Special Issue: Electromagnetic Induction in the Earth
- Open Access
Multisheet modelling of the electrical conductivity structure in the Fennoscandian Shield
Earth, Planets and Space volume 54, pages 559–573 (2002)
Electromagnetic multisheet modelling is a powerful tool for large model areas, if they can be approximated by a multilayered heterogeneous conductivity structure of small vertical dimension in comparison with the penetration depth of electromagnetic fields. In this paper, thin sheet technique is applied to the whole Fennoscandian (Baltic) Shield, whose upper mantle conductivity structure is the objective of the long period electromagnetic array experiment BEAR (Baltic Electromagnetic Array Research). Three thin sheets, each of about 120,000 model cells with the base length of 10 km, describe a-priori crustal inhomogeneities in terms of conductances. The three sheets represent i) upper crust from surface to the depth of 10 km including continental and ocean bottom sediments and seawater, ii) middle crust ranging from 10 km to 30 km and iii) lower crust from 30 km to 60 km. Thus, modelling is taking into account distortions caused by crustal conductivity anomalies. Additionally, distortions due to inhomogeneous external current systems are investigated by introducing an equivalent current system of a polar electrojet model at ionosphere height. Modelling results are illustrated by induced current distribution at different depth levels and by various electromagnetic transfer functions. The latter demonstrate the resolution of crustal conductivity anomalies and their screening effect even at long periods. The predicted behavior of transfer functions in the very complex conductivity structure is compared with the experimental BEAR data, showing qualitatively a first order agreement for most of the sites. Modeled phases for periods of a few thousands of seconds are considerably biased in comparison with experimental data if the background 1-D model has monotonously decreasing resistivity. However, the bias from phases is removed if a conducting asthenosphere having a resistivity of 20 Ωm is emplaced between the depths of 200 km and 300 km. Thus, multisheet modelling indicates a well conducting upper mantle under the Fennoscandian Shield. All modelling has been performed using a multisheet code by Avdeev, Kuvshinov and Pankratov.
Agarwal, A. K. and J. T. Weaver, A three-dimensional numerical study of induction in southern India by an electrojet source, Phys. Earth Planet. Int., 60, 1–17, 1990.
Amm, O. and A. Viljanen, Ionospheric disturbance magnetic field continuation from the ground to the ionosphere using spherical elementary current systems, Earth Planets Space, 51, 431–440, 1999.
Arora, B. R., A. Rigoti, I. Vitorello, A. L. Padilha, N. B. Trivedi, and F. H. Chamalaun, Electrical imaging of the intracratonic Parnaiba Basin, north-northeast Brazil, J. Geomag. Geoelectr., 49, 1631–1648, 1997.
Arora, B. R., A. Rigoti, I. Vitorello, A. L. Padilha, N. B. Trivedi, and F. H. Chamalaun, Magnetometer array study in north-northeast Brazil: Conductivity image building and functional induction modes, Pure a. Applied Geophys., 152, 349–375, 1998.
Avdeev, D. B., A. V. Kuvshinov, O. V. Pankratov, and G. A. Newman, High-performance three-dimensional electromagnetic modeling using modified Neumann series. Wide-band numerical solution and examples, J. Geomag. Geoelectr., 49, 1519–1539, 1997.
Avdeev, D. B., A. V. Kuvshinov, O. V. Pankratov, and G. A. Newman, Three-dimensional frequency-domain modeling of airborne electromagnetic responses, Exploration Geophysics, 29, 1–9, 1998.
Avdeev, D. B., A. V. Kuvshinov, O. V. Pankratov, and G. A. Newman, Modeling induction log responses in 3D geometries using integral equation approach, Second International Symposium on three-dimensional electromagnetics, University of Utah, Salt Lake City, Utah, USA, Expanded Abstracts, 99–103, 1999.
Avdeev, D. B., A. V. Kuvshinov, O. V. Pankratov, and G. A. Newman, 3-D EM modeling using fast integral equation approach with Krylov subspaces accelerator, Extended abstracts book, Volume 2, 62nd EAGE Conference & Technical Exhibition, Glasgow, Scotland, P-183, 4 p., 2000.
