Correlation Based Time Evolution of the Archeomagnetic Field

Abstract

In a previous study, a new snapshot modeling concept for the archeomagnetic field was introduced (Mauerberger et al., 2020, https://doi.org/10.1093/gji/ggaa336). By assuming a Gaussian process for the geomagnetic potential, a correlation‐based algorithm was presented, which incorporates a closed‐form spatial correlation function. This work extends the suggested modeling strategy to the temporal domain. A space‐time correlation kernel is constructed from the tensor product of the closed‐form spatial correlation kernel with a squared exponential kernel in time. Dating uncertainties are incorporated into the modeling concept using a noisy input Gaussian process. All but one modeling hyperparameters are marginalized, to reduce their influence on the outcome and to translate their variability to the posterior variance. The resulting distribution incorporates uncertainties related to dating, measurement and modeling process. Results from application to archeomagnetic data show less variation in the dipole than comparable models, but are in general agreement with previous findings.

Plain Language Summary: Global reconstructions of the past geomagnetic field are useful tools to study the geodynamo process that generates the Earth's magnetic field in the outer core. Data‐based field reconstructions are traditionally represented by a fixed number of coefficients in space and time. In a previous study, a new modeling concept for individual epochs of the magnetic field was introduced, which is better adapted to inhomogeneous data distributions as found in archeomagnetic data, and which provides more realistic uncertainty estimates. This new modeling concept effectively has one coefficient per data point. Here, the new method is expanded to also consider the time evolution and build continuous models of the past geomagnetic field. Uncertainties in archeomagnetic input data and in their ages are taken into account and contribute to estimating reasonable uncertainties for the resulting model. The application of the new method to archeomagnetic data over the past 1,200 years gives general agreement with previous findings with less variation in the dipole field contribution than seen in comparable models.

Key Points:

Extension of a previous study on spatial correlation based archeomagnetic modeling to the temporal domain.

Dating uncertainties are incorporated by the noisy input Gaussian process formalism.

Results show general agreement with comparable models with less variation in the dipole field contribution.