Encyclopedia of Geomagnetism and Paleomagnetism

2007 Edition
| Editors: David Gubbins, Emilio Herrero-Bervera

Main Field, Ellipticity Correction

  • Stuart R. C. Malin
Reference work entry
DOI: https://doi.org/10.1007/978-1-4020-4423-6_211

The first spherical harmonic analyses of the geomagnetic main field ignored the ellipticity of the Earth. This was not a serious omission, since the radial departures of the Earth's surface from a sphere never amount to more than 0.17%. However, as the quality of data improved, it was thought that they might justify inclusion of a correction for ellipticity.

The Earth's surface is closely approximated by an oblate spheroid with eccentricity 0.082. This affects both the position of an observation and the observation itself, since the horizontal component, for example, is measured tangential to the spheroid rather than perpendicular to the line joining the site to the Earth's center. Early analyses that took account of this ellipticity (Schmidt, 1898; Adams, 1900; Jones and Melotte, 1953) first determined coefficients for a spherical Earth, then adjusted these for ellipticity. A better method (Cain et al., 1963) was based directly on the original observations.

Adjustment from geodetic to...

This is a preview of subscription content, log in to check access.


  1. Adams, J.C., 1900. Terrestrial Magnetism. Scientific Papers, Vol. 2. Cambridge: Cambridge University Press, pp. 243–640.Google Scholar
  2. Cain, J.C., Daniels, W.E., Hendricks, S.J., and Jensen, D.C., 1965. An evaluation of the main geomagnetic field, 1940–1962. Journal of Geophysical Research, 70: 3647–3674.Google Scholar
  3. Jones, H.S., and Melotte, P.J., 1953. The harmonic analysis of the Earth's magnetic field for epoch 1942. Monthly Notices of the Royal Astronomical Society, Geophysical Supplement, 6: 409–430.Google Scholar
  4. Kahle, A.B., Kern, J.W., and Vestine, E.H., 1964. Spherical harmonic analyses for the spheroidal Earth. Journal of Geomagnetism and Geoelectricity, 16: 229–237.Google Scholar
  5. Malin, S.R.C., and Pocock, S.B., 1969. Geomagnetic spherical harmonic analysis. Pure and Applied Geophysics, 75: 117–132.CrossRefGoogle Scholar
  6. Schmidt, A., 1898. Der magnetische Zustand der Erde zur Epoch 1885.0. Archiv der deutschen Seewarte, Hamburg, 21(2): 76 pp.Google Scholar
  7. Winch, D.E., 1967. An application of oblate spheroidal harmonic functions to the determination of geomagnetic potential. Journal of Geomagnetism and Geoelectricity, 19: 49–61.Google Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Stuart R. C. Malin

There are no affiliations available