Advertisement

Applied Geophysics

, Volume 13, Issue 2, pp 257–266 | Cite as

Finite element numerical simulation of 2.5D direct current method based on mesh refinement and recoarsement

  • Qian-Jiang Zhang
  • Shi-Kun Dai
  • Long-Wei Chen
  • Jian-Ke Qiang
  • Kun Li
  • Dong-Dong Zhao
Article

Abstract

To deal with the problem of low computational precision at the nodes near the source and satisfy the requirements for computational efficiency in inversion imaging and finite-element numerical simulations of the direct current method, we propose a new mesh refinement and recoarsement method for a two-dimensional point source. We introduce the mesh refinement and mesh recoarsement into the traditional structured mesh subdivision. By refining the horizontal grids, the singularity owing to the point source is minimized and the topography is simulated. By recoarsening the horizontal grids, the number of grid cells is reduced significantly and computational efficiency is improved. Model tests show that the proposed method solves the singularity problem and reduces the number of grid cells by 80% compared to the uniform grid refinement.

Keywords

Direct current resistivity method mesh refinement and recoarsement finite-element method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Blome, M., Marer, H. R., and Schidt, K., 2009, Advances in three-dimensional geoelectric forward solver techniques: Geophys. J. Int., 176(3), 740–752.CrossRefGoogle Scholar
  2. Coggon, J. H., 1971, Electromagnetic and electric modeling by the finite element method: Geophysics, 36(6), 132–155.CrossRefGoogle Scholar
  3. Di, Q. Y., and Wang, M. Y., 1998, The real-like 2D FEM modeling research on the field characteristics of direct electric current field: Chinese J. Geophys. (in Chinese), 41(2), 252–260.Google Scholar
  4. Günther, T., Rücker, C., and Spitzer, K., 2006, Threedimensional modelling and inversion of dc resistivity data incorporating topography-II. Inversion: Geophys. J. Int., 166(2), 506–517.CrossRefGoogle Scholar
  5. Hu, H. L., Xiao, X., Pan, K. J., Tang, J. T., and Xie, W., 2014, Finite element modeling of 2.5D DCresistivity based on locally refined graded mesh: Journal of Central South University (Science and Technology), 45(7), 2259–2267.Google Scholar
  6. Huang, L. P., and Dai, S. K., 2002, Finite Element calculation method of 3D electromagnetic field under complex condition: Earth Science-Journal of China University of Geosciences (in Chinese), 27(6), 776–779.Google Scholar
  7. LaBrecque, D. J., Miletto, M., Daily, W., Ramirez, A., and Owen, E., 1996, The effects of noise on Occam’ s inversion of resistivity tomography data: Geophysics, 61(2), 538–548.CrossRefGoogle Scholar
  8. Li, J. M., 2005, Geoelectric field and electrical exploration (in Chinese): Beijing, Geological Publishing House, Beijing.Google Scholar
  9. Li, S. C., Nie, L. C., Liu, B., Song, J., Liu, Z. Y., Su, M. X., Xu, L., and Sun, H. F., 2013, 3D electrical resistivity inversion using prior spatial shape constraints: Applied Geophysics, 10(4), 361–372.CrossRefGoogle Scholar
  10. Loke, M. H., Chambers, J. E., Rucker, D. F., Kuras, O., and Wilkinson, P. B., 2013, Recent developments in the direct-current geoelectrical imaging method: Journal of Applied Geophysics, 95(8), 135–156.CrossRefGoogle Scholar
  11. Luo, Y. Z., and Meng, Y. L., 1986, Some problems on resistivity modeling for two-dimensional structures by the finite element method: Chinese J. Geophys. (in Chinese), 29(6), 613–621.Google Scholar
  12. Moucha, R., and Bailey, R. C., 2004, An accurate and robust multigrid algorithm for 2D forward resistivity modelling: Geophysical Prospecting, 52(3), 197–212.CrossRefGoogle Scholar
  13. Pan, K. J., and Tang, J. T., 2013, Optimized selection of discrete wavenumbers for inverse Fourier transform in 2.5D DCresistivity modeling: Journal of Central South University (Science and Technology) (in Chinese), 44(7), 2819–2826.Google Scholar
