Agnes Genevey

Claudia Principe

Yves Gallet

Maxime Giuseppe Clemente

Le Goff

Alexandre Fournier

Pasquino Pallecchi

Agnès Genevey

Maxime Le Goff

Refining the high-fidelity archaeointensity curve for western Europe over the past millennium: analysis

Keywords: Archaeomagnetism, Archaeointensity, Palaeomagnetic secular variation, Italy, Western Europe, Past Millennium

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Introduction

Due to its active volcanoes and particularly rich cultural heritage, Italy can certainly be viewed as a privileged "playground" for palaeomagnetists to trace back recent variations of the Earth's magnetic field. Analysis of lava and pyroclastic flows emitted by Italian volcanoes has enabled important steps in understanding and describing the main lines of the geomagnetic directional variations over the past few millennia (e.g. [START_REF] Sodi | Secular variation of the geomagnetic field direction recorded in lavas from Etna and Vesuvius during the last two millennia[END_REF][START_REF] Tanguy | Archaeomagnetic dating of Mediterranean volcanics of the last 2100 years: validity and limits[END_REF][START_REF] Tanguy | Mount Etna eruptions of the last 2,750 years: revised chronology and location through archaeomagnetic and 226 Ra-230 Th dating[END_REF][START_REF] Tanguy | New archaeomagnetic and Ra-226-Th-230 dating of recent lavas for the Geological map of Etna volcano[END_REF][START_REF] Principe | Chronology of Vesuvius' activity from A.D. 79 to 1631 based on archaeomagnetism of lavas and historical sources[END_REF][START_REF] Arrighi | Eruption of the last 2200 years at Vulcano and Vulcanello (Aeolian Islands, Italy) dated by high-accuracy archaeomagnetism[END_REF]Vezzoli et al. 2009;Branca et al. 2015a).

Additionally, these studies further allowed re-dating of some lava flows -in the case of Mount Etna and Vesuvius, these archaeomagnetic constraints were ultimately incorporated for drawing their respective most recent geological map, underlining the potential of such studies for the comprehension of volcanic edifices (Branca et al. 2015b;[START_REF] Paolillo | Volcanology of the South-Western sector of Vesuvius, Italy[END_REF] On the other hand, during the past 15 years or so, there has been in Italy a dynamic development of archaeomagnetic research sensu stricto. New archaeodirectional data were acquired from in situ fired structures, which, together with volcanic data, have allowed a continuous and accurate description of the main lines of the geomagnetic directional variations in the Italian Peninsula from 1200 BC onwards (see the compilation of [START_REF] Tema | Archaeomagnetism in Italy: a compilation of data including new results and a preliminary Italian secular variation curve[END_REF] updated in 2011 by Tema, and new results acquired since then: [START_REF] Malfatti | Archaeomagnetic Directional Investigation of a Metallurgical Furnace in Pisa (Italy)[END_REF][START_REF] Kapper | Linking site formation processes to magnetic properties. Rock-and archaeomagnetic analysis of the combustion levels at Riparo Gaban (Italy)[END_REF]Tema et al. 2016).

In contrast, archaeointensity data in Italy remains very few, despite recent progress.

Only 31 results are currently available for a large time interval of eight millennia, with a quite uneven temporal distribution [START_REF] Evans | Paleointensity estimates from Italian kilns[END_REF](Evans , 1981;;[START_REF] Aitken | Determination of the intensity of the Earth's magnetic field during archaeological times: Reliability of the Thellier technique[END_REF][START_REF] Hedley | A magnetic investigation of roman andpre-roman pottery[END_REF][START_REF] Hill | An archaeomagnetic investigation of a Roman amphorae workshop in Albinia (Italy)[END_REF][START_REF] Hill | Archaeomagnetic investigation of bricks from the VIIIth-VIIth century BC Greek-indigenous site of Incoronata (Metaponto, Italy)[END_REF][START_REF] Donadini | Archaeointensity determinations from Finland, Estonia, and Italy[END_REF][START_REF] Gallet | On the use of archaeology in geomagnetism, and vice-versa: Recent developments in archaeomagnetism[END_REF][START_REF] Tema | Archaeointensity determination from Italy: new data and Earth's magnetic field strength variation over the past three millennia[END_REF]Tema et al. , 2013Tema et al. , 2016 see also Tema et al. 2011). A few other archaeointensity results were obtained in Italy, but they mostly relied on archaeomagnetic dating, and for this reason they were not further considered in this study (e.g. Tema et al. 2015;[START_REF] Principe | Archaeomagnetic dating of Copper Age furnaces at Croce di Papa village and relations on Vesuvius and Phlegraean Fields volcanic activity[END_REF]. Most of the available results (21) are dated between the 3rd century BC and the 8th century AD, with a strong concentration of data (12) between 100 BC and AD 100. Three archaeointensity results were recently obtained for the Early Neolithic period (c. 7500 years ago; Tema et al. 2016), two results are dated for the 8th century BC and the five remaining results of 31document the past five centuries. New archaeointensity data are thus required before a full description of the geomagnetic field variations in Italy over the past two to three millennia can be achieved.

This study aims to contribute to this long-term project with the archaeointensity analysis of groups of brick fragments collected in and around Pisa. Fourteen brick buildings dated from between the middle of the 12th century and the end of the 17th century were sampled. From a broader geomagnetic perspective, this study also addresses the issue of the maximum time resolution of the recording of the geomagnetic field intensity variations accessible from archaeomagnetic data. This is particularly important as several short-term (maximum of two centuries) intensity peaks have been proposed over the past millennium in Western Europe from a dense set of French data [START_REF] Genevey | Evidence for rapid geomagnetic field intensity variations in Western Europe over the past 800 years from new archaeointensity French data[END_REF][START_REF] Genevey | Geomagnetic field intensity variations in Western Europe over the past 1100 years[END_REF][START_REF] Genevey | New archaeointensity data from French Early Medieval ceramic production (6th-10th century AD). Tracing 1500 years of geomagnetic field intensity variations in Western Europe[END_REF]. The intensity variation rates associated with these peaks are quite strong (~0.10 µT/yr), similar to the maximum rate observed in the recent field (e.g. [START_REF] Livermore | Core-flow constraints on extreme archaeomagnetic intensity changes[END_REF].

