3D electromagnetic modeling with vector finite element for a complex-shaped loop source

LI Jianhui1,2 HU Xiangyun1 CHEN Bin1 LIU Yajun1 GUO Shiming1

(1.Institute of Geophysics and Geomatics, China University of Geosciences (Wuhan), Wuhan, Hubei, China 430074)
(2.State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining & Technology, Xuzhou, Jiangsu, China 221116)

【Abstract】The transmitting loop shape is easily changed in a transient electromagnetic field survey. This type of distortion affects the accuracy of data interpretation. Based on the total-field approach and vector finite element (FE) method, we propose a forward modeling for the electromagnetic field excited by a complex-shaped loop source laid on a flat surface. In the forward modeling, a complex-shaped loop laid on a flat surface is firstly divided into dozens of segments, and every segment can be considered as a horizontal electric dipole (HED) source. If a HED is not parallel with the axes in a Cartesian coordinate system, the current density for this HED source is decomposed into a couple of orthogonal HEDs in the axes. We consider first a homogeneous model for a circular loop, which could be seen as a special case for a complex-shaped loop source from the view of enforcing the source item in the vector FE method. The analytic solutions and the FE solutions agree well with each other for the magnetic induction at the loop center. Then, this forward algorithm is applied to calculate the magnetic induction of a complex model respectively for a rectangular loop, a circular loop and a general quadrilateral loop. The results show that the transmitting loop shape has major influence on the early-time magnetic inductions.

【Keywords】 complex-shaped loop source; vector finite element algorithm; unstructured tetrahedron;


【Funds】 National Natural Science Foundation of China (41504088, 41474055) Open Fund of State Key Laboratory for Geomechanics & Underground Engineering, CUMT (SKLGDUEK1312)

Download this article


    [1] Xue G Q, Qin K Z, Li X et al. Discovery of a large-scale porphyry molybdenum deposit in Tibet through a modified TEM exploration method. Journal of Environmental and Engineering Geophysics, 2012, 17 (1): 19–25.

    [2] Yang D, Oldenburg D W. Survey decomposition: A scalable framework for 3D controlled-source electromagnetic inversion. Geophysics, 2016, 81 (2): E31–E49.

    [3] Liu Shucai, Liu Zhixin, Jiang Zhihai. Application of TEM in hydrogeological prospecting of mining district. Journal of China University of Mining & Technology, 2005, 34 (4): 414–417. (in Chinese)

    [4] Xue Guoqiang, Li Xiu, Guo Wenbo et al. Characters of response of large-loop transient electro-magnetic field. OGP, 2007, 42 (5): 586–590. (in Chinese)

    [5] Xue G Q, Bai C Y, Yan S et al. Deep sounding TEM investigation method based on a modified fixed centralloop system. Journal of Environmental and Engineering Geophysics, 2012, 76 (17): 23–32.

    [6] Porsani J L, Bortolozo C A, Almeida E R et al. TDEM survey in urban environmental for hydrogeological study at USP campus in São Paulo city, Brazil. Journal of Applied Geophysics, 2012, 76: 102–108.

    [7] Li Jianhui, Liu Shucai, Jiao Xianfeng et al. Three-dimensional forward modeling for surface-borehole transient electromagnetic method. OGP, 2015, 50 (3): 556–564. (in Chinese)

    [8] Hu Zuzhi, Shi Yanling, He Zhanxiang et al. Application of transient electromagnetic method to detect loess layer in Western China. OGP, 2016, 51 (S): 131–136. (in Chinese)

    [9] Wang T, Hohmann G W. A finite-difference, time-domain solution for three-dimensional electromagnetic modeling. Geophysics, 1993, 58 (6): 797–809.

    [10] Commer M, Newman G. A parallel finite-difference approach for 3D transient electromagnetic modeling with galvanic sources. Geophysics, 2004, 69 (5): 1 192–1 202.

    [11] Qiu Zhipeng, Li Zhanhui, Li Dunzhu et al. Nonorthogonal–grid–based three dimensional modeling of transient electromagnetic field with topography. Chinese Journal of Geophysics, 2013, 56 (12): 4 245–4 255. (in Chinese)

    [12] Um E S, Harris J M, Alumbaugh D L. 3D time–domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics, 2010, 75 (4): F115–F126.

    [13] Newman G A, Hohmann G W, Anderson W L. Transient electromagnetic response of a three-dimensional body in a layered earth. Geophysics, 1986, 51 (8): 1608–1627.

