Studia Geophysica et Geodaetica

, Volume 60, Issue 2, pp 332–347 | Cite as

A finite-volume approach for 2D magnetotellurics modeling with arbitrary topographies

  • Hua-Kun Du
  • Zheng-Yong Ren
  • Jing-Tian Tang


A novel finite-volume approach for complicated 2D magnetotellurics (MT) problems with arbitrarily surface topography is presented. An edge-surface integral balance equation is derived by employing a conservation law on the generalized 2D MT boundary value problem. A triangular grid is used to discretize the 2D conductivity model so that we can deal with arbitrarily complex cases with surface topography. The node-centered finite-volume algorithm is used to derive the final system of linear equations on a dual mesh of the triangular grid, which is solved by a robust direct solver. Three synthetic models verify the accuracy of the presented finite-volume algorithm and its capability of dealing with surface topography.


magnetotellurics unstructured grid finite-volume method 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aprea C., Booker J. and Smith J., 1997. The forward problem of electromagnetic induction: Accurate finite-difference approximations for two-dimensional discrete boundaries with arbitrary geometry. Geophys. J. Int., 129, 29–40.CrossRefGoogle Scholar
  2. Avdeev D., 2005. Three-dimensional electromagnetic modelling and inversion from theory to application. Surv. Geophys., 26, 767–799.CrossRefGoogle Scholar
  3. Avdeev D., Kuvshinov A., Pankratov O. and Newman G., 2002. Three-dimensional induction logging problems, Part I: An integral equation solution and model comparisons. Geophysics, 67, 413–426.CrossRefGoogle Scholar
  4. Azeez K.K.A., Kumar T.S., Basava S., Harinarayana T. and Dayal A.M., 2011. Hydrocarbon prospects across Narmada-Tapti rift in Deccan trap, central India: Inferences from integrated interpretation of magnetotelluric and geochemical prospecting studies. Mar. Pet. Geol., 28, 1073–1082.CrossRefGoogle Scholar
  5. Berdichevsky M., Dmitriev V. and Pozdnjakova E., 1998. On two-dimensional interpretation of magnetotelluric soundings. Geophys. J. Int., 133, 585–606.CrossRefGoogle Scholar
  6. Berdichevsky M.N. and Dmitriev V.I., 2008. Models and Methods of Magnetotellurics. Springer-Verlag, Berlin and Heidelberg, Germany.CrossRefGoogle Scholar
  7. Bibby H.M., Risk G.F., Caldwell T.G. and Heise W., 2009. Investigations of deep resistivity structures at the Wairakei geothermal field. Geothermics, 38, 98–107.CrossRefGoogle Scholar
  8. Cagniard L., 1953. Basic theory of the magnetotelluric method of geophysical prospecting. Geophysics, 18, 605–635.CrossRefGoogle Scholar
  9. Campanya J., Ledo J., Queralt P., Marcuello A., Liesa M. and Munoz J.A., 2012. New geoelectrical characterisation of a continental collision zone in the West-Central Pyrenees: Constraints from long period and broadband magnetotellurics. Earth Planet. Sci. Lett., 333, 112–121.CrossRefGoogle Scholar
  10. Connell D. and Key K., 2013. A numerical comparison of time and frequency-domain marine electromagnetic methods for hydrocarbon exploration in shallow water. Geophys. Prospect., 61, 187–199.CrossRefGoogle Scholar
  11. Diaz D., Brasse H. and Ticona F., 2011. Conductivity distribution beneath Lascar volcano (Northern Chile) and the Puna, inferred from magnetotelluric data. J. Volcanal. Geotherm. Res., 217, 21–29.Google Scholar
  12. Geiermann J. and Schill E., 2010. 2-D Magnetotellurics at the geothermal site at Soultz-sous-Forets: Resistivity distribution to about 3000 m depth. C. R. Geosci., 342, 587–599.CrossRefGoogle Scholar
  13. Grayver A.V., Streich R. and Ritter O., 2013. Three-dimensional parallel distributed inversion of csem data using a direct forward solver. Geophys. J. Int., 193, 1432–1446.CrossRefGoogle Scholar
