Forward and inverse modeling of the magnetotelluric field in 2D anisotropic media with an adaptive finite element method
Huang Yifan1, Hu Xiangyun1, Han Bo2
1. Hubei Key Laboratory of Subsurface Multi-scale Imaging, Institute of Geophysics and Geomatics, China University of Geosciences (Wuhan), Wuhan, Hubei 430074, China;
2. College of Marine Geosciences, Ocean University of China, Qingdao, Shandong 266100, China
Abstract：Electrical anisotropy, which widely exists in the crust and upper mantle, has shown great influence on the observation of the electromagnetic field in earth. This electrical anisotropy will affect on magnetotellurics sounding (MT), an electromagnetic geophysical method for inferring the earth subsurface electrical resistivity from measurements of natural geomagnetic and geoelectric field variation at the earth surface. We propose in the paper forward and inverse modeling of magnetotelluric fields in 2D anisotropic media. MT governing equations of electromagnetic field in 2D medium with tri-axial anisotropy are derived, and solved with an adaptive finite element method based on unstructured grids. The unstructured triangle grids can easily simulate general models with not only bathymetry and topography, but also large-range scales and complex structures. The anisotropic inversion strategy employs the classical model space Occam method, so that the model searching is very stable and the reasonable inversion results can be achieved with a few iteration steps. This proposed method is tested on two models, a four-layer 1D model and a 2D anisotropic block model, which are respectively compared with the standard quasi-analytic solution and the standard finite difference solution. A complex 2D anisotropic seafloor model with bathymetry is also designed to test the inversion method. All the test results demonstrate the validity of the proposed algorithms.
黄一凡, 胡祥云, 韩波. 自适应有限元法的大地电磁二维各向异性正反演[J]. 石油地球物理勘探, 2016, 51(4): 809-820.
Huang Yifan, Hu Xiangyun, Han Bo. Forward and inverse modeling of the magnetotelluric field in 2D anisotropic media with an adaptive finite element method. OGP, 2016, 51(4): 809-820.
Pommier A, Leinenweber K, Kohlstedt D L et al. Experimental constraints on the electrical anisotropy of the lithosphere-asthenosphere system. Nature, 2015, 522: 202-206.
[2]
Eaton D W, Jones A G, Ferguson I J. Lithospheric anisotropy structure inferred from collocated teleseismic and magnetotelluric observations: Great Slave Lake shear zone, northern Canada. Geophysical Research Letters, 2004, 31(19): L19614.
[3]
Wannamaker P. Anisotropy versus heterogeneity in continental solid Earth electromagnetic studies: Fundamental response characteristics and implications for physicochemical state. Survey in Geophysics,2005, 26(6):733-765.
[4]
Zhang B, Yoshino T, Yamazaki D et al. Electrical conductivity anisotropy in partially molten peridotite under shear deformation. Earth and Planetary Science Letters, 2014, 405: 98-109.
[5]
Martí A. The role of electrical anisotropy in magnetotelluric responses: from modelling and dimensionality analysis to inversion and interpretation. Surveys in Geophysics, 2014, 35(1): 179-218.
[6]
O'Brien D P, Morrison H F. Electromagnetic fields in an n-layer anisotropic half-space. Geophysics, 1967, 32(4): 668-677.
[7]
Reddy I K, Rankin D R. Magnetotelluric response of laterally inhomogeneous and anisotropic media. Geophysics, 1975, 40(6): 1035-1045.
[8]
Pek J, Verner T. Finite-difference modelling of magnetotelluric fields in two-dimensional anisotropic media. Geophysical Journal International, 1997,128(3): 505-521.
[9]
Li Y. A finite-element algorithm for electromagnetic induction in two-dimensional anisotropic conductivity structures. Geophysical Journal International, 2002,148(3): 389-401.
[10]
Qin L, Yang C, Chen K. Quasi-analytic solution of 2-D magnetotelluric fields on an axially anisotropic infinite fault. Geophysical Journal International, 2013, 192(1): 67-74.
Hu Xiangyun, Huo Guangpu, Gao Rui et al. The magnetotelluric anisotropic two-dimensional simulation and case analysis. Chinese Journal of Geophy-sics, 2013, 56(12): 4268-4277.
[12]
Li Y, Luo M, Pei J.Adaptive finite element modeling of marine controlled-source electromagnetic fields in two-dimensional general anisotropic media. Journal of Ocean University of China, 2013, 12(1): 1-5.
[13]
蔡红柱,熊彬,Zhdanov M. 电导率各向异性的海洋电磁三维有限单元法正演.地球物理学报,2015,58(8): 2839-2850.
Cai Hongzhu, Xiong Bin,Zhdanov M. Three dimensional marine controlled source electromagnetic modelling in anisotropic medium using finite element method. Chinese Journal of Geophysics, 2015,58(8): 2839-2850.
Lin Changyou, Wu Yuxia, Yang Changfu et al. Magnetotelluric inversion for symmetrically anisotropic layered medium. Chinese Journal of Geophysics, 1996, 39(S): 342-348.
[16]
Yin C. Inherent nonuniqueness in magnetotellurics inversion for 1D anisotropic models. Geophysics, 2003, 68(1): 138-146.
[17]
Kirkby A, Heinson G, Holford S et al.Mapping fractures using 1D anisotropic modelling of magnetotelluric data:a case study from the Otway Basin,Victoria, Australia. Geophysical Journal International, 2015, 201(3): 1961-1976.
[18]
Pek J, Santos F A M. Magnetotelluric inversion for anisotropic conductivities in layered media. Physics of the Earth and Planetary Interiors, 2006, 158(2-4): 139-158.
[19]
Constable S C, Parker R L, Constable C G. Occam's inversion: A practical algorithm for generating smooth models from EM sounding data. Geophysics, 1987, 52(3): 289-300.
Yang Changfu, Lin Changyou, Sun Chongchi et al. Inversion for MT data in 2-D symmetrical anisotropic media. Acta Seismologica Sinica, 2005,27(3): 339-345.
[21]
Rodi W, Mackie R L. Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion. Geophysics, 2001, 66(1): 174-187.
[22]
Baba K, Chave A D, Evans R L et al.Mantle dynamics beneath the East Pacific Rise at 178S: insights from the mantle electromagnetic and tomography (MELT) experiment. Journal of Geophysical Research, 2006, 111(B2): B02101.
[23]
Mandolesi E. Inversion of Magnetotelluric Data in An Anisotropic Domain[D]. National University of Ireland,Galway,Ireland,2013.
[24]
Chen X. Two-dimensional Constrained Anisotropic Inversion of Magnetotelluric Data[D]. University Potsdam,Potsdam,2012.
[25]
Li Y, Pek J. Adaptive finite element modelling of two-dimensional magnetotelluric fields in general anisotropic media. Geophysical Journal International, 2008, 175(3): 942-954.
[26]
Key K, Ovall J. A parallel goal-oriented adaptive finite element method for 2.5-D electromagnetic modeling.Geophysical Journal International,2011,186(1):137-154.
Zhao Hui, Liu Ying, Li Yuguo. Adaptive finite ele-ment forward modeling for two-dimensional marine magnetotelluric fields. OGP, 2014, 49(3): 578-585.
[30]
Shewchuk J R. Reprint of: Delaunay refinement algorithms for triangular mesh generation. Computational Geometry,2014, 47(7): 741-778.
[31]
Pek J, Santos F A M. Magnetotelluric impedances and parametric sensitivities for 1-D anisotropic layered media. Computers & Geosciences, 2002,28(8): 939-950.
