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1. Introduction                  Presentation of the archaeological          site          Antibes is a French municipality situated in the          Alpes-Maritimes department in the Provence-Alpes -          Côte d'Azur region at the Mediterranean seashore, 205 km from          Marseille in the east and 23 km from Nice in the south-west. First          traces of an organized human settlement appear in the Early Iron Age          with a dwelling implanted in the Rocher (the          rock cliff in the actual city center). The foundation of the Antipolis colony is closely related to the          expansion of Greeks from Marseille in the 4th          century B.C. The Greek town was probably set at the foot of the          Antibes cliff under the actual city.          The Grimaldi castle, known          these days for the famous Picasso art collection, was built in the          Middle-Ages at the top of the Rocher          suceeding a vast monumental edifice from the Gallo-Roman period. The          foundations of the castle (Figure 1, Figure 2a), faced with quarried          stones and bricks visible at a height of several meters, belonged to          this monument of an unknown origin. In order to determine the date          of the construction of this monument, the part of the foundations          was subjected to an archaeometric study within an archaeological          research programme (PCR 2011-2013) Antipolis, des          origines au royaume des Francs directed by Eric Delaval, M.          Bats, L. Mercuri and R. Thernot.          Figure 1:  Plan of the Gallo-Roman          masonries observed at Grimaldi Castle (in red) / Figure 1 : Plan des structures antiques observées dans          le château Grimaldi                    Topographical ground Ville d’Antibes, record of the castle Albéric          Olivier CNRS, topography Laurent Vallières Inrap. / Fond topographique Ville d’Antibes, relevé du château          Albéric Olivier CNRS, topographie Laurent Vallières Inrap.          Figure 2: a) View on the west face          of the castle, the gallo-roman foundations marked in a red circle;          b) Wall MR 10003 after sampling of both bricks and mortars, before          restoration / Figure 2 : a) Vue extérieur du          château, face ouest avec des soubassements gallo-romains marqués en          cercle rouge ; b) Mur MR 10003 après l’échantillonnage des briques          et des mortiers, avant la restauation                                    Archaeological background          The dating of the Grimaldi castle foundations is          based on the archaeological hypotheses that emerged from          archaeological sondages realized on the square located in the west          flank of the castle under the supervision of Philippe Mellinand          (INRAP; Mellinand et al. 2007).          During these excavations in 2007, the          archaeologists focused on the foundation fosse of the west perimeter          wall MR10002 belonging to the same construction phase as the          parallel wall MR10003 (Figure 1). These two walls formed a vaulted          gallery. The width of the foundation fosse of the wall MR10002,          which was dug into the rock, is identical to the width of the          masonry and thus did not have to be filled up. However, this fosse          crosses over a circular pit dug into the rock at the same place          before the construction of the masonry. Prior to the erection of the          castle foundations, the pit was cleaned out and it was filled up          with construction mortar in the bottom level and with clay sediment          in the upper level. The sediment contained nine ceramic shards,          gravels, charcoals and plaster fragments. One of the shards was          precisely dated as the fragment of south-Gallic terra sigillata (type Drag-37a, study realized by          Emmanuel Pellegrino) which characterizes the period 60-100 A.D.          Since it does not seem likely that the circular          pit remained uncovered or that it was cleaned and filled up again          after the construction of the masonry, the terminus post quem of this stratigraphic unit          containing the shards is the last third of the 1st century A.D. That is also the terminus post quem of the construction of the          Gallo-Roman monument, the remains of which correspond to the          Grimaldi castle foundations.          Above the backfilled circular fosse, three          stratigraphic units are visible in the following order: the          homogeneous backfilling layer covering the fosse and supporting the          wall, another backfilling layer and an artificial ground level. The          dating of these stratigraphic units indicates the period between          17th and 18th century.                          Objectives of the study          The small number of found shards as well as the          chronological hiatus happening in the stratigraphy casts doubt on          the archaeological interpretations. Therefore, archaeometric          analyses of construction materials were performed in order to          support the hypotheses on the established chronology. Two physical          methods were employed with the following objectives:                      to date the construction of the            foundation wall MR 10003 by means of archaeomagnetic dating (AM)            of bricks assuming that the bricks originated from the original            structure and have been used shortly after their            making;            to date archaeological mortars by            optically stimulated luminescence using a single grain technique            (SG-OSL).                    Whereas the AM dating approach followed a          well-established, reliable measurement protocol (e. g. Lanos, 1998),          the dating of archaeological mortar by SG-OSL represents a new,          innovative and exploratory approach. A development of this new          application was part of the PhD. research resulting in several          publications (Urbanova et al., 2015 ;          Urbanova &#38; Guibert, accepted) where its principles are described          and its significance explained. The originality and the significance          of dating archaeological mortar by SG-OSL consist in the possibility          to date directly the moment of the edification of the masonry by          means of dating the last exposure of sand grains in mortar aggregate          to daylight. Contrary to dating of bricks, the risks of potential          re-use of construction materials (e. g. Guibert et          al., 2012) are eliminated when dating the mortar, since the          latter can only be used fresh during the building process.                      2. Materials and methods                  Sampling          During the sampling campaign that took place in          2012, five fragments of bedding mortar for luminescence dating and          92 brick pieces for archaeomagnetic dating were sampled. All          elements were taken from the wall MR 10003 using a core drill          designed for wet cutting with a 50 mm diameter coring auger for          mortars and a 25 mm diameter one for bricks. As visible in the          Figure 2b, mortars come from different levels of the masonry,          whereas all the bricks originate from the course located 205 cm          above the actual ground. In 2014, the sampled spots were filled with          repair mortar, whose external parts were colored by mineral oxides          in order to mask the intervention.                          Dating of bricks by archaeomagnetism          (AM)          The archaeomagnetic dating method is based on the          ability of baked clay to acquire a thermoremanent magnetization          (TRM) during the cooling process following heating above the so          called Curie temperatures (up to 680 °C) of magnetic carriers in the          clay. Hence, baked clay fossilizes the direction and the intensity          of the ambient geomagnetic field for a particular geographical          location in the form of a very stable magnetization. The direction          is represented by its inclination (I) versus the local horizontal          plane and by its declination (D), the angle between the Magnetic          North and the Geographical North. The magnetization intensity (F)          acquired is proportional to the geomagnetic field intensity which is          expressed in micro-tesla (µT).          