Spherical Harmonic Analysis of Palaeomagnetic Inclination Data

Abstract

Summary A method for determining the relative values of the low-order Gauss coefficients for the palaeomagnetic field from inclination data only, i.e. in the absence of declination and intensity information, has been used to extend the analysis carried out by Creer, Georgi & Lowrie to include the core data published by Opdyke & Henry. The 20 regional average Quaternary palaeomagnetic inclination directions given by Creer et al. were combined with 12 new regional average data points derived from the deep-sea sediment core data published by Opdyke & Henry to form a grand population of 32 inclination directions. The analysis was carried out to determine both the second-order and third-order coefficients. It was found that the normalized amplitudes of the second-and third-order terms dropped of€ at least as rapidly as those of the present-day field. The Cartesian co-ordinate positions of the eccentric dipole for the grand populations were found to be in general agreement with those found by Creer et al. The input data were also perturbed to determine the sensitivity of the offsets to errors in the data. It was generally found that the offset along the rotation axis was least affected by input errors. Various authors have used palaeomagnetic observations to determine the nature of the Earth's palaeomagnetic field. Watkins (1972) has proposed that hemispherical differences in Brunhes inclination data can best be accounted for with double axialdipole model. Wilson (1970) proposed that the inclination data for the Quaternary and upper Tertiary can best be represented by an axial dipole displaced from the geocentre along the rotation axis. In terms of standard spherical harmonic analysis Wilson determined the values of 8,' and 8,'. Creer, Georgi & Lowrie (1973) developed three new methods to determine all Gauss coefficients of degree one and two (g,', . . ., h,'). These terms in turn were used to calculate the position and orientation of a single dipole displaced from the geocentre, for the Quaternary and late Tertiary geomagnetic field.