Testing statistical palaeomagnetic field models against directional data affected by measurement errors

Abstract

In a previous paper, Khokhlov et al. introduced a method to test the compatibility of so-called 'giant Gaussian process' (GGP) statistical models of the palaeomagnetic field against any palaeosecular variation database. This method did not take measurement errors into account. It therefore lacked practical usefulness. In the present paper, we remedy this and generalize the method to account for measurement errors in a way consistent with both the assumptions underlying the GGP approach and the nature of those errors. The method is implemented to test GGP models against any directional data set affected by Fisherian errors. Simulations show that the method can usefully discriminate which GGP model best explains a given data set. Applying the method to test six published GGP models against a test Bruhnes stable polarity data set extracted from the Quidelleur et al. database, it is found that all but one model (that of Quidelleur & Courtillot) should be rejected. Although this result should be taken with care, and does not necessarily imply that this model is superior to other models (Quidelleur & Courtillot precisely used the Quidelleur et al. database to infer their model), it clearly shows that in practice also, and with the databases currently available, the method can discriminate various candidate GGP models. It also shows that the statistical behaviour of the geomagnetic field at times of stable polarity can indeed be described in a consistent way in terms of a GGP model. This 'forward' testing method could ultimately be used to design an 'inverse' approach to GGP modelling of the palaeomagnetic field. © 2006 The Authors Journal compilation © 2006 RAS.