Description of the historical baked-brick buildings investigated

Since the Middle Ages, Pisa and its province have been an important area in Tuscany for ceramic production, particularly using clay from the Arno River and the Serchio River [START_REF] Clemente | Fornaci da mattoni e fornaciai a Pisa tra XV e XVI secolo attraverso le fonti documentarie[END_REF][START_REF] Clemente | Ceramisti e produzione ceramica a Pisa tra Medioevo ed età Moderna[END_REF]. Bricks are still produced in Pisa, and numerous buildings made of bricks were built during the past eight centuries of Pisa's history.

Our sampling focused on the baked-brick architectural heritage of the city of Pisa and its neighbouring territory, encompassing almost five and a half centuries, from the middle of the 12th century to the end of the 17th century. It thus explores the history of Pisa from its apogee as a maritime and commercial power to its decline at the end of the 13th century, followed by a lengthy period under the domination of Florence.

We selected a series of fourteen ensembles of bricks based on careful analysis of available historical and archaeological data, incorporating documentary, iconographic and cartographic sources. In one case, the year of inauguration was directly inscribed on the building (Figure 1a,b). All bricks were collected from important buildings commissioned by the political and/or religious authorities. Even though the year of construction/inauguration of such buildings do not necessarily correspond exactly to the year of production of the bricks, it is nevertheless certain that the time lag between their production and their use was very short (most probably less than a year). According to historical and archaeological evidence, the bricks used were produced specifically for each construction and were not recycled, also because the quantities of bricks required were extremely high. Furthermore, in order to avoid the sampling of possibly re-used bricks, we have taken great care to take all our samples from parts of the walls characterized by homogeneous bricks in terms of colour, aspect, and dimension. No damaged brick, particularly with traces of burning or chipped portions, were sampled. In addition, to ensure that the sampled bricks had a size characteristic of the expected period, we used mensiochronology, a chronological tool based on the temporal evolution of brick size (e.g. [START_REF] Castillo | La mensiocronologia dei laterizi della Toscana: problematiche e prospettive della ricerca[END_REF]. Although this tool requires improvement, it was observed that the thickness of the bricks gradually decreased from ~6 cm around 1200 to ~4 cm at ~1700 (Quiros [START_REF] Castillo | La mensiocronologia dei laterizi della Toscana: problematiche e prospettive della ricerca[END_REF]. Furthermore, our selection of sites was dictated by their accessibility to our sampling (Table 1). This sampling was performed using a portable driller. Between 10 and 16 cores were taken per group, and the holes were later filled with tinted mortar in order to restore the visual aspect of the sampled walls as much as possible (Figure 1c,d,e).

Nine groups were collected in Pisa. The two oldest (Pise11 and Pise12) are from the medieval ramparts built between the middle of the 12th century and the 14th century. These are largely preserved and still partly surround the historical centre of the city. Drilling was performed on the same wall located on the edge of the present Scotto Garden (south bank of the Arno River), where two different phases of construction of the rampart are observed [START_REF] Gattiglia | Archaeologia e storia delle trasformazioni di un'area urbana a Pisa tra XI e XX secolo[END_REF]. The construction of this medieval wall was initiated in AD 1155 and the bricks of group Pise12 document this first phase, as confirmed by their thickness, between 6.5 and 7.5 cm, larger than the one observed since. The second, more recent, sampled phase (Pise11) dates from the first half of the 14th century -i.e., the end of the construction of the city wall [START_REF] Castillo | La mensiocronologia dei laterizi della Toscana: problematiche e prospettive della ricerca[END_REF].

Two groups were sampled in the Florentine fortress located in the same area of the Scotto Garden. This large building was erected during the middle of the 15th century (AD 1440), after the end of the Pisan Republic and under Florentine domination [START_REF] Gattiglia | Archaeologia e storia delle trasformazioni di un'area urbana a Pisa tra XI e XX secolo[END_REF]. The first group of samples (Pise10) collected in the Santa Barbara tower (northern part of the fortress) dates from its construction, whereas the second group from the Sangallo bastion (Pise09; north-western part near the Florentine bridge over the Arno River, inside the Corsini building) corresponds to a renovation phase, during AD 1531-1533, which occurred after a short period of revolt in Pisa and its subsequent reconquest by Florence.

Another group (Pise02) was collected from the Oratory of San Bernardino, which was built at the end of the 15th century to ward off epidemics of medieval plague [START_REF] Sodi | L'Oratorio di S. Bernardino e la sua confraternita[END_REF].

In addition to group Pise09, three other archaeomagnetic groups allow us to document the 16th century. Group Pise01 was collected from the hydraulic regimentation structure of the 'Bocchette', positioned at the entrance of a canal built during the years of Cosimo I de' Medici's government and located a little to the east of the city (Figure 1a,b). This structure was constructed to divert excess waters of the Arno River towards the Pisan plain, thus avoiding devastating flooding inside the city [START_REF] Ciuti | Pisa Medicea. Itinerario Storico Artistico tra Cinquecento e Seicento[END_REF]. Group Pise08 was sampled in the important structure of the Medici arsenal, built between 1543 and 1563 on the banks of the Arno River towards its mouth [START_REF] Ciuti | Pisa Medicea. Itinerario Storico Artistico tra Cinquecento e Seicento[END_REF]. Our sampling concerns a well-known renovation phase carried out few years later in 1588. The third group (Pise06) was sampled in the structure of the Medici aqueduct, the construction of which was decided upon by Grand Duke Ferdinando I de' Medici. This aqueduct provided Pisa with fresh and drinkable water from the source, located near the little town of Asciano in the Monti Pisani area [START_REF] Gasperini | a cura di, Il Principe, la città, l'acqua[END_REF]. This archaeomagnetic fragment group was collected in a pillar of the terminal segment of the structure.