Dawson, T. W. and J. T. Weaver, Three-dimensional induction in a non-uniform thin sheet at the surface of a uniformly conducting earth, Geophys. J. R. astr. Soc., 59, 445–462, 1979.
Dmitriev, V. I. and M. N. Berdichevsky, The fundamental model of magnetotelluric sounding, Proc. IEEE, 67, 1034–1044, 1979.
Fukushima, N., Electric current systems for polar substorms and their magnetic effect below and above the ionosphere, Radio Sci., 6, 269–275, 1971.
Fukushima, N., Generalized theorem for no ground magnetic effect of vertical currents connected with Pedersen currents in the uniform-conductivity ionosphere, Rep. Ionos. Space Res. Japan, 30, 35–40, 1976.
Garcia, X., A. D. Chave, and A. G. Jones, Robust Processing of Magnetotelluric Data from the Auroral Zone, J. Geomag. Geoelectr., 49, 1451–1468, 1997.
Gharibi, M., T. Korja, and L. B. Pedersen, Magnetotelluric soundings across the Scandinavian Caledonides, Jämtland, Sweden, in Electromagnetic Studies of the Continental Crust in Sweden, edited by M. Gharibi, Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, Uppsala, Sweden, 513, 1–50, 2000.
Gorbatschev, R. and S. Bogdanova, Frontiers in the Baltic Shield, Precambrian Res., 64, 3–21, 1993.
Greenbaum, A., Iterative Methods for Solving Linear Systems, Society for Industrial and Applied Mathematics, Philadelphia, 1997.
Hjelt, S.-E. and S. Daly, SVEKALAPKO, Evolution of Palaeoproterozoic and Archaean Lithosphere, in EUROPROBE 1996—Lithosphere Dynamics Origin and Evolution of Continents, edited by D. G. Gee and H. J. Zeyen, pp. 57–67, published by the EUROPROBE Secretariate, Uppsala University, 1996.
Jones, A. G., Geomagnetic induction studies in Scandinavia. II Geomagnetic depth sounding, induction vectors and coast effect, J. Geophys., 50, 23–36, 1981.
Jones, A. G., The electrical structure of the lithosphere and asthenosphere beneath the Fennoscandian shield, J. Geomag. Geoelectr., 35, 811–827, 1983.
Kaikkonen, P., Thin-Sheet Modelling for Deep Electromagnetic Studies in the Fennoscandian Shield, in Deep Electromagnetic Exploration, edited by K. K. Roy, S. K. Verma, and K. Mallick, pp. 365–386, Narossa Publishing House, New Delhi, India, 1998.
Korja, T., S.-E. Hjelt, P. Kaikkonen, K. Koivukoski, T. M. Rasmussen, and R. G. Roberts, The geoelectric model of the POLAR profile, Northern Finland, Tectonophys., 162, 113–133, 1989.
Korja, T. and S.-E. Hjelt, Electromagnetic studies in the Fennoscandian Shield—electrical conductivity of Precambrian crust, Phys. Earth Planet. Inter., 81, 107–138, 1993.
Korja, T. and K. Koivukoski, Crustal conductors of the SVEKA Profile in the Early Proterozoic Fennoscandian (Baltic) Shield, Finland, Geophys. J. Int., 116, 173–197, 1994.
Korja, T., Electrical Conductivity of the Lithosphere—Implications for the Evolution of the Fennoscandian Shield, Geophysica, 33(1), 17–50, 1997.
Korja, T. and S.-E. Hjelt, The Fennoscandian Shield: A treasury box for deep electromagnetic studies, in Deep Electromagnetic Exploration, edited by K. K. Roy, S. K. Verma, and K. Mallick, pp. 31–73, Narossa Publishing House, New Delhi, India, 1998.
Korja, T., M. Engels, A. A. Zhamaletdinov, A. A. Kovtun, N. A. Palshin, M. Yu. Smirnov, A. D. Tokarev, V. E. Asming, L. L. Vanyan, and the BEAR Working Group, Crustal conductivity in Fennoscandia—a compilation of a database on crustal conductance in the Fennoscandian Shield, Earth Planets Space, 54, this issue, 535–558, 2002.
