Three-Dimensional Resistivity Modeling by Serendipity Element

Serendipity 요소법에 의한 전기비저항 3차원 모델링

  • Lee, Keun-Soo (Department of Geophysics, Kangwon National University) ;
  • Cho, In-Ky (Department of Geophysics, Kangwon National University) ;
  • Kang, Hye-Jin (Department of Geophysics, Kangwon National University)
  • Received : 2012.02.01
  • Accepted : 2012.02.24
  • Published : 2012.02.29


A resistivity method has been applied to wide range of engineering and environmental problems with the help of automatic and precise data acquisition. Thus, more accurate modeling and inversion of time-lapse monitoring data are required since resistivity monitoring has been introduced to quantitatively find out subsurface changes With respect to time. Here, we used the finite element method (FEM) for 3D resistivity modeling since the method is easy to realize complex topography and arbitrary shaped anomalous bodies. In the FEM, the linear elements, also referred to as first order elements, have certain advantages of simple formulation and narrow bandwidth of system equation. However, the linear elements show the poor accuracy and slow convergence of the solution with respect to the number of elements or nodes. To achieve the higher accuracy of finite element solution, high order elements are generally used. In this study, we developed a 3D resistivity modeling program using high order Serendipity elements. Comparing the Serendipity element solutions for a cube model with the linear element solutions, we assured that the Serendipity element solutions are more accurate than the linear element solutions in the 3D resistivity modeling.


Supported by : 한국연구재단


  1. 박권규, 1994, 유한요소법을 이용한 3차원 전기비저항 모델링 및 지형보정에 관한 연구, 공학석사 학위논문, 서울대학교.
  2. 오석훈, 1994, 유한요소법을 이용한 2차원 전기탐사의 지형보정, 교육학석사 학위논문, 서울대학교.
  3. 조인기, 1989, 전기 및 자기 비저항법의 3차원 모델링 및 해석, 공학박사학위논문, 서울대학교.
  4. Baker, R. and Moore, J., 1998, The application of time-lapse electrical tomography in groundwater studies, The Leading Edge, 1454-1458.
  5. Chun, K. S., and Kassegne, S. K., 2005, A new, efficient 8-node Serendipity element with explicit and assumed strains formulations, International Journal for Computational Methods in Engineering Science Mechanics, 6, 285-292.
  6. Coggon, J. H., 1971, Electromagnetic and electrical modeling by the finite element method, Geophysics, 36, 132-155.
  7. Ergatoudis, J. G., Irons, B. M., and Zienkiewicz, O. C., 1968, Curved isoparametric quadrilateral elements for finite element analysis, International Journal of Solids Structure, 4, 31-42.
  8. Fox, R. C., Hohmann, G. W., Killpack., T. J, and Rijo, L., 1980, Topographic effects in resistivity and induced-polarization surveys, Geophysics, 45, 75-93.
  9. Hohmann, G. W., 1975, Three-dimensional induced polarization and electromagnetic modeling, Geophysics, 40, 309-324.
  10. Horlin, N. E., Nordstrom, M., and Goransson, P., 2001, A 3-D hierarchical FE formulation of BIOT'S equations for elastoacoustic modelling of porous media, Journal of Sound and Vibration, 245, 633-652.
  11. Kotigua, P. R., and Silvester, P. P., 1982, Vector potential formulation for three-dimensional magnetostatics, Journal of Applied Physics, 53, 8399-8401.
  12. Rathod, H. T., and Sridevi, K., 2001, General complete Lagrange interpolation with applications to three-dimensional finite element analysis, Computer Methods in Applied Mechanics and Engineering, 190, 3325-3368.