  14. Pan, K. J., and Tang, J. T., 2014, 2.5D and 3D DCresistivity modelling using an extrapolation cascadic multigrid method: Geophys. J. Int., 197(3), 1459–1470.CrossRefGoogle Scholar
  15. Pan, K. J., Tang, J. T., Hu, H. L., and Chen, C. M., 2012, Extrapolation cascadic multigrid method for 2.5D direct current resistivity modeling: Chinese J. Geophys. (in Chinese), 55(8), 2769–2778.Google Scholar
  16. Ren, Z. Y., and Tang, J. T., 2009, Finite element modeling of 3D DCresistivity using locally refined unstructured meshes: Chinese J. Geophys. (in Chinese), 52(10), 2627–2634.Google Scholar
  17. Rijo, L., 1977, Modeling of electric and electromagnetic data: PD. University of Utah.Google Scholar
  18. Ruan, B. Y., and Xu, S. Z., 1998, FEM for modeling resistivity sounding on 2D geoelectric model with line variation of conductivity with in each block: Earth Science-Journal of China University of Geoscience(in Chinese), 23(3), 303–307.Google Scholar
  19. Rücker, C., Günther, T., and Spitzer, K., 2006, Threedimensional modelling and inversion of dc resistivity data incorporating topography-I. Modeling: Geophys. J. Int., 166(2), 495–505.CrossRefGoogle Scholar
  20. Rucker, D. F., Loke, M. H., Levitt, M. T., and Noonan, G. E., 2010, Electrical resistivity characterization of an industrial site using long electrodes: Geophysics, 75(4), WA95–WA104.CrossRefGoogle Scholar
  21. Su, B. Y., Yasuhiro, F., Xu, J. L., and Song, J. Y., 2012, A model study of residual oil distribution jointly using crosswell and borehole-surface electric potential methods: Applied Geophysics, 9(1), 19–26.CrossRefGoogle Scholar
  22. Tang, J. T., Wang, F. Y., and Ren, Z. Y., 2010, 2.5D dc resistivity modelling by adaptive finite-element method with unstructured triangulation: Chinese J. Geophys. (in Chinese), 53(3), 708–716.Google Scholar
  23. Wu, X. P., Liu, Y., and Wang, W., 2015, 3D resistivity inversion incorporating topography based on unstructured meshes: Chinese J. Geophys. (in Chinese), 58(8), 2706–2717.Google Scholar
  24. Xiong, B., and Ruan, B. Y., 2002, A numerical simulation of 2D geoelectric section with biquadratic change of potential for resistivity sounding by the finite element method: Chinese J. Geophys. (in Chinese), 45(2), 285–295.Google Scholar
  25. Xu, S. Z., 1994, The Finite Element Method in Geophysics: Beijing, Science Press, Beijing.Google Scholar
  26. Ye, Y. X., Li, Y. G., Deng, J. Z., and Li, Z. L., 2014, 2.5D induced polarization forward modeling using the adaptive finite-element method: Applied Geophysics, 11(4), 500–507.CrossRefGoogle Scholar
  27. Zhang, Z. Y., and Liu, Q. C., 2013, 2D MTnumerical simulation using FEM based on bitree grid: Oil Geophysical Prospecting (in Chinese), 48(3), 482–487.Google Scholar
  28. Zhao, D. D., Zhang, Q. J., Dai, S. K., Chen, L. W., and Li, K., 2015, Fast inversion for two-dimensional direct current resistivity method based on Gauss-Newton method: The Chinese Journal of Nonferrous Metals(in Chinese), 25(6), 1662–1671.Google Scholar
  29. Zhou, X. X., Zhong, B. S., Yan, Z. Q., and Jiang, Y. L., 1983, Point-source two-dimensional electrical forward finite element method: Computing Techniques for Geophysical and Geochemical Exploration (in Chinese), 3, 19–40.Google Scholar
  30. Zou, G. H., Liang, H. Q., and Geng, M., 2014, Finite element 2.5D direct current resistivity modeling based on quadtree mesh: Science & Technology Review(in Chinese), 32(4/5), 100–104.Google Scholar

Copyright information

© Editorial Office of Applied Geophysics and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Qian-Jiang Zhang
    • 1
    • 2
  • Shi-Kun Dai
    • 1
  • Long-Wei Chen
    • 2
  • Jian-Ke Qiang
    • 1
  • Kun Li
    • 1
  • Dong-Dong Zhao
    • 1
  1. 1.School of Geosciences and info-physicsCentral South UniversityChangshaChina
  2. 2.College of Earth SciencesGuilin University of TechnologyGuilinChina

Personalised recommendations