Mapping the Gauss Coefficients to the Pole and the Models of Paleosecular Variation

Abstract

The present magnetic field is usually described by models such as the IGRF which are described by Gauss coefficients obtained by spherical harmonic analysis of the geomagnetic field. The use of Gauss coefficients in paleosecular variation (PSV) studies will therefore make it possible to compare field structures obtained through paleomagnetism with those observed directly. For making such comparisons, it is important to understand how the magnetic field maps into geomagnetic poles and what are their statistical properties, because geomagnetic poles are frequently used in PSV studies. We show how Gauss coefficients map into pole positions, and we develop statistical tools to treat the angular scatter of magnetic poles calculated from models based on Gauss coefficients. We use these methods to evaluate the models of Constable and Parker (1988) and McFadden et al. (1988) which are typical of PSV models using Gauss coefficients. Our results suggests the importance of the (l = 2, m = 1) harmonic in the dynamo process of the earth.