The parallelism between the acquired          magnetization and the ambient geomagnetic field and the fields          variation in intensity and in direction over time are the bases of          the archaeomagnetic dating method. If the variation curve of the          direction is known on the grounds of a number of well dated          archaeological materials prior to the measurement, it is then          possible to date the last firing of baked clay. The date of the last          firing is obtained by transferring the determined mean inclination          and declination values after the latitude correction on the          reference secular variation curve of the past geomagnetic field.          When a in situ structure          (kiln, oven…) is studied, the three geomagnetic characteristics can          be restored. This is not the case of displaced material such as          bricks. Indeed, these building materials were removed from the          original place of their manufacture and transferred to the building          site. This displacement means a definitive loss of the geographic          co-ordinates (North, East, Vertical) in which the bricks were fired.          However, it is reasonable to assume that a rectilinear object would          preferentially lie on one of its flat sides during firing: on flat,          upright or on (long) edge. Given that the floor of the kiln is more          likely to be horizontal and smooth, the horizontal plane may be          conserved as one of the three planes which constitute the basic          trihedral system of the object. In practice, the magnetisation          direction is determined for each of the three firing positions on          flat, on edge or upright. As the secular variation of the          inclination varies between 45 and 75° in France during the          historical period, we may select from the three possible positions          the one which gives an inclination within an enlarged interval 45°          to 90° (Lanos, 1987, 1994, 1998 and 1999): the solution is to all          intents and purposes unequivocal, provided that the latitude of the          firing site is greater than 35° (North or South). It has to be          specified that the declination cannot be determined. However, it is          possible to characterize the orientation of the vertical plane of          the brick with respect to the magnetic north at the date of firing.          This angle is called “deviation”. It represents the angle between          the vertical flattening plane of the brick and the magnetic north          indicated by the magnetization vector, for the selected firing          position. The declination between this magnetic north direction and          the geographic north remains unknown. The deviation lies between          -90° and +90°.          A set of displaced materials (tiles, bricks,          paving tiles) can be statistically processed by archaeomagnetism if          it is composed of at least a hundred different objects originating          from a single “archaeomagnetic unit” (firing at the same date in the          same archaeological entity). Such a number is necessary in order to          compensate positioning errors of the bricks along the vertical in          the kiln. Observations during excavation are essential to detect a          possible mixing of the material or a re-use of materials of          different origins.                          Dating of mortars by optically stimulated          luminescence (OSL)          The principle of OSL dating is discussed in a          number of publications (Aitken, 1998; Wintle, 2008). The OSL age of          a sample is calculated as a ratio of an average archaeological dose          (also called “paleodose” for old samples) to annual dose rate. The          specificity of the present study lies in the analyses of quartz          grains extracted from mortar that were performed exclusively with          the single grain technique (SG-OSL; Duller &#38; Murray, 2000;          Duller, 2008) in order to overcome the problems of heterogeneous          bleaching and therefore to avoid the age overestimation (as observed          during previous attempts: Goedicke, 2003 and 2011, Panzeri, 2013;          Urbanova, et al., 2015).                      OSL sample preparation            The mortar preparation for OSL and gamma            spectrometry measurements has been discussed in detail in previous            publications (Urbanova et al., 2015 ;            Urbanova &#38; Guibert, accepted). We remind briefly the basics.            2-mm thick outer surface of the core drills was removed using a            water-lubricated diamond saw. The internal part of the core drills            was crushed. One part of the powder obtained was taken to prepare            sealed tubes for gamma spectrometry measurements whereas the other            part was submitted to chemical treatments resulting in the            extraction of the 200-250 µm size quartz used for the SG-OSL            analyses. The compact parts of the studied samples were used to            prepare thin and thick sections for material characterization.                                OSL instrumentation, measurements and data            evaluation            All OSL measurements were performed using a            TL/OSL DA20 Risø reader. The light detection system of the reader            consists of an EMI Q9235 photomultiplier tube and 7.5 mm of Hoya            U-340 filter for detection in the UV-blue wavelength range (about            280-370 nm). A 90Sr/90Y            beta source was used as an irradiation source (dose rate            0.150±0.005 mGy/s). Two different luminescence stimulation systems            depending on the measurement protocol were used. The OSL            measurements following a standard multigrain technique use Blue            LEDs (NISHIA type NSPB-500s) with a peak emission at 470 nm for            the stimulation, while a single grain analyses was performed with            a 10 mV Nd: YVO4 solid state diode-pumped            laser emitting at 532 nm. The total dissolution of feldspar in the            etched fractions from mortars was verified before the dating            procedure by IRSL test on multigrain discs (described in Urbanova            et al., 2015). The measurements of recovery            dose and archaeological doses were realized applying the SAR            protocol (Murray &#38; Wintle, 2000) with the regeneration doses            4.8, 9.6, 14.4, 19.2, 0, 4.8 Gy, the preheat and cut-heat            temperatures of 240°C et 190°C, respectively, and the recovery            dose 4.8 Gy.            OSL signals from the multi-grain aliquots are            based on the summation of the first 0.8 s of stimulation corrected            for background derived from the last 8 s (time of stimulation: 40            s). The single-grain OSL signals are derived from the summation of            the first 0.05 s of stimulation less the sum of the last 0.2 s            (time of stimulation: 1 s). For each grain or disc, the            sensitivity-corrected regenerated OSL signals (Lx/Tx) were fitted with an            exponential function and each individual archaeological dose (De) was estimated by            projecting the sensitivity-corrected natural signal (LN/TN) onto the fitted curve.            The standard error on the individual archaeological dose was            obtained by Analyst version 4.11 from counting statistics, curve            fitting and the instrumental reproducibility error of 2.7 % (the            value calculated from the series of measurements performed in the            IRAMAT-CRPAA laboratory in Bordeaux). For more details and the            discussion concerning the experimental parameters and data            evaluation, the reader can refer to thepublications on this topic            related directly to this study (Urbanova, 2015; Urbanova &#38;            Guibert, accepted) or to other studies on young samples (Thomsen            et al., 2005; Panzeri, 2013; Sim et al., 2014; Medialdea et            al., 2014).                                