UC San Diego

Stochastic models have been developed to describe the time-varying axial dipole moment of the geomagnetic field sustained by turbulent fluid motions in Earth’s outer core. Previous stochastic models failed to predict the high-frequency variations present in the frequency spectrum of the axial dipole moment. In this study, we recast the Langevin model - which describes temporal variations in the axial dipole moment as a nonlinear tug-of-war between the moment’s slow drift towards and higher-frequency fluctuations away from equilibrium - as an order-3 continuous-autoregressive model, which is a linear differential equation driven by white noise. Both models are parametrized by a diffusion coefficient $D_{eq}$ that dictates the relative influence between fluctuations and drift on axial dipole behavior, timescales $\{\tau_m, \tau_s\}$ by which fluctuations away from steady state occur, and a drift timescale $\tau_l$ by which the axial dipole moment returns to steady state. Numerical simulations of our new model have frequency spectra that resemble a recently-published composite spectrum for the geomagnetic axial dipole moment. The latter goes like $f^0$ at lowest frequencies, $f^{-2}$ at intermediate frequencies, $f^{-4}$ at higher frequencies and $f^{-6}$ at highest frequencies. Our model parameters facilitate such a shape; $D_{eq}$ dictates the scale of the total spectrum and $\{\tau_l, \tau_m, \tau_s\}$ dictate the transition frequencies between adjacent regimes. Estimating the model parameters by comparison with the composite spectrum, we infer that $\{\tau_l, \tau_m, \tau_s\}$ correspond to the timescales expected for Ohmic diffusion, MAC waves, and torsional oscillations, respectively in Earth’s outer core while $D_{eq}$ reflects a rate at which Ohmic diffusion re-stabilizes the axial dipole field on ten-thousand year timescales while MAC waves and torsional oscillations render it unstable on decadal and sub-decadal timescales.