Stochastic modelling of regional archaeomagnetic series

We report a new method to infer continuous time-series of the declination, inclination and intensity of the magnetic field from archaeomagnetic data. Adopting a Bayesian perspective, we need to specify a priori knowledge about the time evolution of the magnetic field. It consists in a time correlation function that we choose to be compatible with present knowledge about the geomagnetic time spectra. The results are presented as distributions of possible values for the declination, inclination or intensity. We find that the methodology can be adapted to account for the age uncertainties of archaeological artefacts and we use Markov chain Monte Carlo to explore the possible dates of observations. We apply the method to intensity data sets from Mari, Syria and to intensity and directional data sets from Paris, France. Our reconstructions display more rapid variations than previous studies and we find that the possible values of geomagnetic field elements are not necessarily normally distributed. Another output of the model is better age estimates of archaeological artefacts.