In Pisa, the 17th century is represented by a group of fragments collected from the Santo Stefano Dei Cavaleiri church located in the city centre. Although it was founded around the middle of the 16th century under the direction of Cosimo I de' Medici, some parts of its external walls are more recent and precisely date to 1683-1691 [START_REF] Sodi | Secular variation of the geomagnetic field direction recorded in lavas from Etna and Vesuvius during the last two millennia[END_REF], where archaeomagnetic group Pise07 comes from.

Five more groups of fragments were collected in the province of Pisa. The first group (Tosc03) dates from the second half of the 13th century and was sampled in a tower of the castle of Calcinaia, a small medieval city of the Pisan plain along the Arno River (17 km from Pisa), that was built and fortified by the Pisans [START_REF] Alberti | a cura di, Dal castello alla "terra murata[END_REF]. A second group (Tosc04) was precisely dated to 1331, as ascertained by archives, and was drilled in the external wall of the church of Marti in the municipality of Montopoli Valdarno [START_REF] Febbraro | La pieve di S. Maria Novella di Marti. Spunti interpretativi per una conoscenza dell'architettura in laterizi nel Valdarno inferiore[END_REF]. Finally, three archaeomagnetic fragment groups were also sampled in other segments of the Medici aqueduct dated to slightly more recent ages (first half of the 17th century) than group Pise06 located in Pisa, because of later construction and/or a renovation. Group Pise03 comes from the start of the aqueduct (cistern of Ascabo Pisano, Figure 1c), while Pise04 and Pise05, drilled from the arch, come from intermediate but close segments along its path.

A total of 179 cores were drilled from the 14 archaeomagnetic sites described above, and they were subjected to archaeointensity experiments.

Archaeomagnetic investigation and brick composition

The intensity experiments were carried out using three Triaxe magnetometers housed at the paleomagnetic laboratory of the Institut de Physique du Globe de Paris (IPGP), of which one belongs to the Laboratoire d'Archéologie Moléculaire et Structurale (LAMS).

The Triaxe protocol has been specially designed to take advantage of the specificities of this equipment, which allows the three magnetisation components of a small specimen (less than 1 cm 3 in volume) to be measured continuously up to high temperatures, either in a zero field or in a laboratory field, whose intensity and direction are controlled (Le [START_REF] Goff | A new three-axis vibrating sample magnetometer for continuous high-temperature magnetization measurements: applications to paleo-and archaeo-intensity determinations[END_REF]. This procedure, derived from the Thellier and Thellier (1959) method, was detailed in previous papers (e.g. [START_REF] Gallet | High-temperature archaeointensity measurements from Mesopotamia[END_REF][START_REF] Genevey | Evidence for rapid geomagnetic field intensity variations in Western Europe over the past 800 years from new archaeointensity French data[END_REF][START_REF] Hartmann | Archaeointensity in Northeast Brazil over the past five centuries[END_REF].

Table 2 summarises the five heating and cooling steps involved in the Triaxe procedure, which are carried out between a low temperature, T1 (between 110 °C and 150 °C), and a high temperature, T2, chosen such that a large part of the natural remanent magnetization (NRM) is involved. Here, T2 was fixed between 400 °C and 450 °C, as almost total demagnetisation was achieved at this temperature.

The ancient geomagnetic field intensity is inferred from the series of measurements of steps #1, #3 and #5 (with increasing temperatures) -more precisely, from the averaging of the R'(Ti) data computed over the temperature range where the primary component is isolated.

Each R'(Ti) value is equal to the ratio, multiplied by the applied laboratory field intensity, between the demagnetised fractions of NRM (step #1) and thermoremanent magnetisation (TRM; step #5) between T1 and Ti, with both fractions being corrected from the thermal variations of the NRM fraction still blocked at T2 (step #3) (see discussion in [START_REF] Goff | A new three-axis vibrating sample magnetometer for continuous high-temperature magnetization measurements: applications to paleo-and archaeo-intensity determinations[END_REF]). When a second component is observed, the R'(Ti) data are computed from a higher temperature referred to as T1' up to T2.

It should be emphasised that this protocol takes into account the anisotropy of the thermoremanent magnetisation since the laboratory field direction is automatically chosen so as to induce a TRM parallel to the original NRM (Le [START_REF] Goff | A new three-axis vibrating sample magnetometer for continuous high-temperature magnetization measurements: applications to paleo-and archaeo-intensity determinations[END_REF]). Additionally, it was experimentally observed that the Triaxe protocol allows the cooling-rate effect to be overcome when the intensity values are derived from the R'(Ti) data. This characteristic was verified for different archaeological collections of various ages and origins from the Near East, Europe, Russia and Brazil (Le [START_REF] Goff | A new three-axis vibrating sample magnetometer for continuous high-temperature magnetization measurements: applications to paleo-and archaeo-intensity determinations[END_REF][START_REF] Genevey | Evidence for rapid geomagnetic field intensity variations in Western Europe over the past 800 years from new archaeointensity French data[END_REF][START_REF] Genevey | Geomagnetic field intensity variations in Western Europe over the past 1100 years[END_REF][START_REF] Hartmann | Archaeointensity in Northeast Brazil over the past five centuries[END_REF][START_REF] Hervé | Fast geomagnetic field intensity variations between 1400 and 400 BCE: new archaeointensity data from Germany[END_REF][START_REF] Salnaia | New archaeointensity data from Novgorod (North-Western Russia) between c. 1100 and 1700 AD. Implications for the European intensity secular variation[END_REF]. Finally, it is worth noting that an effect of multidomain grains (if any) would be mitigated with this protocol since the laboratory magnetisation acquired from T2 is almost a full TRM.

