Abstract
AbstractIn 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.
Highlights
Existing models of the Earth's magnetic field (EMF) for the past millennia show a variety of time-dependent features: The evolution of the South Atlantic Anomaly, the observed dipole decay in recent centuries and the movement of flux patches all take place on timescales of several hundred years
The presented work extends the Bayesian strategy for correlation-based modeling of the archeomagnetic field introduced in MSKH20 to the temporal domain
In contrast to previous works (Hellio & Gillet, 2018; Hellio et al, 2014; Korte et al, 2009; Licht et al, 2013; Senftleben, 2019), using a noisy input Gaussian process (NIGP) (McHutchon & Rasmussen, 2011) to incorporate dating uncertainties does not rely on sampling techniques
Summary
Existing models of the Earth's magnetic field (EMF) for the past millennia show a variety of time-dependent features: The evolution of the South Atlantic Anomaly, the observed dipole decay in recent centuries and the movement of flux patches all take place on timescales of several hundred years (see e.g., Hartmann & Pacca, 2009; Jackson & Finlay, 2015). Existing models differ in the approach to global modeling, but are usually constructed using inversion for spherical harmonics (SH) coefficients, truncated at a certain degree. In the low degrees, and to exploit the data to its fullest, we suggest a Bayesian modeling approach based on Gaussian processes (GPs), both in space and time. With this already in mind, we implemented a closed-form covariance function for the spatial domain in a previous study (Mauerberger et al, 2020, hereafter referred to as MSKH20). We provide further insight into the mathematical footing of the introduced methods
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