Dose rate determination, scanning electron            microscopy and beta-imaging            The practical aspects and the measurement            details on all the below-mentioned analyses are described in            Urbanova et al. (2015). Contributions of            the different dose rate components used for the age calculation            were measured. The contribution of sample matrix was determined by            low background gamma spectrometry that allows obtaining K, U and            Th contents of dated material, converted into the related dose            rates using the conversion factors published by Guérin et al. (2011). The environmental contribution            was measured by Al2O3:C            dosimetry. Internal radioactivity of the quartz grains used for            dating was evaluated by inductively coupled plasma mass            spectrometry (ICP-MS). Distributions of β emitting minerals within            mortar matrix were mapped by beta-imaging system. A scanning            electron microscopy coupled with an energy dispersive X-ray            analysis spectrometer (SEM-EDS) was used for mapping the potassium            content in the different zones of mortar matrix as described in            Urbanova et al. (2015).            An approximate contribution of water content to            the annual dose rate was estimated from the difference in the            weight between the dry sample and the same sample saturated with            water, assuming 50 % of the saturation value for the masonry ( 4).            The standard deviation on estimated water content was taken equal            to 29 %.                                3. Results and discussion                  Dating of bricks by archaeomagnetism                      Sampling on the field and specimen            preparation            From 94 bricks within the wall MR 10003, ~5 cm            long cores were taken using a portable, water cooled, hand-held            drill. The field sampling method involved drawing a line parallel            to the long edge of the brick (ox axis) with a carbide needle.            Samples were drilled so their axis was perpendicular to this line            and parallel to the plane of the bricks inserted in the wall. In            the laboratory, these cores were cut to 10.8 cm3 cores with a diameter of 25 mm and a length of            22 mm. Thus, a local coordinate system is attached to each            specimen: ox axis along the long edge, oy axis perpendicular to            the flattening plane of the brick, oz axis along the short edge of            the brick (which goes inwardly of the wall, in            situ). Each specimen is referred to by a core number (1 to            94), a letter (B for brick) and a specimen number (1 or 2): for            instance 40B1.                                Magnetic measurements, demagnetization and            anisotropy correction            Magnetization measurements have been carried            out in Rennes Laboratory using the “Molspin” spinner magnetometer. Thermal            demagnetizations in zero field and TRM anisotropy determinations            have been performed using the MMTD oven (Magnetic Measurements). Low field            susceptibility was measured after each heating step using a            Bartington MS2 susceptibility-meter (Bartington            instruments) in order to monitor mineralogical changes during            heatings.            Detailed stepwise thermal demagnetization (at            100, 150, 200, 250, 300, 350, 400, 450 and 500°C) was performed on            the first 36 specimens to identify if they contain one or two            components of magnetization. As seen in Figure 3, all of the            specimens present only one magnetization component which            corresponds to the manufacture of the bricks. We consider this is            also the case for the rest of the specimens.            Figure 3:  Demagnetization diagram            (Zijderveld diagram) for specimen 1B1 / Figure            3 : Diagramme de désaimantation (diagramme de Zijderveld) du            spécimen 1B1.                         Thermal step points are aligned to the            origin. This shows that there is only one magnetization component            which corresponds to baking of the brick. / Les            étapes thermiques sont alignées à l'origine. Ceci indique qu'il            n'y a qu'une composante d'aimantation correspondant à la cuisson            de la brique.            The TRM anisotropy tensor was determined on the            same 36 specimens following the procedure described by Chauvin et al. . Four successive heating steps at 450°C            were performed with a laboratory field of 60 µT applied along the            +Z, +X, +Y axis of each specimen. A thermal stability check along            the +Z axis was also performed. The alteration factor (0.6% in            average) determined via the stability check is much less than 5%            for the anisotropy correction to be applied. The principal axes of            anisotropy ellipsoids show that the anisotropy is quite oblate and            correlated to the shape of the bricks. Samples were then            individually corrected for anisotropy using the mean            Eigenvalues:            F13= 1.077 F12= 1.030 F23= 1.046                                Statistical analysis of the TRM            Magnetic measurements and thermal            demagnetizations showed that the set of bricks is homogeneous. The            bricks were produced at the same date and in the same place. The            magnetization directions of the 94 specimens can thus be directly            related to the geomagnetic field prevailing at the time of the            manufacture. Directional results are plotted in Figure 4.            Figure 4: Directional results (inclination,            deviation) for the 94 bricks, plotted in a stereogram. /            Figure 4 : Résultats des directions            (inclinaison, déviation) pour les 94 briques, placés sur un            diagramme stéréo.                        Deviation and inclination histograms,            magnetization magnitude (A/m) and susceptibility (SI) histograms.            Values are concentrated which is typical to a homogeneous set of            bricks. / Histogrammes de la déviation et de            l'inclinaison, histogramme de l'intensité de l'aimantation (A/m)            et histogramme de la susceptibilité (SI). Les valeurs sont            concentrées ce qui est typique d'un lot homogène de            briques.            It is not possible to use the Fisher statistics            for calculating the mean direction because the declination cannot            be determined. The only geomagnetic parameter accessible is the            inclination. Therefore, we use the McFadden statistics applied to            inclination values. With n = 93 specimens, we obtain:                          Site location: Lat. : 45° 50' 48''              North Long. : 0° 46' 14'' East              Inc site = 60.7°              alpha95 (equivalent Fisher) = 1.7°              (directional error)                        In order to convert this mean inclination in            calendar date, it is necessary beforehand to transfer it at the            location of Paris, the place for which the French reference curves            are established. Using the VADM (virtual axial dipole moment)            correction, the mean inclination at Paris becomes:                          Inc Paris = 65.2° ± 1.7°                                            Archaeomagnetic dating results of            bricks            The determination of the inclination allows            conducting archaeomagnetic dating for the manufacture of the            bricks using the ChronoModel 1.5 software (Lanos et al., 2015). The inclination curve used is            the reference secular variation curve at Paris for the last two            millennia calculated with Rencurve software (Lanos, 2004) and            using Gallet et al. (2002) directional            data. As shown in Figure 5, the inclination value at Paris for the            manufacture (last firing) of the bricks corresponds to six time            periods at 95 % confidence level (HPD region):                          [-1000; -799] (26.4%),              [-208; -102] (5.0%),              [-9; 72] (16.0%),              [434; 556] (20.1%),              [934; 1025] (17.1%),              [1527; 1584] (10.3%)                        By combining this data with luminescence dating            results and with the archaeological interpretation, one of these            intervals will be preferred (see part 4).            Figure 5: Dating with ChronoModel 1.5            software, based on the inclination value determined for Paris. /            Figure 5 : Datation avec le logiciel ChronoModel            1.5, en utilisant la valeur de l'inclinaison déterminée à            Paris.                        