A NEW METHOD FOR GAMMA DOSE-RATE ESTIMATION

OF HETEROGENEOUS MEDIA IN TL DATING

PIERRE GUIBERT,1* FRANC°OISE BECHTEL,1 MAX SCHVOERER,1 PIERRE MUÈ LLER2 andSANDA BALESCU3

1Universite M. de Montaigne, Bordeaux III, CNRS ESA 5060, Centre de Recherche en PhysiqueApplique e aÁ l'Arche ologie (CRPAA), Maison de l'Arche ologie, F 33405 Talence Cedex, France,

2Universite de Marseille, CRMC2-CNRS, Campus de Luminy, case 913, F 13288 Marseille Cedex 9,France and 3Universite du Que bec aÁ Montre al, De partment des Sciences de la Terre, CP 8888, succ.

Centre-Ville, Montre al, Canada H3C 3P8

(Received 16 February 1997; revised 12 May 1998; in ®nal form 21 May 1998)

AbstractÐIn this paper we develop a new method for gamma dose rate estimation of heterogeneousarchaeological deposits. This method is based upon a computerised reconstruction of the gamma irra-diating environment of the sample to be dated when applying any paleodosimetric methods such asthermoluminescence (TL), optically stimulated luminescence (OSL) and electron spin resonance (ESR).If the deposits overlying the sample to be dated have already been excavated, the missing upper en-vironment (i.e. the relative position, the shape and the size of each lithologic component) is graphicallyreconstructed using the information recorded in ®eld documents. For this purpose, the space surround-ing the dated sample, within a 50 cm radius sphere, is decomposed into spherical volume elements, con-tiguous and centred on the dated sample. Within each volume element, the proportion of each lithilogiccomponent is estimated. The K, U and Th contents of each lithologic component are determined. Thisenables us to quantify the e�ective radiochemical composition of any lithologic component. The relativeweight of each volume element, which is related to the absorption properties of the g rays by the radio-active system being studied (i.e. the dated sample and the surrounding environment) is estimated by acomputation whose potentialities and limitations are discussed.

Both this reconstruction and in situ radioactivity measurements were applied at the cave known as``Grotte XVI'' in Dordogne (southwestern France), in order to assess the g dose-rate of TL dated burntsediments extracted from a Mousterian combustion structure. In spite of its complexity, this reconstruc-tion method yields a more suitable and more accurate determination of the environmental dose ratethan the classical and/or simpli®ed approaches. # 1998 Elsevier Science Ltd. All rights reserved

1. INTRODUCTION

Application of any paleodosimetric dating methods

such as thermoluminescence (TL), optically stimu-

lated luminescence (OSL) and electron spin reson-

ance (ESR) requires determination of the annual

dose-rate. However, this determination is made dif-

®cult by the presence of heterogeneities in the radi-

ation ®eld due to spatial variations in the

radiochemical composition within the irradiating

medium. Any heterogeneity in the radiochemical

composition can generate, at various scales, gradi-

ents in particle or photon ¯uence. The scale of

these e�ects varies depending on the irradiating par-

ticle: around 10 mm for a particles, 1 mm for b par-

ticles and secondary electrons and 10 cm for gphotons.

The e�ect of dose gradients related to a and bparticles can be minimised by adopting speci®c ana-

lytical procedures: for example, the removal of the

outer layer of the thermoluminescent grains

(Mejdahl, 1982) or the removal of the external parts

of the samples to be dated. However, locally distrib-

uted heterogeneities in a and b radiations within a

sample induce variations of accumulated dose from

one grain to another. The use of a large number of

grains (multigrain aliquots) generally can compen-

sate for this dose heterogeneity.

In the case of g photons, however, problems

raised by heterogeneities in the radioactive environ-

ment of the sample to be dated cannot be mini-

mised by speci®c sample treatment (Schwarcz,

1994). For practical reasons, this problem cannot

be solved by applying the same kind of procedure

as for a and b local heterogeneity compensation

(i.e. by increasing the number of dated samples).

In this paper, we discuss the problem raised by

the existence of gamma gradients when estimating

the environmental dose-rate and present our sol-

ution to the challenge of TL dating burnt sediments

of a Mousterian combustion structure from an im-

Radiation Measurements Vol. 29, No. 5, pp. 561±572, 1998# 1998 Elsevier Science Ltd. All rights reserved

Printed in Great Britain1350-4487/98 $19.00+0.00PII: S1350-4487(98)00069-9

*To whom all correspondence should be addressed. Tel: (33 or 0) 5-56-84-51-60; Fax: (33 or 0) 5-56-84-51-57; E-mail:crpaa@montaigne.u-bordeaux.fr

561

portant cave of Dordogne (France) known as``Grotte XVI''.

