Spherical Harmonic Analysis in Terms of Unevenly Distributed Observation Points and Its Applications to Geomagnetic Data

Spherical harmonic expansion is affected by uneven distribution of observation points. A weighting scheme is proposed in order to reduce the effects. The weights of observation points are determined in order to homogenize the distribution. Spherical harmonic expansion of the synthetic geomagnetic data is demonstrated; the weighting works in terms of decrease of truncation error of the expansion. The method is applicable to find a new observation site and to prioritize present geomagnetic observatories.