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A computing method for 3D magnetotelluric modelling directed by polynomials


A computational method for automatic 3D MT modelling is described. Making use of a recent publicly available forward algorithm, our method allows unattended search for a 3D conductivity model. The geometry of the conductivity features is described by a set of mathematical functions of the horizontal coordinates x and y and of a fixed number of parameters. Starting from a presumed conductivity distribution, our scheme automatically varies the parameters in a steepest descent control loop, until the misfit between the model response and the measured data reaches an allowable value. To illustrate the method, we apply it to MT and induction data gathered in the Swiss Alps and determine the depth and lateral extension of a highly conductive, graphite-bearing layer.


  1. Beiner, J., FORTRAN Routine MINDEF for Function Minimization, 5 pp., Institut de Physique, Univ. of Neuchatel, Switzerland, 1970.

    Google Scholar 

  2. de Groot-Hedlin, C. D. and S. C. Constable, Occam’s inversion to generate smooth, two-dimensional models from magnetotelluric data, Geophysics, 55(12), 1613–1624, 1990.

    Article  Google Scholar 

  3. Ellis, R. G. and D. W. Oldenburg, Applied geophysical inversion, Geophys. J. Int., 116, 5–11, 1994.

    Article  Google Scholar 

  4. Fischer, G. and B. V. Le Quang, Topography and minimization of the standard deviation in one-dimensional magnetotelluric modelling, Geophys. J. R. astr. Soc., 67, 279–292, 1981.

    Article  Google Scholar 

  5. Glover, P. W. J. and F. J. Vine, Electrical conductivity of carbon-bearing granulite at raised temperatures and pressures, Nature, 360, 723–726, 1992.

    Article  Google Scholar 

  6. Jones, A. G., The Coprod2 Dataset: Tectonic Setting, Recorded MT Data, and Comparison of Models, J. Geomag. Geoelectr., 45, 933–955, 1993.

    Article  Google Scholar 

  7. Klingelé, E., M. Cocard, M. Halliday, and H.-G. Kahle, The Airborne Gravimetric Survey of Switzerland, Matériaux pour la Gétologie de la Suisse, 31, 104 pp., Swiss Geophysical Commission, 1996.

  8. Livelybrooks, D., M. Mareschal, E. Blais, and J. T. Smith, Magnetotelluric delineation of the Trillabelle massive sulfide body in Sudbury, Ontario, Geophysics, 61(4), 971–986, 1996.

    Article  Google Scholar 

  9. Mackie, R. L. and T. R. Madden, Instructions for Running 3D MT Forward Modeling Program, 5 pp., MIT Earth Resources Laboratory, Cambridge, Massachusetts 02142, 1994.

    Google Scholar 

  10. Mackie, R. L., T. R. Madden, and P. E. Wannamaker, Three-dimensional magnetotelluric modeling using difference equations—theory and comparison to integral equation solutions, Geophysics, 58, 215–226, 1993.

    Article  Google Scholar 

  11. Mackie, R. L., J. T. Smith, and T. R. Madden, Three-dimensional electromagnetic modeling using finite difference equations: the magnetotelluric example, Radio Sci., 923–935, 1994.

  12. Masero, W., G. Fischer, and P.-A. Schnegg, Crustal deformation in the region of the Araguainha impact, Brazil, Phys. Earth Planet. Inter., 101, 271–289, 1997.

    Article  Google Scholar 

  13. Park, S. K. and R. J. Mackie, Crustal structure at Nanga Parbat, northern Pakistan, from magnetotelluric soundings, Geophys. Res. Lett. (USA), 24(19), 2415–2418, 1997.

    Article  Google Scholar 

  14. Pous, J., C. Ayala, J. Ledo, A. Marcuello, and F. Sabat, 3D modelling of magnetotelluric and gravity data of Mallorca island (Western Mediterranean), Geophys. Res. Lett. (USA), 22(6), 735–738, 1995.

    Article  Google Scholar 

  15. Schnegg, P.-A., An Automatic Scheme for 2-D Magnetotelluric Modelling, Based on Low-Order Polynomial Fitting, J. Geomag. Geoelectr., 45(9), 1039–1043, 1993.

    Article  Google Scholar 

  16. Schnegg, P.-A., Comparison of 2D modelling methods: rapid inversion vs polynomial fitting, in Elektromagnetische Tiefenforschung, edited by K. Bahr and A. Junge, pp. 74–79, Deutsche Geophysikalische Gesellschaft, Burg Ludwigstein, 1996.

    Google Scholar 

  17. Schnegg, P.-A., The Magnetotelluric Survey of the Penninic Alps of Valais, Matériaux pour la Géologie de la Suisse, 32, 76 pp., Swiss Geophysical Commission, 1998.

  18. Valasek, P. and St. Mueller, A 3D Crustal Model of the Swiss Alps Based on an Integrated Interpretation of Seismic Refraction and NRP 20 Seismic Reflection Data, Deep structure of the Swiss Alps, pp. 305–326, Birkhäuser Verlag, 1997.

  19. Wannamaker, P. E., J. A. Stodt, and L. Rijo, PW2D-finite element program for solution of magnetotelluric responses of two-dimensional earth resistivity structure, Earth Science Laboratory, University of Utah, Salt Lake City, 1985.

    Google Scholar 

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Correspondence to Pierre-André Schnegg.

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Schnegg, P. A computing method for 3D magnetotelluric modelling directed by polynomials. Earth Planet Sp 51, 1005–1012 (1999).

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  • Apparent Resistivity
  • Seismic Line
  • Resistivity Variation
  • Salt Dome
  • Conductivity Distribution