1887
Volume 50, Issue 1
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

ABSTRACT

It is important to study the responses of the magnetotelluric (MT) method in anisotropic media. However, MT anisotropy research has focused mainly on one-dimensional (1D) and two-dimensional (2D) solutions. Therefore, we developed a three-dimensional (3D) finite element (FE) algorithm for MT modelling in anisotropic media. This approach is based on the weak formulation of the governing Maxwell equations using Coulomb-gauged potentials. The node-based FE method is adopted here, and the values of the coefficient matrixes are obtained with hexahedral meshes. To validate the correctness and accuracy of this method, its results are compared with previous solutions for a 2D anisotropic model and a 3D arbitrary anisotropic model, respectively. Different solvers with different preconditioners are tested, and the results show that the quasi-minimum residual method with the incomplete LU preconditioner is more stable and faster compared with the other schemes. We then studied a 3D anisotropic model in three different conditions, and analysed the results in detail. Finally, three main conclusions are obtained: the xy- and yy-mode apparent resistivities remain almost unchanged if a principal conductivity is in the -direction; the yx- and xx-mode apparent resistivities remain almost the same if a principal conductivity is in the -direction; a principal conductivity in the -direction has almost no influence on apparent resistivities.

© 2019 Australian Society of Exploration Geophysics
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2019-01-02
2026-01-12