  14. Haber E. and Heldmann S., 2007. An octree multigrid method for quasi-static Maxwells equations with highly discontinuous coefficients. J. Comput. Phys., 223, 783–796.CrossRefGoogle Scholar
  15. Haber E., Ascher U., Aruliah D. and Oldenburg D., 2000. Fast simulation of 3D electromagnetic problems using potentials. J. Comput. Phys., 163, 150–171.CrossRefGoogle Scholar
  16. He Z., HuW. and Dong W., 2010. Petroleum Electromagnetic Prospecting Advances and Case Studies in China. Surv. Geophys., 31, 207–224.CrossRefGoogle Scholar
  17. Hohmann G., 1975. Three-dimensional induced polarization and electromagnetic modeling. Geophysics, 40, 309–324.CrossRefGoogle Scholar
  18. Hou J., Mallan R.K. and Torres-Verdin C., 2006. Finite-difference simulation of borehole EM measurements in 3D anisotropic media using coupled scalar-vector potentials. Geophysics, 71, G225–G233.CrossRefGoogle Scholar
  19. Jahandari H. and Farquharson C., 2013. Forward modeling of gravity data using finite-volume and finite element methods on unstructured grids. Geophysics, 78, G69–G80.CrossRefGoogle Scholar
  20. Jahandari H. and Farquharson C., 2014. A finite-volume solution to the geophysical electromagnetic forward problem using unstructured grids. Geophysics, 79, E287–E302.CrossRefGoogle Scholar
  21. Jahandari H. and Farquharson C., 2014. Forward modelling of geophysical electromagnetic data on unstructured grids using a finite-volume approach. Extended Abstract. 76th EAGE Conference and Exhibition 2014, DOI: 10.3997/2214-4609.20141097CrossRefGoogle Scholar
  22. Jin J.M., 2002. The Finite Element Method in Electromagnetics. Wiley-IEEE Press, New York.Google Scholar
  23. Keast P., 1986. Moderate-degree tetrahedral quadrature formulas. Comput. Meth. Appl. Mech. Eng., 55, 339–348.CrossRefGoogle Scholar
  24. Li Y. and Key K., 2007. 2D marine controlled-source electromagnetic modeling: Part 1 - An adaptive finite-element algorithm. Geophysics, 72, WA51–WA62.Google Scholar
  25. Mogi T., 1996. Three-dimensional modeling of magnetotelluric data using finite element method. J. Appl. Geophys., 35, 185–189.CrossRefGoogle Scholar
  26. Mukherjee S. and Everett M.E., 2011. 3D controlled-source electromagnetic edge-based finite element modeling of conductive and permeable heterogeneities. Geophysics, 76, F215–F226.CrossRefGoogle Scholar
  27. Naidu G.D., Veeraswamy K. and Harinarayana T., 2011. Electrical signatures of the Earth’s crust in central India as inferred from magnetotelluric study. Earth Planets Space, 63, 1175–1182.CrossRefGoogle Scholar
  28. Newman G. and Alumbaugh D., 2002. Three-dimensional induction logging problems, Part 2: A finite difference solution. Geophysics, 67, 484–491.CrossRefGoogle Scholar
  29. Pedersen L. and Engels M., 2005. Routine 2D inversion of magnetotelluric data using the determinant of the impedance tensor. Geophysics, 70, G33–G41.CrossRefGoogle Scholar
  30. Penz S., Chauris H., Donno D. and Mehl C., 2013. Resistivity modelling with topography. Geophys. J. Int., 194, 1486–1497.CrossRefGoogle Scholar
  31. Ren Z., 2014. A C++ based 2D magnetotellurics and radio-magnetotellurics finite element solver using unstructrued grids. Scholar
  32. Schenk O. and Gärtner K., 2004. Solving unsymmetric sparse systems of linear equations with PARDISO. Future Gener. Comput. Syst., 20, 475–487.CrossRefGoogle Scholar
  33. Schwarzbach C. and Haber E., 2013. Finite element based inversion for time-harmonic electromagnetic problems. Geophys. J. Int., 193, 615–634.CrossRefGoogle Scholar
  34. Shewchuk J.R., 1996. Triangle: engineering a 2D quality mesh generator and Delaunay triangulator. In: Lin M.C. and Manocha D. (Eds), Applied Computational Geometry: Towards Geometric Engineering. Lecture Notes in Computer Science 1148. Springer-Verlag, Berlin, Germany, 203–222.CrossRefGoogle Scholar