Korsman, K., T. Korja, M. Pajunen, P. Virransalo, and the GGT/SVEKA Working Group, The GGT/SVEKA Transect: Structure and Evolution of the Continental Crust in the Palaeoproterozoic Svecofennian Orogen in Finland, International Geology Review, 41, 4, 287–333, 1999.
Kovtun, A. A., S. A. Vagin, I. L. Vardaniants, N. P. Legenkova, N. I. Uspenskiy, and M. Yu. Smirnov, Structure of the crust and upper mantle by the MT soundings on the profile Murmansk-Suoyarvy-Vyborg, Rossiyaskaya geofizika, 11–12, 57–67, 1998 (in Russian).
Kuvshinov, A. V., D. B. Avdeev, O. V. Pankratov, and S. A. Golyshev, Modeling EM fields in 3D spherical earth using integral equation approach, The Second International Symposium on 3D electromagnetics, University of Utah, Salt Lake City, Utah, USA, Expanded Abstracts, 84–88, 1999.
Mareschal, M., Modelling of natural sources of magnetospheric origin in the interpretation of regional induction studies: A review, Surveys in Geophysics, 8, 261–300, 1986.
McKirdy, D. McA., J. T. Weaver, and T. W. Dawson, Induction in a thin sheet of variable conductance at the surface of a stratified earth—II. Three-dimensional theory, Geophys. J. R. astr. Soc., 80, 177–194, 1985.
Osipova, I. L., S.-E. Hjelt, and L. L. Vanyan, Source field problems in northern parts of the Baltic Shield, Phys. Earth Planet. Inter., 53, 337–342, 1989.
Pajunpää, K., Conductivity anomalies in the Baltic Shield in Finland, Geophys. J. R. astr. Soc., 91, 657–666, 1987.
Pajunpää, K., Magnetometer array studies in Finland, Acta Univ. Oul., A 205, 32 pp., 1989.
Pankratov, O. V., Electromagnetic field modeling in presence of subsurface and deep inhomogeneities, Ph.D. Thesis, Institute of Physics of the Earth, Moscow, 162 pp., 1991 (in Russian).
Pankratov, O. V., D. B. Avdeev, and A. V. Kuvshinov, Electromagnetic field scattering in a heterogeneous earth: A solution to the forward problem, Physics of the Solid Earth, 31, 201–209, 1995 (English edition).
Pankratov, O. V., A. V. Kuvshinov, and D. B. Avdeev, High-performance three-dimensional electromagnetic modeling using modified Neumann series. Anisotropic case, J. Geomag. Geoelectr., 49, 1541–1547, 1997.
Parkinson, W. D., The influence of continents and oceans on geomagnetic variation, Geophys. J. R. astr. Soc., 6, 441–449, 1962.
Pirjola, R., On magnetotelluric source effects caused by an auroral electrojet system, Radio Sci., 27(4), 463–468, 1992.
Pirjola, R. and A. Viljanen, Complex image method for calculating electric and magnetic fields produced by an auroral electrojet of finite length, Ann. Geophys., 16, 1434–1444, 1998.
Price, A. T., The induction of electric currents in non-uniform thin sheets and shells, Q. J. Mech. appl. Math., 2, 283–310, 1949.
Rasmussen, T. M., R. G. Roberts, and L. B. Pedersen, Magnetotellurics along the Fennoscandian Long Range Profile, Geophys. J. R. astr. Soc., 89, 799–820, 1987.
Rasmussen, T. M., Magnetotellurics in southwestern Sweden: evidence for electrical anisotropy in the lower crust, J. Geophys. Res., 93, 7897–7907, 1988.
Rokityansky, I. I., Geoelectromagnetic Investigation of the Earth’s Crust and Mantle, Springer Verlag, New York, 1982.
Schmucker, U., Anomalies of geomagnetic variations in the southwestern United States, Bull. Scripps, Institution of Oceanography, University of California, 13, 1–165, 1970.
Schmucker, U., Induktion in geschichteten Halbräumen durch inhomogene Felder, Protokoll Koll. Elektromagnetische Tiefenforschung, Berlin-Lichtenrade, 197–210, 1980 (in German).
