Skip to main content
SpringerLink
Log in

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

  • Published:
Studia Geophysica et Geodaetica Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • 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.

    Article  Google Scholar 

  • Avdeev D., 2005. Three-dimensional electromagnetic modelling and inversion from theory to application. Surv. Geophys., 26, 767–799.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Berdichevsky M., Dmitriev V. and Pozdnjakova E., 1998. On two-dimensional interpretation of magnetotelluric soundings. Geophys. J. Int., 133, 585–606.

    Article  Google Scholar 

  • Berdichevsky M.N. and Dmitriev V.I., 2008. Models and Methods of Magnetotellurics. Springer-Verlag, Berlin and Heidelberg, Germany.

    Book  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Cagniard L., 1953. Basic theory of the magnetotelluric method of geophysical prospecting. Geophysics, 18, 605–635.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Haber E., Ascher U., Aruliah D. and Oldenburg D., 2000. Fast simulation of 3D electromagnetic problems using potentials. J. Comput. Phys., 163, 150–171.

    Article  Google Scholar 

  • He Z., HuW. and Dong W., 2010. Petroleum Electromagnetic Prospecting Advances and Case Studies in China. Surv. Geophys., 31, 207–224.

    Article  Google Scholar 

  • Hohmann G., 1975. Three-dimensional induced polarization and electromagnetic modeling. Geophysics, 40, 309–324.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Jahandari H. and Farquharson C., 2014. A finite-volume solution to the geophysical electromagnetic forward problem using unstructured grids. Geophysics, 79, E287–E302.

    Article  Google Scholar 

  • 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: 10.3997/2214-4609.20141097

    Book  Google Scholar 

  • Jin J.M., 2002. The Finite Element Method in Electromagnetics. Wiley-IEEE Press, New York.

    Google Scholar 

  • Keast P., 1986. Moderate-degree tetrahedral quadrature formulas. Comput. Meth. Appl. Mech. Eng., 55, 339–348.

    Article  Google Scholar 

  • 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 

  • Mogi T., 1996. Three-dimensional modeling of magnetotelluric data using finite element method. J. Appl. Geophys., 35, 185–189.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Newman G. and Alumbaugh D., 2002. Three-dimensional induction logging problems, Part 2: A finite difference solution. Geophysics, 67, 484–491.

    Article  Google Scholar 

  • Pedersen L. and Engels M., 2005. Routine 2D inversion of magnetotelluric data using the determinant of the impedance tensor. Geophysics, 70, G33–G41.

    Article  Google Scholar 

  • Penz S., Chauris H., Donno D. and Mehl C., 2013. Resistivity modelling with topography. Geophys. J. Int., 194, 1486–1497.

    Article  Google Scholar 

  • Ren Z., 2014. A C++ based 2D magnetotellurics and radio-magnetotellurics finite element solver using unstructrued grids. http://sourceforge.net/projects/mt2d/.

    Google Scholar 

  • Schenk O. and Gärtner K., 2004. Solving unsymmetric sparse systems of linear equations with PARDISO. Future Gener. Comput. Syst., 20, 475–487.

    Article  Google Scholar 

  • Schwarzbach C. and Haber E., 2013. Finite element based inversion for time-harmonic electromagnetic problems. Geophys. J. Int., 193, 615–634.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Simpson F. and Bahr K., 2005. Practical Magnetotellurics. Cambridge University Press, Cambridge, U.K.

    Book  Google Scholar 

  • Strack K.M., 2014. Future directions of electromagnetic methods for hydrocarbon applications. Surv. Geophys., 35, 157–177.

    Article  Google Scholar 

  • Stratton J., 2007. Electromagnetic Theory. Wiley-IEEE Press, New York.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Tai C.T., 1997. Generalized Vector and Dyadic Analysis: Applied Mathematics in Field Theory. Wiley-IEEE Press, ISBN: 978-0-7803-3413-7.

    Book  Google Scholar 

  • 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.

  • 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.

    Article  Google Scholar 

  • Tikhonov A., 1950. On determining electrical characteristics of the deep layers of the earth’s crust. Dokl. Acad. Nauk SSSR, 73, 295–297.

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Wannamaker P., Stodt J. and Rijo L., 1986. Two dimensional topographic responses in magnetotellurics modeled using finite elements. Geophysics, 51, 2131–2144.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring, Central South University, Ministry of Education, Hunan Province, China

    Hua-Kun Du, Zheng-Yong Ren & Jing-Tian Tang

  2. Key Laboratory of Non-ferrous Resources and Geological Hazard Detection, Hunan Province, China

    Hua-Kun Du, Zheng-Yong Ren & Jing-Tian Tang

  3. School of Geosciences and Info-Physics, Central South University, Changsha, China

    Hua-Kun Du, Zheng-Yong Ren & Jing-Tian Tang

Authors
  1. Hua-Kun Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zheng-Yong Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jing-Tian Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zheng-Yong Ren.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Du, HK., Ren, ZY. & Tang, JT. A finite-volume approach for 2D magnetotellurics modeling with arbitrary topographies. Stud Geophys Geod 60, 332–347 (2016). https://doi.org/10.1007/s11200-014-1041-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11200-014-1041-9

Keywords

Search

Navigation