The mean curve in blue with its confidence            envelop at 95% is the reference secular variation curve at Paris            for the last three millennia. See text for the predicated calendar            dates obtained. / La courbe moyenne en bleu avec            son enveloppe d'erreur à 95 % est la courbe de variation séculaire            de référence à Paris pour les trois derniers millénaires. Voir            texte pour les dates calendaires présumées obtenues.                                    Dating of mortars by optically stimulated          luminescence (SG-OSL)                      Preliminary tests            Preliminary tests consisting in a study of            physical properties of the quartz grains used for OSL dating are            essential to optimize the measurement protocol used for the            determination of the archaeological dose. A plateau test (e.g. Murray and Olley, 2002;            Wintle and Murray, 2006; Medialdea et al.,            2014), a thermal transfer test (e.g. Murray &#38; Olley, 2002;            Jain et al., 2004) and a LM-OSL test were            executed on one sample of the series, BDX 16045, showing the same            luminescent properties and identical chemical and mineralogical            composition with other samples. For the reason of time, these            three measurements were realized by the multigrain technique.            According to the thermal transfer test realized            on the artificially bleached discs, the pre-heat temperatures            lower or equal to 240°C do not provoke a noticeable thermal            transfer (Figure 6a). On the contrary, from the pre-heat            temperature of 260°C a slight increase of the signal is observed            which indicates optical and thermal drainage of electron charge            from the deep traps towards the OSL traps. This tendency was noted            by some other authors for young quartz samples (e.g. Murray and            Clemmensen, 2001; Rhodes, 2000; Madsen et            al., 2007; Medialdea et al.,            2014).            As showed clearly by the LM-OSL measurement,            the OSL signal of Antibes mortars is predominated by the fast            component (Figure 6b), which is a precondition to date mortar by            SG-OSL. The plateau test did not show any            clear dependence of the measured dose on the pre-heat temperature.            The smallest variations of the measured dose between the repeated            measurements seem to correspond to the pre-heat temperature of            240°C as seen in Figure 6c, which was therefore selected for the            archaeological dose determination.            Figure 6 / Figure            6                        a) Thermal transfer test for the mortar            BDX 16045 : the test consists in the measurement of the dose on            artificially bleached discs at several preheat temperatures. Each            point in the graph represents the mean of 6 independent            measurements; b) LM-OSL test for the mortar BDX 16045: the test            reflects the dependence of the measured luminescence on the            stimulation power which is linearly increased during the test. The            classical SG-OSL quartz dating is based on the dominant fast            component detectable during the first seconds of the stimulation;            c) Plateau test for the mortar BDX 16045: the test consists in the            measurement of the archaeological dose at different preheat            temperatures. Each point in the graph represents the mean of 6            independent measurements; d) Histogram of the measured doses from            the recovery dose experiment: CAM = average dose calculated            following the Central age model (Galbraith et            al., 1999), OD = over-dispersion, n = number of measured            grains. / a) Test de transfert thermique pour le            mortier BDX 16045: Le test consiste aux mesures de la dose sur des            disques artificiellement blanchis à plusieurs températures de            préchauffe. Chaque point du graphique représente la moyenne des            six mesures indépendantes ; b) Test LM-OSL du mortier BDX 16045 :            le test consiste à une mesure de la luminescence en fonction de la            puissance de la stimulation qui est linéairement augmentée pendant            le test. La datation par OSL classique est basée sur l’existence            du composant rapide du signal détectable lors des premières            secondes d’excitation ; c) Test de plateau pour le mortier BDX            16045 : Le test consiste aux mesures de la dose archéologique à            plusieurs températures de préchauffe effectuées sur des disques de            multigrain. Chaque point du graphique représente la moyenne des            six mesures indépendantes ; d) Histogrammes des distributions de            doses mesurées pour des grains individuels lors de tests de            recovery. CAM = la dose moyenne calculée en utilisant le modèle            d’âge central (Galbraith et al., 1999), OD = over-dispersion, n =            nombre des grains mesurés.            The recovery dose tests, contrary to three            preliminary tests discussed above, were realized by the single            grain technique on the artificially bleached grains and followed            entirely the measurement protocol used for the archaeological dose            determination described in the section 2. The tests were performed            for all the studied samples (Table 1). The recovery dose histogram            of the sample BDX 16046 which is presented in Figure 6d shows that            the measured individual doses are homogeneously distributed around            the given recovery dose of 9.6 Gy. The average ratio (DR ratio) of            the measured dose to the given recovery dose is 1.04 which enters            into the interval 0.9-1.1 considered generally as an indicator of            a suitable measurement procedure.            Table 1: Number of grains with            signal after the dose recovery, recovery dose calculated using the            Central age model (Galbraith et al., 1999),            over-dispersion values and dose recovery ratios between the            measured dose and the given recovery dose / Tableau 1 : Nombre de grains            avec le signal après la dose de recovery, dose de recovery            calculée en utilisant le modèle d’age central (Galbraith et al.,            1999), valeurs de l’over-dispersion et les rapports entre la dose            mesurée et la dose donnée                                          Sample                Nb of grains with recovery                signal                CAM recovery dose (Gy)                Over-dispersion (%)                DR ratio                                            BDX 16045                41                10.3±0.3                14                1.07                                            BDX 16046                58                10.0±0.2                12                1.04                                            BDX 16047                62                9.9±0.2                8                1.03                                            BDX 16048                53                10.0±0.2                7                1.04                                            BDX 16049                88                9.9±0.1                5                1.02                                                          Archaeological dose determination            To determine the archaeological dose, about            4000 grains per sample were measured. Between 3.9 and 5 % of these            grains emitted a detectable signal. The measurement results are            summed up in the Table 2.            