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

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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.

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References

  • Blome, M., Marer, H. R., and Schidt, K., 2009, Advances in three-dimensional geoelectric forward solver techniques: Geophys. J. Int., 176(3), 740–752.

    Article  Google Scholar 

  • Coggon, J. H., 1971, Electromagnetic and electric modeling by the finite element method: Geophysics, 36(6), 132–155.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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.

    Article  Google Scholar 

  • Li, J. M., 2005, Geoelectric field and electrical exploration (in Chinese): Beijing, Geological Publishing House, Beijing.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • Moucha, R., and Bailey, R. C., 2004, An accurate and robust multigrid algorithm for 2D forward resistivity modelling: Geophysical Prospecting, 52(3), 197–212.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • Rijo, L., 1977, Modeling of electric and electromagnetic data: PD. University of Utah.

    Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • Xu, S. Z., 1994, The Finite Element Method in Geophysics: Beijing, Science Press, Beijing.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

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Authors and Affiliations

  1. School of Geosciences and info-physics, Central South University, Changsha, 410083, China

    Qian-Jiang Zhang, Shi-Kun Dai, Jian-Ke Qiang, Kun Li & Dong-Dong Zhao

  2. College of Earth Sciences, Guilin University of Technology, Guilin, 541006, China

    Qian-Jiang Zhang & Long-Wei Chen

Authors
  1. Qian-Jiang Zhang
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  2. Shi-Kun Dai
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  3. Long-Wei Chen
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  4. Jian-Ke Qiang
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  5. Kun Li
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  6. Dong-Dong Zhao
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Corresponding author

Correspondence to Shi-Kun Dai.

Additional information

This work was financially supported by the National Natural Science Foundation of China (No 41574127 and 41174104) and the National Key Technology R&D Program for the 13th five-year plan (No 2016ZX05018006-006).

Zhang Qian-Jiang: See biography and photo in the Applied Geophysics September 2015 issue, P. 388.

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Zhang, QJ., Dai, SK., Chen, LW. et al. Finite element numerical simulation of 2.5D direct current method based on mesh refinement and recoarsement. Appl. Geophys. 13, 257–266 (2016). https://doi.org/10.1007/s11770-016-0562-0

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  • DOI: https://doi.org/10.1007/s11770-016-0562-0

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