Archaeomagnetic dating of a High Middle Age likely iron working site in Corroy-le-Grand (Belgium)

Physics and Chemistry of the Earth 33 (2008) 544–556

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Archaeomagnetic dating of a High Middle Age likely iron working site in Corroy-le-Grand (Belgium) Simo Spassov a,*, Jozef Hus a, Raoul Geeraerts a, Frédéric Heller b a b

Centre de Physique du Globe de l’Institut Royal Météorologique de Belgique, B-5670 Dourbes (Viroinval), Belgium Direction générale de l’Aménagement du Territoire, du Logement et de Patrimoine (DGATLP), 88 Rue de Nivelles, B-1300 Wavre, Belgium

a r t i c l e

i n f o

Available online 2 March 2008

Keywords: Archaeomagnetism Archaeomagnetic dating Belgium Iron working site Goethite Rock magnetism

a b s t r a c t Archaeological burnt materials and structures provide unique records of direction and intensity of the Earth’s magnetic field in the past, elements that can be absolutely determined applying the archaeomagnetic method. At present, such records within Europe are irregular in both space and time. Presented here is the archaeomagnetic investigation of three kilns that were discovered during a preventive excavation of an archaeological site considered of High Middle Age in Corroy-le-Grand (Belgium) and that are assumed to be related to iron working activities. Archaeological context dating points to kiln operation between the second half of the 10th century until the 12th century AD. As the site is not far from Paris, declination and inclination of the characteristic remanent magnetisation of the kilns were compared with the standard directional secular variation curve for France in order to propose archaeomagnetic dates for the cessation of kiln operation by using probability densities [Lanos, Ph., 2004. Bayesian inference of calibration curves, application to archaeomagnetism. In: Buck, C.E., Millard, A.R. (Eds.), Tools for Constructing Chronologies: Crossing Disciplinary Boundaries. Lecture Notes in Statistics. Springer Verlag, London, pp. 43–82; Lanos, Ph., Le Goff, M., Kovacheva, M., Schnepp, E., 2005. Hierarchical modelling of archaeomagnetic data and curve estimation by moving average technique. Geophysical Journal International 160 (2), 440–476]. This confirms the presumed archaeological age and resulted in more precise time constraints for the last kiln operation. Rock magnetic techniques, proposed by Spassov and Hus [Spassov, S., Hus, J., 2006. Estimating baking temperatures in a Roman pottery kiln by rock magnetic properties: implications of thermochemical alteration for archaeointensity determinations. Geophysical Journal International 167, 592–604], were applied to examine the suitability of the burnt materials from the kilns for archaeointensity determinations and to increase the success rate of the Thellier–Thellier double heating technique. An average value for the field intensity of 69.4 ± 2.5 lT was estimated from 10 specimens from a single kiln, which corresponds reasonably well with published data for Western Europe. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction Many regions in Europe are undergoing rapid economic expansion, inevitably involving the loss of part of our shared cultural heritage and in particular of baked structures, like kilns, that are precious for improving our knowledge of past geomagnetic field behaviour. Archaeological sites are often destroyed and have to make way for new construction projects, as is the case in the present examined site in Corroy-le-Grand (Belgium) close to Brussels. A preventive excavation of this High Middle Age archaeological site led to the discovery of three baked structures, which seem to be related to metal working as burnt pieces of ferruginous sandstones were found in the fillings of kiln CLGa02 (F13). Moreover, several iron slags were found in pits near the baked structures. In the * Corresponding author. Tel.: +32 60 395 424; fax: +32 60 395 423. E-mail address: [email protected] (S. Spassov). 1474-7065/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.pce.2008.02.037

following, these baked structures will be called kilns, although this designation may be archaeologically speaking inappropriate depending on their exact function. The main purpose of the archaeomagnetic study of the kilns is to provide a site archaeomagnetic dating solution based on the recorded magnetic declination (D) and inclination (I) and the standard directional secular variation diagram of France. This may verify the preliminary archaeological dating and provide more precise time constraints for the last heating/cooling cycle of the kilns. Indeed, a first examination of the ceramics found in pits and living floors point to site occupation between the second half of the 10th century until the 12th century (unpublished report by Sylvie de Longueville). The suitability of burnt materials collected from one kiln was examined and several intensity determinations performed applying the Thellier–Thellier double heating method. The field intensity result was in the first place compared with available data for the

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time span concerned to strengthen the proposed archaeomagnetic date based on directional data only. Also charcoal has been collected in the three kilns for 14C dating in the near future. Consequently, once the kilns are independently dated and the study of the typology of the ceramics is finished, the directional and intensity data obtained may be appropriate for improving and/or as a supplement of archaeomagnetic secular variation standard curves for Western Europe. This is important as archaeomagnetic data for the High Middle Age (11–13th century AD) are rather rare for Western Europe and not well dated (Hus and Geeraerts, 1998; Chauvin et al., 2000; Genevey and Gallet, 2002; Le Goff et al., 2002 and references therein). As the three kilns were installed in Tertiary ferruginous sands and the floor of two kilns partly consisted of burnt ferruginous sand, the rock magnetic properties, including thermo-magnetic properties, of burnt kiln materials and of non-baked ferruginous sand close to the kilns were examined in detail.

pling and besides the calcareous sandstone blocks, one burnt piece of ferruginous sandstone was present in the eastern wall. The floor had been destroyed; only a few tiny brown reddish patches were still visible in the northern part of the floor, as well as a moreor-less 5 cm thick charcoal rich layer. In total 14 oriented samples were taken in the walls at the southern part of the kiln (11 baked clay samples, 2 burnt calcareous sandstone blocks and 1 burnt piece of ferruginous sandstone). Kiln CLGa02 (F13) differs from the other two as stones are absent (Fig. 1b). The floor consisted here of six burnt layers separated by non-baked brown yellowish ferruginous sands and/or charcoal. At the moment of sampling only the two oldest (bottom) floors were still visible. In total 17 oriented samples were taken (13 samples in the floor and 4 in the walls) at the southern part of the kiln.

