ARTICLE

Compressed FWI inversion with non-monotone line search LBFGS

CHAORAN DUAN1 FENGJIAO ZHANG1,2 LIGUO HAN1 AO CHANG1 XIAOCHUN YANG1 FEI HUANG2
Show Less
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: 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/ )
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
  1. Abdi, H. and Williams, L., 2010. Principal component analysis: Wiley
  2. Interdisciplinary Reviews. Computat. Statist., 2: 433-459.
  3. Benhadjali, H., Operto, S. and Virieux, J., 2011. An efficient frequency-domain full
  4. waveform inversion method using simultaneous encoded sources, Geophysics,
  5. 76(4): 109-124. DOE:10.1190/1.3581357.
  6. Brossier, R., 2011. Two-dimensional frequency-domain visco-elastic full waveform
  7. inversion: Parallel algorithms, optimization and performance. Comput. Geosci.,
  8. 37: 444-455. DOL:10.1016/j.cageo.2010.09.013.
  9. Broyden, C.G., 1965. A class of methods for solving nonlinear simultaneous
  10. equations. Mathemat. Computat., 19(92): 577-593.
  11. DOI:10.1090/S0025-5718-1965-0198670-6.
  12. Broyden, C.G., 1967. Quasi-Newton methods and their application to function
  13. minimization. Mathemat. Computat., 21(99): 368-381. DOI:10.2307/2003239.
  14. Byrd, R.H. and Nocedal, J., 1989. A tool for the analysis of quasi-Newton methods
  15. with application to unconstrained minimization. SIAM J. Numer. Analys., 26:
  16. 727-739. DOI:10.1137/0726042.
  17. Cheng, W.Y. and Li, D.H., 2010. Spectral scaling BFGS method. J. Optimizat.
  18. Theory Applicat., 146: 305-319. DOI:10.1007/s10957-010-9652-y.
  19. Grippo, L., Lampariello, F. and Lucidi, S., 1986. A nonmonotone line search
  20. technique for Newton’s Method. SIAM J. Numer. Analys., 23: 707-716.
  21. DOI:10.1137/0723046.
  22. Grippo, L., Lampariello, F. and Lucidi, S., 1989. A truncated Newton method with
  23. nonmonotone line search for unconstrained optimization. J. Optimizat. Theory
  24. Applicat., 60: 401-419. DOI:10.1007/BF00940345.
  25. Han, J. and Liu, G., 1997. Global convergence analysis of a new nonmonotone BFGS
  26. algorithm on convex objective functions. Computat. Optimizat. Applicat., 7:
  27. 277-289. DOI:10.1023/A:1008656711925.
  28. Huang, Z.H., Hu, S.L. and Han, J.Y., 2009. Convergence of a smoothing algorithm
  29. for symmetric cone complementarity problems with a non-monotone line search.
  30. Sci. China, 52: 833-848. DOI:10.1007/s11425-008-0170-4.
  31. Liu, C.C., Han, M., Han, L.G., Huang, F. and Deng, W., 2012. Application of
  32. principal component analysis for frequency-domain full waveform inversion.
  33. Expanded Abstr., 82nd Ann. Internat. SEG Mtg., Las Vegas: 1-5.
  34. DOI:10.1190/segam2012-0909.1.
  35. Liu, D.C. and Nocedal, J., 1989. On the Limited Memory BFGS Method for large
  36. scale optimization. Mathemat. Program., 45: 503-528.
  37. DOI:10.1007/BF01589116.
  38. Ma, Y.and Hale, D., 2012. Quasi Newton full-waveform inversion with a projected
  39. Hessian matrix. Geophysics, 77(5): 207-216. DOI:10.1190/geo02011-0519.1.
  40. Moore, B., 1981. Principal component analysis in linear systems: Controllability,
  41. observability, and model reduction. IEEE Transact. Automat. Contr., 26:
  42. 17-32.
  43. Nocedal, J., 1980. Updating quasi-Newton matrices with limited storage. Mathemat.
  44. Comput., 35: 773-782. DOI: 10.2307/2006193.
  45. Panier, E.R. and Tits, A.L., 1991. Avoiding the Maratos effect by means of a
  46. non-monotone linear search I , general constrained problems. SIAM J. Numer.
  47. Analys., 28: 1183-1195.
  48. Pratt, R.G., 1999. Seismic waveform inversion in the frequency domain, Part 1:
  49. Theory and verification in a physical scale model. Geophysics, 64: 888-901.
  50. DOI:10.1190/1.1444597.
  51. Raydan, M., 1997. The Barzilai and Borwein gradient method for the large scale
  52. unconstrained minimization problem. SIAM J. Optimizat., 7: 26-33.
  53. DOI:10.1137/S1052623494266365.
  54. Schiemenz, A. and Igel, H., 2013. Accelerated 3-D full-waveform inversion using
  55. simultaneously encoded sources in the time domain: application to Valhall
  56. ocean-bottom cable data. Geophys. J. Internat., 195: 1970-1988.
  57. DOI:10.1093/gji/ggt362.
  58. Shi, Z.J. and Shen, J., 2006. Convergence of non-monotone line search method. J.
  59. Computat. Appl. Mathemat., 193: 397-412. DOI:10.1016/j.cam. 2005. 06.003.
  60. Sun, W.Y., Han, J.Y., Sun, J., 2002. Global convergence of non-monotone descent
  61. method for unconstrained optimization problems. J. Computat. Appl. Mathemat.,
  62. 146: 89-98. DOI:10.1016/S0377-0427(02)00420-X.
  63. Tarantola, A., 1984. Inversion of seismic reflection data in the acoustic approximation.
  64. Geophysics, 49: 1259-1266. DOI:10.1190/1.1441754.
  65. Wang, Y.H. and Rao, Y., 2009. Reflection seismic waveform tomography. J. Geophys.
  66. Res., 114(B3): 63-73. DOI:10.1029/2008JB005916
  67. Zhang, H.C. and Hager, W.W., 2004. A Non-monotone Line search technique and its
  68. application to unconstrained optimization. SIAM J. Optimizat., 14: 1043-1056.
  69. DOI:10.1137/S1052623403428208.
  70. Zhao, H. and Gao, Z.Y., 2005. Equilibrium algorithms with non-monotone line search
  71. technique for solving the traffic assignment problems. J. Systems Sci.
  72. Complex., 18: 543-555.
  73. Zhu, D.T., 2003. Non-monotonic back-tracking trust region interior point algorithm
  74. for linear constrained optimization. J. Computat. Appl. Mathemat., 155: 285-305.
  75. DOI:10.1016/S0377-0427(02)00870-1.
Share
Back to top
Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing