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Compressed FWI inversion with non-monotone line search LBFGS
CHAORAN DUAN1 ,
FENGJIAO ZHANG1,2 ,
LIGUO HAN1 ,
AO CHANG1 ,
XIAOCHUN YANG1 ,
FEI HUANG2
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1
College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, P.R. China,
2
Department of Earth Sciences, Uppsala University, Uppsala 75236, Sweden,
JSE 2017, 26(6), 561–585;
Submitted: 15 May 2017 | Accepted: 12 September 2017 | Published: 1 December 2017
© 2017 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/ )
Abstract
Duan, C., Zhang, F., Han, L., Chang, X. and Yang, F., 2017. Journal of Seismic Exploration, 26: 561-585. Full waveform inversion (FWI) is a high quality seismic imaging method. It is a nonlinear inversion problem which usually needs the monotone line search method to be solved. However, the speed of convergence for such a simple search technique is relatively slow. In this paper, we combine the non-monotone line search technique with the LBFGS method and apply them to the frequency-domain FWI. We test this new method on a two-dimensional Marmousi model. The results show that the method is robust. Comparing with the monotone line search method, the new method could improve the convergence rate of FWI. We also test the new method with a two-dimensional conventional streamer data set and the results show some improvements compared with the conventional FWI method.
Keywords
full waveform inversion (FWI)
LBFGS method
non-monotone line search
principal component analysis
References
- Abdi, H. and Williams, L., 2010. Principal component analysis: Wiley
- Interdisciplinary Reviews. Computat. Statist., 2: 433-459.
- Benhadjali, H., Operto, S. and Virieux, J., 2011. An efficient frequency-domain fullwaveform inversion method using simultaneous encoded sources, Geophysics,76(4): 109-124. DOE:10.1190/1.3581357.
- Brossier, R., 2011. Two-dimensional frequency-domain visco-elastic full waveforminversion: Parallel algorithms, optimization and performance. Comput. Geosci.,37: 444-455. DOL:10.1016/j.cageo.2010.09.013.
- Broyden, C.G., 1965. A class of methods for solving nonlinear simultaneousequations. Mathemat. Computat., 19(92): 577-593.DOI:10.1090/S0025-5718-1965-0198670-6.
- Broyden, C.G., 1967. Quasi-Newton methods and their application to functionminimization. Mathemat. Computat., 21(99): 368-381. DOI:10.2307/2003239.
- Byrd, R.H. and Nocedal, J., 1989. A tool for the analysis of quasi-Newton methodswith application to unconstrained minimization. SIAM J. Numer. Analys., 26:727-739. DOI:10.1137/0726042.
- Cheng, W.Y. and Li, D.H., 2010. Spectral scaling BFGS method. J. Optimizat.
- Theory Applicat., 146: 305-319. DOI:10.1007/s10957-010-9652-y.
- Grippo, L., Lampariello, F. and Lucidi, S., 1986. A nonmonotone line searchtechnique for Newton’s Method. SIAM J. Numer. Analys., 23: 707-716.DOI:10.1137/0723046.
- Grippo, L., Lampariello, F. and Lucidi, S., 1989. A truncated Newton method withnonmonotone line search for unconstrained optimization. J. Optimizat. TheoryApplicat., 60: 401-419. DOI:10.1007/BF00940345.
- Han, J. and Liu, G., 1997. Global convergence analysis of a new nonmonotone BFGSalgorithm on convex objective functions. Computat. Optimizat. Applicat., 7:277-289. DOI:10.1023/A:1008656711925.
- Huang, Z.H., Hu, S.L. and Han, J.Y., 2009. Convergence of a smoothing algorithmfor symmetric cone complementarity problems with a non-monotone line search.
- Sci. China, 52: 833-848. DOI:10.1007/s11425-008-0170-4.
- Liu, C.C., Han, M., Han, L.G., Huang, F. and Deng, W., 2012. Application ofprincipal component analysis for frequency-domain full waveform inversion.
- Expanded Abstr., 82nd Ann. Internat. SEG Mtg., Las Vegas: 1-5.DOI:10.1190/segam2012-0909.1.
- Liu, D.C. and Nocedal, J., 1989. On the Limited Memory BFGS Method for largescale optimization. Mathemat. Program., 45: 503-528.DOI:10.1007/BF01589116.
- Ma, Y.and Hale, D., 2012. Quasi Newton full-waveform inversion with a projected
- Hessian matrix. Geophysics, 77(5): 207-216. DOI:10.1190/geo02011-0519.1.
- Moore, B., 1981. Principal component analysis in linear systems: Controllability,observability, and model reduction. IEEE Transact. Automat. Contr., 26:17-32.
- Nocedal, J., 1980. Updating quasi-Newton matrices with limited storage. Mathemat.Comput., 35: 773-782. DOI: 10.2307/2006193.
- Panier, E.R. and Tits, A.L., 1991. Avoiding the Maratos effect by means of anon-monotone linear search I , general constrained problems. SIAM J. Numer.Analys., 28: 1183-1195.
- Pratt, R.G., 1999. Seismic waveform inversion in the frequency domain, Part 1:
- Theory and verification in a physical scale model. Geophysics, 64: 888-901.DOI:10.1190/1.1444597.
- Raydan, M., 1997. The Barzilai and Borwein gradient method for the large scaleunconstrained minimization problem. SIAM J. Optimizat., 7: 26-33.DOI:10.1137/S1052623494266365.
- Schiemenz, A. and Igel, H., 2013. Accelerated 3-D full-waveform inversion usingsimultaneously encoded sources in the time domain: application to Valhallocean-bottom cable data. Geophys. J. Internat., 195: 1970-1988.DOI:10.1093/gji/ggt362.
- Shi, Z.J. and Shen, J., 2006. Convergence of non-monotone line search method. J.
- Computat. Appl. Mathemat., 193: 397-412. DOI:10.1016/j.cam. 2005. 06.003.
- Sun, W.Y., Han, J.Y., Sun, J., 2002. Global convergence of non-monotone descentmethod for unconstrained optimization problems. J. Computat. Appl. Mathemat.,146: 89-98. DOI:10.1016/S0377-0427(02)00420-X.
- Tarantola, A., 1984. Inversion of seismic reflection data in the acoustic approximation.Geophysics, 49: 1259-1266. DOI:10.1190/1.1441754.
- Wang, Y.H. and Rao, Y., 2009. Reflection seismic waveform tomography. J. Geophys.Res., 114(B3): 63-73. DOI:10.1029/2008JB005916
- Zhang, H.C. and Hager, W.W., 2004. A Non-monotone Line search technique and itsapplication to unconstrained optimization. SIAM J. Optimizat., 14: 1043-1056.DOI:10.1137/S1052623403428208.
- Zhao, H. and Gao, Z.Y., 2005. Equilibrium algorithms with non-monotone line searchtechnique for solving the traffic assignment problems. J. Systems Sci.Complex., 18: 543-555.
- Zhu, D.T., 2003. Non-monotonic back-tracking trust region interior point algorithmfor linear constrained optimization. J. Computat. Appl. Mathemat., 155: 285-305.DOI:10.1016/S0377-0427(02)00870-1.
