Towards a self-consistent approach to palaeonmagnetic field modelling

Abstract

Recent studies of the palacomagnetic field behaviour over the past 5 Myr rely on statistical analysis of mainly directional data. However, the data are quite sparse and ill-distributed, and directional parameters are non-linear functions of the local field, rendering such statistical analysis non-trivial. Up to now these difficulties have usually been ignored or removed by relying on simplifications (linearization, neglecting internal correlations, etc.) that are unfortunately not justified if the field contains some amount of complexity. The purpose of the present paper is to present a rigorous statistical forward approach to palaeomagnetic field modelling. Starting from a statistical model of the field defined in terms of the statistics of its Gauss coefficients (along the lines pioneered by Constable & Parker 1988), we show how such a model may be exactly tested against any given data set, either on a local regional or a global scale. A method to implement this approach is outlined and examples based on published models are provided. In particular we focus on the treatment of directional data, for which the method is most relevant. The corresponding local probability density functions are derived and shown to be non-Fisherian, which we note may be a significant source of artefacts for standard mean-field modelling. Although the method we propose is already useful in its present state, some slight improvements are possible in order to account for noise in the data better.