Towards a self-consistent approach to palaeomagnetic field modelling

Recent studies of the palaeomagnetic field behaviour over the past 5 Myr re ly on statistical analysis of mainly directional data. However, the data ar e quite sparse and ill-distributed, and directional parameters are non-line ar functions of the local field, rendering such statistical analysis non-tr ivial. Up to now these difficulties have usually been ignored or removed by relying on simplifications (linearization, neglecting internal correlation s, etc.) that are unfortunately not justified if the field contains some am ount of complexity. The purpose of the present paper is to present a rigorous statistical forwa rd approach to palaeomagnetic field modelling. Starting from a statistical model of the field defined in terms of the statistics of its Gauss coeffici ents (along the lines pioneered by Constable & Parker 1988), we show how su ch a model may be exactly tested against any given data set, either on a lo cal regional or a global scale. A method to implement this approach is outl ined 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 functi ons are derived and shown to be non-Fisherian, which we note may be a signi ficant source of artefacts for standard mean-field modelling. Although the method we propose is already useful in its present state, some slight impro vements are possible in order to account for noise in the data better.