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Three dimensional magnetotelluric inversion using L BFGS

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The gradient-based optimization methods are preferable for the large-scale three-dimensional (3D) magnetotelluric (MT) inverse problem. Compared with the popular nonlinear conjugate gradient (NLCG) method, however, the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) method is less adopted. This paper aims to implement a L-BFGS-based inversion algorithm for the 3D MT problem. And we develop our code on top of the ModEM package, which is highly extensible and popular among the MT community. To accelerate the convergence speed, the preconditioning technique by the afne linear transformation of the original model parameters is used. Two modifcations of the conventional L-BFGS algorithm are also made to get a comparable convergence rate with the NLCG method. The impacts of the preconditioner parameters, the regularization parameters, the starting model, etc., on the inversion are evaluated by synthetic examples for both L-BFGS and NLCG methods. And the real MT Kayabe dataset is also inverted by the inversion algorithms. The synthetic tests show that through our L-BFGS inversion algorithm the similar resistivity models can be obtained with that from the NLCG method. For the real data inversion, the L-BFGS method performs more efciently and reasonable results could be obtained by less iterations of the inversion process than the NLCG method. Thus, we suggest the common usage of the L-BFGS method for the 3D MT inverse problem.
Słowa kluczowe
EN
3D   MT   NLCG   quasi-Newton   line search  
PL
3D   MT   NLCG   quasi-Newton  
Czasopismo
Rocznik
Strony
1049--1066
Opis fizyczny
Bibliogr. 30 poz.
Twórcy
autor
  • School of Geophysics and Information Technology, China University of Geosciences (Beijing), Beijing 100083, China
autor
  • College of Geophysics, Chengdu University of Technology, Chengdu 610059, China
autor
  • School of Geophysics and Information Technology, China University of Geosciences (Beijing), Beijing 100083, China
autor
  • College of Geophysics, Chengdu University of Technology, Chengdu 610059, China
Bibliografia
  • 1. Avdeev D, Avdeeva A (2009) 3D magnetotelluric inversion using a limited-memory quasi-Newton optimization. Geophysics 74(3):F45–F57
  • 2. Avdeeva A, Avdeev D (2006) A limited-memory quasi-Newton inversion for 1D magnetotellurics. Geophysics 71(5):G191–G196
  • 3. Avdeeva A, Avdeev D, Jegen M (2012) Detecting a salt dome overhang with magnetotellurics: 3D inversion methodology and synthetic model studies. Geophysics 77(4):E251–E263
  • 4. Byrd RH, Lu P, Nocedal J et al (1995) A limited memory algorithm for bound constrained optimization. SIAM J Sci Comput 16(5):1190–1208
  • 5. Byrd RH, Nocedal J, Schnabel RB (1994) Representations of quasi-Newton matrices and their use in limited memory methods. Math Program 63(1–3):129–156
  • 6. Devi A, Israil M, Gupta PK et al (2019) Transverse tectonics structures in the Garhwal Himalaya Corridor inferred from 3D inversion of magnetotelluric profile data. Pure Appl Geophys 176(11):4921–4940
  • 7. Egbert GD, Kelbert A (2012) Computational recipes for electromagnetic inverse problems. Geophys J Int 189(1):251–267
  • 8. Jahandari H, Farquharson CG (2017) 3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids. Geophys J Int 211(2):1189–1205
  • 9. Kelbert A, Egbert GD, Schultz A (2008) Non-linear conjugate gradient inversion for global EM induction: resolution studies. Geophys J Int 173(2):365–381
  • 10. Kelbert A, Meqbel N, Egbert GD et al (2014) ModEM: a modular system for inversion of electromagnetic geophysical data. Comput Geosci 66:40–53
  • 11. Koyama T, Khan A, Kuvshinov A (2014) Three-dimensional electrical conductivity structure beneath Australia from inversion of geomagnetic observatory data: evidence for lateral variations in transition-zone temperature, water content and melt. Geophys J Int 196(3):1330–1350
  • 12. Lin C, Tan H, Tong T (2011) Three-dimensional conjugate gradient inversion of magnetotelluric impedance tensor data. J Earth Sci 22(3):386–395
  • 13. Liu DC, Nocedal J (1989) On the limited memory BFGS method for large scale optimization. Math Program 45(1–3):503–528
  • 14. Liu Y, Yin C (2013) 3D inversion for frequency-domain HEM data. Chin J Geophys Chin Ed 56(12):4278–4287
  • 15. Lorenc A (1992) Iterative analysis using covariance functions and filters. Q J R Meteorol Soc 118(505):569–591
  • 16. Moorkamp M, Heincke B, Jegen M et al (2011) A framework for 3-D joint inversion of MT, gravity and seismic refraction data. Geophys J Int 184(1):477–493
  • 17. Newman GA, Alumbaugh DL (2000) Three-dimensional magnetotelluric inversion using non-linear conjugate gradients. Geophys J Int 140(2):410–424
  • 18. Newman GA, Boggs PT (2004) Solution accelerators for large-scale three-dimensional electromagnetic inverse problems. Inverse Prob 20(6):S151–S170
  • 19. Newman GA, Gasperikova E, Hoversten GM et al (2008) Three-dimensional magnetotelluric characterization of the Coso geothermal field. Geothermics 37(4):369–399
  • 20. Ni Q, Yuan YX (1997) A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization. Math Comput 66(220):1509–1520
  • 21. Nocedal J, Wright S (2006) Numerical optimization. Springer, New York, pp 135–163
  • 22. Purser RJ, Wu WS, Parrish DF et al (2003) Numerical aspects of the application of recursive filters to variational statistical analysis. Part I: spatially homogeneous and isotropic Gaussian covariances. Mon Weather Rev 131(8):1524–1535
  • 23. Rodi W, Mackie RL (2001) Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion. Geophysics 66(1):174–187
  • 24. Sass P, Ritter O, Ratschbacher L et al (2014) Resistivity structure underneath the Pamir and Southern Tian Shan. Geophys J Int 198(1):564–579
  • 25. Siripunvaraporn W, Egbert G (2000) An efficient data-subspace inversion method for 2-D magnetotelluric data. Geophysics 65(3):791–803
  • 26. Siripunvaraporn W, Sarakorn W (2011) An efficient data space conjugate gradient Occam's method for three-dimensional magnetotelluric inversion. Geophys J Int 186(2):567–579
  • 27. Siripunvaraporn W, Egbert G, Lenbury Y et al (2005) Three-dimensional magnetotelluric inversion: data-space method. Phys Earth Planet Int 150(1–3):3–14
  • 28. Takasugi S, Tanaka K, Kawakami N et al (1992) High spatial resolution of the resistivity structure revealed by a dense network MT measurement—a case study in the Minamikayabe Area, Hokkaido Japan. J Geomagn Geoelectr 44(4):289–308
  • 29. Yamane K, Takasugi S (1997) Data processing procedures for Minami-Kayabe magnetotelluric soundings. J Geomagn Geoelectr 49(11–12):1697–1715
  • 30. Zhang K, Dong H, Yan J et al (2013) A NLCG inversion method of magnetotellurics with parallel structure. Chin J Geophys Chin Ed 56(11):3922–3931
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a7ebc59b-0673-4180-83e8-159b4aacb46f
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