Table 2: Number of analyzed grains, number            of grains emitting an OSL signal and number of grains selected for            the calculation of the archaeological dose, values of average            archeological doses with the standard deviation for each sample            calculated according to Central age model (CAM) and            over-dispersion values describing the spread between individual            archaeological doses within the same sample caused by another            factor than by a statistical uncertainty / Tableau 2 : Nombre de grains            de quartz étudiés, du nombre de grains de quartz ayant montré une            sensibilité suffisante, du nombre de grains retenus pour la            détermination de la dose archéologique, repart de la dose            archéologique mesurée selon le modèle d’âge central (CAM,            Galbraith et al., 1999) avec son écart-type statistique, et le            terme d’over-dispersion qui rend compte de l’accroissement de            dispersion de la distribution des doses lié à d’autres causes            que la seule incertitude statistique des            mesures des doses archéologiques individuelles                                          Sample                Nb of analyzed grains                Nb of grains with OSL                signal                % of grains with OSL                signal                Nb of selected grains                % of selected grains                Archeological dose                (Gy)                Over-dispersion (%)                                            BDX 16045                4085                200                5.0                196                4.1                3.85±0.10                31                                            BDX 16046                3800                193                5.0                180                4.7                3.56±0.09                31                                            BDX 16047                3800                179                4.8                175                4.6                4.60±0.16                43                                            BDX 16048                3990                205                4.9                189                4.7                3.66±0.08                27                                            BDX 16049                4085                163                3.9                152                3.7                3.89±0.13                36                                      Distributions of individual archeological doses            for the series of Antibes mortars seem relatively narrow which            indicates a good degree of bleaching of these mortars. Apart from            some isolated grains with higher doses, all the values are            concentrated around the central dose. For this reason, the central            age model (CAM; Galbraith et al., 1999) is            used to calculate the average archaeological dose. The grains            retained for the calculation meet following selection criteria            (discussed in detail in the article Urbanova &#38; Guibert,            accepted or by other authors: Medialdea et            al., 2013; Sim et al., 2014):                          (a) the relative recycling ratio error              &#60; 25%              (b) the error associated with the TN signal &#60; 25%              (c) the signal higher than 3 sigma              above background                        The application of these criteria eliminates            only a very small number of grains (comparison of the 3rd and 5th column in the Table            2). The selected grains are presented in the below histograms            (Figure 7). Also, we do not observe any dependence between the            relative standard errors and the associated archeological doses,            which is the basic condition to justify the use of the central age            model (CAM) for the calculation of the average archaeological            dose. The relative standard errors vary between 5 and 20 %.            Figure 7: Histograms (a, b, c,d, e) show            the distributions of individual archaeological doses from the            single grain measurements / Figure 7 :            Histogrammes des distributions de doses archéologiques pour des            grains individuels                        The dispersion of the data is caused            probably by the combination of intrinsic variability (occurring            naturally between the single grains) and microdosimetric effects            (see paragraph 3) rather than by insufficient bleaching (that            would show as a long tail at the right side of each distribution,            which is not the case). Average archaeological doses (CAM) and            over-dispersion values (OD) for the number of grains n calculated using the central age model (CAM,            Galbraith et al., 1999). / La dispersion des données résulte probablement de la            combinaison de la variabilité intrinsèque (naturellement existant            entre des grains) et de la variabilité microdosimétrique (voir            paragraphe 3) plutôt que du blanchiment insuffisant (qui se            projetterait dans la distribution des doses comme un queue à            droite). Les doses archéologiques moyennes (CAM) et les valeurs de            l’over-dispersion (OD) pour le nombre de grains n étaient            calculées en utilisant le modèle d’âge central (CAM, Galbraith et            al., 1999).            Since the mortar samples from Grimaldi castle            in Antibes seem to be well-bleached, which is rather rare for            mortar samples (compare with Goedicke, 2003 and 2011, Panzeri,            2013; Urbanova, et al., 2015), the            measurements of the archaeological dose by the classical            multigrain (single aliquot) technique were executed. The            conditions of the analyses were identical to those of the single            grain measurements. Each disc contained about 50 grains.            The results of the multigrain and the single            grain measurements are in a very good agreement. The exception is            the sample BDX 16049 for which the deviation between these two            measurements exceeds their standard errors. Nevertheless, the            general agreement for the whole series of samples is            satisfactory.            Since the samples were analyzed by two            independent OSL techniques (single grain and multigrain), the            average archaeological dose used for the age calculation was            determined for each mortar sample by inverse-variance weighting            associated to each of these measurements. To take into account            possible anomalous deviations (greater than expected by            statistical uncertainties) between the measurements, the            experimental deviation between the single grain and the multigrain            measurement was integrated in the establishment of the measurement uncertainty calculated according            to the following equation (1):                        Where D1 and D2 are average archaeological doses for the single            grain and the multigrain measurement, respectively, σ1 and σ2 the associated            standard deviations, w1 and w2 the corresponding calculated weights and Dm the average archaeological dose calculated by            inverse-variance weighting. For the samples BDX 16048 and BDX            16049, the measurement uncertainty is higher because of the larger            difference between the single grain and the multigrain            measurement. For the final age calculation, the average            archaeological doses in the 6th column of            Table 3 were taken into account.            Table 3: Values of the average            archaeological dose from the single grain measurements, number of            analyzed discs, values of the average archeological doses with the            standard deviation for each sample from the multigrain            measurements, the Euclidian distance between the multigrain and            the single grain measurements and the final value of the average            archaeological dose calculated by inverse-variance weighting with            the associated standard deviation / Tableau            3 : Rappel de la dose archéologique moyenne obtenue par OSL            monograin, nombre de disques multi-grains utilisés selon la            méthode conventionnelle, dose archéologique et écart-type            statistique correspondants, distance euclidienne réduite entre les            mesures monograin et multi-grains, et valeur moyenne finale de la            dose archéologique avec écart-type statistique associé                                          Sample                Archaeological dose monograin                (Gy)                Nb of multigrain discs                Archaeological dose multi-grain                (Gy)                Euclidian distance                (monograin-multi-grain)                Average archaeological dose                (Gy)                                            BDX 16045                3.85±0.10                21                3.78±0.21                -0.30                3.84±0.09                                            BDX 16046                3.56±0.09                24                3.69±0.20                0.59                3.58±0.09                                            BDX 16047                4.60±0.16                22                4.54±0.15                -0.27                4.57±0.11                                            BDX 16048                3.66±0.08                23                4.01±0.16                1.96                3.73±0.11                                            BDX 16049                3.89±0.13                24                3.30±0.10                -3.60                3.52±0.21                                                          Microdosimetry caracteristics            The over-dispersion values associated to the            archaeological (natural) doses are higher (from 27 to 44 %,            Table 1) than the over-dispersion values of dose recovery            measurements (from 5 to 14 %, Table 2). This difference indicates            the presence of some external dispersive factor that provokes this            supplementary variability between the archaeological (natural)            doses. In Urbanova et al. (2015) dealing            with OSL dating of mortars, two principal possible sources of            dispersion of archaeological doses were discussed: heterogeneous            bleaching and differences in dose rate at the grain scale.            