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References

  1. Badea, E.A., M.E. Everett, G.A. Newman, and O. Biro 2001 Finite-element analysis of controlled-source electromagnetic induction using Coulomb-gauged potentials. Geophysics66 no. 3: 786–799. doi:10.1190/1.1444968.
     [Google Scholar]
  2. Bai, D., M.J. Unsworth, M.A. Meju, X. Ma, J. Teng, X. Kong, and C. Zhao 2010 Crustal deformation of the eastern Tibetan plateau revealed by magnetotelluric imaging. Nature Geoscience3 no. 5: 358–362. doi:10.1038/ngeo830.
     [Google Scholar]
  3. Biro, O., and K. Preis 1989 On the use of the magnetic vector potential in the finite-element analysis of three-dimensional eddy currents. IEEE Transactions on Magnetics25 no. 4: 3145–3159. doi:10.1109/20.34388.
     [Google Scholar]
  4. Cai, H., B. Xiong, M. Han, and M. Zhdanov 2014 3D controlled-source electromagnetic modeling in anisotropic medium using edge-based finite element method. Computers and Geosciences73: 164–176. doi:10.1016/j.cageo.2014.09.008.
     [Google Scholar]
  5. Cai, H.Z., B. Xiong, and M. Zhdanov 2015 Three-dimensional marine controlled-source electromagnetic modeling in anisotropic medium using finite element method. Chinese Journal of Geophysics58 no. 8: 2839–2850. doi:10.6038/cjg20150818.
     [Google Scholar]
  6. Cao, H., K. Wang, T. Wang, and B. Hua 2018 Three-dimensional magnetotelluri axial anisotropic forward modeling and inversion. Journal of Applied Geophysics. doi:10.1016/j.jappgeo.2018.04.015.
     [Google Scholar]
  7. Christensen, N.I. 1984 The magnitude, symmetry and origin of upper mantle anisotropy based on fabric analyses of ultramafic tectonites. Geophysical Journal International76 no. 1: 89–111. doi:10.1111/j.1365-246X.1984.tb05025.x.
     [Google Scholar]
  8. Dekker, D.L., and L.M. Hastie 1980 Magneto-telluric impedances of an anisotropic layered Earth model. Geophysical Journal International61 no. 1: 11–20. doi: 10.1111/j.1365‑246X.1980.tb04300.x
     https://doi.org/10.1111/j.1365-246X.1980.tb04300.x [Google Scholar]
  9. Evans, R.L., G. Hirth, K. Baba, D. Forsyth, A. Chave, and R. Mackie 2005 Geophysical evidence from the MELT area for compositional controls on oceanic plates. Nature437 no. 7056: 249. doi:10.1111/j.1365-246X.1980.tb04300.x.
     [Google Scholar]
  10. Everett, M.E. 2012 Theoretical developments in electromagnetic induction geophysics with selected applications in the near surface. Surveys in Geophysics33 no. 1: 29–63. doi:10.1007/s10712-011-9138-y.
     [Google Scholar]
  11. Farquharson, C.G., and J.A. Craven 2009 Three-dimensional inversion of magnetotelluric data for mineral exploration: An example from the McArthur River uranium deposit, Saskatchewan, Canada. Journal of Applied Geophysics68 no. 4: 450–458. doi:10.1016/j.jappgeo.2008.02.002.
     [Google Scholar]
  12. Haber, E., U.M. Ascher, D.A. Aruliah, and D.W. Oldenburg 2000 Fast simulation of 3D electromagnetic problems using potentials. Journal of Computational Physics163 no. 1: 150–171. doi:10.1006/jcph.2000.6545.
     [Google Scholar]
  13. Häuserer, M., and A. Junge 2011 Electrical mantle anisotropy and crustal conductor: a 3-D conductivity model of the Rwenzori Region in western Uganda. Geophysical Journal International185 no. 3: 1235–1242. doi:10.1111/j.1365-246X.2011.05006.x.
     [Google Scholar]
  14. Heise, W., and J. Pous 2001 Effects of anisotropy on the two-dimensional inversion procedure. Geophysical Journal International147 no. 3: 610–621. doi:10.1046/j.0956-540x.2001.01560.x.
     [Google Scholar]
  15. Heise, W., and J. Pous 2003 Anomalous phases exceeding 90° in magnetotellurics: anisotropic model studies and a field example. Geophysical Journal International155 no. 1: 308–318. doi:10.1046/j.1365-246X.2003.02050.x.
     [Google Scholar]
  16. Hu, X.Y., G.P. Huo, R. Gao, H.Y. Wang, Y.F. Huang, Y.X. Zhang, B.X. Zuo, and J.C. Cai 2013 The magnetotelluric anisotropic two-dimensional simulation and case analysis. Chinese Journal of Geophysics56 no. 12: 4268–4277. doi:10.6038/cjg20131229.
     [Google Scholar]
  17. Huo, G.P., X.Y. Hu, Y.F. Huang, and B. Han 2015 MT modeling for two-dimensional anisotropic conductivity structure with topography and examples of comparative analyses. Chinese Journal of Geophysics58 no. 12: 4696–4708. doi:10.6038/cjg20151230.
     [Google Scholar]
  18. Jin, J.M. 2002 The finite element method in electromagnetics. 2nd ed. New York: John Wiley and Sons.
  19. Kirkby, A., G. Heinson, S. Holford, and S. Thiel 2015 Mapping fractures using 1D anisotropic modelling of magnetotelluric data: A case study from the Otway Basin, Victoria, Australia. Geophysical Journal International201 no. 3: 1961–1976. doi:10.1093/gji/ggv116.
     [Google Scholar]
  20. Klein, K.A., and J.C. Santamarina 2003 Electrical conductivity in soils: Underlying phenomena. Journal of Environmental and Engineering Geophysics8 no. 4: 263–273. doi:10.4133/JEEG8.4.263.
     [Google Scholar]
  21. Kong, W., C. Lin, H. Tan, M. Peng, T. Tong, and M. Wang 2018 The effects of 3D electrical anisotropy on magnetotelluric responses: synthetic case studies. Journal of Environmental and Engineering Geophysics23 no. 1: 61–75. doi:10.2113/JEEG23.1.61.
     [Google Scholar]
  22. Li, J., G. Farquharson, and X. Hu 2016 3D vector finite-element electromagnetic forward modeling for large loop sources using a total-field algorithm and unstructured tetrahedral grids. Geophysics82: E1–E16. doi:10.1190/geo2016-0004.1.