The Triaxe results were assessed on the basis of selection criteria presented in Supplementary Table 1 (see also e.g. [START_REF] Genevey | New archaeointensity data from French Early Medieval ceramic production (6th-10th century AD). Tracing 1500 years of geomagnetic field intensity variations in Western Europe[END_REF]. Firstly, they allow us to judge the quality of the determination at the specimen level, checking both the directional and intensity behaviours. Two specimens per fragment must then be successfully investigated, and their results must agree within a limit of 5%. A mean value is computed at the site level when deriving from at least three different fragments, and its standard deviation must be less than 5 µT and 10% to be retained. The consistency of the results is thus tested at both the fragment and group levels. The relevance of these criteria, and those related to the selection of archaeological artefacts, was in fine further tested through the consistency of the intensity values obtained between sites of similar age.

For those groups of fragments successfully analysed for intensity, the magnetic mineralogy was explored through progressive thermal demagnetisation of three orthogonal isothermal remanent magnetization (IRM) acquired on cubic specimen (of side 1 cm) in high (1.5 T), medium (0.4 T) and low (0.2 T) fields [START_REF] Lowrie | Identification of ferromagnetic minerals in a rock by coercivity and unblocking temperatures properties[END_REF]). The IRM was imparted using a MMPM10 pulse magnetiser, while the magnetisation measurements were carried out using a JR-6 spinner (Agico) magnetometer. One fragment per site was subjected to these experiments. In addition, magnetic susceptibility measurements were performed for at least two fragments per site along a heating-cooling cycle between 20 °C and a high temperature chosen close to temperature T2 considered for the Triaxe experiments (here 400 °C-450 °C).

These experiments aimed to confirm the thermal stability of the magnetic mineralogy on the same temperature range involved in the intensity analysis. The measurements were performed using a KLY-3 Kappabridge coupled to a CS3 unit (Agico). Note that in our previous studies (e.g. [START_REF] Hartmann | New historical archaeointensity data from Brazil : Evidence for a large regional non-dipole field contribution over the past few centuries[END_REF][START_REF] Genevey | New archaeointensity data from French Early Medieval ceramic production (6th-10th century AD). Tracing 1500 years of geomagnetic field intensity variations in Western Europe[END_REF], these experiments were systematically conducted on all the fragments retained in intensity. Here, this has not been the case because the magnetic susceptibility versus temperature curves were found to be almost identical for the entire collection (see below).

Brick fragments were further analysed in the laboratory of the Archaeological Superintendence of Florence in order to define their composition. After a first description by means of a Nikon SMZ800 stereo-microscope, thin sections of about 30 µm were analysed using a Leitz Ortoluz POL polarising microscope connected to a DIGIMAT image processor in order to define their petrographic paragenesis and textures, and microanalyses were also carried out using an FEI Quanta 200 electronic microscope connected to a EDX Edax DX-4 spectrometer in order to explore the chemical composition variability.

Results

One important feature of this collection of brick fragments is its remarkable homogeneity in terms of paleomagnetic behaviour. This behaviour is characterised by an almost total thermal demagnetisation of the NRM at relatively low temperatures -i.e., around 400 °C-450 °C, with a single magnetization component isolated from 135°C-220°C up to the highest temperatures (Supplementary Table 2). This collection also appears to be very suitable for intensity experiments. Indeed, of the 149 fragments investigated using the Triaxe magnetometers, only 24 fragments were rejected, leading to a very good success rate of 84% (Supplementary Table 2). For 11 groups of fragments, this percentage ranges from 80% to 100% at the group level, while it is more modest, between 45% and 55%, for the other three groups. It is worth noting that these percentages refer to the fragments whose magnetisation was strong enough in relation to the Triaxe sensitivity; 27 fragments were found to be too weakly magnetised. The retained specimens (Supplementary Table 2) possess a NRM between 30 and 700 10 -8 A.m 2 with a NRM below 250 10 -8 A.m 2 for 90% of the collection. For 14 fragments, failures in intensity experiments were linked to a non-ideal behaviour during the thermal treatment, as illustrated in Figure 2a by the Tosc04-04B specimen. For this specimen (and corresponding fragment), the R'(Ti) data decrease continuously all over the temperature interval investigated, although only one magnetisation component is observed (Figure 2b), which prevents the recovery of a reliable intensity of the ancient magnetic field.

By contrast, the Pise04-05A specimen displays an appropriate behaviour for intensity determination, with quasi-constant R'(Ti) data observed over the temperature range where the primary component is isolated (Figures 2a,c). The other reason for rejection is related to the non-fulfilled coherence test at the fragment level (10 fragments).

The very homogeneous magnetic behaviour above is associated with an almost identical magnetic mineralogy for the whole collection of fragments (at least for the fragments successfully analysed for intensity). The three-axis IRM curves show a systematic predominance of low coercivity (<0.2 T) minerals, with unblocking temperatures ranging from 450 °C to 600 °C, which are likely to be from the magnetite family with impurities of various contents (Figure 3). The thermal demagnetisation of the 1.5-T IRM also shows the presence of a small fraction of high-coercivity minerals, likely being hematite. For some fragments, we observe a fraction of minerals with unblocking temperatures below 200 °C-250 °C and high coercivity, which probably indicates the presence of epsilon iron oxide, as recently identified by López-Sánchez et al. (2017, Figure 3). The susceptibility vs temperature curves, although providing no additional information on the magnetic mineralogy, also emphasise the homogeneity of the collection, as well as the thermal stability of the magnetic mineralogy over the temperature range used for intensity determinations (inserts in Figure 3). This consistency in the magnetic response to all the experiments above is most probably due to the use of the same raw material.

A total of 276 specimens associated to 125 brick fragments were successfully analysed for intensity. This allowed 14 new mean well-defined intensity values (Table 1) to be derived. This is illustrated in Figure 4, where each panel displays for one group all the results obtained at the specimen level.

