A comprehensive model for the kyr and Myr timescales of Earth's axial magnetic dipole field

Abstract

Abstract. We consider a stochastic differential equation model for Earth's axial magnetic dipole field. Our goal is to estimate the model's parameters using diverse and independent data sources that had previously been treated separately, so that the model is a valid representation of an expanded paleomagnetic record on kyr to Myr timescales. We formulate the estimation problem within the Bayesian framework and define a feature-based posterior distribution that describes probabilities of model parameters given a set of features derived from the data. Numerically, we use Markov chain Monte Carlo (MCMC) to obtain a sample-based representation of the posterior distribution. The Bayesian problem formulation and its MCMC solution allow us to study the model's limitations and remaining posterior uncertainties. Another important aspect of our overall approach is that it reveals inconsistencies between model and data or within the various data sets. Identifying these shortcomings is a first and necessary step towards building more sophisticated models or towards resolving inconsistencies within the data. The stochastic model we derive represents selected aspects of the long-term behavior of the geomagnetic dipole field with limitations and errors that are well defined. We believe that such a model is useful (besides its limitations) for hypothesis testing and give a few examples of how the model can be used in this context.

Simple stochastic model for geomagnetic excursions and reversals reproduces the temporal asymmetry of the axial dipole moment

“…The doubledisk dynamo proposed by Rikitake (8), which showed a chaotic behavior and underwent stochastic reversals, was a historic model of this kind. Since then, several simple models have been studied including both fully deterministic models (8,9) and models containing stochastic terms (10)(11)(12)(13)(14).…”

Variability of Millennial‐Scale Trends in the Geomagnetic Axial Dipole

“…Model parameters for the stochastic model are recovered from a wide variety of paleomagnetic observations using a Bayesian feature‐based inversion (Morzfeld & Buffett, ). The input data sets include 2‐Myr records of paleointensity from the SINT‐2000 (Valet et al, ) and PADM2 M (Ziegler et al, ) models, as well as high‐resolution records from the CALS10k.2 model (Constable et al, ) and the average reversal rate from the last 10 Myr (Ogg, ).…”

“…This assumption is reasonable when the time step, , is large, but it becomes questionable when approaches the correlation time of the noise model. Morzfeld and Buffett () recovered a correlation time of years from the high‐resolution CALS10k.2 model. This time interval is comparable to the length of the historical record, so our assessment of the historical record using the stochastic model may require an explicit treatment of correlated noise.…”

“…This is implemented in the stochastic model by replacing with an exponentially correlated noise source. The required modifications are fairly standard and the details can be found in Morzfeld and Buffett ().…”

“…This is implemented in the stochastic model by replacing dW t with an exponentially correlated noise source. The required modifications are fairly standard and the details can be found in Morzfeld and Buffett (2019). Figure 4 shows the standard deviation of the trend computed from a simulation of the stochastic model with correlated noise.…”