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\begin{document}

\title{Correlation based time evolution of the archeomagnetic field}



\author[1]{Maximilian Schanner}%
\author[2]{Stefan Mauerberger}%
\author[1]{Monika Korte}%
\author[2]{Matthias Holschneider}%
\affil[1]{German Research Centre for Geosciences GFZ, Section 2.3, Potsdam, Germany}%
\affil[2]{Applied Mathematics, University of Potsdam, Potsdam, Germany}%


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  \date{June 11, 2024}


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\begin{abstract}
In a previous study, a new snapshot modeling concept for the
archeomagnetic field was introduced (Mauerberger et al. 2020). 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.%
\end{abstract}%



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