Hierarchical modelling of archaeomagnetic data and curve estimation by moving average technique

Abstract

ISSN : 0956-540XInternational audienceA Bayesian hierarchical modelling is proposed for the different sources of scatter occurring in archaeomagnetism, which follows the natural hierarchical sampling process implemented by laboratories in field. A comparison is made with the stratified statistics commonly used up to now. The Bayesian statistics corrects the disturbance resulting from the variability in the number of specimens taken from each sample or site. There is no need to publish results at sample level if a descending hierarchy is verified. In this case, often verified by archaeomagnetic data, only results at site level are useful for geomagnetic reference curve building. Typically, a study with at least 20 samples will give an α95i 5 per cent close to the optimal α95i for a fixed site number mi and if errors are random with zero mean (no systematic errors). The precision on the curve itself is essentially controlled, through hierarchical elliptic statistics, by the number of reference points per window and by dating errors, rather than by the confidence angles α95ij at site level (if a descending hierarchy). The Bayesian elliptic distribution proposed reveals the influence of the window width. The moving average technique is well adapted to numerous and very well dated data evenly distributed along time. It is not a global functional approach, but a (linear) local one

Archaeomagnetic Studies in Kilns From N. Greece

“…In the last decade archaeomagnetic dating became an attainable and common practice due to the development in statistical treatment of archaeomagnetic data based on bivariate statistics or Bayesian hierarchical technique (Le Goff et al, 2002;Lanos et al, 2005). …”

“…The relocation was made by using the virtual geomagnetic pole (VGP) method proposed by Noel and Batt (1990). The dating was performed by using the Bayesian hierarchical approach (Lanos et al, 2005). This method allows the calculation of the probability densities separately for each geomagnetic field element after comparison with the reference SV curves.…”

The historic magmatic-hydrothermal eruption of the Breccia di Commenda, Vulcano, Italy

“…To obtain the archeomagnetic age for the eruption, the mean direction from the BC clasts was first relocated to Paris using the relocation via pole method. Dating was then done using the RenDate software (Lanos et al 2005) and the French Secular Variation (SV) curve (Gallet et al 2002) as reference. This method uses the Bayesian statistics approach, in which the probability density obtained from the inclination and declination SV curves are combined.…”

Limitations in paleomagnetic data and modelling techniques and their impact on Holocene geomagnetic field models

“…Potential sources of the uncertainty in archeomagnetic data include: (1) dating errors; (2) cooling rate differences; (3) magnetic anisotropy (Lanos et al 2005); as well as (4) uncertainties related to the thermal remanence acquisition, local magnetic field anomalies, and errors during sampling (Constable et al 2000). Data from archeomagnetic and lava flows are often obtained by averaging several measurements from individual samples.…”