Skip to main content


We’d like to understand how you use our websites in order to improve them. Register your interest.

Magnetotelluric source effect due to 3D ionospheric current systems using the complex image method for 1D conductivity structures


The complex image method (CIM) is an efficient tool to calculate the electromagnetic field at the earth’s surface produced by 3D ionospheric current systems when the earth has a layered conductivity structure. The calculations are applicable to the estimation of source effects on magnetotelluric data. In this paper CIM is used in connection with some typical high-latitude ionospheric events: a westward travelling surge, a Harang discontinuity, an omega band, and a giant pulsation. The complicated ionospheric current systems are constructed of short horizontal current filaments with vertical currents at both ends. The currents are given numerically on a 50 km × 50 km grid covering a region of even 1000 km × 2000 km. The investigations indicate that the source distortion very much depends on the event, and may be significant in a wide period range, especially for a resistive earth structure. The source effect seems quite unpredictable. Sometimes the apparent resistivity is larger and sometimes smaller than the plane wave value. At times the source effect is very small even if the ionospheric current is strongly inhomogeneous.


  1. Amm, O., Direct determination of the local ionospheric Hall conductance distribution from two-dimensional electric and magnetic field data: Application of the method using models of typical ionospheric electrodynamic situations, J. Geophys. Res., 100(A11), 21473–21488, 1995.

  2. Amm, O., Improved electrodynamic modeling of an omega band and analysis of its current system, J. Geophys. Res., 101, 2677–2683, 1996.

  3. Boteler, D. H. and R. J. Pirjola, The complex-image method for calculating the magnetic and electric fields at the surface of the Earth by the auroral electrojet, Geophys. J. Int., 132, 31–40, 1998.

  4. Chave, A. D., D. J. Thomson, and M. E. Ander, On the robust estimation of power spectra, coherences, and transfer functions, J. Geophys. Res., 92, 633–648, 1987.

  5. Egbert, G. D. and J. R. Booker, Multivariate analysis of geomagnetic array data. 1. The response space, J. Geophys. Res., 94, 14227–14247, 1989a.

  6. Egbert, G. D. and J. R. Booker, Multivariate analysis of geomagnetic array data. 2. Random source models, J. Geophys. Res., 94, 14249–14265, 1989b.

  7. 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.

  8. Glassmeier, K.H., Magnetometer array observations of a giant pulsation event, J. Geophys., 48, 127–138, 1980.

  9. Häkkinen, L. and R. Pirjola, Calculation of electric and magnetic fields due to an electrojet current system above a layered earth, Geophysica, 22, 31–44, 1986.

  10. Häkkinen, L., R. Pirjola, and C. Sucksdorff, EISCAT magnetometer cross and theoretical studies connected with the electrojet current system, Geophysica, 25, 123–134, 1989.

  11. Korja, T. and the BEAR Working Group, BEAR. Baltic Electromagnetic Array Research, EUROPROBE News, No. 12, 4–5, 1998.

  12. Larsen, J. C., R. L. Mackie, A. Manzella, A. Fiordelisi, and S. Rieven, Robust smooth magnetotelluric transfer function, Geophys. J. Int., 124, 801–819, 1996.

  13. Mareschal, M., Modelling of natural sources of magnetospheric origin in the interpretation of regional induction studies: areview, Surv. Geophys., 8, 261–300, 1986.

  14. 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.

  15. Padilha, A. L., I. Vitorello, and L. Rijo, Effects of the Equatorial Electrojet on magnetotelluric surveys: Field results from Northwest Brazil, Geophys. Res. Lett., 24, 89–92, 1997.

  16. Pirjola, R., On magnetotelluric source effects caused by an auroral electrojet system, Radio Sci., 27 (4), 463–468, 1992.

  17. Pirjola, R. and A. Viljanen, Complex image method for calculating electric and magnetic fields produced by an auroral electrojet of a finite length, Ann. Geophys., 16, 1434–1444, 1998.

  18. Pirjola, R., D. Boteler, A. Viljanen, and O. Amm, Prediction of geomagnetically induced currents in power transmission systems, Adv. Space Res., 1999 (accepted for publication).

  19. Szarka, L. and G. Fischer, Electromagnetic parameters at the surface of a conductive halfspace in terms of the subsurface current distribution, Geophysical Transactions, 25 (3), 157–172, 1989.

  20. Thomson, D. J. and J. T. Weaver, The complex image approximation for induction in a multilayered Earth, J. Geophys. Res., 80 (1), 123–129, 1975.

  21. Untiedt, J. and W. Baumjohann, Studies of polar current systems using the IMS Scandinavian magnetometer array, Space Science Reviews, 63, 245–390, 1993.

  22. 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.

  23. Viljanen, A., Source effect on geomagnetic induction vectors in the fennoscandian auroral region, J. Geomag. Geoelectr., 48, 1001–1009, 1996.

  24. Viljanen, A. and R. Pirjola, On the possibility of performing studies on the geoelectric field and ionospheric currents using induction in power systems, J. Atmos. Terr. Phys., 56, 1483–1491, 1994.

  25. Viljanen, A., R. Pirjola, and L. Häkkinen, An attempt to reduce induction source effects at high latitudes, J. Geomag. Geoelectr., 45, 817–831, 1993.

  26. Wait, J. R., Wave Propagation Theory, 348 pp., Pergamon Press, 1981.

  27. Wait, J. R. and K. P. Spies, On the representation of the quasi-static fields of a line current source above the ground, Can. J. Phys., 27, 2731–2733, 1969.

  28. Weidelt, P., The Inverse Problem of Geomagnetic Induction, Z. Geophys., 38, 257–289, 1972.

Download references

Author information



Corresponding author

Correspondence to Ari Viljanen.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Viljanen, A., Pirjola, R. & Amm, O. Magnetotelluric source effect due to 3D ionospheric current systems using the complex image method for 1D conductivity structures. Earth Planet Sp 51, 933–945 (1999).

Download citation


  • Apparent Resistivity
  • Source Effect
  • Auroral Electrojet
  • Geomagnetically Induce Current
  • Giant Pulsation