The homogeneity of this archaeological collection is further supported by petrographic and spectrometric measurements. The original clayey material contains silicate debris attributable to quartz in both single crystal and polycrystalline aggregate forms with a sub-angular to angular morphology. There is no addition of sandy sediments, as would be the case if the material source was along the course of the Arno River. The absence of fine silt and of well rounded clasts also militate against a supply of clay from the small quarries that were active in Pisa from at least the 13th century [START_REF] Clemente | Fornaci da mattoni e fornaciai a Pisa tra XV e XVI secolo attraverso le fonti documentarie[END_REF][START_REF] Clemente | Ceramisti e produzione ceramica a Pisa tra Medioevo ed età Moderna[END_REF]. On another hand, it should be noted that the huge quantity of clay necessary for the construction of the large buildings studied likely exceeded the resources of these small in-town quarries [START_REF] Clemente | Fornaci da mattoni e fornaciai a Pisa tra XV e XVI secolo attraverso le fonti documentarie[END_REF][START_REF] Clemente | Ceramisti e produzione ceramica a Pisa tra Medioevo ed età Moderna[END_REF].

In contrast, the quartz and the other silicate (feldspars, micas) components are typical of alluvial deposits coming from the eastern part of the Monti Pisani sedimentary succession [START_REF] Carratori | Carta 1:50.000 degli elementi naturalistici e storici della pianura di Pisa e dei rilievi contermini. CSGDSA-CNR e Provincia di Pisa, SELCA. In "La Pianura di Pisa ed i rilievi contermini. La natura e la storia[END_REF]. The sharped edges and the clasts typologies suggest a short transport along small watercourses contributing to the paleo-course of the Serchio River.

All fragments have in common a red-coloured isotropic matrix due to iron oxidation, as well as recrystallisation of calcium carbonate during the thermal processes, probably resulting from the addition of limestone fragments to the clay to increase the porosity of the bricks and reduce their weight. A fine granulometry is systematically observed in the limestone clasts, which are present in variable quantities and evenly distributed in the matrix. The microanalytical investigations show the same qualitative composition. All fragments appear to be made of clayey material fired in furnaces with excess oxygen (oxidising environment) at temperatures between ~800 °C and ~980 °C. Comparison of the textural and compositional characteristics of the bricks of Pisa with those of Calcinaia and Marti shows strong similarities, except for the quantity of the limestone clasts.

Based on the results above, we suggest that the bricks used in huge quantity for the construction of the studied buildings in Pisa were manufactured in the Calcinaia area, where the presence of brick kilns since the 15th century [START_REF] Alberti | La forace Coccapani di Calcinaia. Recupero della Memoria e musealizzazione[END_REF] is documented, and where their transport to Pisa was easy thanks to the proximity of the Arno River.

Discussion

Our new data obtained in Tuscany are reported in Figure 5 together with the five other archaeointensity results available in Italy for the past millennium [START_REF] Evans | Paleointensity estimates from Italian kilns[END_REF][START_REF] Aitken | Determination of the intensity of the Earth's magnetic field during archaeological times: Reliability of the Thellier technique[END_REF][START_REF] Tema | Archaeointensity determination from Italy: new data and Earth's magnetic field strength variation over the past three millennia[END_REF], 2013, Tema 2011, see also Figure 6 for their geographical distribution). Alone, the Tuscan data show a decreasing trend in intensity from the middle of the 12th century to c. 1500. There was then an increase until the beginning of the 17th century, followed by a decrease in intensity for about a century. At this stage, it can be noted that the two other Italian data available for the time period (1500-1700) cannot be easily reconciled with this variation pattern. This could be the case, however, for the result with the widest dating interval if its true age would lie at either extremities of that interval. In contrast, the three most recent data appear in good agreement with the direct measurements and/or the gufm1 model predictions at Pisa (Jacskon et al. 2000).

Considering the small number of Italian intensity data, Tema et al. (2013) relied on other data available within a 900 km radius around Viterbo (central Italy) to construct an intensity variation curve for the Italian peninsula. This curve is composed of two segments, the ages of which range between 100BC and AD 400, and AD 1300 and AD 1800, respectively. These two intervals are those where the data selected on the basis of quality criteria are sufficiently numerous. Interestingly, for the period of 1300-1800, the Italian curve is in fact largely determined from the data obtained in the south of France (e.g. [START_REF] Genevey | Evidence for rapid geomagnetic field intensity variations in Western Europe over the past 800 years from new archaeointensity French data[END_REF]. For this reason, to compare our new Tuscan data with the other results available regionally, we preferred to move the reduction site to an intermediate city between Paris and Pisa and then to integrate into this comparison the data obtained within a 700 km radius around this new reduction site. Here, we chose Beaune in the Burgundy region, home to the famous Hôtel-Dieu de Beaune (Figure 6). Note that one of the French data, precisely dated to the mid-15th century from archival documents, has been obtained from analysis of pavement tiles from the so-called King's Room in the Hospices de Beaune [START_REF] Genevey | Evidence for rapid geomagnetic field intensity variations in Western Europe over the past 800 years from new archaeointensity French data[END_REF].

