Skip to main content

One-dimensional upward continuation of the ground magnetic field disturbance using spherical elementary current systems


Ionospheric equivalent currents are defined as spherical sheet currents, which reproduce the observed magnetic disturbances below the ionosphere. One way of determining these currents is to place several so called spherical elementary current systems (SECS) in the ionospheric height and to solve an inversion problem for the amplitudes of these systems. In previous studies this method has been applied to two-dimensional data sets, having both latitudinal and longitudinal spatial coverage (2D SECS method). In this paper a one-dimensional variant of this method (1D SECS) is developed. The 1D SECS method can be used even in those situations where the data set is one dimensional, e.g. with one meridionally aligned magnetometer chain. The applicability of the 1D SECS method is tested using both synthetic and real data. It is found that in real situations the errors in the 1D SECS results are 5—10% in current density profiles and ~5% in integrated currents, when compared to the results of the more accurate 2D SECS method.


  • 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 the ionosphere using spherical elementary current systems, Earth Planets Space, 51, 431–440, 1999.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Gradshteyn, I. and I. Ryzhik, Table of Integrals, Series and Products, 4th ed., 1086 pp, Academic Press, New York, 1965.

    Google Scholar 

  • Haines, G., Spherical Cap Harmonic Analysis, J. Geophys. Res., 90(B3), 2583–2591, 1985.

    Article  Google Scholar 

  • Kauristie, K., T. Pulkkinen, R. Pellinen, and H. Opgenoorth, What can we tell about global auroral-electrojet activity from a single meridional magnetometer chain?,Ann. Geophys., 14, 1177–1185, 1996.

    Article  Google Scholar 

  • Mersmann, U., W. Baumjohann, F. Küppers, and K. Lange, Analysis of an eastward electrojet by means of upward continuation of ground-based magnetometer data, J. Geophys., 45, 281–298, 1979.

    Google Scholar 

  • Popov, V., V. Papitashvili, and J. Watermann, Modeling of equivalent ionospheric currents from meridian magnetometer chain data, Earth Planets Space, 53, 129–137, 2001.

    Article  Google Scholar 

  • Press, W., S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in Fortran 77. The Art of Scientific Computing, 2nd ed., 973 pp, Cambridge Univ. 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(A2), 1053, doi:10.1029/2001JA005085, 2003a.

    Article  Google Scholar 

  • Pulkkinen, A., O. Amm, A. Viljanen, and BEAR Working Group, Separation of the geomagnetic variation field on the ground into external and internal parts using the spherical elementary current system method, Earth Planets Space, 55, 117–129, 2003b.

    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 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Heikki Vanhamäki.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Vanhamäki, H., Amm, O. & Viljanen, A. One-dimensional upward continuation of the ground magnetic field disturbance using spherical elementary current systems. Earth Planet Sp 55, 613–625 (2003).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Current Distribution
  • Earth Planet Space
  • Fourier Method
  • Equivalent Current
  • Upward Continuation