Finite element numerical simulation of 2.5D direct current method based on mesh refinement and recoarsement
Zhang Qian-Jiang1,2, Dai Shi-Kun1, Chen Long-Wei2, Qiang Jian-Ke1, Li Kun1, and Zhao Dong-Dong1
1. School of Geosciences and info-physics, Central South University, Changsha 410083, China.
2. College of Earth Sciences, Guilin University of Technology, Guilin 541006, China.
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.
. Finite element numerical simulation of 2.5D direct current method based on mesh refinement and recoarsement[J]. APPLIED GEOPHYSICS, 2016, 13(2): 257-266.
[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.
[2]
Coggon, J. H., 1971, Electromagnetic and electric modeling by the finite element method: Geophysics, 36(6), 132−155.
[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.
[4]
Günther, T., Rücker, C., and Spitzer, K., 2006, Three-dimensional modelling and inversion of dc resistivity data incorporating topography-II. Inversion: Geophys. J. Int., 166(2), 506−517.
[5]
Hu, H. L., Xiao, X., Pan, K. J., Tang, J. T., and Xie, W., 2014, Finite element modeling of 2.5D DC resistivity based on locally refined graded mesh: Journal of Central South University (Science and Technology), 45(7), 2259−2267.
[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.
[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.
[8]
Li, J. M., 2005, Geoelectric field and electrical exploration (in Chinese): Beijing, Geological Publishing House, Beijing.
[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.
[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.
[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.
[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.
[13]
Pan, K. J., and Tang, J. T., 2013, Optimized selection of discrete wavenumbers for inverse Fourier transform in 2.5D DC resistivity modeling: Journal of Central South University (Science and Technology) (in Chinese), 44(7), 2819−2826.
[14]
Pan, K. J., and Tang, J. T., 2014, 2.5D and 3D DC resistivity modelling using an extrapolation cascadic multigrid method: Geophys. J. Int., 197(3), 1459−1470.
[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.
[16]
Ren, Z. Y., and Tang, J. T., 2009, Finite element modeling of 3D DC resistivity using locally refined unstructured meshes: Chinese J. Geophys. (in Chinese), 52(10), 2627−2634.
[17]
Rijo, L., 1977, Modeling of electric and electromagnetic data: PD. University of Utah.
[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.
[19]
Rücker, C., Günther, T., and Spitzer, K., 2006, Three-dimensional modelling and inversion of dc resistivity data incorporating topography-I. Modeling: Geophys. J. Int., 166(2), 495−505.
[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.
[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.
[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.
[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.
[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.
[25]
Xu, S. Z., 1994, The Finite Element Method in Geophysics: Beijing, Science Press, Beijing.
[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.
[27]
Zhang, Z. Y., and Liu, Q. C., 2013, 2D MT numerical simulation using FEM based on bitree grid: Oil Geophysical Prospecting (in Chinese), 48(3), 482−487.
[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.
[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.
[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.
2016, Vol. 13 
