Skip to main content

Advertisement

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

Revision of the high-degree Gauss coefficients in the IGRF 1945–1955 models by using natural orthogonal component analysis

Abstract

The high-degree Gauss coefficients (n ≥ 7) in the IGRF models for 1945–1955 exhibit some unusual and unreliable behaviors in comparison with the models for other epochs. In this paper the method of Natural Orthogonal Components (NOC) is used to revise these coefficients. The obtained result shows that the main geomagnetic field can be approximated very well by the first a few NOC eigen modes. The high-degree Gauss coefficients (n ≥ 7) are deduced for each of IGRF models using the first 6 eigen modes and low-degree Gauss coefficients (n ≤ 6). The deduced high-degree coefficients are in very good agreement with the original ones for all models except those for 1945, 1950 and 1955. In comparison with the unusual behaviors in the IGRF1945–1955 models, the deduced high-degree coefficients for these models exhibit fairly smooth time-variations. Besides, the magnetic energy and magnetic flux calculated by the revised Gauss coefficients show more continuous secular variations and consistent characteristics.

References

  1. Barton, C. E., International geomagnetic field: the seventh generation, J. Geomag. Geoelectr., 49, 123, 1997.

    Article  Google Scholar 

  2. Frynberg, E. B., Separation of the geomagnetic field into a normal and anomalous part, Geomagn. Aeron., 15, 117, 1975.

    Google Scholar 

  3. Golovkov, V. P., N. E. Papitashvili, Y. S. Tyupkin, and E. P. Kharin, Separation of geomagnetic field variations on the quiet and disturbed components by the MNOC, Geomagn. Aeron., 18, 511, 1978.

    Google Scholar 

  4. Golovkov, V. P., T. N. Bondar, and I. A. Burdelnaya, Spatial-temporal modeling of the Geomagnetic field for 1980–2000 period and a candidate IGRF secular-variation model for 2000–2005, Earth Planets Space, 52, 1125, 2000.

    Article  Google Scholar 

  5. IAGA Commission 2 Working Group 4, International Geomagnetic ReferenceField 1965.0, J. Geophys. Res., 74, 4407, 1969.

    Article  Google Scholar 

  6. IAGA Division 5, Working Group 8, International Geomagnetic Reference Field 2000, Geophys. J. Int., 141, 259, 2000.

    Article  Google Scholar 

  7. Kendall, M. G. and A. Stuart, The Advanced Theory of Statistics, vol. 3, chap. 35, Charles Griffin, London, 1976.

    Google Scholar 

  8. Langel, R. A., The Main Field, in Geomagnetism, Vol. 1, edited by J. A. Jacobs, pp. 249–512, Academic Press, London, 1987.

  9. Langel, R. A. and R. H. Estes, Derivation of proposed International Geomagnetic Reference Field models for 1945, 1950, 1955, and 1960, Phys. Earth Planet. Int., 48, 293, 1987.

    Article  Google Scholar 

  10. Langel, R. A., D. R. Barraclough, D. J. Kerridge, V. P. Golovkov, T. J. Sabaka, and R. H. Estes, Definitive IGRF models for 1945, 1950, 1955, and 1960, J. Geomag. Geoelectr., 40, 645, 1988.

    Article  Google Scholar 

  11. Leove, M., Probability Theory, second edition, D Van Nosthand Company Inc., New York, 1963.

  12. Lowes, F. J., An estimate of the errors of the IGRF/DGRF fields 1945–2000, Earth Planets Space, 52, 1207, 2000.

    Article  Google Scholar 

  13. Pushkov, A. N., E. B. Frynberg, T. A. Chernova, and M. V. Fiskina, Analysis of the space-time structure of the main geomagnetic field by expansion into natural orthogonal components, Geomagn. Aeron., 16, 196, 1976.

    Google Scholar 

  14. Rotanova, N. M., N. E. Papitashvili, and A. N. Pushkov, Use of natural orthogonal components to distinguish and analyze the 60-yr geomagnetic field variations, Geomagn. Aeron., 22, 821, 1982.

    Google Scholar 

  15. Sabaka, T. J., R. A. Langel, R. T. Baldwin, and J. A. Conrad, The geomagnetic field 1900–1995, including the large-scale field from magnetospheric sources, and the NASA candidate models for the 1995 revision of the IGRF, J. Geomag. Geoelectr., 49, 157, 1997.

    Article  Google Scholar 

  16. Sun, W., W.-Y. Xu, and S.-I. Akasofu, Mathematical separation of directly driven and unloading components in the ionospheric equivalent currents during substorms, J. Geophys. Res., 103, 11695, 1998.

    Article  Google Scholar 

  17. Sun, W., W.-Y. Xu, and S.-I. Akasofu, An improved method to deduce the unloading component for magnetospheric substorms, J. Geophys. Res., 105, 13131, 2000.

    Article  Google Scholar 

  18. Xu, W.-Y., Unusual behaviour of the IGRF during the 1945–1955 period, Earth Planets Space, 52, 1227, 2000.

    Article  Google Scholar 

  19. Yamada, Y., 2-day, 3-day, and 5-6-day oscillations of the geomagnetic field detected by principal component analysis, Earth Planets Space, 54, 379, 2002.

    Article  Google Scholar 

  20. Zmuda, A. J., The International Geomagnetic Reference Field, 1965.0, in IAGA Bulletin 28, World Magnetic Survey, IUGG, Paris, 1971.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Wen-Yao Xu.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Xu, W. Revision of the high-degree Gauss coefficients in the IGRF 1945–1955 models by using natural orthogonal component analysis. Earth Planet Sp 54, 753–761 (2002). https://doi.org/10.1186/BF03351728

Download citation

Keywords

  • Secular Variation
  • Earth Planet Space
  • Truncation Level
  • International Geomagnetic Reference Field
  • Gauss Coefficient