This paper focuses on the forward modeling of the direct current resistivity method. To this end, the Gmsh software-a 3D finite element grid generator-was used to model the anomalous bodies under undulating terrain and conduct relevant irregular grid division. Then partial grid data generated by Gmsh were applied to a 2.5D finite element forward modeling program, and the forward calculation results were analyzed using the well-ground joint observation method. The analytical results show that good effects can be obtained by using irregular grids to fit the undulating terrain and using the well-ground joint observation method to explore the geological conditions under the undulating terrain. The effects of the valley terrain on the anomalous response below using different observation devices were also studied. The results achieved are practically significant and they also prove that the Gmsh software has great application value in the forward modeling and meshing based on the finite element method.
张宇哲, 孟麟, 王智. 基于Gmsh的起伏地形下井—地直流电法正演模拟[J]. 物探与化探, 2022, 46(1): 182-190.
ZHANG Yu-Zhe, MENG Lin, WANG Zhi. Forward modeling of well-ground direct current resistivity method for undulating terrain based on Gmsh. Geophysical and Geochemical Exploration, 2022, 46(1): 182-190.
Geuzaine C, Remacle J. Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities[J]. International Journal for Numerical Methods in Engineering, 2009,79(11):1309-1331.
doi: 10.1002/nme.2579
[2]
Coggon J H. Electromagnetic and electrical modeling by the finite element method[J]. Geophysics, 1971,36(2):132-155.
doi: 10.1190/1.1440151
[3]
Rijo L. Modeling of electric and electromagnetic data [D]. Phd Thesis, Univ. of Utah, 1977.
[4]
Dey A, Morrison H F. Resistivity modeling for arbitrarily shaped three-dimensional structured[J]. Geophysics, 1979,44(4):753-780.
doi: 10.1190/1.1440975
[5]
Wu X P. A 3-D finite-element algorithm for DC resistivity modelling using the shifted incomplete Cholesky conjugate gradient method[J]. Geophysical Journal International, 2003,154(3):947-956.
doi: 10.1046/j.1365-246X.2003.02018.x
[6]
Cardarelli E, Fischanger F. 2D data modelling by electrical resistivity tomography for complex subsurface geology[J]. Geophysical Prospecting, 2006,54(2):121-133.
doi: 10.1111/gpr.2006.54.issue-2
Tang J T, Wang F Y, Ren Z Y. 2.5-D DC resistivity modeling by adaptive finite-element with unstructured triangulation[J]. Chinese Journal of Geophysics, 2010,53(3):708-716.
[8]
Ren Z Y, Tang J T. 3D direct current resistivity modeling with unstructured mesh by adaptive finite-element method[J]. Geophysics, 2010,75(1):7-17.
[9]
Ren Z Y, Thomas K, Stewart G. A goal-oriented adaptive finite-element approach for plane wave 3-D electromagnetic modelling[J]. Geophysical Journal International, 2013,194(2):700-718.
doi: 10.1093/gji/ggt154
[10]
Ren Z Y, Tang J T. A goal-oriented adaptive finite-element approach for multi-electrode resistivity system[J]. Geophysical Journal International, 2014,199(1):136-145.
doi: 10.1093/gji/ggu245
[11]
Pan K J, Tang J T. 2.5-D and 3-D DC resistivity modelling using an extrapolation cascadic multigrid method[J]. Geophysical Journal International, 2014,197(3):1459-1470.
doi: 10.1093/gji/ggu094
[12]
Zhang Q J, Dai S K, Chen L W, et al. Finite element numerical simulation of 2.5D direct current method based on mesh refinement and recoasement [J]. Applied Geophysics, 2016, 13(2): 257-266,416-417.
[13]
Kuang X T, Yang H, Zhu X Y, et al. Singularity-free expression of magnetic field of cuboid under undulating terrain[J]. Applied Geophysics, 2016,13(2):238-248,416.
doi: 10.1007/s11770-016-0565-x
Wang Z, Wu A P, Li G. Forward modeling of borehole-ground induced polarization method under undulating topography[J]. Geophysical Prospecting for Petroleum, 2018,57(6):927-935.
Wu J P, Zhang C, Chen J P, et al. Three dimensional finite element simulation of wide field electromagnetic method[J]. Geophysical and Geochemical Exploration, 2020,44(5):1066-1072.
Yan B, Liu Y, Ye Y X. 2.5D direct current resistivity adaptive finite-element numerical modeling based on dual weighted posteriori error estimation[J]. Geophysical and Geochemical Exploration, 2014,38(1):145-150.
[17]
徐世浙. 地球物理中的有限单元法[M]. 北京: 科学出版社, 1994.
[17]
Xu S Z. The finite element method in geophysics [M]. Beiing: Science Press, 1994.
Huang J G, Ruan B X, Wang J L, et al. A study on anomaly of borehole-to-ground joint resistivity surveying system[J]. Chinese Journal of Geophysics, 2009,52(5):1348-1362.