A stochastic model for palaeomagnetic field variations

Abstract

Regeneration of the Earth's magnetic field by convection in the liquid core produces a broadspectrum of time variation. Relative palaeointensity measurements in marine sediments providea detailed record over the past 2 Myr, but an explicit reconstruction of the underlyingdynamics is not feasible. A more practical alternative is to construct a stochastic model fromestimates of the virtual axial dipole moment. The deterministic part of the model (drift term)describes time-averaged behaviour, whereas the random part (diffusion term) characterizescomplex interactions over convective timescales. We recover estimates of the drift and diffusionterms from the SINT2000 model of Valet et al. and the PADM2M model of Ziegleret al. The results are used in numerical solutions of the Fokker-Planck equation to predictstatistical properties of the palaeomagnetic field, including the average rates of magnetic reversalsand excursions. A physical interpretation of the stochastic model suggests that thetimescale for adjustments in the axial dipole moment is set by the dipole decay time td. Weobtain td = 29 kyr from the stochastic models, which falls within the expected range for theEarth's core.We also predict the amplitude of convective fluctuations in the core, and establisha physical connection to the rates of magnetic reversals and excursions. Chrons lasting longerthan 10 Myr are unlikely under present-day conditions. However, long chrons become morelikely if the diffusion term is reduced by a factor of 2. Such a change is accomplished byreducing the velocity fluctuations in the core by a factor ofv2, which could be attributedto a shift in the spatial pattern of heat flux from the core or a reduction in the total coreheat flow. © The Authors 2013 Published by Oxford University Press on behalf of The Royal Astronomical Society.