Interpreting the Paleomagnetic Field Using Stochastic Models

Abstract:

Stochastic models are often applied to problems where only a small subset of variables are accessible by direct observation. This approach is well suited to paleomagnetism because we usually want to characterize the dipole field without explicitly accounting for all of the details of the internal field. Instead, the evolution of the dipole field is divided into two parts, based on the inherent timescales. One part describes slow adjustments of the dipole field toward a time-averaged state. The second part represents the effect of short-period convective fluctuations, which may be due to turbulent flow at smaller scales. Both parts of the stochastic model can be reconstructed from a time series of paleomagentic estimates. In this study we consider an example from (Buffett et al., 2013), which is based on the virtual axial dipole moment (VADM) from (Ziegler et al., 2011). The resulting stochastic model permits testable predictions, including the mean time between magnetic reversals or excursions. We extend these capabilities by predicting a geomagnetic power spectrum. The spectrum is nearly flat at low frequencies with a shoulder defined by the decay time of dipole fluctuations. At higher frequencies the spectrum decreases with frequency as $f^{-2}$. Geodynamo models suggest that dipole fluctuations involve the first few decay modes. When these results are applied to geomagnetic spectrum we obtain an average electrical conductivity of $1.5\times 10^6$ S/m, which is compatible with recent estimates. The stochastic model also yields predictions for the duration of a magnetic reversal. A key input parameter is the amplitude of convective fluctuations when the dipole is weak. The model inferred from VADM estimates implies a 50\% increase in convective fluctuations when the field is weak, yielding a mean reversal duration of 15 kyr. Interestingly, the model also predicts multiple flips in the dipole before a new polarity is established. For the predicted duration we expect two changes in polarity before a strong dipole emerges.