2. Site description and sampling

In total, 58 oriented decimetre-sized samples were collected from the three kilns (Fig. 1a). Each sample was covered in the field with gypsum in order to protect it and to realise a horizontal surface for the angle of dip. Lines of known geographical azimuth, obtained by measuring the zenithal distance of the sun at a certain instant of time with a Wild T2 theodolite, were scribed on the horizontal reference planes with a precision better than 0.5°, before removing the samples. From the large samples, small 2.2  2.2  2.2 cm and 4.0  4.0  4.0 cm cubes were cut in the laboratory, keeping their original orientation marks, for respectively demagnetisation tests and the archaeomagnetic directional analysis. Remanent magnetisations, including the natural remanent magnetisation (NRM) of the samples, were measured in an upgraded three-axis, model 760, 2G Enterprises, cryogenic magnetometer with DC SQUIDS and sample access of 7.6 cm. The magnetometer is equipped with a Cryomech 4K, model PT405, pulse tube cryorefrigerator, which creates the requested working temperatures for the detection system without the necessity of a liquid helium reservoir. In-line is a manual sample handler to measure 4 cm cubes in different positions, guaranteeing high precision in directional measurements. Magnetic stability of the NRM in the coercivity range between 0 and 100 mT was tested on oriented pilot specimens (cubes of 2.2 cm size) using the in-line alternating field demagnetiser and automated sample handling system of the 2G cryogenic magnetometer. The 4 cm cubes on the other hand were stepwise demagnetised along three perpendicular sample axes in a large alternating field solenoid coil set up in three orthogonal Helmholtz coils, in peak fields of 15, 20 and 25 mT. The remaining NRM was measured after each step in the 2G cryogenic magnetometer. The characteristic remanent magnetisation (ChRM) was estimated by principal component analysis as proposed by Kirschvink (1980) including the origin of the coordinate system. Loose powder specimens were taken from the burnt kiln materials and non-baked ferruginous sands for the examination of their rock magnetic properties. About three grams of powder were pressed into small paper boxes for measuring acquisition curves of isothermal remanent magnetisation (IRM), backfield curves and short-term remanence decay, after different heating steps, in a J-coercivity ‘‘rotation” magnetometer (Burov et al., 1986; Jasonov et al., 1998). The thermal treatments took place in air. Magnetisation was measured between +500 mT and 500 mT with averaged field increments of 0.5 mT per magnetisation step. The magnetisation duration at each magnetisation step is in the order of tenths of a second. When the backfield curve is finished, the direct current is switched off automatically,

The kilns investigated in the present paper were discovered in Corroy-le-Grand (about 30 km SE of Brussels in the province Walloon Brabant, 50° 390 5100 N, 4° 400 3800 E) in a small Mediaeval rural settlement at the first terrace of the brook Piou, a tributary of the river Dyle. Three kilns, probably related to metal working, were unearthed by F. Heller of DGATLP in 2005 in a Mediaeval parcel west of three other parcels with the rural housing. In addition to the kilns, the floors of some workshops were discovered in this parcel that was limited by a V-shaped ditch with an earth wall on the inner side. Archaeological findings in the ditch fillings, mainly sherds, suggest that the ditch was abandoned in the 11th century AD. Middle-Eocene, medium to coarse, glauconite containing, nearly decalcified sands of the Brussels Formation, which are in some places strongly ferruginous with iron pans, are outcropping in this area and visible immediately east from the kilns (Houthuys, 1990; Laga et al., 2001). The Tertiary sands are covered with a thin Pleistocene loess blanket. The three kilns (F135-146, F92 and F13) had been installed in the ferruginous sands and are all three oriented in the NNW-SSE direction. They are rectangular in shape and were probably semi-sunken, single-chambered, and open at the smallest sides (Fig. 1). The walls of two kilns (F135-146 and F92) were made from calcareous sandstone blocks, cemented and lined on the inner side with clay or loam, which may correspond to a facies of the Brabant Formation that is found in the east of the province of Walloon Brabant, known as the Gobertange stones. Kiln F13 differs from the other ones as walls in stone are lacking. Kiln CLGa01 (between the walls F135 and F146) is of rectangular shape, opens at both smaller sides and is lined with cemented calcareous sandstone blocks along the longer sides (Fig. 1a and b). The inner side of the walls had been covered with a fine-grained clay or loam and burnt pieces were still attached to the calcareous sandstone blocks in certain places. An undisturbed part of the kiln floor was still preserved at the southern side, consisting of a hard light brown burnt clay crust (about 2 cm thick) and underlying more reddish burnt sand (about 5 cm thick). Only a small part of the kiln floor was present at the northern side, but this was less well preserved as the hard crust was missing. In total 27 oriented samples were taken: 8 in the fine-grained burnt material covering the walls, 15 in the floor at the southern side and 4 in a small burnt spot at the northern side (Fig. 1a). Kiln CLGa03 (F92) is of similar shape and dimensions and oriented in the same direction as kiln CLGa01. It is also rectangular in shape with two openings at both small ends, and bordered with calcareous sandstone blocks along the long sides (Fig. 1a). Only some parts of the walls were still visible at the moment of sam-

3. Methods

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Fig. 1. (a) Sampling scheme (plane view) of the three kiln remains, CLGa01 (F135/F146), CLGa02 (F13) and CLGa03 (F92), unearthed in the High Middle Age archaeological site at Corroy-le-Grand (Belgium). Numbers indicate the positions of independently oriented samples. (b) Left side: picture of kiln CLGa01 taken from the north; right side: picture of kiln CLGa02 taken from the south. Notice the presence of several floors, separated by ferruginous sands and/or charcoal in the latter.

and the magnetising field decreases towards a constant residual field of about 0.4 mT within the following 0.4 s. The decay of the remaining remanence (IRM500 mT,0.4 s) is monitored during 100 s, hereafter called short-term remanence loss.

