Applied Geophysics

, Volume 14, Issue 3, pp 419–430 | Cite as

3D anisotropic modeling and identification for airborne EM systems based on the spectral-element method

  • Xin Huang
  • Chang-Chun Yin
  • Xiao-Yue Cao
  • Yun-He Liu
  • Bo Zhang
  • Jing Cai
Electrical & electromagnetic methods


The airborne electromagnetic (AEM) method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element (SE) method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell’s equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic geology.


Spectral-element method anisotropy frequency-domain AEM GLL interpolation basis function forward modeling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



We are very grateful to the reviewers and AP editors for their comments and suggestions, which have helped improve the clarity of this paper.


  1. Avdeev, D. B., Newman, G. A., Kuvshinov, A. V., and Pankratov, O. V., 1998, Three-dimensional frequencydomain modeling of airborne electromagnetic responses: Exploration Geophysics, 29, 111–119.CrossRefGoogle Scholar
  2. Chen, H., Deng, J. Z., Yin, M., Yin, C. C., and Tang, W. W., 2017, Three-dimensional forward modeling of DC resistivity using the aggregation-based algebraic multigrid method: Applied Geophysics, 14(1), 154–164.CrossRefGoogle Scholar
  3. Cohen, G., Joly, P., and Tordjman, N., 1993, Construction and analysis of higher-order finite elements with mass lumping for the wave equation: in Kleinman R. (Ed.). Proceedings of the Second: International Conference on Mathematical and Numerical Aspects of Wave Propagation, SIAM, Philadephias.Google Scholar
  4. Farquharson, C. G., and Oldenburg, D. W., 2002, Chapter 1 An integral equation solution to the geophysical electromagnetic forward-modelling problem: Methods in Geochemistry & Geophysics, 35(2), 3–19.CrossRefGoogle Scholar
  5. Harrington, R. F., and Harrington, J. L., 1968, Field computation by moment methods: Macmillan.Google Scholar
  6. Hu, Y. C., Li, T. L., Fan, C. S., Wang, D. Y., and Li, J. P., 2015, Three-dimensional tensor controlled-source electromagnetic modeling based on the vector finiteelement method: Applied Geophysics, 12(1), 35–46.CrossRefGoogle Scholar
  7. Jin, J. M., 2002, The Finite Element Method in Electromagnetics: Wiley-IEEE Press Wiley, New York.Google Scholar
  8. Li, J. H., Farquharson, C. G., Hu, X. Y., and Zeng, S. H., 2016, A vector finite element solver of three-dimensional modelling for a long grounded wire source based on total electric field: Chinese J. Geophys, (in Chinese), 59(4), 1521–1534.Google Scholar
  9. Li, W. B., Zeng, Z. F., Jing, L., Xiong, C., Wang, K., and Zhao, X., 2016, 2.5d forward modeling and inversion of frequency-domain airborne electromagnetic data: Applied Geophysics, 13(1), 37–47.CrossRefGoogle Scholar
  10. Liu, N., Cai, G., Zhu, C., Tang, Y., and Liu, Q. H., 2015, The Mixed Spectral-Element Method for Anisotropic, Lossy, and Open Waveguides: IEEE Transactions on Microwave Theory & Techniques, 63(10), 3094–3102.CrossRefGoogle Scholar
  11. Liu, N., Tobón, L. E., Zhao, Y., and Tang, Y., 2015, Mixed spectral-element method for 3-d Maxwell’s eigenvalue problem: IEEE Transactions on Microwave Theory & Techniques, 63(2), 317–325.CrossRefGoogle Scholar
  12. Liu, Y. H., and Yin, C. C., 2014, 3D anisotropic modeling for airborne EM systems using finite-difference method: Journal of Applied Geophysics, 109, 186–194.CrossRefGoogle Scholar
