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Volume 70, Issue 4
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

An investigation of forward modelling 3‐D wire source electromagnetic data in the frequency domain using nodal and edge finite‐element basis functions is presented. The equations solved are those for the coupled secondary vector–scalar potentials (i.e. magnetic vector potential and electric scalar potential ), which give rise to a less ill‐conditioned system of equations to be solved. The effectiveness of these two methods is validated with two 3‐D examples, i.e. multi‐blocks models and topography models, which considered the computation of the potentials and the electromagnetic fields due to a grounded electric line source by inter‐comparing the numerical solutions computed from each method and by comparing them against the equivalent solutions for the same model computed using other methods. Based on the multiple‐blocks models, we compare the relative contributions of the inductive and galvanic parts to the E‐field for different frequencies. Results show that for the type of source considered in this paper, the galvanic parts dominate for a relatively low frequency (10 Hz), but that for a relatively high frequency (10 kHz), the inductive parts also contribute. The extent to which the Coulomb gauge condition is satisfied when using nodal basis functions for is also investigated, with results showing that the divergence of the numerically calculated is almost zero as desired. Based on the topography models, we analyse the electromagnetic response characteristics at different survey planes, with results of this investigation indicating that the electromagnetic responses measured over a plane close to the target will carry more accurate geometry information (such as position, shape and size) of the target, which is expected, and less distortion due to topography compared to those measured at the earth's surface. This suggests that when conducting electromagnetic prospecting in an area with complex topography, it is possible to obtain better anomaly detection affected less by topography if the electromagnetic measurement is carried out underground (such as in a borehole).

© 2022 European Association of Geoscientists & Engineers © 2022 European Association of Geoscientists & Engineers
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2022-04-14
2024-04-23