Filtered backfield curves were used for the calculation of remanence coercivity spectra applying the software MAGMIX (Egli, 2003). In order to quantify remanence contributions of different magnetic phases, the spectra were fitted with a linear combination

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of so-called maximum entropy Skewed Generalised Gaussian functions (SGG) as proposed and introduced by Egli (2003). An example is given in Fig. 2. The temperature dependence of low field magnetic susceptibility from ambient temperature to 700 °C was measured on selected natural and burnt specimens in a CS-3 heating unit of a KLY-3 Kappabridge, in air, at a heating rate of 6 °C/min. The archaeointensity experiments were carried out following the classical Thellier–Thellier double heating ‘‘in field” technique as described in Thellier and Thellier (1959). Heating and cooling (without forced cooling), both lasting about 45 min, took place in a Schonstedt thermal demagnetiser. As the applied axial DC field, controlled with a tri-axial applied physics fluxgate magnetometer, varies with distance in the cooling chamber, the position of each specimen on the sample holder was determined with millimetre accuracy. Each specimen was put in exactly the same place during successive heating/cooling cycles in order to guarantee the application of a constant field at all temperature steps. After each completed temperature step, magnetic low field susceptibility was measured in a KLY-3 Kappabridge in order to trace changes of mineral magnetic alterations. 4. Rock magnetic properties 4.1. Kiln material

20 0 – 1 cm 0 –20 –40 1

10

100 Field [mT]

IRM500 mT [mA m²/kg]

2 1 3 – 4 cm 0 –1 –2 1

10

100 Field [mT]

Log. IRM500 mT derivative [mA m²/kg]

IRM500 mT [mA m²/kg]

Backfield curves 40

L og. IRM500 mT derivative

[mA m²/kg]

Rock magnetic investigations aid in assessing the confidence of directional and archaeointensity results and give an indication for successful specimen pre-selection (e.g., Spassov and Hus, 2006). A schematic cross-section through a typical kiln floor sample from kiln CLGa01 is shown in Fig. 3. High magnetic susceptibility and

IRM values, low remanent coercive forces and a short-term remanence loss up to 10% characterise the topmost centimetres, consisting of well-baked hard crust of moderate brown colour. Immediately below (from 1.5 to 8.5 cm) is light brown well-baked clay in which both magnetic susceptibility and short-term remanence loss decrease, remanent coercive force increases, but IRM intensity remains rather constant. In the less baked clay (8.5–12 cm) and the non-baked sand (12–14 cm), magnetic susceptibility and IRM continue to decrease, while remanent coercive force decreases and the short-term remanence loss increases. Coercivity spectra analysis of the kiln floor sample indicates the presence of multiple co-existing magnetic mineral assemblages (components) with different remanent coercive force distributions (cf. Fig. 2) in all specimens from this sample. A low coercivity component dominates the IRM intensity of the well-baked topmost centimetres, as well as in the less baked material and unbaked sands in the lower part. The intermediate coercivity component increases in depth between 1.5 and 8.5 cm, whereas the low coercivity component decreases (Fig. 4). Thermomagnetic curves are useful indicators for the thermal stability of baked materials. The moderate brownish well-baked hard crust from the topmost centimetres of the kiln floor samples shows an irreversible low-field magnetic susceptibility vs. temperature behaviour (CLGa01e14 in Fig. 5a). Magnetic susceptibility at room temperature is higher after heating to 700 °C. The same is true for the well-baked light brown coloured baked clay from the wall (CLGa01e21 and e26), but here two magnetic phases are present. In contrast, kiln floor sample CLGa01e01, from a depth between 3 and 5 cm in kiln CLGa01, displays reversible behaviour.

Remanent coercivity spectra 100 0 – 1 cm

80 60

C 21 mT

40 20

C 88 mT UL

0 1

10 Field [mT]

100

4 3 – 4 cm 3 C 21 mT

2 1

C 65 mT

H

UL

0 1

100

10 Field [mT]

Fig. 2. Backfield curves (left), remanent coercivity spectra and their interpretation (right) of two specimens from sample CLGa01e1 taken at different depths. The thickness of the black band represents the spectral error. The spectra are fitted with a linear combination (white) of three (c) or four (d) SGG functions (grey), representing magnetic mineral phases with different remanent coercive forces (for details see Egli, 2003).

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Susceptibility [m³/kg] 10 100

1

Remanent coercive force

IRM500 mT [mAm²/kg] 1000 0.01 0.1 1 10

0

well baked hard crust moderate brown

100

20

30

[mT] 40

50

Remanence loss 0

2

[%] 4 6

8

10

5 Y R 4/4

2

Depth [cm]

4 well baked clay light brown

6

5 YR 5/6

8 10

less baked clay moderate yellowish brown

10 YR 5/4

non baked sand moderate to dark yellowish brown

10 YR 5.5/5

12 14

Fig. 3. Bulk rock magnetic properties in function of depth for a typical kiln floor sample (CLGa01e01) of kiln CLGa01. The different layers are characterised by different colours according to the Munsell colour chart (Munsell, 1905) and have different magnetic properties (see text). The rather constant IRM500 mT and the increasing coercivity of remanence within the well-baked light brown layer indicate different co-existing magnetic mineral phases with variable contribution (cf. Fig. 4).

Relative IRM contribution low coercivity minerals [%]

intermediate coercivity minerals [%]

30 40 50 60 70 80 0

2

2

C 21 mT

6 8

4

Depth [cm]

4

Depth [cm]

10 20 30 40 50 60

0

C 65 mT

6 8

10

10

12

12

14

C 88 mT

C 72 mT

14

Fig. 4. Quantified relative contribution of low (21 mT) and intermediate (65, 72, 88 mT) coercivity components to the IRM500 mT in function of depth for kiln floor sample CLGa01e01. At shallow depths, i.e., close to the heat source, the IRM500 mT is dominated by low coercivity components, whereas further away intermediate coercivity components gain in importance in the well-baked part. This variable contribution explains the increasing remanent coercive force in the well-baked part, as seen in Fig. 3.

4.2. Material near kiln CLGa02 As almost all samples of kiln CLGa02 consist of burnt ferruginous sand, non-baked material surrounding the kiln was also investigated in order to study possible magnetic phase transformations and to assess the degree of newly formed magnetic mineral during laboratory treatment. Ferruginous sand and sandstones containing oxyhydroxides alter strongly during thermal treatment and this may considerably influence ChRM directions and intensity if they are not sufficiently baked. The heating curve of the hard brown crust of a natural limonite sample collected near kiln CLGa02 is characterised by a two-step transformation between about 300 and 550 °C (Fig. 6a). This can be attributed to the presence of both goethite and lepidocrocite.