  35. Simpson F. and Bahr K., 2005. Practical Magnetotellurics. Cambridge University Press, Cambridge, U.K.CrossRefGoogle Scholar
  36. Strack K.M., 2014. Future directions of electromagnetic methods for hydrocarbon applications. Surv. Geophys., 35, 157–177.CrossRefGoogle Scholar
  37. Stratton J., 2007. Electromagnetic Theory. Wiley-IEEE Press, New York.Google Scholar
  38. Streich R., Becken M. and Ritter O., 2010. Imaging of CO2 storage sites, geothermal reservoirs, and gas shales using controlled-source magnetotellurics: Modeling studies. Chem Erde-Geochem., 70, 63–75.CrossRefGoogle Scholar
  39. Tai C.T., 1997. Generalized Vector and Dyadic Analysis: Applied Mathematics in Field Theory. Wiley-IEEE Press, ISBN: 978-0-7803-3413-7.CrossRefGoogle Scholar
  40. Tang J. and Yuan Y., 2014. MT2DFWD-A program in FORTRAN for finite element modeling of magnetotelluric TE/TM mode responses over 2D earth, in The 22nd Workshop on Electromagnetic Induction in the Earth, Weimar, Germany.Google Scholar
  41. Tezkan B., Goldman M., Greinwald S., Hordt A., Muller I., Neubauer F. and Zacher G., 1996. A joint application of radiomagnetotellurics and transient electromagnetics to the investigation of a waste deposit in Cologne (Germany). J. Appl. Geophys., 34, 199–212.CrossRefGoogle Scholar
  42. Tikhonov A., 1950. On determining electrical characteristics of the deep layers of the earth’s crust. Dokl. Acad. Nauk SSSR, 73, 295–297.Google Scholar
  43. Tournerie B. and Chouteau M., 2002. Analysis of magnetotelluric data along the Lithoprobe seismic line 21 in the Blake River Group, Abitibi, Canada. Earth Planets Space, 54, 575–589.CrossRefGoogle Scholar
  44. Unsworth M., Jones A., Wei W., Marquis G., Gokarn S., Spratt J., Bedrosian P., Booker J., Leshou C., Clarke G. and the INDEPTH-MT Team, 2005. Crustal rheology of the Himalaya and Southern Tibet inferred from magnetotelluric data. Nature, 438, 78–81.CrossRefGoogle Scholar
  45. Volpi G., Manzella A. and Fiordelisi A., 2003. Investigation of geothermal structures by magnetotellurics (MT): an example from the Mt. Amiata area, Italy. Geothermics, 32, 131–145.CrossRefGoogle Scholar
  46. Wannamaker P., Stodt J. and Rijo L., 1986. Two dimensional topographic responses in magnetotellurics modeled using finite elements. Geophysics, 51, 2131–2144.CrossRefGoogle Scholar
  47. Ward S. and Hohmann G., 1987. Electromagnetic theory for geophysical applications: Electromagnetic methods in applied geophysics. In: Nabighian M.N. (Ed.), Electromagnetic Methods in Applied Geophysics: Voume 1, Theory. Society of Exploration Geophysicists, Tulsa, OK, 130–311.Google Scholar
  48. Zhdanov M., Varentsov I., Weaver J., Golubev N. and Krylov V., 1997. Methods for modelling electromagnetic fields: Results from COMMEMI - the international project on the comparison of modelling methods for electromagnetic induction. J. Appl. Geophys., 37, 133–271.CrossRefGoogle Scholar
  49. Zhdanov M.S., Lee S.K. and Yoshioka K., 2006. Integral equation method for 3D modeling of electromagnetic fields in complex structures with inhomogeneous background conductivity. Geophysics, 71, G333–G345.CrossRefGoogle Scholar

Copyright information

© Institute of Geophysics of the ASCR, v.v.i 2016

Authors and Affiliations

  • Hua-Kun Du
    • 1
    • 2
    • 3
  • Zheng-Yong Ren
    • 1
    • 2
    • 3
  • Jing-Tian Tang
    • 1
    • 2
    • 3
  1. 1.Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment MonitoringCentral South University, Ministry of EducationHunan ProvinceChina
  2. 2.Key Laboratory of Non-ferrous Resources and Geological Hazard DetectionHunan ProvinceChina
  3. 3.School of Geosciences and Info-PhysicsCentral South UniversityChangshaChina

Personalised recommendations