Correlation Based Time Evolution of the Archeomagnetic Field

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.

Automated summary

The study extends the previous archeomagnetic field modeling concept to the temporal domain by introducing a space-time correlation kernel, and reduces uncertainties and translates variability into posterior variance by marginalizing hyperparameters. Results from applying the method to archeomagnetic data show less variation in the dipole compared to previous models, but are generally in agreement with previous findings.