Conversion of lepidocrocite to maghaemite occurs between about 200 and 300 °C, depending on its degree of crystallinity, carbon content and heating rate (Gehring and Hofmeister, 1994). Hanesch et al. (2006) showed that the transformation to maghaemite starts at lower temperature when carbon is present but that the presence of the latter is not necessary for the transformation to occur. At higher temperatures it is expected to transform to haematite. Dehydroxylation of goethite to haematite occurs between 200 and 400 °C. In natural samples the formation of a strongly magnetic mineral, maghaemite or magnetite, is observed and is generally attributed to the presence of organic carbon (Dekkers, 1990). In the present case, transformation starts after 250–260 °C in the hard brown and the yellow crust of the limonite samples (Fig. 6a and b inset) but after 290 °C in the ferruginous sand sample (Fig. 6c). In all three cases, transformation into a strongly ferrimagnetic mineral occurs during further heating, but haematite is not revealed. This suggests the formation of maghaemite and the stabilising effect of substituted iron (Stacey and Banerjee, 1974). The yellow crust sample (Fig. 6b), in which transformation already sets in from 250 °C, has a magnetic susceptibility after the heating/ cooling cycle that is several orders of magnitude higher than in the hard crust sample (Fig. 6a). As the heating rate was the same, this can be explained by different degrees of crystallinity resulting in higher reactivity in the yellow crust. In contrast to lepidocrocite, goethite transforms to a strongly magnetic mineral only when organic carbon is present. The formation of the strongly magnetic phase during heating in air of the three samples can be explained by the reducing conditions due to the presence of trace amounts of organic matter in the limonite samples and sands and ferrous iron that occurs by decomposition of the clay minerals in the ferruginous, glauconite bearing sands. Substitution of iron by aluminium is a plausible explanation for the stabilising effect of the formed strongly magnetic phase, preventing its transformation towards haematite. Goethite in the sands and sandstones of the Brussels formation probably formed by direct precipitation in solution via a nucleation-crystal growth process, and organic matter may become trapped during this process. In carbonate-rich solutions the formation of lepidocrocite is prevented and goethite forms instead (Schwertmann and Cornell, 2000). Lepidocrocite is less common and is thermodynamically less stable than its polymorph goethite but is frequently formed in clays near a fluctuating water table and in reductomorphic soils, by the presence of bivalent iron ions, due to alternating oxidation and reducing conditions. Once formed,

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CLGa01e1–baked clay, kiln floor (3–5 cm depth cooling)

CLGa01e14–hard crust kiln floor

1.2

0.6

1

g atin

ting

hea

0.8

he

0.6

/

23ºC

/

1 0.8

ling

coo

23ºC

1.4

0.4

0.4

0.2

0.2 100

200 300 400 500 Temperature [ºC]

600

100

700

CLGa01e21–baked clay from wall 1.2

in 23ºC

23ºC

heating

0.75

/

/

1

g

1

700

co

ol

1.25

600

CLGa01e26–baked clay from wall

co

1.5

200 300 400 500 Temperature [ºC]

oli

hea

ng

tin

0.8

g

0.6

0.5

0.4

0.25

0.2

0 100

200 300 400 500 Temperature [ºC]

600

700

100

200 300 400 500 Temperature [ºC]

600

700

Fig. 5. High temperature dependence of low-field magnetic susceptibility of two floor (a, b) and two wall (c, d) specimens. Heating to 700 °C considerably changes the magnetic mineralogy in all specimens except in the one taken from 3 to 5 cm below the kiln floor (b).

CLGa01l2 – natural limonite(hard brown crust)

CLGa02l2–natural limonite(yellow crust) 350

15

1.4

cool

10

ing

7.5 heating

5

23ºC

250 200

/

/

23ºC

12.5

150

50

0

0 200 300 400 500 Temperature [ºC]

600

200 300 400 500 Temperature [˚C]

700

ng

oli

heating

200 300 400 500 Temperature [ºC]

600

700

Baked sand from floor of kiln CLGa02

coolin

1.2

g

3

600

co

100

700

Sand near kiln CLGa02

3.5

1

2.5

cooling

0.8

g tin

23ºC

2

hea

23ºC

0.6

100

100

0.6

1.5

/

/

1 0.8

100

2.5

1

1.2

/ 23˚C

300

0.4

heating

0.2

0.5

0 100

200 300 400 500 Temperature [ºC]

600

700

100

200 300 400 500 Temperature [ºC]

600

700

Fig. 6. High temperature dependence of low-field magnetic susceptibility of two natural limonite samples recovered near kiln CLGa01 (a) and kiln CLGa02 floor (b). Limonite dehydration results in the formation of two transient ferrimagnetic phases at 260 and 300 °C. A superparamagnetic ferrimagnetic phase forms after heating to 700 °C. Sand near kiln CLGa02 shows somewhat similar behaviour. Baked sand from the bottom of kiln CLGa02 (d) is apparently thermally unstable. Initially present, limonite had already been transformed during ancient baking.

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the transformation of lepidocrocite to the thermodynamically more stable goethite is an extremely slow process. 5. Archaeomagnetic analyses 5.1. Archaeodirections Typical detailed stepwise natural remanent magnetisation (NRM) demagnetisations of 2.2  2.2  2.2 cm pilot specimens are given in Fig. 7. Alternating fields with peak amplitudes of 30–35 mT are sufficient to demagnetise 90% of the NRM in most specimens. However, in some specimens about 20–30% of the NRM is carried by magnetic mineral assemblages with remanent coercive forces above 30 mT (cf. CLGa01e22 in Fig. 7). Only a single component is present, except in the specimen from kiln CLGa02, where a small viscous overprint is removed in AF fields of 10 mT. The calculated characteristic remanent magnetisation (ChRM) has small maximum angular deviation (MAD) values, in the order of 1°, guaranteeing high quality of the estimated directions. Large cubes of 4.0  4.0  4.0 cm in size have been used for the determination of the archaeodirections as mentioned in Section 3, in order to reduce the effect of material inhomogeneities and to obtain accurate archaeodirections. As the previously studied pilot specimens have rather small MAD values, all the other specimens were partially demagnetised only at three steps in alternating peak fields of 15, 20 and 25 mT. This yielded MAD’s < 5° for specimen ChRM directions from kilns CLGa01 and CLGa03. Two additional demagnetisation steps at 30 and 35 mT were added for the specimens from kiln CLGa02, consisting of less consolidated baked sand, in order to obtain MAD’s < 5°. The ChRM has been estimated for each specimen by principal component analysis (Kirschvink, 1980) including the origin of the coordinate system. The Fisherian mean of each sample was calculated, followed by averaging of the sample directions in order to obtain the mean magnetisation direc-