However, as seen in the paragraph above, Antibes mortars are            well-bleached, which was confirmed by the agreement of the            multigrain and the single grain measurements. Thick sections of            the studied samples were thus analyzed by SEM-EDX cartography and            beta-imaging system in order to evaluate qualitatively            microdosimetric properties of Antibes mortars. All the samples had            very similar character.            The images from beta autoradiography show quite            an important number of beta emitters that are relatively            homogeneously spread in mortar matrix (Figure 8a). For a better            visual interpretation, these images are presented together with            macroscopic photos of the studied thick sections. The brightest            tiny points correspond probably to apatite minerals identified            sporadically by SEM-EDX analyses.            Figure 8 / Figure            8                        a) Image from beta-autoradiography of the            mortar sample BDX 16048. The brightest spots correspond to the            most intense beta emitters; b) Macroscopic picture of the mortar            sample BDX 16048; c) Observation (x50) of the thin section of the            sample BDX 16048 in cross-polarized light; d) Interpretation of            the SEM-EDX carthography performed on the thick section of the            sample BDX 16048. Each colour corresponds to the most represented            element: in red – silicium (quartz minerals), in blue – potassium            (potassium minerals), en green – calcium (carbonated matrix); e)            Histogram representing the distribution of potassium in the mortar            sample BDX 16048 based on the spot analyses including a radius of            2 mm around the quartz grains used for SG-OSL measurements; f)            SEM-EDX carthography of potassium rich minerals in the sample BDX            16048. The grey level corresponds to the number of X rays emitted            by potassium detected by the instrument. Magnification: 60, pixel            size: 0.03 mm. / a) Images de l’autoradiographie            beta de l’échantillon BDX 16048. Les points plus clairs            correspondent aux endroits plus radioactifs (émissions beta) ; b)            Photos macroscopiques du mortier correspondant ; c) Observation            (x50) de la lame mince de l’échantillon BDX 16045 en lumière            polarisée analysée ; d) Interprétation d’une cartographie            élémentaire par EDX-MEB, effectuée sur la lame épaisse de            l’échantillon BDX 16048. Chaque couleur correspond à un élément            majeur d’un endroit analysé: en rouge – silicium (minéraux de            quartz), en bleu – potassium (minéraux potassiques), en vert –            calcium (liant calcaire) ; e) Histogramme de distribution du            potassium dans le mortier BDX 16048 basés sur les mesures            ponctuelles du rayon de 2 millimètres réalisées autour des grains            de quartz utilisés pour la datation par SG-OSL ; f) Images de            répartition du potassium, obtenues par cartographie EDX-MEB pour            l’échantillon BDX 16048. Le niveau de gris correspond au nombre de            rayons X émis par potassium atteignant le détecteur en fonction            d’un endroit analysé. Grandissement : 60. Taille du pixel : 0.03            mm.             In general terms, the mortars seem to be            homogeneous, fine-grained, containing rather angular grains            smaller than 1 mm in diameter, quartz being the most abundant of            all minerals. Petrographic observations (Figure 8c) confirm a            significant amount of potassium feldspars and micas in the thin            sections of Antibes mortars. All these minerals seem to be            uniformly distributed.            According to the SEM-EDX mapping the mortars            contain a large quantity of K2O rich minerals            (Figure 8d,f) which is in agreement with the petrographic            observations. Point SEM-EDX analyses show that K2O content can vary from 1 to 3 % in different            areas of mortar matrix (Figure 8e), which causes microdosimetric            variations of the dose rate.                                Dose rate            The concentrations of radioelements in the            studied mortar samples determined by low-background gamma            spectrometry (Guibert and Schvoerer, 1991, Guibert et al., 2009) are showed in the Table 4. No            particular relationship between the position of the samples in the            structure and the content of radioelements was observed.            Table 4: Water content taken into account            for age determination and K, U and Th content detected by            low-background gamma spectrometry / Tableau 4 : Mesure de            l’humidité à saturation (% de masse d’eau à saturation par rapport            à la masse de matériau sec), teneurs en K, U et Th déterminées par            spectrométrie gamma à bas bruit de fond                                          Sample                Water content[%]                K[%]                U(238U)[ppm]                U(226Ra)[ppm]                U(210Pb)[ppm]                Th[ppm]                                            BDX 16045                5.0±1.5                1.43 ± 0.03                1.68 ± 0.12                1.77 ± 0.04                1.66 ± 0.21                2.31 ± 0.07                                            BDX 16046                6.0±1.7                1.44 ± 0.03                1.46 ± 0.11                1.81 ± 0.04                1.43 ± 0.19                2.11 ± 0.06                                            BDX 16047                13.0±3.8                1.88 ± 0.03                1.60 ± 0.12                1.86 ± 0.04                1.27 ± 0.21                2.89 ± 0.07                                            BDX 16048                10.0±2.9                1.94 ± 0.03                2.02 ± 0.10                2.36 ±0.04                1.66 ± 0.17                2.67 ± 0.06                                            BDX 16049                13±3.8                1.74 ± 0.04                1.99 ± 0.13                1.42 ± 0.04                1.43 ± 0.24                2.83 ± 0.08                                      210Pb and 226Ra are in disequilibrium. In general, the            activity of 226Ra is higher than the activity            of 210Pb which is interpreted as a continuous            loss of radon since the last 30 years in the corresponding part of            the building. If the castle foundations have never been buried, a            permanent loss of radon since the construction of the structure            can be supposed. Therefore, the ages are estimated taking into            account this hypothesis according to which 210Pb indicates the average activity of 222Rn and its daughters since the erection of the            masonry.            238U and 226Ra are also slightly in disequilibrium. Whereas            the U/Th ratios indicate low variability, variability of Ra is            according to the Ra/Th ratios much more important (Table 4). The            number of samples is insufficient to interpret with absolute            certainty the cause of the mentioned disequilibrium (contrary to            some other studies such as Guibert et al.,            2009). Nevertheless, since the 226Ra content            varies more than the 238U content, a            hypothesis of the Ra alteration rather than of the U alteration            can be raised (as observed for example on the series of bricks            from the church St Martin in Angers; Blain et            al., 2011).            