At first, we only considered our datasets [START_REF] Genevey | Intensity of the geomagnetic field in western Europe over the past 2000 years: new data from ancient French pottery[END_REF]Genevey et al. 2009, 2013 andthis study), as together they form a very homogeneous data collection from an experimental point of view (i.e., same experimental protocol and selection criteria). Their geographic distribution is shown in Figure 6 (blue and pink circles), and their intensity values reduced to the latitude of Beaune are reported in Figure 7a. We observe that they are remarkably consistent and complementary. The Tuscan data confirm some of the rapid intensity variations previously observed only from the French dataset [START_REF] Genevey | Evidence for rapid geomagnetic field intensity variations in Western Europe over the past 800 years from new archaeointensity French data[END_REF][START_REF] Genevey | Geomagnetic field intensity variations in Western Europe over the past 1100 years[END_REF][START_REF] Genevey | New archaeointensity data from French Early Medieval ceramic production (6th-10th century AD). Tracing 1500 years of geomagnetic field intensity variations in Western Europe[END_REF]. It is worth recalling that the latter dataset showed that these variations were characterised throughout the past millennium by three peaks in intensity detected during the 12th century, the second part of the 14th century, and around AD 1600. The Tuscan data allow us to constrain the intensity maximum at the transition of the 16th and 17th centuries, with a peak that now appears better defined and more pronounced (Figure 7a). The new result dated from the middle of the 12th century is also important because it further documents the peak of intensity observed during this century, in particular the rapid decrease in intensity between c. 1150 and c. 1250.

In a second step, we also reported in Figure 7b all available data obtained within a 700 km radius of Beaune (Figure 6), which fulfil modern quality criteria (as defined by, for example, [START_REF] Genevey | New archaeointensity data from French Early Medieval ceramic production (6th-10th century AD). Tracing 1500 years of geomagnetic field intensity variations in Western Europe[END_REF]. We only kept data with age uncertainties of less than 100 years, considering that for this recent period of European history, it is possible to access such accurate dating when the aim is to recover rapid geomagnetic field intensity variations.

Overall, the data available are very consistent. The additional data included here [START_REF] Chauvin | Paleointensity of the geomagnetic field recovered on archaeomagnetic sites from France[END_REF][START_REF] Casas | High-quality microwave archaeointensity determinations from an early 18 th century AD English brick kiln[END_REF][START_REF] Donadini | Palaeointensity determination on an early medieval kiln from Switzerland and the effect of cooling rate[END_REF][START_REF] Gómez-Paccard | Improving our knowledge of rapid geomagnetic field intensity changes observed in Europe between 200 and 1400 AD[END_REF]) allow, in particular, a better description of intervals characterised by a decrease in intensity -i.e., during the 10th, 15th and 17th centuries.

From the data selection above, we constructed a reference intensity variation curve using the method recently developed by [START_REF] Livermore | Transdimensional inference of archaeomagnetic intensity change[END_REF]. This method relies on a trans-dimensional Bayesian approach that aims to fit a series of linear segments to the data, the number of which is self-determined by the data themselves. A great asset of this technique is the minimum regularisation imposed on the fit to the dataset (see discussion in [START_REF] Livermore | Transdimensional inference of archaeomagnetic intensity change[END_REF]. The average curve obtained, and its 95% confidence interval, is shown in Figure 7b. The results are very similar to those previously discussed by [START_REF] Genevey | New archaeointensity data from French Early Medieval ceramic production (6th-10th century AD). Tracing 1500 years of geomagnetic field intensity variations in Western Europe[END_REF] and [START_REF] Livermore | Transdimensional inference of archaeomagnetic intensity change[END_REF] using different averaging techniques, which further demonstrates the robustness of the three intensity peaks observed over the past millennium. Note that this result is particularly interesting for the attempts to find a correlation (and possible causal link) between geomagnetic field intensity peaks and cooling episodes in Western Europe as documented by advances and retreats of alpine glaciers, as well as with fluctuations in the C14 production rate [START_REF] Gallet | Does Earth's magnetic field secular variation control centennial climate change?[END_REF][START_REF] Genevey | Evidence for rapid geomagnetic field intensity variations in Western Europe over the past 800 years from new archaeointensity French data[END_REF][START_REF] Genevey | Geomagnetic field intensity variations in Western Europe over the past 1100 years[END_REF]. Furthermore, it is also worth reminding that the three intensity peaks, now better defined thanks to the new Tuscan data, are part of a set of five maxima regularly spaced since about 1500 years ago, with a pseudo period of ~250 years [START_REF] Genevey | New archaeointensity data from French Early Medieval ceramic production (6th-10th century AD). Tracing 1500 years of geomagnetic field intensity variations in Western Europe[END_REF][START_REF] Livermore | Transdimensional inference of archaeomagnetic intensity change[END_REF].

Moving away from the area of 700 km around Beaune or Paris, the past millennium in Europe is well documented by sets of data mainly acquired in northern Germany [START_REF] Schnepp | Geomagnetic paleointensity between 1300 and 1750[END_REF]), Spain (Gómez-Paccard et al. 2006, 2008, 2012[START_REF] Clemente | Ceramisti e produzione ceramica a Pisa tra Medioevo ed età Moderna[END_REF] and further east in Bulgaria [START_REF] Kovacheva | Extended and revised archaeomagnetic database and secular variation curves from Bulgaria for the last eight millennia[END_REF]. Comparison between, on the one hand, these results and, on the other hand, the variations predicted in Paris from different global and regional field models [START_REF] Pavón-Carrasco | A regional archaeomagnetic model for Europe for the last 3000 years, SCHA.DIF.3K: Applications to archaeomagnetic dating[END_REF], 2014a;[START_REF] Korte | Geomagnetic field for 0-3 ka: 2. A new series of time-varying global models[END_REF][START_REF] Licht | Ensembles of low degree archaeomagnetic field models for the past three millennia[END_REF], has already been widely discussed in our previous publications [START_REF] Genevey | Evidence for rapid geomagnetic field intensity variations in Western Europe over the past 800 years from new archaeointensity French data[END_REF][START_REF] Genevey | Geomagnetic field intensity variations in Western Europe over the past 1100 years[END_REF][START_REF] Genevey | New archaeointensity data from French Early Medieval ceramic production (6th-10th century AD). Tracing 1500 years of geomagnetic field intensity variations in Western Europe[END_REF]; see also in Pavón-Carrasco et al., 2014b). It should be noted that extending the area around Beaune for instance to 900 km or 1000 km would lead to a dataset almost identical to that available in a radius of 1250 km around Paris [START_REF] Genevey | New archaeointensity data from French Early Medieval ceramic production (6th-10th century AD). Tracing 1500 years of geomagnetic field intensity variations in Western Europe[END_REF]; we recall that in this case, the data appears significantly more scattered than the dataset available in a 700-km radius, which results in the smoothing of most of the rapid intensity variations mentioned (see Fig. 7 in [START_REF] Genevey | New archaeointensity data from French Early Medieval ceramic production (6th-10th century AD). Tracing 1500 years of geomagnetic field intensity variations in Western Europe[END_REF]. Redoing this comparison work would not provide new information compared to the conclusions of [START_REF] Genevey | New archaeointensity data from French Early Medieval ceramic production (6th-10th century AD). Tracing 1500 years of geomagnetic field intensity variations in Western Europe[END_REF] and for this reason, we chose here to perform a comparison with a new dataset obtained in Spain [START_REF] Molina-Cardín | Updated Iberian Archaeomagnetic Catalogue: New Full Vector Paleosecular Variation Curve for the Last Three Millennia[END_REF].

