Three-dimensional Electromagnetic Modeling in Frequency Domain

주파수영역 전자법의 3차원 모델링

  • Jang, Hannuree (Green Energy Research Institute, Sejong University, Energy Resources Institute, Pukyong National University) ;
  • Kim, Hee Joon (Department of Energy Resources Engineering, Pukyong National University)
  • 장한누리 (세종대학교 그린에너지연구소, 부경대학교 에너지자원연구소) ;
  • 김희준 (부경대학교 에너지자원공학과)
  • Received : 2013.05.10
  • Accepted : 2014.07.08
  • Published : 2014.08.31


Development of a modeling technique for accurately interpreting electromagnetic (EM) data is increasingly required. We introduce finite difference (FD) and finite-element (FE) methods for three-dimensional (3D) frequency-domain EM modeling. In the controlled-source EM methods, formulating the governing equations into a secondary electric field enables us to avoid a singularity problem at the source point. The secondary electric field is discretized using the FD or FE methods for the model region. We represent iterative and direct methods to solve the system of equations resulting from the FD or FE schemes. By applying the static divergence correction in the iterative method, the rate of convergence is dramatically improved, and it is particularly useful to compute a model including surface topography in the FD method. Finally, as an example of an airborne EM survey, we present 3D modeling using the FD method.


Supported by : 한국연구재단, 한국에너지기술평가원(KETEP)


  1. Anderson, W. L., 1982, Fast Hankel transforms using related and lagged convolutions, ACM Trans. Math. Software, 8, 344-368.
  2. Chung, Y., Son, J.-S., Lee, T. J., Kim, H. J., and Shin, C., 2011, 3D CSEM modeling and inversion algorithms for a surfaceto-borehole survey, 81st Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 645-649.
  3. Chung, Y., Son, J.-S., Lee, T. J., Kim, H. J., and Shin, C., 2014, Three-dimensional modelling of controlled-source electromagnetic surveys using an edge finite-element method with a direct solver, Geophysical Prospecting, doi: 10.1111/1365-2478.12132.
  4. Dey, A., and Morrison, H. F., 1979, Resistivity modeling for arbitrarily shaped three-dimensional structures, Geophysics, 44, 753-780.
  5. Farquharson, C. G., and Miensopust, M. P., 2011, Three-dimensional finite-element modelling of magnetotelluric data with a divergence correction, J. Appl. Geophys., 75, 699-710. doi: 10.1016/j.jappgeo.2011.09.025
  6. Guptasarma, D., and Singh, B., 1997, New digital linear filters for Handel $J_0$ and $J_1$ transforms, Geophysical Prospecting, 45, 745-762.
  7. Han, N., Nam, M. J., Kim, H. J., Song, Y., and Suh, J. H., 2009, A comparison of accuracy and computation time of threedimensional magnetotelluric modeling algorithms, J. Geophys. Eng., 6, 136-145. doi:10.1088/1742-2132/6/2/005.
  8. Han, N., Nam, M. J., Ku, B., and Kim, H. J., 2012, Threedimensional modeling of marine controlled-source electromagnetic surveys based on finite difference method, Jigu-Mulli-wa-Mulli-Tamsa, 15, 66-74. (in Korean with English abstract)
  9. Kim, H. J., Nam, M. J., Song, Y., and Suh, J. H., 2004, Review on the three-dimensional magnetotelluric modeling, Mulli-Tamsa, 7, 148-154. (in Korean with English abstract)
  10. Kim, H. J., Choi, J., Han, N., Song, Y., and Lee, K. H., 2009, Primary solution evaluations for interpreting electromagnetic data, Jigu-Mulli-wa-Mulli-Tamsa, 12, 361-366. (in Korean with English abstract)
  11. Kim, H. J., 2011, A scheme for computing primary fields in modeling of marine controlled-source electromagnetic surveys, Jigu-Mulli-wa-Mulli-Tamsa, 14, 185-190. (in Korean with English abstract)
  12. Mackie, R. I., Smith, J. T., and Madden, T. R., 1994, Threedimensional electromagnetic modeling using finite difference equations: The magnetotelluric example, Radio Science, 29, 923-935.
  13. McGillivray, P. R., D. W. Oldenburg, R. G. Ellis, and T. M. Habashy, 1994, Calculation of sensitivities for the frequencydomain electromagnetic problem, Geophys. J. Int., 116, 1-4.
  14. Nam, M. J., Kim, H. J., Song, Y., Lee, T. J., Son, J.-S., and Suh, J. H., 2007a, Three-dimensional magnetotelluric modeling including surface topography, Geophysical Prospecting, 55, 277-287.
  15. Nam, M. J., Kim, H. J., Song, Y., Lee, T. J., and Suh, J. H., 2007b, Effects of 3D topography on Magnetotelluric responses, Mulli-Tamsa, 10, 275-284. (in Korean with English abstract)
  16. Nam, M. J., Kim, H. J., Song, Y., Lee, T. J., and Suh, J. H., 2009, Three-dimensional topographic and bathymetric effects on magnetotelluric responses in Jeju Island, Korea, Geophys. J. Int., 176, 457-466.
  17. Nam, M. J., Han, N., Kim, H. J., and Song, Y., 2011, Modeling of magnetotelluric data based on finite element method: Calculation of auxiliary fields, Jigu-Mulli-wa-Mulli-Tamsa, 14, 164-175. (in Korean with English abstract)
  18. Newman, G. A., and Alumbaugh, D. L., 1995, Frequency-domain modeling of airborne electromagnetic responses using staggered finite differences, Geophysical Prospecting, 43, 1021-1042.
  19. Pridmore, D. F., Hohmann, G. W., Ward, S. H., and Sill, W. R., 1981, An investigation of finite-element method, Geophysics, 46, 1009-1024.
  20. Reddy, I. K., Rankin, D., and Phillips, R. J., 1977, Three-dimensional modeling in magnetotelluric and magnetic variational sounding, Geophys. J. Roy. Astr. Soc., 51, 313-325.
  21. Sasaki, Y., 1999, Three-dimensional frequency-domain electromagnetic modeling using the finite-difference method, Butsuri- Tansa, 52, 421-431. (in Japanese with English abstract)
  22. Smith, J. T., 1996, Conservative modeling of 3-D electromagnetic fields, Part II: Biconjugate gradient solution and an accelerator, Geophysics, 61, 1319-1324.
  23. Son, J.-S., Song, Y., Chung, S.-H., and Suh, J. H., 2002, Threedimensional high-frequency electromagnetic modeling using vector finite elements, Mulli-Tamsa, 5, 280-290. (in Korean with English abstract)
  24. Yee, K. S., 1966, Numerical solution of initial boundary value problems involving Maxwell's equation in isotropic media, IEEE Trans. Antenn. Prop., AP-14, 302-307.