A physical interpretation of stochastic models for fluctuations in the Earth's dipole field

Abstract

Several recent studies have used palaeomagnetic estimates of the virtual axial dipole moment to construct a quantitative stochastic model for fluctuations and reversals in the Earth's dipole field. We investigate the physical significance of the terms in a standard stochastic (Langevin) model using output from a numerical geodynamo model. The first term, known as the drift term, characterizes the slow adjustment of the dipole field toward a time-averaged state. We find that the timescale for this slow adjustment is set by the magnetic decay time of dipole fluctuations. These fluctuations are typically be represented by the first few decay modes. The second term is often called the noise term because it characterizes the influence of short-period convective fluctuations in the core. We establish a connection between the noise term and the rms variation in magnetic induction. Applying these results to the palaeomagnetic field suggests that the rms variation in dipole generation exceeds the mean rate of generation. Such large fluctuations may be necessary to permit magnetic reversals. Palaeomagnetic estimates of the drift term favour a high electrical conductivity in the core. A lower bound on electrical conductivity is 0.6 × 106 S m−1. Similarly, we establish an upper bound on turbulent magnetic diffusivity (0.8 m2 s−1), although realistic estimates may be much less.