Probabilistic approach to geomagnetic field modelling of data with age uncertainties and post-depositional magnetisations

Abstract

Holocene geomagnetic field models are used to study processes in Earth's core, millennial scale variations in solar activity and to relatively date geological and archaeological archives. Constructing models from magnetic field directions and intensities stored in archaeological artefacts, igneous rocks and sediment records is challenging due to the sparse data distribution and the large chronological and magnetic uncertainties associated with the data. In addition, data from sediment records are further complicated by the effects of post-depositional remanent magnetisations (pDRMs) that lead to a magnetic signal which is smoothed and offset in time. Here we present a new probabilistic modelling approach that addresses these problems by co-estimating the geomagnetic field and the age of the data as well as accounting for the effects of pDRM and systematic directional errors in the sedimentary data. The use of a flexible Student's t-distribution in the likelihood function removes the need for outlier rejection which may otherwise lead to excessive smoothing of the model when applied to data with uncertain ages. A final ensemble of models is obtained through Hamiltonian Monte Carlo simulation of the posterior distribution. The modelling approach is tested and evaluated using synthetic data generated from the prior with an equivalent spatial and temporal distribution to the real data and corrupted with realistic noise.