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References

  1. Ansari, S. (2014) Three dimensional finite‐Element numerical modeling of geophysical electromagnetic problems using tetrahedral unstructured grids. PhD thesis, Memorial University of Newfoundland.
  2. Ansari, S. and Farquharson, C.G. (2014) 3D finite‐element forward modeling of electromagnetic data using vector and scalar potentials and unstructured grids. Geophysics, 79(4), 149–165.
     [Google Scholar]
  3. Badea, B., Everett, M., Newman, G. and Biro, O. (2001) Finite element analysis of controlled‐source electromagnetic induction using coulomb‐gauged potentials. Geophysics, 66, 786–799.
     [Google Scholar]
  4. Bartel, L.C. and Jacobson, R.D. (1987) Results of a controlled‐source audio frequency magnetotelluric survey at the Puhimau thermal area, Kilauea volcano, Hawaii. Geophysics, 52(5), 665–677.
     [Google Scholar]
  5. Biro, O. (1999) Edge element formulations of eddy current problems. Computer Methods in Applied Mechanics and Engineering, 169, 391–405.
     [Google Scholar]
  6. Biro, O. and Preis, K. (1989) On the use of the magnetic vector potential in the finite element analysis of three‐dimensional eddy currents. IEEE Transactions on Magnetics, 25, 3145–3159.
     [Google Scholar]
  7. Coggon, J.H. (1971), Electromagnetic and electrical modeling by the finite element method. Geophysics, 36, 132–155.
     [Google Scholar]
  8. Dey, A. and Morrison, H.F. (1979) Resistivity modelling for arbitrary shaped three‐dimensional structures. Geophysics, 44, 753–780.
     [Google Scholar]
  9. Everett, M.E. and Schultz, A. (1996) Geomagnetic induction in a heterogenous sphere: azimuthally symmetric test computations and the response of an undulating 660‐km discontinuity. Journal of Geophysical Research, 101, 2765–2783.
     [Google Scholar]
  10. Farquharson, C.G. and Miensopust, M. (2011) Three‐dimensional finite‐element modelling of magnetotelluric data with a divergence correction. Journal of Applied Geophysics, 75, 699–710.
     [Google Scholar]
  11. Farquharson, C.G. and OldenburgD.W. (2002) An integral equation solution to the geophysical electromagnetic forward‐modelling problems. In: Zhdanov, M.S. and Wannamaker, P.E. (Eds) Three‐Dimensional Electromagnetics. New York: Elsevier, Inc., pp. 3–19.
     [Google Scholar]
  12. Franke‐Börner, A., Börner, R.U. and Spitzer, K. (2012) On the efficient formulation of the MT boundary value problem for 3D finite‐element simulation: 21th International Workshop on Electromagnetic Induction in the Earth, Australia, Expanded Abstracts.
  13. Haber, E., Ascher, U.M., Aruliah, D.A. and Oldenburg, D.W. (2000) Fast simulation of 3D electromagnetic problems using potentials. Journal of Computational Physics,163(1), 150–171.
     [Google Scholar]
  14. Hohmann, G.W., (1975) Three‐dimensional induced polarization and electromagnetic modeling. Geophysics, 40, 309–324.
     [Google Scholar]
  15. Jahandari, H. and Farquharson, C.G. (2014) A finite‐volume solution to the geophysical electromagnetic forward problem using unstructured grids. Geophysics, 79, 287–302,
     [Google Scholar]
  16. Jin, J.M. (2002) The Finite Element Method in Electromagnetics (2nd ed.). New York: John Wiley and Sons.
     [Google Scholar]
  17. Li, J., Liu, J.X., Egbert, G.D., Liu, R., Guo, R. and Pan, K. (2020) An efficient preconditioner for 3‐D finite difference modeling of the electromagnetic diffusion process in the frequency domain. IEEE Transactions on Geoscience and Remote Sensing, 58(1), 500–509.
     [Google Scholar]
  18. Liu, C., RenZ., TangJ. and YanY. (2008) Three‐dimensional magnetotellurics using edge‐based finite element usnstructured meshes. Applied Geophysics, 5, 170–180.
     [Google Scholar]
  19. Lowry, T., AllenM.B. and ShiveP.N. (1989) Singularity removal: a refinement of resistivity modeling techniques. Geophysics, 54, 766–774.
     [Google Scholar]
  20. Mulder, W.A. (2006) A multigrid solver for 3D electromagnetic diffusion. Geophysical Prospecting, 54(5), 633–649.
     [Google Scholar]
  21. Nabighian, M.N. (Ed.) (1988) Electromagnetic Methods in Applied Geophysics 1, Theory. Tulsa, OK: Society of Exploration Geophysicists.
     [Google Scholar]
  22. Nabighian, M.N. (Ed.) (1991) Electromagnetic Methods in Applied Geophysics 2, Applications. Tulsa, OK: Society of Exploration Geophysicists.
     [Google Scholar]
  23. Newman, G.A. and Alumbaugh, D.L. (1995) Frequency‐domain modeling of air borne electromagnetic responses using staggered finite differences. Geophysical Prospecting, 43, 1021–1042.
     [Google Scholar]
  24. Raiche, A.P. (1974) An integral equation approach to three‐dimensional modelling. Geophysical Journal of the Royal Astronomical Society, 36, 363–376.
     [Google Scholar]
  25. Smith, J.T. (1996) Conservative modeling of 3‐D electromagnetic fields, Part I, properties and error analysis. Geophysics, 61, 1038–1318.
     [Google Scholar]
  26. Sugeng, F. (1998) Modelling the 3D TDEM responses using the 3D full‐domain finite element method based on the hexahedral edge‐element technique. Exploration Geophysics, 29, 615–619.
     [Google Scholar]
  27. Walker, P.W. and West, G.F. (1991) A robust integral equation solution for electromagnetic scattering by a thin plate in conductive media. Geophysics, 56(8), 1140–1152.
     [Google Scholar]
  28. Yavich, N. and Zhdanov, M.S. (2016) Contraction preconditioner in finite‐difference electromagnetic modeling. Geophysical Journal International, 206(3), 1718–1729.
     [Google Scholar]
  29. Yavich, N. and Zhdanov, M.S. (2020) Finite‐element EM modelling on hexahedral grids with an FD solver as a pre‐conditioner. Geophysical Journal International, 223(2), 840–850.
     [Google Scholar]
  30. Yee, K.S. (1966) Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Transactions on Antennas and Propagation, 14, 302–309.
     [Google Scholar]
  31. Zhang, M., Farquharson, C.G. and Liu, C.S. (2020) Response characteristics of gradient data from the frequency‐domain controlled‐source electromagnetic method. Journal of Applied Geophysics, 172(103873).
     [Google Scholar]
  32. Zhdanov, M., Varentsov, I., Weaver, J., Golubev, N.G. and Krylov, V.A. (1997) Methods for modelling electromagnetic fields results from COMMEMI the international project on the comparison of modelling methods for electromagnetic induction. Journal of Applied Geophysics, 37(3–4), 133–271.
     [Google Scholar]
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Comparison of nodal and edge basis functions for the forward modelling of three‐dimensional frequency‐domain wire source electromagnetic data using a potentials formulation
Geophysical Prospecting 70, 828 (2022); https://doi.org/10.1111/1365-2478.13187
/content/journals/10.1111/1365-2478.13187
/content/journals/10.1111/1365-2478.13187
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  • Article Type: Research Article
Keyword(s): A–φ potentials; Coulomb‐gauged condition; Edge–nodal FE method; Forward modelling; Frequency‐domain controlled‐source electromagnetic; Nodal FE method

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