Studying the Geomagnetic Polarity Time Scale and Superchrons by Scalar Models and Feature Based Data Assimilation

Paleomagnetic data have been used to create a scalar stochastic model that produces time-series representative of Earth's magnetic dipole field, and correctly captures mean reversal rates. The stochastic model is characterized by two components: a deterministic drift coefficient modeling "resolved" dynamics, and a stochastic diffusion term modeling the effects of turbulent fluid motion at the earth's core. The validity of the model may be suspect over long time periods, due to significant variation in core dynamics. A means of extending the model's applicability to longer time periods involves adjusting the drift or diffusion coefficient based on geomagnetic polarity time scale data, describing Earth's dipole polarity over the past 150 Myr. The model adjustment can be handled via numerical data assimilation. In typical data assimilation setups, e.g., numerical weather prediction or hydrological problems, one attempts to identify model parameters such that simulations by the numerical model adequately approximate measured data.This approach is neither feasible nor appropriate for the stochastic models and data we consider. It is infeasible because assimilation of the polarity only effects the resulting state estimates when the field reverses, and it is inappropriate since the main goal is to match reversal rates which depend on the distribution of reversals as opposed to their specific occurrences. We thus perform the data assimilation by preprocessing the data to produce a feature: an estimated reversal rate as a function of time over the past 150 Myr. We then base our data assimilation on this feature, rather than the entirety of the data, and estimate a scaling for the diffusion term to match the feature. Thus the scalar stochastic model and the geomagnetic polarity time-scale can be used to estimate the strength of the diffusion term over the past 150 Myr. In particular, we find that the model generates superchrons lasting 10 Myr or longer, contingent upon a properly tuned scaling of the diffusion term. The stochastic model combined with the feature based data assimilation can in fact reproduce the entire range of reversal rates found over the past 150 Myr. This in turn, allows us to draw conclusions about important aspects of core dynamics happening over very long time scales.