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)

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This Article



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