An Application of Oblate Spheroidal Harmonic Functions to the Determination of Geomagnetic Potential

Abstract

The general theory of harmonic analysis of the potential of the Earth's main magnetic field is presented in terms of oblate spheroidal harmonic functions, treating the figure of the Earth as an oblate spheroid. It is a modification of the theory given originally by Schmidt, but removes the requirement of 48 multiplicative constants pnm and qnm. The theory is applied to Schmidt's data for epoch 1885 and for comparison the same data has been analyzed using sperical harmonic functions and treating the Earth as a sphere. Both analyses have been done both considering and ignoring the external field. Of the 48 coefficients for the external field, 18 are found to be significant at the 95 per cent confidence level and the magnitude of the external component of g10 is found to be significantly reduced from 226γ for a spherical Earth to 139γ for an oblate Earth. This reduction is shown to be theoretically necessary, and application of the theory to spherical harmonic coefficients for epoch 1965, shows that the magnitude of the external component of g10 is reduced from 82γ to 0γ. © 1967, Society of Geomagnetism and Earth, Planetary and Space Sciences. All rights reserved.