An evaluation of the main geomagnetic field, 1940-1962

Abstract

A set of 21,695 selected survey and observatory annual mean data available for the interval 1940–1963 is used to make a new determination of the geomagnetic field and its secular change. The field is given by a series of 63 spherical harmonics (gnm and hnm to n = m = 7) and 35 time derivatives (ġnm and to n = m = 5). Although it is inferred from these results that a better fit could be made with existing data if more coefficients were used, the improvement is substantial enough for us to recommend that the coefficients be used as a replacement for previously derived coefficients to evaluate the field at the current epoch. One refinement in the present determination is the use of an oblate earth in place of the spherical approximation. It is illustrated that this modification is necessary to obtain meaningful extrapolations above the earth's surface. The standard errors and confidence levels are given for the coefficients to show that almost all are well determined. It is shown that, when the field components computed using this new series are compared with several weighted selections of survey data, the rms deviations average only 210 γ (1955–1963), a value smaller than that obtained by other spherical harmonic series known to us.

Spherical disharmonies in the Earth sciences and the spatial solution: Ridges, hotspots, slabs, geochemistry and tomography correlations

“…Typically, a least squares fitting technique is used. The most straightforward way of doing this is to take the sampled points and directly fit the spherical harmonics to the data points [Cain et al, 1965]. Other possibilities include fitting to interpolated values [Leaton et al, Copyright 1994 by the American Geophysical Union.…”

The Canadian Geomagnetic Reference Field 1995

“…Since total field is non-linear in the coefficients used to express vector components, the expression for total field must be linearized. The usual technique of considering only the linear terms in a Taylor series expansion (Cain et al, 1965) has been used here.…”

An Equation for Estimating Westward Drift

“…The values of U and UH for the three epochs 1945 (Vestine et al 1947), 1960(Cain et al 1965(Leaton et al 1965 are given in Table 1. Equality of UV and UH would only be expected for a field rotating uniformly about the polar axis; the discrepancies in Table 1 merely emphasise that the geomagnetic secular variation cannot be completely accounted for by a uniform westward drift.…”