tion of each kiln. Specimens with MAD’s > 5° were hereby excluded, as well as outliers (at specimen level), which were identified by an angular deviation from the mean kiln direction larger than 5°. The Fisherian mean directions of all three kilns are given in Table 1, including concentration parameter k and confidence factor a95. The distribution of individual sample mean directions of each of the three kilns has been checked positively to represent Fisherian distributions and application of the latter is therefore justified. The average magnetisation directions of the three kilns do not differ considerably from each other, taking the error limits into account, suggesting contemporaneous kiln operation. 5.2. Archaeomagnetic dating As the site examined is close to Paris (about 260 km), the directional secular variation standard curve of France (Gallet et al., 2002), which refers to Paris, can be used as a reference for archaeomagnetic dating of the three investigated kilns. The calculated kiln mean directions of the three kilns (Table 1) were relocated to the geographical coordinates of Paris and compared with the French secular variation D–I reference curve. In order to compare the directions from different geographic locations, the kiln mean declination and inclination have to be transferred to the geographical coordinates for which the reference secular variation curve is calculated. This reduction or relocation can be done by transferring the directions via the virtual geomagnetic pole (Shuey et al., 1970), which seems to be the most efficient reduction procedure at present (Noel and Batt, 1990). Applying this method, one assumes that the geomagnetic field is mainly a geocentric axial dipole field and that secular variation at the reference site and the examined site is identical. The archaeomagnetic dating is implemented using probability densities as suggested by Lanos (2004) and Lanos et al. (2005), with

Fig. 7. Detailed alternating field demagnetisation and principal component analysis of four specimens with different NRM intensities from the wall and the floor of the kilns CLGa01 and CLGa02. ChRM directions are given at the bottom. The direction of the NRM is very stable during the demagnetisation treatment, resulting in low maximum angular deviation (MAD) values, which are in the order of 1°. A viscous overprint, if present, is usually very small (cf. specimen CLGa02e6) and is removed in AF peak fields of 5–10 mT. In the Zijderveld diagram, the vertical component (V) is plotted with open squares and the horizontal component (H) with filled circles.

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Table 1 Number of samples N used for archaeomagnetic dating, mean archaeomagnetic directions (D, I), concentration parameter k, and confidence factor a95 for each of the three examined kilns Kiln

Presumed age (centuries AD)

N

D (°)

I (°)

k

a95 (°)

DParis (°)

IParis (°)

Archaeomagnetic dating (95% c.l.) (years AD)

CLGa01 CLGa02 CLGa03

2nd half of 10–12th 2nd half of 10–12th 2nd half of 10–12th

19 10 12

15.0 13.4 15.7

64.7 65.6 64.9

1530 1790 575

0.9 1.1 1.8

14.2 12.7 14.9

63.0 64.0 63.2

1022–1167 990–1162 991–1163

Inclinations and declinations reduced to Paris (DParis, IParis) have been used for dating with the French secular variation master curve after Bucur (1994) and Gallet et al. (2002). The last column gives the archaeomagnetic dates at a 95% confidence level.

the software RENDATE. The region of intersection of the declination (inclination) reference curve with the estimated kiln mean declination (inclination), including the errors of both, represents a probability density of possible dates (Fig. 8a and b). The multiplicative combination of declination and inclination probability density is used for final dating (shaded region in Fig. 8c and d). The dating solutions for all three kilns are given in Table 1. Relying on the average ChRM directions, the three kilns had probably been operated at the same time. The dating interval for kilns CLGa02 and

CLGa03 is larger compared to CLGa01 and therefore may suggest an earlier use of these two kilns. As a95 of both kilns is larger, they must however be considered to have been in operation in the same period as kiln CLGa01. The archaeomagnetic dating estimate refines the presumed archaeological age (cf. Table 1), particularly for a confidence level of 68% (cf. Fig. 8d). The dating solution obtained by probability densities after Lanos (2004) is in agreement with the method proposed by Le Goff et al. (2002) using a bivariate extension of Fisherian statistics

Fig. 8. Archaeomagnetic dating with probability densities using the method of Lanos (2004). Mean declination (a) and inclination (b) of kiln CLGa01, relocated to the geographical coordinates of Paris, are compared with the known archaeomagnetic reference curve for Paris after Bucur (1994) and Gallet et al. (2002). Red points are individual observations of reference data. The region of intersection of both, reference curves inclusive error envelope and site directions inclusive error represent probability densities of possible dates. The variables fb and tb/2 are the confidence coefficients of the Fisherian and the Students distribution, respectively, for a probability b = 0.05. The multiplicative combination of declination and inclination probability density is used for final dating (shaded region in c and d). (For the interpretation of color in this figure legend the reader is referred to the Web version of this article.)

S. Spassov et al. / Physics and Chemistry of the Earth 33 (2008) 544–556

For all specimens, the lower limit of the regression interval is not below 175 °C and the upper limit does not exceed 450 °C (Table 2). More TRM is acquired than NRM demagnetised at each temperature step above 450 °C, and the Arai diagram becomes non-linear. The results of all archaeointensity determinations are given in Table 2. From the 12 specimens analysed, two were rejected for calculation of the mean, because of high maximum angular deviation (MAD) values during NRM demagnetisation (specimen clga01e6s60) and because of thermochemical alteration (specimen clga01e5s61), i.e., one negative pTRM check in the regression interval. The average archaeointensity of kiln CLGa01 in Table 2 represents an arithmetic mean from the remaining specimens that

f (log10 h) heated

40 60 80 f (log10 h) non heated

100

CLGa01e1 – 6 to 8 cm below kiln floor 4 3.5 3 log10 (38 mT) 2.5 2 1.5 1 0.5 0.5

1

1.5 2 2.5 3 f (log10 h) non heated

3.5

0.5

120

4

300 ºC

300 ºC

20

4 3.5 3 2.5 2 1.5 1 0.5

1

1.5 2 2.5 3 f(log10 h) non heated

3.5

4

CLGa01e1 – 8 to 9 cm below kiln floor

log10 (40 mT) log10 (1 mT)

ng

20

g

40

log10 (32 mT)

afte

60

CLGa01e1 – 3 to 4 cm below kiln floor

rh eati

300 ºC

f (log10 h) heated

80

f(log10 h) heated

f (log10 h) heated

300 ºC

log10 (25 mT)

