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Ionospheric disturbance magnetic field continuation from the ground to the ionosphere using spherical elementary current systems


A new technique for continuation of the ground magnetic field caused by ionospheric currents to the ionosphere in spherical geometry is presented that makes use of elementary ionospheric current systems, which were introduced by Amm (1997) in extension of an earlier work by Fukushima (1976). The measured ground magnetic disturbance is expanded in terms of the ground magnetic effect of a spatial distribution of such elementary current systems. Using a matrix inversion technique, the scaling factors for each elementary current system, and therefrom the ionospheric equivalent currents are calculated. The technique can be applied to both global and local scales. Its advantages compared to the common field continuation techniques with Fourier (local scale), spherical cap (local to medium scale), or spherical (global scale) harmonic expansions are: 1) No fixed limitation of the spectral content has to be given for the whole analysis area, as it has to be done for the other techniques by truncation of a series expansion. 2) The locations of the elementary current systems can be chosen freely, such that they are most suitable with respect to the available measurement sites or the type of current system to be analysed. Results of the new technique are discussed in comparison to results of the spherical cap harmonic expansion method for a model of a Cowling channel.


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

  2. Amm, O., Method of characteristics in spherical geometry applied to a Harang discontinuity situation, Ann. Geophys., 16, 413–424, 1998.

  3. Arfken, G., Mathematical Methods for Physicists, Academic Press, pp. 985, San Diego, U.S.A., 1985.

  4. Baumjohann, W., R.J. Pellinen, H.J. Opgenoorth, and E. Nielsen, Joint two-dimensional observations of ground magnetic and ionospheric electric fields associated with auroral zone currents: Current system associated with local auroral break-ups, Planet. Space Sci, 29, 431–447, 1981.

  5. Boström, R., Ionosphere-magnetosphere coupling, in Magnetospheric Physics, edited by B. M. McCormack, p. 45, D. Reidel, Norwell, Mass., 1974.

  6. Chapman, S. and J. Bartels, Geomagnetism, vol. II, pp. 1049, Oxford University Press, New York, 1940.

  7. De Santis, A., D. J. Kerridge, and D. R. Barraclough, A spherical cap harmonic model of the crustal magnetic anomaly field in Europe observed by MAGSAT, in Geomagnetism and Palaeomagnetism, edited by F. J. Lowes et al, pp. 1–17, 1989.

  8. De Santis, A., C. Falcone, and J. M. Torta, SHA vs. SCHA for modelling secular variation in a small region such as Italy, J. Geomag. Geoelectr., 49, 359–371, 1997.

  9. 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.

  10. Gauß, C. F., Erdmagnetismus und Erdmagnetometer, in: Gauß, C. F., Werke, hrsg. von der Königlichen Gesellschaft der Wissenschaften, Göttingen, 1863–1933, 1836.

  11. Gustafsson, G., W. Baumjohann, and I. Iversen, Multi-method observations and modeling of the three-dimensional currents associates with a very strong Ps 6 event, J. Geophys., 49, 138–145, 1981.

  12. Haines, G. V., Spherical cap harmonic analysis of geomagnetic secular variation over Canada 1960-21983, J. Geophys. Res., 90, 12563–12574, 1985a.

  13. Haines, G. V., Spherical cap harmonic analysis, J. Geophys. Res., 90, 2583–2591, 1985b.

  14. Haines, G. V., Computer programs for spherical cap harmonic analysis of potential and general fields, Comput. Geosci., 14, 413–447, 1988.

  15. Haines, G. V., Regional magnetic field modelling: a review, J. Geomag. Geoelectr, 42, 1001–1018, 1990.

  16. Haines, G. V. and J. M. Torta, Determination of equivalent current sources from spherical cap harmonic models of geomagnetic field variations, Geophys. J. Int., 118, 499–514, 1994.

  17. Hobson, E. W., The Theory of Spherical and Ellipsoidal Harmonics, pp. 500, Cambridge University Press, New York, 1931.

  18. Inhester, B., J. Untiedt, M. Segatz, and M. Kürschner, Direct determination of the local ionospheric Hall conductance distribution from two-dimensional electric and magnetic field data, J. Geophys. Res., 97, 4073–4083, 1992.

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

  20. Richmond, A. D. and W. Baumjohann, Three-dimensional analysis of magnetometer array data, J. Geophys., 54, 138–156, 1983.

  21. Torta, J. M. and A. De Santis, On the derivation of the Earth’s conductivity structure by means of spherical cap harmonic analysis, Geophys. J. Int., 127, 441–451, 1996.

  22. Torta, J. M., A. Garcia, J. J. Curto, and A. De Santis, New representation of geomagnetic secular variation over restricted regions by means of spherical cap harmonic analysis: application to the case of Spain, Phys. Earth Planet. Inter, 74, 209–217, 1992.

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

  24. Viljanen, A., K. Kauristie, and K. Pajunpää, On induction effects at EIS-CAT and IMAGE magnetometer stations, Geophys. J. Int., 121, 893–906, 1995.

  25. Walker, J. K., V. Y Semenov, and T. L. Hansen, Synoptic models of high latitude magnetic activity and equivalent ionospheric and induced currents, J. Atmos. Terr. Phys., 59, 1435–1452, 1997.

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Amm, O., Viljanen, A. Ionospheric disturbance magnetic field continuation from the ground to the ionosphere using spherical elementary current systems. Earth Planet Sp 51, 431–440 (1999).

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  • Elementary System
  • Equivalent Current
  • Upward Continuation
  • Spherical Harmonic Analysis
  • Equivalent Current System