A stochastic model for palaeomagnetic field variations

Regeneration of the Earth's magnetic field by convection in the liquid core produces a broad spectrum of time variation. Relative palaeointensity measurements in marine sediments provide a detailed record over the past 2 Myr, but an explicit reconstruction of the underlying dynamics is not feasible. A more practical alternative is to construct a stochastic model from estimates of the virtual axial dipole moment. The deterministic part of the model (drift term) describes time-averaged behaviour, whereas the random part (diffusion term) characterizes complex interactions over convective timescales. We recover estimates of the drift and diffusion terms from the SINT2000 model of Valet <it>et al.</it> and the PADM2M model of Ziegler <it>et al.</it> The results are used in numerical solutions of the Fokker–Planck equation to predict statistical properties of the palaeomagnetic field, including the average rates of magnetic reversals and excursions. A physical interpretation of the stochastic model suggests that the timescale for adjustments in the axial dipole moment is set by the dipole decay time τ<inf>d</inf>. We obtain τ<inf>d</inf> = 29 kyr from the stochastic models, which falls within the expected range for the Earth's core. We also predict the amplitude of convective fluctuations in the core, and establish a physical connection to the rates of magnetic reversals and excursions. Chrons lasting longer than 10 Myr are unlikely under present-day conditions. However, long chrons become more likely if the diffusion term is reduced by a factor of 2. Such a change is accomplished by reducing the velocity fluctuations in the core by a factor of √2, which could be attributed to a shift in the spatial pattern of heat flux from the core or a reduction in the total core heat flow.