These authors constructed a new intensity variation curve for the Iberian Peninsula, spanning the past 3000 years, using both new data and previous results that fulfil a set of quality criteria, available in a radius of 900 km around Madrid. For the past millennium, this data selection is essentially different from the one considered around Beaune, even if some data obtained in France are common to both selections (Figure 6). Let us note that the selection criteria used by [START_REF] Molina-Cardín | Updated Iberian Archaeomagnetic Catalogue: New Full Vector Paleosecular Variation Curve for the Last Three Millennia[END_REF] are slightly less restrictive than those used to select the data reported in Figure 7b [START_REF] Genevey | Geomagnetic field intensity variations in Western Europe over the past 1100 years[END_REF]. The criteria relative to the intensity methods are the same (Thellier method with pTRM-checks and TRM anisotropy effect taken into account for artefacts recognized as more anisotropic), but they differ for the dating uncertainties and data accuracy. In [START_REF] Molina-Cardín | Updated Iberian Archaeomagnetic Catalogue: New Full Vector Paleosecular Variation Curve for the Last Three Millennia[END_REF], the age uncertainties are required to be of less than 250 years and there is no threshold value relative to the uncertainty on the intensity mean, whereas, our selection is based on a dating accuracy of less than 100 years and an uncertainty of less than 15% on the intensity mean. Applying our selection criteria to the Spanish dataset would have comparatively resulted in the rejection of 13 data, mainly on the basis of the age uncertainties (11 of the 13 data indicated by crosses in Figure 7c). Regardless of the criteria considered, the data selected around Madrid are significantly more scattered than those presented in Figure 7b. A mean intensity variation curve was constructed in Figure 7c using the data selection used by [START_REF] Molina-Cardín | Updated Iberian Archaeomagnetic Catalogue: New Full Vector Paleosecular Variation Curve for the Last Three Millennia[END_REF]. The dispersion of the data leads to a smooth evolution showing a continuous decrease between c. 1100 and c. 1850, followed in continuity by the intensity decrease predicted by gufm1 at Madrid since 1850 (Figure 7c). It should be noted that the very same evolution is obtained when the Spanish data are selected according to our selection criteria. The same overall trend is observed from the Beaune dataset, but thanks to a higher coherence between the results, it allows us to detect the existence of faster intensity variations occurring on the century timescale (Figure 7b). It therefore seems likely that a reduction of the scatter in the Madrid dataset would allow the emergence of the same three intensity peaks observed in France and partly in Italy. From this point of view, the data obtained in France and in Tuscany indicate that the construction of a mean intensity variation curve with a resolution on a 100year timescale is an achievable objective, although it must be acknowledged that this is clearly a difficult task. Tema, E., 2011. Archaeomagnetic Research in Italy: Recent achievements and future perspectives. In: The Earth's Magnetic Interior, IAGA Special Sopron Book Series, Volume 1, Chapter 15, pp. 213-233. Eds: Petrovsky, E., Herrero-Bervera, E., Harinarayana, T., Ivers, D., Springer. Tema, E., Morales, J., Goguitchaichvili, A., Camps, P., 2013. New archaeointensity data from Italy and geomagnetic field intensity variation in the Italian Peninsula. Geophys. J. Int. 193, 603-614. Tema, E., Camps, P., Ferrara, E., Poidras, T., 2015. Directional [START_REF] Genevey | Intensity of the geomagnetic field in western Europe over the past 2000 years: new data from ancient French pottery[END_REF][START_REF] Genevey | Evidence for rapid geomagnetic field intensity variations in Western Europe over the past 800 years from new archaeointensity French data[END_REF][START_REF] Genevey | Geomagnetic field intensity variations in Western Europe over the past 1100 years[END_REF] and from direct measurements (http://www.bcmt.fr/). (b) Intensity data fulfilling quality criteria and available within 700 km around Beaune, and mean geomagnetic field intensity variation curve, and its 95% confidence envelope, computed from this dataset using the AH-RJMCMC algorithm developed by [START_REF] Livermore | Transdimensional inference of archaeomagnetic intensity change[END_REF]. The computational parameters are as follows: s move = 200 yr, s change = 15 µT, s birth = 8 µT, s ages = 5 yr, b = 20, K max =80, with a chain length of 50 million samples and intensity priors of 30 µT for the minimum and 100 µT for the maximum (see details in [START_REF] Livermore | Transdimensional inference of archaeomagnetic intensity change[END_REF]. Following [START_REF] Genevey | ArchaeoInt: An upgraded compilation of geomagnetic field intensity data for the past ten millennia and its application to the recovery of the past dipole moment[END_REF], the datum obtained by [START_REF] Casas | High-quality microwave archaeointensity determinations from an early 18 th century AD English brick kiln[END_REF] marked by '*' was decreased by 5% to account for the cooling-rate effect, which was not evaluated in this study. (c) Intensity data selected by [START_REF] Molina-Cardín | Updated Iberian Archaeomagnetic Catalogue: New Full Vector Paleosecular Variation Curve for the Last Three Millennia[END_REF] for a region of 900 km around Madrid and the corresponding mean intensity variation curve computed using the same method as in (b) and with the same computational parameters except for the intensity priors set at 25 µT for the minimum and 95 µT for the maximum. Note that the time-order relationship existing for two datasets was taken into account in these estimates. The symbol "x" indicates the thirteen data that would not have been retained if the same selection criteria as in Figure 7b had been chosen. The intensity values expected in Madrid since 1850 from the gufm1 model [START_REF] Jackson | Four centuries of geomagnetic secular variation from historical records[END_REF] are also exhibited.

