Geomagnetic spherical harmonic analyses: 1. Techniques

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Abstract
Improved techniques for direct least squares analysis of the main geomagnetic field are introduced and tested with simulated data. One improvement involves adding secular change data to the least squares analysis (as well as the usual spatial data). As a result, the secular variation (SV), as observed at fixed magnetic observatories and repeat stations, directly adjusts the SV terms of the spherical harmonic coefficients, while spatial data adjust both the spatial and SV terms. Simulations show that SV errors can be reduced by factors of 2 or 3 by introducing SV as data. The second refinement involved obtaining uncorrelated spherical harmonic coefficient sets through employment of a uniform distribution of data by area or by a compromise of an area‐weighting scheme. The latter was shown to reduce high cross correlations between spherical harmonic coefficients by up to a factor of 3 in simulated tests. This technique is especially useful in analyses of data sets which are unevenly distributed. Justification is given for the area‐weighting scheme and also for the employment of evenly distributed data sets, as may readily be obtained in the case of satellite data. A third refinement, though used previously, that of incorporating declination data weighted by the horizontal intensity and inclination data weighted by total intensity, was shown to have merit on the basis of observed error distributions.

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