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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

. Extended and revised archaeomagnetic database and secular variation curves from Bulgaria for the last eight millennia. Physics of the Earth and Planetary Interiors, Elsevier, 2014, 236, pp.79-94

S U M M A R YThe German archaeomagnetic data set was supplemented with 35 new directions from German sites mainly dating from the past 3000 yr. Together with archaeomagnetic data from the neighbouring countries of Germany a database of 166 reliable archaeomagnetic directions has been compiled for the reference area, which is defined by a 500-km-radius circle around Göttingen. The retrieved directions come from well-dated archaeological structures and about 40 per cent of the dating relay on natural science methods such as radiocarbon, thermoluminescence, dendrochronology dating or historical documents. From this data set a secular variation (SV) reference curve has been calculated using a bivariate algorithm, which fits a natural cubic spline based on roughness penalty to declination, inclination and time, simultaneously. The error tube surrounding this curve was obtained from Bayesian modelling of the experimental errors, which can also take stratigraphic information into account. The obtained SV reference curve for the past 2500 yr is similar to that from France, but also significant differences are seen. Comparison of the curves does not show a simple westward drift of the SV pattern. The German reference curve allows archaeomagnetic dating in the reference area and extends this dating technique to sites situated in middle Europe.

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[1] A first secular variation (SV) curve for the Iberian Peninsula was computed by hierarchical Bayesian method using a total of 134 archaeomagnetic directions with ages ranging from À775 to 1959 A.D. A general agreement is observed between the Iberian curve and the French and German SV curves, although some interesting differences were found, such as the occurrence of lower inclinations between the 11th and 14th centuries in the Iberian curve. The analysis of these three reference curves indicates that SV in western Europe is characterized by three major directional changes at À125, 200, and 1350 A.D. It is suggested that these cusps are regional features of the geomagnetic field. The Iberian curve has been compared with the predictions of the Jackson, CALSK7K.2, and Hongre global models. Despite large differences recognized between these models, even for the dipolar terms, they predict reasonably well the Iberian archaeomagnetic SV.