100

4 3.5 3 2.5 2 1.5 1 0.5

tin

CLGa01e1 – 0 to 1 cm below kiln floor 120

hea

Kilns CLGa02 and CLGa03 show moderate directional NRM stability during demagnetisation, as most of the MAD values are above 2°. Moreover, the floor of kiln CLGa02 consists of several baked layers, separated by insufficiently baked material, which strongly alters during thermal treatment (Fig. 6c). Also well-baked sand from the kiln floor is thermally unstable (Fig. 6d). Only kiln floor specimens from CLGa01 are therefore considered to be appropriate for archaeointensity determinations. Thermomagnetic curves indicate that the light brownish coloured baked clay from the kiln floor sample of CLGa01 at 3–5 cm depth shows very little alteration (cf. Fig. 5b) and seems to be most promising for the application of the Thellier–Thellier double heating method. In order to test the degree of alteration of the remanence carriers, another part of the kiln floor material was heated in air for about 4 h at 300 °C. Fig. 9 shows that only a narrow depth interval appears to be suitable for archaeointensity analyses, characterised by only very minor alteration of the remanence carrying mineral content during thermal treatment. This material presents the well-baked light brownish material closest to the heat source. Archaeointensity experiments were carried out on 12 specimens prepared from 7 samples from kiln CLGa01 with variable concentration of magnetic mineral phases (Table 2). An archaeointensity determination example of a representative pilot specimen is illustrated in Fig. 10. The choice of the temperature interval for linear regression is based on the following criteria:

re

5.3. Archaeointensity

(a) the degree of smoothness of the NRM demagnetisation and the TRM acquisition curves (Fig. 10a); (b) the linearity of the Arai diagram (R2 higher than 0.95, Fig. 10b and d, Table 2); (c) the directional stability during NRM demagnetisation, TRM acquisition and of residual NRM and partial TRM checks (Fig. 10c, grey points); (d) the degree of thermochemical alteration, i.e., partial TRM checks should fall within the 95% confidence intervals for the predicted responses of single observations in the Arai diagram (grey empty squares in Fig. 10d); (e) the equality of blocking and unblocking temperatures, i.e., the NRM of a partial TRM check should equal the NRM of the previous temperature step and should fall also within the 95% confidence intervals for the predicted responses of single observations in the Arai diagram (grey filled squares in Fig. 10d).

log10 (40 mT)

0.5

1

befo

(Le Goff, 1990), which tests the degree of compatibility between an individual Fisherian mean direction and the reference curve.

f log10 h

552

1.5 2 2.5 3 f(log10 h) non heated

log10 h

3.5

4

Fig. 9. Parametric plots of coercivity spectra of selected specimens from sample CLGa01e1 taken at different depths. The spectrum after heating f(log10h)heated300 °C is plotted vs. the spectrum before heating f(log10h)non-heated in function of the parameter log10h that is the Briggs logarithm of the magnetising h field given in mT. The powder specimens were heated for about 4 h at 300 °C in air. In the ideal case of absolutely no alteration, the coercivity spectra should be equal before and after heating resulting in a straight line of slope equal to one (black line). All specimens are strongly affected by alteration, except the specimen taken at 3–4 cm depth. Only little alteration occurs in the latter. For better understanding, the inset in (d) shows the coercivity spectra f(log10h) before (black) and after (grey) heating in function of the magnetising field log10h of the same sample.

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S. Spassov et al. / Physics and Chemistry of the Earth 33 (2008) 544–556 Table 2 Results of archaeointensity determinations applying the Thellier–Thellier double heating technique Specimen

NRM Distance Susceptibility, Laboratory Regression range below kiln (mA m2/kg) v (108 m3/kg) field, floor (cm) FL (lT) Tbeg Tend

clga01e1s60a 3.0–5.0 0.147 94.0 30.3 clga01e3s60 2.7–4.7 0.150 141.5 37.1 clga01e3s61 2.7–4.7 0.170 103.5 32.6 clga01e4s60 1.5–3.5 0.058 64.7 31.2 clga01e4s61 1.5–3.5 0.079 60.0 31.3 clga01e5s60a 4.0–6.0 0.044 45.6 30.7 clga01e5s61a 4.0–6.0 0.048 47.0 31.5 clga01e6s60 3.0–5.0 0.056 67.1 30.4 clga01e6s61 3.0–5.0 0.040 38.4 31.0 clga01e9s60 0.4–2.4 0.054 42.6 31.7 clga01e9s61 0.4–2.4 0.068 53.9 32.1 clga01e11s60 4.0–6.0 0.056 69.7 39.7 Mean and standard deviation (SD) 69.4 ± 1.1 Confidence interval at 95% level for expected value 66.9–71.8 Mean and random error at 95% c.l. 69.4 ± 2.5

250 275 300 225 200 200 175 250 275 275 250 225

400 375 450 350 375 350 325 375 375 375 375 400

Number ChRM of points, NF D I (°C) (°C) 8 5 6 6 8 7 7 6 5 5 6 7

334.3 29.5 30.4 10.8 18.1 57.8 86.4 29.1 11.7 13.6 34.3 359.9

ChTRM MAD D (°C) (°C)

63.8 3.6 61.9 4.2 62.1 4.4 63.0 6.1 62.6 2.3 74.8 8.6 80.1 5.9 51.1 13.5 61.7 4.6 63.0 3.3 65.5 6.2 60.3 8.9

261.1 144.4 206.0 189.1 136.4 67.9 142.3 258.6 210.6 153.9 22.7 92.6

I (°C)

MAD (°C)

83.6 87.5 87.2 84.9 87.8 82.5 88.7 79.0 81.2 83.2 83.2 87.1

7.1 9.6 2.7 11.6 6.0 15.0 7.6 13.2 6.2 12.0 9.6 17.1

Archaeointensity, Coefficient of Fa ± SD (lT) determination, R2

68.6 ± 2.0 76.7 ± 5.7 70.1 ± 4.3 73.3 ± 2.0 74.5 ± 1.7 72.4 ± 2.3 85.1 ± 4.4 48.4 ± 3.1 53.4 ± 3.7 76.6 ± 4.6 56.9 ± 2.8 71.3 ± 3.0

0.995 0.984 0.985 0.997 0.997 0.991 0.987 0.984 0.986 0.989 0.991 0.992

Specimens CLGa01e5s61 and CLGa01e6s60 (italics) were omitted for the mean calculation, because of negative pTRM checks and because of a maximum angular deviation >10° of the ChRM within the regression interval, respectively. a Non-oriented specimens.