Schmucker, U., Electromagnetic induction in thin sheets: integral equations and model studies in two dimensions, Geophys. J. Int., 121, 173–190, 1995.
Singer, B. Sh., Method for solution of Maxwell’s equations in non-uniform media, Geophys. J. Int., 120, 590–598, 1995.
Singer, B. Sh. and E. B. Fainberg, Electromagnetic induction in nonuniform thin layers, IZMIRAN, Moscow, 234 pp., 1985 (in Russian).
Singer, B. Sh. and E. B. Fainberg, Generalization of the iterative-dissipative method for modeling electromagnetic fields in nonuniform media with displacement currents, J. Applied Geophysics, 34, 41–46, 1995.
Singer, B. Sh. and E. B. Fainberg, Fast and stable method for 3-D modelling of electromagnetic field, Exploration Geophysics, 28, 130–135, 1997.
Singer, B. Sh., A. Mezzatesta, and T. Wang, 3D IDM modeling of EM field, The Second International Symposium on 3D electromagnetics, University of Utah, Salt Lake City, Utah, USA, Expanded Abstracts, 29–33, 1999.
Sokolova, E. Yu., Iv. M. Varentsov, and BEAR Working Group, Investigation and elimination of polar magnetotelluric source distortions in the BEAR project transfer functions, Earth Planets Space, 2002 (to be submitted).
Vanyan, L. L., T. A. Demidova, N. A. Palshin, A. A. Zhamaletdinov, Yu. I. Kuksa, P. Kaikkonen, and T. Korja, Interpretation of the deep DC soundings in the northeastern Baltic Shield, Phys. Earth Planet. Inter., 54, 149–155, 1989.
Vanyan, L. L. and V. A. Kouznetsov, A crustal conducting layer in Central Finland: myth or reality?, Fizica Zemli, 3, 62–64, 1999 (in Russian).
Varentsov, Iv. M., E. Yu. Sokolova, E. R. Martanus, K.V. Nalivaiko, and BEAR Working Group, Estimation of MT and GDS transfer functions in the Baltic Electromagnetic Array Research (BEAR), Earth Planets Space, 2002 (to be submitted).
Vasseur, G. and P. Weidelt, Bimodal electromagnetic induction in nonuniform thin sheets with an application to the northern Pyrenean induction anomaly, Geophys. J. R. astr. Soc., 51, 669–690, 1977.
Viljanen, A., Source Effect on Geomagnetic Induction Vectors in the Fennoscandian Auroral Region, J. Geomag. Geoelectr., 48, 1001–1009, 1996.
Viljanen, A. and L. Häkkinen, IMAGE magnetometer network, in Satellite-Ground Based Coordination Sourcebook, edited by M. Lockwood, M. N. Wild, and H. J. Opgenoorth, ESA publications, SP-1198, 111–117, 1997.
Viljanen, A., R. Pirjola, and O. Amm, Magnetotelluric source effect due to 3D ionospheric current systems using the complex image method for 1D conductivity structures, Earth Planets Space, 51, 933–945, 1999.
Weaver, J. T., Mathematical Methods for Geo-electromagnetic Induction, Research Studies Press LTD, 1994.
Yegorov, I. V., E. L. Chernyak, N. A. Palshin, T. A. Demidova, and P. Kaikkonen, Numerical thin-sheet modelling of telluric field distortions by hybrid technique. I Theory and an example for the Baltic Shield, Phys. Earth Planet. Inter., 33, 56–63, 1983.
Zhdanov, M. S., V. I. Dmitriev, G. Hursan, and S. Fang, Quasi-analytical approximations and series in 3-D electromagnetic modeling, The Second International Symposium on 3D electromagnetics, University of Utah, Salt Lake City, Utah, USA, Expanded Abstracts, 16–21, 1999.
About this article
Cite this article
Engels, M., Korja, T. & the BEAR Working Group. Multisheet modelling of the electrical conductivity structure in the Fennoscandian Shield. Earth Planet Sp 54, 559–573 (2002). https://doi.org/10.1186/BF03353045
- Apparent Resistivity
- Thin Sheet
- Baltic Shield
- Source Effect
- Conductivity Structure