    [14] Sugeng F. Modelling the 3D TDEM response using the 3D full-domain finite-element method based on the hexahedral edge-element technique. Exploration Geophysics, 1998, 29 (4): 615–619.

    [15] Li J H, Zhu Z Q, Liu S C et al. 3D numerical simulation for the transient electromagnetic field excited by the central loop based on the vector finite-element method. Journal of Geophysics and Engineering, 2011, 8 (4): 560–567.

    [16] Yin C C, Fraser D C. Attitude corrections of helicopter EM data using a superposed dipole model. Geophysics, 2004, 69 (2): 431–439.

    [17] Ji Yanju, Lin Jun, Guan Shanshan et al. Theoretical study of concentric loop coils attitude correction in helicopter-borne TEM. Chinese Journal of Geophysics, 2010, 53 (1): 171–176. (in Chinese)

    [18] Liu Yunhe, Yin Changchun, Weng Aihua et al. Attitude effect for marine CSEM system. Chinese Journal of Geophysics, 2012, 55 (8): 2 757–2 768 (in Chinese).

    [19] Han Bo, Hu Xiangyun, Schultz A et al. Three-dimensional forward modeling of the marine controlled source electromagnetic field with complex source geometries. Chinese Journal of Geophysics, 2015, 58 (3): 1 059–1 071 (in Chinese).

    [20] Yan Bo, Li Yuguo, Han Bo et al. 3D marine controlled source electromagnetic forward modeling with arbitrarily oriented dipole source. OGP, 2017, 52 (4): 859–868. (in Chinese)

    [21] Weiss C J. Project AphiD: A Lorenz-gauged A-Φ decomposition for parallelized computation of ultrabroadband electromagnetic induction in a fully heterogeneous earth. Computer & Geosciences, 2013, 58: 40–52.

    [22] Jahandari H, Farquharson C G. A finite-volume solution to the geophysical electromagnetic forward problem using unstructured grids. Geophysics, 2014, 79 (6): E287–E302.

    [23] Ansari S, Farquharson C G. 3D finite-element forward modeling of electromagnetic data using vector and scalar potentials and unstructured grids. Geophysics, 2014, 79 (4): E149–E165.

    [24] Yang Jun, Liu Ying, Wu Xiaoping. 3D simulation of marine CSEM using vector finite element method on unstructured grids. Chinese Journal of Geophysics, 2015, 58 (8): 2 827–2 838 (in Chinese).

    [25] Li Jianhui, Farquharson C G, Hu Xiangyun et al. A vector finite element solver of three-dimensional modelling for a long grounded wire source based on total electric field. Chinese Journal of Geophysics, 2016, 59 (4): 1 521–1 534 (in Chinese).

    [26] Jin J M. The Finite Element Method in Electromagnetic II. John Wiley & Sons Inc, New York, 2002.

    [27] Amestoy P R, Guermouche A, L’Excellent J Y et al. Hybrid scheduling for the parallel solution of linear systems. Parallel Computing, 2006, 32 (2): 136–156.

    [28] Anderson W L. Fourier cosine and sine transforms using lagged convolutions in double–precision (subprograms DLAGF0/DLAGF1). Open-File Report 83–320, U.S. Geological Survey, 1983.

    [29] Li J, Farquharson C G, Hu X. Three effective inverse Laplace transform algorithms for computing timedomain electromagnetic responses. Geophysics, 2016, 81 (2): E113–E128.

    [30] Si H. TetGen, a delaunay-based quality tetrahedral mesh generator. ACM Transactions on Mathematical Software, 2015, 41 (2): 11.

    [31] Ayachit U. The ParaView Guide: A Parallel Visualization Application. Kitware Inc, 2015.

    [32] Ward S H, Hohmann G W. Electromagnetic theory for geophysical applications //Electromagnetic Methods in Applied Geophysics: Volume 1, Theory. SEG, 1988, 167–183.

    [33] Guptasarma D, Singh B. New digital linear filters for Hankel J0 and J1 transforms. Geophysical Prospecting, 1997, 45 (5): 745–762.

This Article


CN: 13-1095/TE

Vol 52, No. 06, Pages 1324-1332+1125

December 2017


Article Outline


  • 1 Introduction
  • 2 Vector finite element method
  • 3 Homogeneous model test
  • 4 Complex model test
  • 5 Conclusions
  • Appendix A: Analytic solution for the circular loop excited at the loop center
  • References