We assumed that the whole series of Antibes            mortars was affected by the same alteration phenomenon. The            influence of different possible alteration phenomena on the dose            rate values was tested by applying two disequilibrium models (each            of them for two different kinetics laws):            1. The disequilibrium is due to a mobility of            uranium isotopes                          We suppose that the disequilibrium is              inherited from raw material at the moment of the mortar              preparation. In this case, the disequilibrium is considered              constant (the age of mortar is much younger than the half-life              of 75200 years of 230Th) and the measured              activities of 238U, 226Ra and 210Pb represent              the average activities since the fabrication of              mortar.              We suppose that the disequilibrium is              recent. Here the alteration process took place quite recently              with regard to the age of the samples. The U content would be              thus represented by the 226Ra              activity.                        2. The disequilibrium is due to a mobility of            radium                          We suppose that the disequilibrium is              inherited from raw material at the moment of the mortar              preparation. The radioactive period for 226Ra (1600 years) is similar to the age of the              samples. It cannot be assumed that the radium concentration              remained constant during the existence of the dated structure.              The progressive return of 226Ra to              equilibrium since the fabrication of mortar was thus assumed. In              this case, the significant indicator of radioactivity during the              existence of the masonry is the average content of U(226Ra). The loss of 222Rn              was considered constant through time and the mean activity of              222Rn and its daughters was recalculated              with this average Ra activity respecting the ratio 210Pb/226Ra              measured.              The Ra disequilibrium is recent. Here              the alteration which took place quite recently with regard to              the age of the samples has modified all the U chain beginning              with 226Ra. The Ra content would be thus              deduced from the 238U activity. Following              the same assumption as for the preceding case, the average              activity of radon and the daughters was calculated respecting              the ratio 210Pb/226Ra              measured.                        The annual dose was determined according to            these four scenarios (Table 5) using the content/annual dose            conversion factors published by Guérin et al.            (2011). It was considered that only the α and β internal            components were affected by this disequilibrium, whereas the            external γ and cosmic doses measured by dosimetry were assumed            constant. As a result, the annual dose does not seem to vary            significantly with regard to the origin of the disequilibrium and            its duration. Negligible variability is related mainly to the fact            that the contribution of uranium to the annual dose rate takes a            minor part. Also, a combination of relative values of U(226Ra), U(238U) and U(210Pb) lead to the values that are very            similar.            Table 5 / Tableau            5                        For each contribution, the annual dose is            calculated following four scenarios of disequilibrium described in            the text (uncertainty = 1 std deviation). OSL age and            corresponding global standard deviation are expressed in years            (with regard to the year of analyses being 2014) and presented            rounded to the closest ten. Statistical component of the standard            deviation is indicated in brackets. / La dose            annuelle absorbée en moyenne par les grains de quartz des mortiers            étudiés dans ce travail a été calculée pour chaque composante les            valeurs de dose annuelle selon les 4 scénarios de déséquilibre au            niveau de l’uranium et du radium explicités dans le texte. L’âge            OSL exprimé en années (par rapport à la date de l’analyse, 2014)            est présenté arrondi à la dizaine d’années la plus proche, associé            à son incertitude globale (estimée à un écart-type), elle aussi            exprimée en années. Entre parenthèses, nous avons indiqué la            composante statistique de l’écart-type.             The Table 5 sums up all the contributions to            the annual dose rate. The uncertainty associated to each value of            the annual dose rate represents a standard deviation resulting            from the quadratic combination of statistical uncertainties            (counting statistics of gamma spectrometry measurements, the OSL            measurement error, the dosimetry measurement error) and systematic            errors. Among the latter ones, the uncertainty on the measurement            of humidity, which is proportional to porosity of the material,            represents an important part to be taken into account.            The major part of the uncertainty on the α            component originates from the estimation of α efficacy factor            (k-value). Finally, for the contribution of environment, a            supplementary uncertainty representing 5 % of the measured value            was added with regard to potential non-identified variations            affecting the masonry in time. This uncertainty is included in the            determination of a systematic error. The environmental dose rate            is constant and rather low for the mortar samples taken from the            parts further from the brick courses, whereas the mortar sample            BDX 16047 originating from the zone located in the close            neighborhood with bricks being naturally more radioactive than            stones shows much higher value.                                SG-OSL dating results of mortars            The final OSL ages of Antibes mortars are            presented in the Table 6. The uncertainties associated to the            SG-OSL ages correspond to the estimation of the total standard            deviation resulting from a quadratic combination of statistical            and systematical uncertainties. The statistical part of the            uncertainty is indicated in brackets. The maximum differences            between the ages of each sample calculated following the four            scenarios defined for the disequilibrium of uranium series are not            very important: 10 years for BDX 16045, 20 for BDX 16047, 30 for            BDX 16048, 40 for BDX 16046 and 70 for BDX 16049 (Table 5). The            ages evaluated according to the scenario of the ancient            disequilibrium of uranium were taken into account to determine the            final OSL age of the masonry that was calculated by            inverse-variance weighting of five individual ages.            