Modeling the global archeomagnetic field based on space-time correlations

Abstract:

For the global geomagnetic core field, a new modeling concept for Holocene archeomagnetic data is presented. Major challenges consist of the uneven data distribution, missing vector field components and non-linear relations between observations and the geomagnetic potential, as well as dating errors. Archeomagnetic models are typically based on truncated spherical harmonics, combined with a spline decomposition. Instead, we propose a Gaussian process based model together with its Bayesian inversion. Inherently, the Bayesian approach provides location dependent uncertainties and allows to account for dating errors.

The geomagnetic potential is assumed to be a Gaussian process whose covariance structure is given by an explicit space-time kernel function, including several hyperparameters. For this kind of semi-parametric models, the full Bayesian posterior is numerically intractable. Therefore, we propose approximate computation using a Bayesian update system. In a first step, the full vector records are used to obtain, within Laplace approximation, a rough field estimate. This estimate serves as a point of linearization for the non-linear observations. Dating errors are incorporated via linearization of a noisy input model. Most prior parameters are marginalized, to reduce their influence on the outcome and to translate their variability to the posterior variance. The approximate posterior is thus given by a Gaussian mixture, including uncertainties related to dating, measurement and modeling process. The modeling concept was tested on synthetic data and to showcase its potential applied to archeomagnetic and volcanic data from the last 1000 years.