  13. Liu, Y. H., Yin, C. C., Ren, X. Y., and Qiu, C. K., 2016, 3D parallel inversion of time-domain airborne EM data: Applied Geophysics, 13(4), 701–711.CrossRefGoogle Scholar
  14. Lee, J. H., Xiao, T., and Liu, Q. H., 2006, A 3-D spectralelement method using mixed-order curl conforming vector basis functions for electromagnetic fields: IEEE Transactions on Microwave Theory & Techniques, 54(1), 437–444.CrossRefGoogle Scholar
  15. Kamm, J., and Pederson, L. B., 2014, Inversion of airborne tensor VLF data using integral equations: Geophysical Journal International, 198(2), 775–794.CrossRefGoogle Scholar
  16. Komatitsch, D., and Vilotte, J. P., 1998, The spectral element method: An efficient tool to simulate the seismic response of 2D and 3D geological structures: Bulletin of the Seismological Society of America, 88(2), 368–392.Google Scholar
  17. Nabigian, N. M., 1992, Electromagnetic Methods in Applied Geophysics (Volume 1) (in Chinese): Geological Publishing House, Beijing.Google Scholar
  18. Newman, G. A., and Alumbaugh, D., 1995, Frequencydomain modeling of airborne electromagnetic responses using staggered finite differences: Geophysical Prospecting, 43(8), 1021–1042.CrossRefGoogle Scholar
  19. Patera, A. T., 1984, A spectral element method for fluid dynamics: Laminar flow in a channel expansion: Journal of Computational Physics, 54(3), 468–488.CrossRefGoogle Scholar
  20. Peterson, A. F., Ray, S. L., and Mittra, R., 1997, Computational Methods for Electromagnetics: IEEE Press, Piscataway.CrossRefGoogle Scholar
  21. Reid, J. E., Pfaffling, A., and Vrbancich, J., 2006, Airborne electromagnetic footprints in 1D earths: Geophysics, 71(2), G63–G72.CrossRefGoogle Scholar
  22. Sasaki, Y., and Nakazato, H., 2003, Topographic modeling and correction in frequency-domain airborne electromagnetics: 16th Geophysical Conference, ASEG Extended Abstracts, 1–4.Google Scholar
  23. Yin, C. C., and Fraser, D. C., 2004, The effect of the electrical anisotropy on the response of helicopterborne frequency-domain electromagnetic systems: Geophysical Prospecting, 52(5), 399–416.CrossRefGoogle Scholar
  24. Yin, C. C., and Hodges, G., 2007, 3D animated visualization of EM diffusion for a frequency-domain helicopter EM system: Geophysics, 72(1), F1–F7.CrossRefGoogle Scholar
  25. Yin, C. C., Huang, X., Liu, Y. H., and Cai, J., 2017, 3-D modeling for airborne E Musing the spectral-element method: Journal of Environmental & Engineering Geophysics, 22(1), 13–23.CrossRefGoogle Scholar
  26. Yin, C. C., Zhang, P., and Cai, J., 2016, Forward modeling of marine DC resistivity method for a layered anisotropic earth: Applied Geophysics, 13(2), 279–287.CrossRefGoogle Scholar
  27. Zhang, Q. J., Dai, S. K., Chen, L. W., Qiang, J. K., Li, K., and Zhao, D. D., 2016, Finite element numerical simulation of 2.5d direct current method based on mesh refinement and recoarsement: Applied Geophysics, 13(2), 257–266.CrossRefGoogle Scholar
  28. Zhou, Y., Shi, L., Liu, N., Zhu, C., Liu, H., and Liu, Q. H., 2016, Spectral element method and domain decomposition for low-frequency subsurface EM simulation: IEEE Geoscience & Remote Sensing Letters, 13(4), 550–554.CrossRefGoogle Scholar

Copyright information

© Editorial Office of Applied Geophysics and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Xin Huang
    • 1
  • Chang-Chun Yin
    • 1
  • Xiao-Yue Cao
    • 1
  • Yun-He Liu
    • 1
  • Bo Zhang
    • 1
  • Jing Cai
    • 1
  1. 1.College of Geo-exploration Science and TechnologyJilin UniversityChangchunChina

Personalised recommendations