Geomagnetic reversals and the stochastic exit problem

We consider a dynamical system consisting of a fundamental mode (amplitude x , nonlinearly stable) and one stable periodic overtone, coupled by multiplicative noise. The problem emerges from attempts to understand the variability of the geomagnetic dipole field. We determine the mean reversal rate of x ( t ) with the help of stochastic exit theory, and analyse the reversal mechanism and the crucial role of the overtone. It is argued that models based on the induction equation of MHD will lead to equations of the same generic type, so that our conclusions on the reversal scenario should also hold for the geomagnetic field. Reversals are relatively rare, fast events, associated with a surge in the nondipole field. The mean reversal rate is very sensitive to the control parameters.