Abstract

Modern observations of the geomagnetic field allow us to peer into the Earth’s interior and recover estimates of fluid motion at the top of the core. Properties of the resulting flow guide our understanding of the underlying dynamics. However, duration of the modern record is relatively short.  The challenge is illustrated by a loose analogy with the dynamics of the atmosphere. Four hundred years of historical magnetic observations is roughly equivalent to four days of sparse meteorological observations. The daunting task of understanding the climate system with such a short atmospheric record is ample motivation for seeking longer records. Unfortunately, a longer record from geological observations comes with fewer spatial details. Our theoretical approach should be adapted to exploit the available information. Stochastic models are well suited to the study of the palaeomagnetic field because we can focus on the observable part of the field (i.e. the axial dipole) and represent the turbulent generation process using a suitable statistical description. One illustrative example is motivated by the work of Eugene Parker. We let the turbulent generation process be represented by a series of short-period convective events. The timing of these events follows a Poisson process and the amplitude of the convective event is a random variable. Sufficient constraints to specify the model come from the mean and variance of the dipole moment, as well as the time required for the dipole to reach the time-averaged amplitude after a reversal. The resulting model is able to reproduce the observed reversal rate and offers useful predictions for other properties of the paleomagnetic field.  Physical insights into the generation process can be drawn from the amplitude and average recurrence time of the convective events.