Table 1: New mean archaeointensity values obtained from the fourteen Tuscan groups of architectural brick fragments analysed in the present study. 'location' indicates the city where the brick fragments were sampled. Note, however, that the study carried out on the composition of the bricks suggests the same production area around Calcinaia (43.68°N ; 10.61°E). '# Group' indicates the archaeomagnetic identification number of each group; 'N Frag. (n Spec)' gives, respectively, the number of fragments and specimens retained to estimate a mean; 'F ± F (µT)' corresponds to the mean value obtained at the sampling site with its standard deviation in µT. Its reduction at the latitude of Beaune (47.02°N) is given in µT in the last column.

Table 2: Sequence of the five series of measurements involved in the Triaxe intensity protocol. The measurements are carried out every 5° C (Le [START_REF] Goff | A new three-axis vibrating sample magnetometer for continuous high-temperature magnetization measurements: applications to paleo-and archaeo-intensity determinations[END_REF].

  results and absolute archaeointensity determination by the classical Thellier and the multi-specimen DSC protocols for two kilns excavated at Osterietta, Italy, Stud. Geophys. Geod., 59, DOI: 10.1007/s11200-015-0413-0. Tema, E., Ferrara, E., Camps, P., Conati Barbaro, C., Spatafora, S., Carvallo, C., Poidras, T., 2016. The Earth's magnetic field in Italy during the Neolithic period: New data from the Early Neolithic site of Portonovo (Marche, Italy). Earth Planet. Sci. Lett. 448, 49-61. Thellier, E., Thellier, O., 1959. Sur l'intensité du champ magnétique tesrrestre dans le passé historique et géologique. Ann. Géophys. 15, 285-376. Vezzoli, L., Principe, C., Malfatti, J., Arrighi, S., Tanguy, J.C., Le Goff, M., 2009. Modes and times of caldera resurgence: The <10 ka evolution of Ischia Caldera, Italy, from archaeomagnetic dating. Journal Volcanol Geotherm Res, 186, 305-319.

Figure

  Figure and Table captions

Figure 1 :

 1 Figure 1: Examples of Tuscan baked-brick buildings sampled for this archaeointensity study.

  (a) 'Bocchette di Putignano'. This dike was built in 1558 as indicated on a plaque affixed to the building (b), which reads 'A PARTV VIRGINIS ANNO M. D. LVIII. CALEN. NOVEMBRIS' and can be translated as 'November 2nd of the 1558th year since the date Mary gave birth [to Jesus]'. (c) Cistern of the Medici aqueduct linking Pisa to Asciano Pisa dated from the beginning of the 17th century. The yellow cross indicates the area selected for the sampling carried out using drilling. For this site, 12 cores were collected, leaving as many visible holes (d), which were then filled with tinted mortar to restore the wall as much as possible (e).

Figure 2 :

 2 Figure 2: Examples of favourable (Pise04-05A) and unfavourable (Tosc04-04B) magnetic

Figure 3 :

 3 Figure 3: Characterisation of the magnetic mineralogy. Typical example of thermal

Figure 4 :

 4 Figure 4: Intensity results obtained for four groups of brick fragments. Each curve in the

Figure 6 :

 6 Figure 6: Geographical distribution of the Italian archaeointensity data (pink circles, the new

Figure 7 :

 7 Figure 7: Archaeointensity variations in Western Europe over the past millennium as inferred

  Figure 2.

  Figure5.

  Figure6.

Acknowledgments

The authors are indebted with Federico Andreazzoli for his great help for the selection of the structures and on the field. Claudia Principe wants to remember here their two-voices speech from the pulpit of the church of Marti about devil and archaeomagnetism. We are also pleased to thank Fiorella Ramacogi and the late Mario Ferretti from the Soprintendenza to Monuments of Pisa, who produced us the due authorization for sampling. We are grateful to two anonymous reviewers for their helpful comments on the manuscript. This research was supported by the CNRS (Projet International de Collaboration Scientifique, PICS n°3063) and by the Simone and Cino Del Duca Foundation of the French Academy of Science (ID 100009515). This is IPGP contribution no. 4093.

Supplementary Table 1: Summary of the selection criteria used to retain the intensity results at the specimen, fragment and group levels.

Supplementary Table 2: Intensity results obtained at the specimen level and mean values obtained at the fragment level. 'Tmin-Tmax': Interval of temperature involved for the intensity computation. 'Flab': Intensity of the laboratory field in µT. 'NRM T1 (T1')' column: Percentage of magnetisation fraction with unblocking temperatures larger than T1 (or T1'). 'Slope R': Slope of the straight line computed from the R'(Ti) data between Tmin and Tmax. 'F Triaxe': Intensity values obtained at the specimen level in µT. 'F Triaxe mean value per fragment F': Mean intensity value obtained at the fragment level with its standard error when computed from 2 values or its standard deviation when computed from 3 values.

*: (n1/n2/n3) indicates successively the number of fragments collected, the number of fragments whose magnetization was strong enough relative to the Triaxe sensitivity and the number of fragments retained to estimate a mean value at the group level.