Fig. 10. Archaeointensity determination of the pilot specimen. Residual NRM checks and partial TRM checks are represented by blue and red circles, respectively. (a) Thermal demagnetisation of NRM and acquisition of TRM. The shaded interval indicates the part of the curves with less noise, which is used for regression. (b) Arai plot: the part between 250 and 400 °C is linear and is used for regression. (c) Equal area plots of NRM demagnetisation, TRM acquisition, residual NRM checks and partial TRM checks. Green squares indicate the regression points. (d) Part of the Arai plot used for archaeointensity determination. The slope (black solid line) has been calculated for eight successive temperature steps, excluding residual NRM and partial TRM checks, ranging from 250 to 400 °C. The dashed lines represent the 95% confidence intervals for the predicted responses of single observations. Although the last residual NRM check does not fall into the error envelope, this point has been considered for slope calculation, because the corresponding partial TRM check is positive. (For the interpretation of color in this figure legend the reader is referred to the Web version of this article.)

fulfilled the criteria mentioned above. The homogeneity of the material varies inside a sample and therefore the calculation of sample averages prior to kiln mean calculation is irrelevant in

the present case. As the kiln is not completely preserved and its function still unclear, it is difficult to guess the exact dimensions of the original kiln and the temperature reached inside the

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S. Spassov et al. / Physics and Chemistry of the Earth 33 (2008) 544–556

combustion chamber, in order to assess the original cooling rates. Hence, a cooling rate correction has not been applied. Test measurements of magnetic susceptibility in three orthogonal axes give no indication for considerable anisotropy. The TRM anisotropy is considered to be negligible, which is often the case in non-moulded baked clay. Therefore a TRM anisotropy correction has not been attempted. Kiln CLGa01 has been dated to 1022–1167 AD on basis of archaeodirections (see Section 5.2 and Table 1). The palaeofield intensity at Paris is between 53 and 67 lT during this time interval (Chauvin et al., 2000; Gómez-Paccard et al., 2006). After latitude correction (reallocation of the data to Paris), the estimated palaeointensity of kiln CLGa01 amounts to 68.2 ± 2.5 lT, which agrees fairly well with data from other regions (Fig. 14 in Gómez-Paccard et al., 2006). The fact that the intensity is rather on the upper boundary may be due to different cooling rates during past kiln operation and laboratory treatment. As laboratory cooling rates are very probably faster than original cooling rates, the laboratory TRM and in turn the obtained archaeointensities may be overestimated (cf. Genevey and Gallet, 2002).

6. Discussion The main objective of the present investigation was to provide independent archaeomagnetic dating of the three kilns that were discovered during a preventive excavation of a likely High Middle Age iron working site in Corroy-le-Grand based on the direction of their ChRM and available secular variation curves of declination and inclination. In the first place, this may verify the presumed archaeological dating that is based on a preliminary examination of ceramic finds near the kilns. Moreover, there is an interest to extend the geomagnetic field record into the past and to combine these results with theoretical field models or to use them for analyses of the geomagnetic field (e.g., Hongre et al., 1998; Jackson et al., 2000). Field intensity determinations were performed to restrict multiple archaeomagnetic dating solutions based on directional data only due to errors or field recurrence. Indeed, when knowing the complete geomagnetic vector (direction and intensity), a burnt archaeological structure can be independently dated based on the direction only and based on intensity only. Combining both, the number of dating solutions can be reduced, and the dating result will gain in confidence. Archaeointensities are also highly needed to improve models of processes that take place in the Earth’s core. Besides, changes of the geomagnetic field strength have become an important issue as it may influence the Earth’s biosphere and be related to climate changes (e.g., Gallet et al., 2005). Geomagnetic field intensities can also be retrieved from sediments. But the latter are often not reliable for an accurate registration of the geomagnetic field, because of delayed recording due to complex sedimentation environments and magnetic mineralogy (Bleil and von Dobeneck, 1999; Spassov et al., 2003). Moreover, they yield only relative field intensity values. Archaeological burnt materials, however, do not have such limitations and provide nearly instantaneous absolute and more reliable records of the magnetic field by acquisition of a stable thermoremanent magnetisation. Unfortunately, at present, such records are irregular in both space and time. In particular, reliable geomagnetic intensity data for the High Middle Age (11–13th century AD) are rather scarce for Western Europe and not well dated (Hus and Geeraerts, 1998; Chauvin et al., 2000; Genevey and Gallet, 2002; Le Goff et al., 2002 and references therein). The archaeomagnetic dating of the three kilns in Corroyle-Grand, using directional data only, strengthens the presumed

archaeological age. It narrows the period of cessation of kiln operation between the end of the 10th century to the middle or third quarter of the 12th century AD, suggesting that the three kilns are contemporaneous within the dating error (Table 1). As mentioned in Section 4, the baked clay from Corroy-le-Grand consists of co-existing magnetic mineral phases with different remanent coercivity distributions (Figs. 2 and 4), and one would not expect such material to yield very reliable palaeointensity results, because of possible interaction of the two phases and violation of the law of independence. The palaeointensity results, however, do not show such complications. Apparently, both major remanence carrying magnetic mineral phases do not interact and have similar blocking temperature spectra. The presence of multidomain grains can not completely be excluded, but their remanence contribution is negligible, as the residual NRM checks are almost positive (Fig. 10d). Kiln CLGa01 yields a palaeointensity of 69.4 ± 2.5 lT (95% c.l.), and a virtual dipole moment (VDM) of (11.1 ± 6.3)  1022Am2, 95% c.l., can be calculated from the measured inclination and archaeointensity (error calculation given in appendix). The VDM value for kiln CLGa01 is slightly higher than the values between 9.8 and 10.3  1022Am2, obtained for Bulgaria by Kovacheva et al. (1998) within the same time interval. The same holds true for composite VDM records for eastern Europe (Valet, 2003 and references therein) and predicted virtual axial dipole moments (VADM) derived from the model of Hongre et al. (1998). The cause for this slight overestimation may be due to not applying a cooling rate correction. Knowledge of kiln function is irrelevant for archaeomagnetic dating, but may be a useful complementary information for interpretation of the rock magnetic properties. The exact function of the three kilns unearthed in Corroy-le-Grand remains an enigma, and the contribution of the archaeomagnetic investigation to answer this question is rather limited at present. The strongly ferruginous sands with iron pans which are outcropping in this area contain hard banks of limonite. Fig. 6a and b indicates that strongly ferrimagnetic compounds are formed after heating limonite to 700 °C in air. Pieces of burnt limonite that were present in the infillings of kiln CLGa02 (F13) suggest an iron working site that exploited the limonite banks that are common in the formation of the Brussel sands and sandstones in the area. Fragments of a crucible found in the ditch cutting one of the corners of one of the kilns (CLGa03, respectively, F92) may suggest metal smelting activities. Several slags, one of them decimetre-sized, were discovered not far from the kilns. The three kilns seem to have been open at the smaller sides, and are probably single-chambered, twin-flued kilns, with the flues linking the stokeholes to the kiln chamber. If this is the case, this particular design creates strong suction, increasing the draught drawing the flames into the heating chamber. It is interesting to mention that single-chambered, twin-flued kilns, but used for pottery production, have been reported for Roman Britain (Svan, 1984). In that case the flues are, in contrast to the kilns examined here, tapered and widened in the centre. Several twinflued kilns of the second half of the third century discovered in a Roman vicus in Baudecet near Gembloux (Belgium), have been reported by Plumier (2006). Due to the presence of numerous slags, these kilns were attributed to iron working activities. Various but not frequent ceramic finds of different cultural epochs in the site of Corroy-le-Grand (including Andenne, Mayen and even Roman wares) in pits and on living floors, as well as the shape of the kilns (narrow, rectangular heating chamber without any widening) point out that the hypothesis of pottery production may reasonably be rejected. It remains the hypothesis that the kilns were related to iron working activities. Iron production starting from limonite consists of multiple processes: iron ore reduction by roasting in order to dehydroxylate the iron-oxyhydroxides,

