Two-dimensional magnetotelluric inversion of topography
XIONG Bin1, LUO Tian-Ya1, CAI Hong-Zhu2, LIU Yun-Long1, WU Yan-Qiang1, GUO Sheng-Nan1
1. College of Earth Sciences, Guilin University of Technology, Guilin 541006, China;
2. College of Mines & Earth Sciences, University of Utah, Salt lake city, UT 84112, USA
In order to simulate the actual geological conditions, the authors present the least squares inversion by incorporating topography into a forward model. In consideration of an ill-posed inverse problem of MT, the authors introduce Tikhonov regularization to obtain the equation of the total objective function and utilize smoothness-constrained least-squares inversion to solve the total objective function. As the regularized factor controls resolution and stability of the inverse problem, the authors put forward active constraint balancing (ACB) to obtain an optimized regularized factor that balances the resolution as well as the stability of the inversion process. Meanwhile, for the purpose of speeding up the calculation of the field Jacobian for 2-D magnetotelluric inversion, the principle of electromagnetic reciprocity is applied. Finally, the authors discuss the inversion results of TE mode, TM mode and joint inversion of TE and TM mode using some synthetic models, in comparison with some of previous work.
[1] 石应骏,刘国栋,吴广耀,等. 大地电磁测深法教程[M]. 北京:地震出版社,1985.
[2] Jupp D L B, Vozoff K. Two-dimensional magnetotelluric inversion [J]. Geophys. J. R. astr. SOC., 1977, 50: 333-352.
[3] Ogawa Y, Uchida T. A two-dimensional magnetotelluric inversion assuming Gaussian static shift [J]. Geophysical Journal International, 1996, 126: 69-76.
[4] Didana Y L, Thiel S, Heinson G. Magnetotelluric imaging of upper crustal partial melt at Tendaho graben in Afar, Ethiopia [J]. Geophysical Research Letters, 2014, 41(9): 3089-3095.
[5] Martí A. The role of electrical anisotropy in magnetotelluric responses: from modelling and dimensionality analysis to inversion and interpretation [J]. Surv. Geophys., 2014, 35(1): 179-218.
[6] Newman G A, Alumbaugh D L. Three-dimensional magnetotelluric inversion using non-linearconjugate gradients [J]. Geophys. J. Int., 2000, 140: 410-424.
[7] Siripunvaraporn W, Egbert G, Lenbury Y, et al. Three dimensional magnetotelluric inversion: data-space method [J]. Physics of the Earth and Planetary Interios, 2005, 150: 3-14.
[8] Siripunvaraporn W. Three-Dimensional magnetotelluric inversion: An introductory guide for developers and users [J]: Surv. Geophys., 2012, 33(1): 5-27.
[9] Zhang L L, Koyama T, Utada H, et al. A regularized three-dimensional magnetotelluric inversion with a minimum gradient support constraint [J]. Geophys. J. Int., 2012, 189 (1): 296-316.
[10] Grayver A V. Parallel three-dimensional magnetotelluric inversion using adaptive finite-element method. Part I: theory and synthetic study [J]. Geophys. J. Int., 2015, 202 (1): 584-603.
[11] Lindsey N J, Newman G A. Improved workflow for 3D inverse modeling of magnetotelluric data: Examples from five geothermal systems [J]. Geothermics, 2015, 53: 527-532.
[12] Kordy M, Wannamaker P, Maris V, et al. 3-D magnetotelluric inversion including topography using deformed hexahedral edge finite elements and direct solvers parallelized on SMP computers — Part I: forward problem and parameter Jacobians [J]. Geophys. J. Int., 2016, 204(1): 74-93.
[13] deGroot-Hedlin C, Constable S. Occam's inversion to generate smooth, two-dimensional models from magnetotelluric data [J]. Geophysics, 1990, 55(12): 1613-1624.
[14] Siripunvaraporn W, Egbert G. An efficient data-subspace inversion method for 2-D magnetotelluric data [J]. Geophysics, 2000, 65(3): 791-803.
[15] deGroot-Hedlin C, Constable S. Inversion of magnetotelluric data for 2D structure with sharp resistivity contrasts [J]. Geophysics, 2004, 69:78-86.
[16] Smith J T,Booker J R. Rapid inversion of two and three dimensional magnetotelluric data [J]. Geophys Res,1991, 96(B3): 3905-3922.
[17] 陈向斌,吕庆田,张昆. 大地电磁测深反演方法现状与评述[J]. 地球物理学进展,2011,26(5):1607-1619.
[18] Portniaguine O, Zhdanov M S. Focusing geophysical inversion images [J]. Geophysics, 1999a, 64: 874-887.
[19] Mehanee S, Zhdanov M. Two-dimensional magnetotelluric inversion of blocky geoelectrical structures [J]. Journal of Geophysical Research, 2002, 107(B4): EPM 2-1-EPM 2-11.
[20] Rodi W L, Mackie R L. Nonlinear conjugate gradient algorithm for 2-D magnetotelluric inversion [J]. Geophysics, 2001, 66(1): 174-187.
[21] Rodi W L. A technique for improving the accuracy of finite element solutions for magnetotelluric data [J]. Geophys. J. Int., 1976, 44 (2): 483-506.
[22] 陈乐寿. 有限元法在大地电磁场正演计算中的应用及改进[J]. 石油勘探,1981,(3):84-103.
[23] Zienkiewicz O C. The finite element method in engineering science [M]. New York: McGraw-Hill, 1971.
[24] Lee S K, Kim H J, Song Y, et al. MT2DInvMatlab-A program in MATLAB and FORTRAN for two-dimensional magnetotelluric inversion [J]. Computers & Geosciences, 2009, 35(8): 1722-1734.
[25] 陈小斌,赵国泽,汤吉,等. 大地电磁自适应正则化反演算法[J]. 地球物理学报,2005,48(4):937-946.
[26] 柳建新,童孝忠,郭荣文,等. 大地电磁测深勘探——资料处理、反演与解释[M]. 北京:科学出版社,2012.
[27] de Lugão P P, Wannamaker P E. Calculating the two-dimensional magnetotelluric Jacobian in finite elements using reciprocity [J]. Geophys. J. Int., 1996, 127(3): 806-810.
[28] Yi M J, Kim J H, Chung S H. Enhancing the resolving power of least-squares inversion with active constraint balancing [J]. Geophysics, 2003, 68(3): 931-941.
[29] 李磊. 湘南骑田岭锡铅锌多金属矿区岩矿石电性研究[J]. 物探与化探,2007,31(S1):77-80.
[30] Wannamaker P E, Stodt J A, Rijo L. Two-Dimensional Topographic Responses in Magnetotellurics Modeled Using Finite Elements [J]. Geophysics, 1986, 51(11): 2131-2144.