

## References

• [1]

A. Y. Anagaw and M. D. Sacchi, Full waveform inversion with total variation regularization, preprint (2011), http://www.cspg.org/documents/Conventions/Archives/Annual/2011/131-Full_Waveform_Inversion.pdf.

• [2]

A. Asnaashari, R. Brossier, S. Garambois, F. Audebert, P. Thore and J. Virieux, Regularized seismic full waveform inversion with prior model information, Geophys. 78 (2013), R25–R36.

• [3]

C. Boonyasiriwat, P. Valasek, P. Routh, W. Cao, G. T. Schuster and B. Macy, An efficient multiscale method for time-domain waveform tomography, Geophys. 74 (2009), WCC59–WCC68.

• [4]

R. Brossier, S. Operto and J. Virieux, Seismic imaging of complex onshore structures by 2D elastic frequency-domain full-waveform inversion, Geophys. 74 (2009), WCC105–WCC118.

• [5]

C. Bunks, F. M. Saleck, S. Zaleski and G. Chavent, Multiscale seismic waveform inversion, Geophys. 60 (1995), 1457–1473.

• [6]

C. Burstedde and O. Ghattas, Algorithmic strategies for full waveform inversion: 1D experiments, Geophys. 74 (2009), WCC37–WCC46.

• [7]

A. Guitton, Blocky regularization schemes for full-waveform inversion, Geophys. Prospecting 60 (2012), 870–884.

• [8]

A. Guitton, G. Ayeni and E. Diaz, Constrained full-waveform inversion by model reparameterization, Geophys. 77 (2012), R117–R127.

• [9]

B. Han, Y. X. Dou and L. Ding, Electrical resistivity tomography by using a hybrid regularization, Chinese J. Geophys. 55 (2012), 970–980.

• [10]

W. Hu, A. Abubakar and T. M. Habashy, Simultaneous multifrequency inversion of full-waveform seismic data, Geophys. 74 (2009), R1–R14.

• [11]

S. I. Kabanikhin, Numerical analysis of inverse problems, J. Inverse Ill-Posed Probl. 3 (1995), no. 4, 278–304. Google Scholar

• [12]

S. I. Kabanikhin, D. B. Nurseitov, M. A. Shishlenin and B. B. Sholpanbaev, Inverse problems for the ground penetrating radar, J. Inverse Ill-Posed Probl. 21 (2013), no. 6, 885–892.

• [13]

P. Lailly, The seismic inverse problem as a sequence of before stack migrations, Conference on Inverse Scattering: Theory and Application (Tulsa 1983), SIAM, Philadelphia (1983), 206–220. Google Scholar

• [14]

Y. Lin and L. Huang, Acoustic-and elastic-waveform inversion using a modified total-variation regularization scheme, Geophys. J. Internat. 200 (2015), 489–502. Google Scholar

• [15]

Y. Ma, D. Hale, B. Gong and Z. Meng, Image-guided sparse-model full waveform inversion, Geophys. 77 (2012), R189–R198. Google Scholar

• [16]

J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed., Springer Ser. Oper. Res. Financ. Eng., Springer, New York, 2006. Google Scholar

• [17]

R. E. Plessix, A review of the adjoint-state method for computing the gradient of a functional with geophysical applications, Geophys. J. Internat. 167 (2006), 495–503.

• [18]

R. G. Pratt, Frequency-domain elastic wave modeling by finite differences: A tool for crosshole seismic imaging, Geophys. 55 (1990), 626–632.

• [19]

R. G. Pratt, Seismic waveform inversion in the frequency domain, Part 1: Theory and verification in a physical scale model, Geophys. 64 (1999), 888–901.

• [20]

A. C. Ramirez and W. R. Lewis, Regularization and full-waveform inversion: A two-step approach, SEG Technical Program Expanded Abstracts 2010, Society of Exploration Geophysicists, Tulsa (2010), 2773–2778. Google Scholar

• [21]

L. I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D 60 (1992), no. 1–4, 259–268.

• [22]

J. Sheng, A. Leeds, M. Buddensiek and G. T. Schuster, Early arrival waveform tomography on near-surface refraction data, Geophys. 71 (2006), U47–U57. Google Scholar

• [23]

C. Shin and Y. H. Cha, Waveform inversion in the Laplace domain, Geophys. J. Internat. 173 (2008), 922–931.

• [24]

L. Sirgue and R. G. Pratt, Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies, Geophys. 69 (2004), 231–248.

• [25]

A. Tarantola, Inversion of seismic reflection data in the acoustic approximation, Geophys. 49 (1984), 1259–1266.

• [26]

A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems, V. H. Winston & Sons, Washington, 1977. Google Scholar

• [27]

J. Tromp, C. Tape and Q. Liu, Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels, Geophys. J. Internat. 160 (2005), 195–216. Google Scholar

• [28]

T. van Leeuwen and F. J. Herrmann, Mitigating local minima in full-waveform inversion by expanding the search space, Geophys. J. Internat. 195 (2013), 661–667.

• [29]

V. V. Vasin, Convergence of gradient-type methods for nonlinear equations, Dokl. Akad. Nauk 359 (1998), no. 1, 7–9. Google Scholar

• [30]

J. Virieux and S. Operto, An overview of full-waveform inversion in exploration geophysics, Geophys. 74 (2009), WCC1–WCC26.

• [31]

Y. Wang, Seismic impedance inversion using ${l}_{1}$-norm regularization and gradient descent methods, J. Inverse Ill-Posed Probl. 18 (2010), no. 7, 823–838.

• [32]

Y. Wang and C. Yang, Inverse problems, optimization and regularization: A multi-disciplinary subject, Optimization and Regularization for Computational Inverse Problems and Applications, Springer, Heidelberg (2010), 3–14. Google Scholar

• [33]

Y. F. Wang, Computational Methods for Inverse Problems and Their Applications, Higher Education Press, Beijing, 2007. Google Scholar

• [34]

Y. F. Wang, Sparse optimization methods for seismic wavefields recovery, Trudy Inst. Mat. i Mekh. UrO RAN 18 (2012), 42–55. Google Scholar

• [35]

Y. F. Wang, I. E. Stepanova, V. N. Titarenko and A. G. Yagola, Inverse Problems in Geophysics and Solution Methods, Higher Education Press, Beijing, 2011. Google Scholar

• [36]

Y. F. Wang and C. C. Yang, Accelerating migration deconvolution using a non-monotone gradient method, Geophys. 75 (2010), S131–S137. Google Scholar

• [37]

Y. X. Yuan, Numerical Methods for Nonlinear Programming, Shanghai Science and Technology Publisher, Shanghai, 1993. Google Scholar

• [38]

W. S. Zhang, J. Luo and J. W. Teng, Frequency multiscale full-waveform velocity inversion, Chinese J. Geophys. 58 (2015), 216–228.

Revised: 2017-08-04

Accepted: 2017-08-24

Published Online: 2017-10-17

Published in Print: 2018-04-01

Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 41325016

Award identifier / Grant number: 91630202

The research is supported by National Natural Science Foundation of China under grant numbers 41325016 and 91630202.

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 26, Issue 2, Pages 243–257, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219,

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