Skip to main content

One-dimensional spherical elementary current systems and their use for determining ionospheric currents from satellite measurements


The method of 1D spherical elementary current systems (SECS) is a new way for determining ionospheric and field-aligned currents in spherical geometry from magnetic field measurements made by a low-orbit satellite. In contrast to earlier methods, the full ionospheric current distribution, including both divergence-free and curl-free horizontal currents, as well as field-aligned currents, can be determined. Placing infinitely many 2D SECSs of identical amplitudes at a constant latitude results in two types of 1D SECSs, which are independent of longitude, and by superposition can reproduce any ionospheric and field-aligned current system with the same property. One type of the 1D SECSs is divergence-free and toroidal with a poloidal magnetic field, and the other type is curl-free and poloidal. Associated with the divergence of the curl-free type are radial currents. The magnetic field of the combined curl-free 1D SECS and field-aligned currents is toroidal and restricted to the region above the ionosphere. Ionospheric currents are determined by placing several 1D SECSs at different latitudes and choosing their amplitudes in such a way that their combined magnetic field as closely as possible fits the one measured by the satellite. The 1D SECS method has been tested using both modeled and real data from the CHAMP satellite, and found to work excellently in 1D cases.


  • Amm, O., Ionospheric elementary current systems in spherical coordinates and their application, J. Geomag. Geoelectr., 49, 947–955, 1997.

    Article  Google Scholar 

  • Amm, O. and A. Viljanen, Ionospheric disturbance magnetic field continuation from the ground to ionosphere using spherical elementary current systems, Earth Planets Space, 51, 431–440, 1999.

    Article  Google Scholar 

  • Arfken, G. and H. Weber, Mathematical Methods for Physicists, Academic Press, 4th ed., 1995.

    Google Scholar 

  • Brekke, A., Physics of the Upper Polar Atmosphere, John Wiley & Sons Ltd, 1997.

    Google Scholar 

  • Fukushima, N., Generalized theorem for no ground magnetic effect of vertical currents connected with Pedersen currents in the uniformconductivity ionosphere, Rep. Ionos. Space. Res. Japan, 30, 35–40, 1976.

    Google Scholar 

  • Olsen, N., A new tool for determining ionospheric currents from magnetic satellite data, Geophys. Res. Lett., 23, 3635–3638, 1996.

    Article  Google Scholar 

  • Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, 2nd ed., 973 pp., Cambridge University Press, Cambridge, 1992.

    Google Scholar 

  • Pulkkinen, A., O. Amm, A. Viljanen, and BEAR Working Group, Ionospheric equivalent current distributions determined with the method of spherical elementary current systems, J. Geophys. Res., 108, 1053, 2003.

    Article  Google Scholar 

  • Ritter, P., H. Lühr, A. Viljanen, O. Amm, A. Pulkkinen, and I. Sillanpää, Ionospheric currents estimated simultaneously from CHAMP satellite and IMAGE ground based magnetic field measurements: a statistical study at auroral latitudes, Ann. Geophys., 22, 417–430, 2004.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Vanhamäki, H., O. Amm, and A. Viljanen, 1-Dimensional upward continuation of the ground magnetic field disturbance using spherical elementary current systems, Earth Planets Space, 55, 613–625, 2003.

    Article  Google Scholar 

  • Viljanen, A., A. Pulkkinen, O. Amm, R. Pirjola, T. Korja, and BEAR Working Group, Fast computation of the geoelectric field using the method of elementary current systems and planar earth models, Ann. Geophys., 22, 101–113, 2004.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Liisa Juusola.

Rights and permissions

Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit

Reprints and permissions

About this article

Cite this article

Juusola, L., Amm, O. & Viljanen, A. One-dimensional spherical elementary current systems and their use for determining ionospheric currents from satellite measurements. Earth Planet Sp 58, 667–678 (2006).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Key words