     [Google Scholar]
  23. Li, Y. 2000 Finite element modeling of electromagnetic fields in two-and three-dimensional anisotropic conductivity structures. Ph.D. Thesis, University of Gottingen.
     [Google Scholar]
  24. Li, Y. 2002 A finite-element algorithm for electromagnetic induction in two-dimensional anisotropic conductivity structures. Geophysical Journal International148 no. 3: 389–401. doi:10.1046/j.1365-246x.2002.01570.x.
     [Google Scholar]
  25. Li, Y., and J. Pek 2008 Adaptive finite element modelling of two-dimensional magnetotelluric fields in general anisotropic media. Geophysical Journal International175 no. 3: 942–954. doi:10.1111/j.1365-246X.2008.03955.x.
     [Google Scholar]
  26. Liu, Y., Z. Xu, and Y. Li 2018 Adaptive finite element modelling of three-dimensional magnetotelluric fields in general anisotropic media. Journal of Applied Geophysics151: 113–124. doi:10.1016/j.jappgeo.2018.01.012.
     [Google Scholar]
  27. Löwer, A., and A. Junge 2017 Magnetotelluric transfer functions: phase tensor and tipper vector above a simple anisotropic three-dimensional conductivity anomaly and implications for 3Disotropic inversion. Pure and Applied Geophysics174 no. 5: 2089–2101. doi:10.1007/s0002. doi: 10.1007/s00024‑016‑1444‑3
     https://doi.org/10.1007/s00024-016-1444-3 [Google Scholar]
  28. Martinelli, P., and A. Osella 1997 MT forward modeling of 3-D anisotropic electrical conductivity structures using the Rayleigh-Fourier method. Journal of geomagnetism and geoelectricity49 no. 11-12: 1499–1518. doi:10.5636/jgg.49.1499.
     [Google Scholar]
  29. Mitsuhata, Y., and T. Uchida 2004 3D magnetotelluric modeling using the T-Ω finite-element method. Geophysics69 no. 1: 108–119. doi:10.1190/1.1649380.
     [Google Scholar]
  30. O’Brien, D.P., and H.F. Morrison 1967 Electromagnetic fields in an n-layer anisotropic half-space. Geophysics32 no. 4: 668–677. doi:10.1190/1.1439882.
     [Google Scholar]
  31. Pek, J., and F.A. Santos 2002 Magnetotelluric impedances and parametric sensitivities for 1-D anisotropic layered media. Computers and Geosciences28 no. 8: 939–950. doi:10.1016/S0098-3004(02)00014-6.
     [Google Scholar]
  32. Pek, J., and T. Verner 1997 Finite-difference modelling of magnetotelluric fields in two-dimensional anisotropic media. Geophysical Journal International128 no. 3: 505–521. doi:10.1111/j.1365-246X.1997.tb05314.x.
     [Google Scholar]
  33. Puzyrev, V., J. Koldan, J. de la Puente, G. Houzeaux, M. Vázquez, and J.M. Cela 2013 A parallel finite-element method for three-dimensional controlled-source electromagnetic forward modelling. Geophysical Journal International193 no. 2: 678–693. doi:10.1093/gji/ggt027.
     [Google Scholar]
  34. Reddy, I.K., and D. Rankin 1971 Magnetotelluric effect of dipping anisotropies. Geophysical Prospecting19 no. 1: 84–97. doi:10.1111/j.1365-2478.1971.tb00586.x.
     [Google Scholar]
  35. Ren, Z.Y., T. Kalscheuer, S. Greenhalgh, and H. Maurer 2014 A finite-element-based domain-decomposition approach for plane wave 3D electromagnetic modeling. Geophysics79 no. 6: E255–E268. doi:10.1190/geo2013-0376.1.
     [Google Scholar]
  36. Sarvandani, M.M., A.N. Kalateh, M. Unsworth, and A. Majidi 2017 Interpretation of magnetotelluric data from the Gachsaran oil field using sharp boundary inversion. Journal of Petroleum Science and Engineering149: 25–39. doi:10.1016/j.petrol.2016.10.019.
     [Google Scholar]
  37. Wang, T., and S. Fang 2001 3-D electromagnetic anisotropy modeling using finite differences. Geophysics66 no. 5: 1386–1398. doi:10.1190/1.1486779.
     [Google Scholar]
  38. Weidelt, P., M. Oristaglio, and B. Spies 1999 3-D conductivity models: Implications of electrical anisotropy. Three-dimensional Electromagnetics7: 119–137. doi:10.1190/1.9781560802154.ch8.
     [Google Scholar]
  39. Xiao, T., H. Xiangyu, and W. Yun. 2018a 3D MT modeling using the T–Ω method in general anisotropic media. Journal of Applied Geophysics. doi:10.1016/j.jappgeo.2018.11.012.
     [Google Scholar]
  40. Xiao, T., Y. Liu, Y. Wang, and L.Y. Fu 2018b Three-dimensional magnetotelluric modeling in anisotropic media using edge-based finite element method. Journal of Applied Geophysics149: 1–9. doi:10.1016/j.jappgeo.2017.12.009.
     [Google Scholar]
  41. Xu, S.Z. 1994 The Finite Element Methods in Geophysics. Beijing, China: Science Press.
  42. Yin, C. 2000 Geoelectrical inversion for a one-dimensional anisotropic model and inherent non-uniqueness. Geophysical Journal International140 no. 1: 11–23. doi:10.1046/j.1365-246x.2000.00974.x.
     [Google Scholar]
  43. Yin, C. 2003 Inherent nonuniqueness in magnetotelluric inversion for 1D anisotropic models. Geophysics68 no. 1: 138–146. doi:10.1190/1.1543201.
     [Google Scholar]
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Three-dimensional magnetotelluric modelling in anisotropic media using the A-phi method
Exploration Geophysics 50, 31 (2019); https://doi.org/10.1080/08123985.2018.1564274
/content/journals/10.1080/08123985.2018.1564274
/content/journals/10.1080/08123985.2018.1564274
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  • Article Type: Research Article
Keyword(s): 3D modelling; anisotropy; Coulomb-gauged potentials; finite element; Magnetotelluric

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