S. Spassov et al. / Physics and Chemistry of the Earth 33 (2008) 544–556

followed by heating in a low furnace where the silicates are liquefied forming slags, re-heating and hammering of the iron bloom in order to remove slags and charcoal still present, and finally fashioning and manufacturing of objects (Forbes, 1950). Roasting is generally done on a surface at ground level or in a shallow depression and this could have been the case for kiln CLGa02 (F13). Whether the other two kilns were used to treat iron bloom or to manufacture or to work objects remains unsolved. The presence of many pieces of burnt sandstone in CLGa02 (F13) and several iron slags in pits near the baked structures, of which one was decimetre-sized, supports the idea that the kilns or baked structures were related to iron working activities. 7. Conclusions The archaeomagnetic investigation of three kiln remains discovered in the High Middle Age archaeological site of Corroy-le-Grand confirms the presumed archaeological age. The preliminary archaeological context dating result could be refined by archaeomagnetic dating based on inclination and declination of the characteristic remanent magnetisation of the kilns between the end of the 10th century to the middle or third quarter of the 12th century AD. Archaeomagnetic dating also suggests that the three kilns are contemporaneous within the dating error. A careful choice of burnt samples based on rock magnetic properties of laboratory heated sister samples resulted in a successful determination of the past geomagnetic field intensity with a rather small error. The estimated local palaeointensity of 69.4 ± 2.5 lT and corresponding virtual dipole moment of 11.1 ± 6.3  1022 A m2 agree fairly well with data from other regions in Western Europe for the considered time interval. The presence of different remanence carrying magnetic mineral phases has no considerable influence on the accuracy of the determined archaeointensity in the present case, as both major remanence phases have similar blocking temperature spectra and do not interact with each other. The three kilns are very probably related to metal working activities, but their exact function remains unclear and only further excavation of the area may help to solve this problem. Acknowledgements

Appendix The virtual dipole moment (VDM) in Section 6 is calculated after the following expression: 4pr 3 1 F a pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l0 1 þ 3 cos2 hm

where r is the median radius of the Earth, equal to 6371  103 m, l0 the magnetic permeability of vacuum equal to 4p  107 V s=A m and Fa the measured archaeointensity in T or V s/m2. The magnetic archaeosite co-latitude hm is obtained from the well-known relation cot hm ¼ 12 tan I, with I the archaeofield inclination. The latter is assumed to be equal to the measured inclination of the characteristic remanent magnetisation. Substituting the expression for the magnetic archaeosite co-latitude into Eq. (1) and rearranging yields the following expression: VDM ¼

4pr3 F a qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 l0 1 þ 1þ4cot 2I

ð2Þ

Eq. (2) is the basis for the calculation of the random error of VDM, which is estimated following the rule of propagation of the random error after C.F. Gauss: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2 oVDM oVDM ~I ~VDM ¼ ~F a r ð3Þ r r þ oF a oI ~VDM ; r ~F a , and r ~I are the (empirical) standard deviations of VDM, r archaeointensity Fa and the inclination I, respectively. The median radius r and the permeability of vacuum l0 can be considered as constants and hence have no standard deviations. The first derivative after Fa is thus oVDM 4pr 3 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi oF a 3 l0 1 þ 1þ4cot 2I

ð4Þ

and the first derivative after I is oVDM ¼ oI

48pr 3 F a cot Icsc2 I 3  2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 l0 1 þ 4cot2 I 1 þ 1þ4cot 2I

ð5Þ

Inserting expression (4) and (5) into Eq. (3) gives ~VDM r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v0 12 0 12ffi u u uB 3 3 2 4pr 48pr F a cotIcsc I C B C ¼u ~I A r ~F a A þ @  3 r t@ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 2 2 3 l0 1 þ 1þ4cot 2I l0 1 þ 4cot I 1 þ 1þ4cot2 I ~I can be derived The standard deviation of Fa is given in Table 2 and r by following the formalisms of Lanos et al. (2005):

This research has been supported by the European research training network Archaeomagnetic Applications for the Rescue of Cultural Heritage (AARCH), contract number HPRN-CT-200200219, which is greatly acknowledged. The authors are highly indebted to the Service de l’Archéologie, Province Brabant-wallon, for authorisation to sample the kilns in Corroy-le-Grand and for the help provided during sampling. Sylvie de Longueville of the Centre de Recherche Archéologique National de l’Université Catholique de Louvain (UCL) is thanked for providing already the preliminary dating results of the ceramics. The authors wish to thank further Ramon Egli for using his software package MAGMIX, Miriam Gómez-Paccard for having provided data for comparison, as well as Philippe Lanos for clarifying discussions and for making available his dating software RENDATE. The authors are grateful to Rob Sternberg and David Starley for their careful and constructive reviews.

VDM ¼

555

ð1Þ

~I ¼ r

a95 fb;i

ð7Þ

with fb,i being the confidence factor of the Fisherian distribution (Table 2 in Lanos et al., 2005), for a certain number of observations i. Parameter a95 is given in Table 1. Finally, the random error of the virtual dipole moment DRVDM for a chosen probability b is then ~VDM tb=2;i DR VDM ¼ r

ð8Þ

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