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

Abstract

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.

References

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  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.

    Article  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  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.

    Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Google Scholar 

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

    Google Scholar 

  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.

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  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.

    Article  Google Scholar 

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

    Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Google Scholar 

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

    Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  23. 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 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

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Correspondence to O. Amm.

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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). https://doi.org/10.1186/BF03352247

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Keywords

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