Table 6: Average OSL age and date of the            construction of Grimaldi castle foundations in Antibes / Tableau 6 : Âge et date OSL            moyenne des échantillons de mortier prélevés sur les fondations            romaines du Château Grimaldi à Antibes                                          Sample                OSL age                Global uncertainty                Statistical                uncertainty                Weighting                Reduced euclidian d                                            Bdx 16045                2102                100                58                0.240                2.05                                            Bdx 16046                2078                104                61                0.217                1.56                                            Bdx 16047                2000                137                58                0.240                0.29                                            Bdx 16048                1800                110                58                0.240                -3.16                                            Bdx 16049                1833                156                114                0.062                -1.32                                            Average weighted                age                1983                115                62                                                                            Average weighted                date                31                AD                                                                      Information presented in the table            includes: global and statistical uncertainties associated to the            OSL ages, a relative weight of each OSL age for the calculation of            the average OSL age and reduced Euclidian distances between            individual OSL ages and the average OSL age. /            Nous avons précisé l’incertitude globale            associée aux âges, ainsi que leur incertitude statistique, la            pondération relative à chaque résultat pour le calcul de la            moyenne et les distances euclidiennes réduites entre les âges            individuels et la valeur moyenne.            The SG-OSL results obtained for mortar samples            from Grimaldi castle foundations served as input data for testing            the accuracy of a Bayesian central-dose model for single-grain OSL            published by Guérin et al. (2015). At the            present time we have slight but not significant differences in the            single grain data between Guérin’s 2015 paper and the present one.            The dose rates in Guérin’s article were calculated without taking            into account the disequilibrium in uranium series. In addition,            the grains with relative uncertainties higher than 30 % were not            included in the determination of the central dose (CAM), so the            number of grains presented in Guérin et al.            (2015) is slightly lower than the number of grains presented in            this paper. The small differences in the data evaluation resulting            from the methodological progress do not provoke significant            differences between the ages presented in these two papers.            The mortars from Grimaldi castle in Antibes            contain quartz aggregate that was well bleached at the moment of            the construction of the building and could have been therefore            easily dated. The good degree of bleaching was demonstrated by a            perfect agreement of the single grain and the multigrain            measurements. The dating results for five mortar samples taken in            different parts of the wall MR 10003 are coherent.                                4. Chronological synthesis and        conclusion        The chronology determining the construction of the        Grimaldi castle foundations results from four independent dating        approaches:                  archaeological analysis of the ceramic          shard found in the upper part of the circular pit located under the          dated masonry reveals the terminus post quem          60-100 A.D. for the construction of the masonry.          archaeomagnetic dating of the series of 94          bricks (Figure 5)          single grain OSL dating of 5          mortars          multigrain OSL dating of the same 5          mortars.                In order to determine a chronological interval of        the construction of the masonry by taking into account all the data        and their relationships, the results of archaeomagnetic dating and OSL        dating were associated to the same event: the construction of the        wall. The bricks are therefore supposed to have been used directly        after their manufacture. This event was considered as subsequent to        the terminus post quem revealed by        typo-chronological dating of the ceramic shard.        A statistical combination of all the data was        performed by means of the ChronoModel procedure (Lanos et al., 2015) at 95% confidence level. The Figure 9        shows the process of data evaluation. The Figures 9a and 9h show final        chronological intervals of the construction of the Grimaldi castle        foundations and terminus post quem,        respectively. The Figures 9b-g and 9i are the results of the        overlapping of:                  a priori probability          distributions of the dating results which are deduced from the          measurements          a posteriori          probability distributions of the chronological intervals resulting          from the combination of all the data                The analysis shows that between four intervals        determined by archaeomagnetic dating (Figure 9b) [-9 BC, +72 A.D.] is        clearly preferred when put in relation with the OSL and the        archaeological results. The probability distributions of different        mortar samples dated by OSL are overlapping, which indicates good        coherence between the individual dating results (Figures 9c-g).        The results indicate that the Grimaldi castle        foundations were constructed between 30 and 220 A.D. at 95% confidence        level. The probability distribution (Figure 9a) is not symmetrical due        to the chronological constraint imposed by the backfilling of the        circular pit (terminus post quem). The        probability reaches the maximum at the year 97 A.D. with the median        value of 105 A.D and the chronological interval spreads up to 220 A.D.        The upper limit is only the result of the combination of OSL and        archaeomagnetic data since no terminus ante        quem (apart from the stratigraphic units from 17th and 18th century) that would        affect the probability distributions on the right side is known.        Figure 9: Presentation of the ChronoModel        procedure (Lanos et al., 2015) at 95 %        confidence level / Figure 9 : Présentation de la        procedure ChronoModel (Lanos et al., 2015) à 95 % de        probabilité                a: a posteriori        interval of the construction Event of the castle foundations; b:        archaeomagnetic dating results for the studied brick set: calibrated        distribution (line) and a posteriori        distributions (light grey color); c-g: SG-OSL dating results for each        mortar sample (a priori and a        posteriori probability distributions); h: final chronological        interval for the terminus post quem of the        construction of the castle foundations; i: archaeological hypothesis        (probability distribution) for the terminus post        quem of the construction of the castle foundations. / a : distribution de probabilité a posteriori du fait        « construction » des soubassements du château ; b : résultats de        datation par l’archéomagnétisme pour la série des briques étudiées :        distribution calibrée (ligne) et distribution de probabilité a        posteriori (gris clair) ; c-g : résultats de datation par SG-OSL pour        chaque échantillon du mortier (distributions de probabilité a priori        and a posteriori ; h : intervalle chronologique final pour le terminus        post quem de la construction des soubassements du château ; i :        hypothèse archéologique (distribution de probabilité) pour le terminus        post quem de la construction des soubassements du château.        In the given context, none of the dating approaches        used would have succeeded to date accurately the construction of the        castle foundations if they were used separately. For archaeomagnetism,        archaeological hypotheses and luminescence dating of mortar enabled to        select the most likely chronological interval for the production of        bricks. For single grain OSL dating, the archaeological hypotheses and        the archaeomagnetic results allowed to validate this new method of        mortar dating. For archaeology, the physical methods helped to confirm        the initial hypothesis on the construction of the castle foundations.        To conclude, thanks to the mutual comparison of the dating results        originating from four different approaches, the reliable chronology        for the construction of the Gallo-Roman structure whose remains are        still visible, as well as the foundations of Grimaldi castle in        Antibes could have been established. Our interdisciplinary approach        proves ancientness of the standing masonry and attests cultural and        historical significance of the monument.