A representation function for a distribution of points on the unit sphere—with applications to analyses of the distribution of virtual geomagnetic poles

Abstract

An arbitrary point distribution consisting of a finite number of points on a unit sphere may be completely and uniquely represented by an analytic function in the form of a spherical harmonic expansion. The applications of this representation function are illustrated in an analysis of the symmetries in the virtual geomagnetic pole (VGP) distribution of the polarity reversal records of the past 10 million years. We find that the longitudinal confinements in the VGP distribution are (a) persistent only in the equatorially symmetric part (of the non-zonal symmetries) of the VGP distribution and (b) strong along the east coast of the North American continent and weak along the longitudes of East Asia-Australia. We also find that the equatorially symmetric patterns in the VGP distribution appear to extend preferentially into the Pacific Ocean and are relatively depleted in the longitude band associated with Africa.