Interpreting long-term changes in the paleomagnetic field using stochastic models and dynamo simulations

Paleomagnetic records show long time scale changes in the Earth's magnetic field, with fluctuations in intensity, mean/variance, and reversal rate. These observed features have been proposed to be governed by changes in core processes and dynamics, such as variations in heat flux across the CMB/ICB or the vigor of convection.

To explore the connection between these processes and the resulting dipole field, we perform numerical dynamo simulations at low Ekman numbers for two cases: (1) a regime with heat flow across the whole outer core, and (2) a purely bottom driven system. To each case, alterations to the Rayleigh number and/or CMB heat flux are prescribed after several magnetic diffusion times. Time variations in the vertical axial dipole moment are treated as a stochastic process governed by deterministic and random components, which are resolved using a kernel based non-parametric approach. This enables comparisons to previously recovered stochastic models from paleomagnetic observations. Deterministic variations and random fluctuations are well represented by linear drift and constant noise functions, respectively.

For case (1), an increased heat flux at the CMB causes a decrease in the gradient of the drift term and an increase in the noise term. Alternatively for case (2), an augmented Rayleigh number increases both the gradient of the drift term and the noise term. This suggests that for both systems, imposed changes increase the fluctuations in dipole generation through greater variations in convective velocity. However these changes affect the slow adjustment of the field in each model differently, possibly due to more or less of the field being partitioned into the slowest dipole decay mode. We apply these relations to paleomagnetic records to infer the evolution of core processes.