2. PROBLEMS RAISED BY

ENVIRONMENTAL HETEROGENEITY: A

CASE STUDY FROM GROTTE XVI

2.1. The site and the TL samples

Grotte XVI is a cave located within the ``LeConte'' karstic cli�s, at Ce nac and St-Julien in

Dordogne (southwestern France). At least 23 cavesand shelters have been discovered in these cli�s,including the well-known site of the Vaufrey Cave

(Grotte XV).The heterogeneous archaeological deposits of

Grotte XVI are composed of sand and coarse lime-

stone fragments. The archaeological sequence(Rigaud et al., 1995) is as follows. The lower levelsinclude, from bottom to top: (1) three nearly sterilelevels (K, J and I) yielding only few Mousterian

artefacts, and (2) four levels (H, G, F and E) con-taining Mousterian assemblages partly produced bythe Levallois method. The upper levels, shown in

Fig. 1 are the following, from bottom to top:

ÐLevel D is a heterogeneous sandy deposit con-taining few large limestone and calcite fragments:

Mousterian artefacts are present but the Levalloisdebitage is uncommon.

ÐLevel C is a complex deposit containing a

Mousterian assemblage of Acheulean Tradition andalso a Mousterian combustion area; the sedimentsare made up of approx. 15 cm of brown yellow

sand and coarser cryoclastic elements are rare.ÐLevel B marks the beginning of the upper

Paleolithic sequence. The artefacts are rare but

include several Castelperronian points.ÐLevel A is a very complex deposit, often more

than 60 cm thick, composed of silty sands and coar-ser limestone fragments of di�erent size. Several

sub-levels have been distinguished, such as Abase

and Asup (Fig. 1) which contain Aurignacian andSolutrean assemblages, respectively.

Finally, the most upper level 0, only found in theremote rear gallery of the cave, contains a very richand varied Magdalenian assemblage.

For dating purpose, six TL samples have beencollected within the burnt sediments (sand) of theMousterian combustion area of level C (BDX 2794,

2800, 3606, 3609, 3612 and 3615).

2.2. The radiochemical composition of the archaeolo-gical deposits of Grotte XVI: evidence of gammairradiation heterogeneities

The natural radioelement concentrations of sedi-ments (sand) and limestone fragments collected

within the upper levels (A, B and C) were measuredby low background gamma spectrometry (Guibertand Schvoerer, 1991). The analytical results dis-cussed in detail by Guibert et al. (1997), are

reported in Table 1).In most samples, a signi®cant deviation between

the two uranium measurements, U(238U) and

U(226Ra), provides evidence for a disequilibrium inU-series. According to the radiochemical study ofGuibert et al. (1997), this disequilibrium is due to a

uranium enrichment (234U, 235U and 238U). A singleperturbation model was used to estimate the age ofthe U ingress; an apparent age of 1426 ka wasobtained using the radiochemical data of the altered

limestone extracted from level C. This suggests thatthis phenomenon is rather recent when comparedwith the TL age of the Mousterian ®res, 64.623.1

ka in weighted average (Guibert et al., 1995). Thedisequilibrium and consequent variations inuranium (and daughters) contents have been taken

into account for the annual dose-rate estimationsbased on g spectrometry measurements, using theannual dose data of Nambi and Aitken (1986) and

considering U (and immediate daughters) and 230Th(and daughters), separately (Guibert et al., 1994).The analytical data reported in Table 1 show that

the radiochemical composition of the sedimentFig. 1. Stratigraphic section of the Grotte XVI excavation:

upper levels D to A after Rigaud et al. (1995).

P. GUIBERT et al.562

(sand) and the buried limestone fragments from

level C are signi®cantly di�erent: the limestone frag-

ments are 5 to 10 times less radioactive than the

sand. Consequently, the archaeological deposits

may exhibit a high variability in radioactivity,

depending on the presence of limestone fragments.

This was con®rmed by direct measurement of the

environmental dose-rate at di�erent locations in the

cave using CaSO4:Tm dosimeters. Values ranged

from 0.36220.036 to 0.81520.050 Gy/ka with a

mean value and associated standard deviation of

0.54520.117 Gy/ka.

Also, it should be pointed out that the sediment

in the combustion area is 20 to 30% more radio-

active than anywhere else in the cave. These di�er-

ences in radiochemical composition (i.e. U, Th, and

Table 1. Radiochemical composition of the sediment and the limestone fragments from Grotte XVI, obtained by lowbackground gamma spectrometry (nd: not determined)

Sample Coordinate K (%) U(238U) (ppm) U(226Ra) (ppm) Th (ppm)

Level Asup

(sediment)BDX 2943 G8 0.7620.01 1.9520.15 1.6520.02 6.2920.07

Level B (sediment)BDX 2940 G9 0.6220.01 1.6520.13 1.2820.02 5.3820.06BDX 4534 G/H8 0.7820.01 1.9420.30 1.4720.02 6.8320.07BDX 3617 I9 0.6920.01 1.4720.14 1.2820.02 5.6720.06

Level C (burntsediments in thecombustion area)

BDX 2794 I9 0.9320.02 2.8520.35 1.9020.05 9.9720.15BDX 2798 H/18 1.0120.03 3.1020.49 2.4020.07 11.9520.20BDX 2800 J8 1.0420.02 3.5220.31 2.3720.04 10.9720.14BDX 3606 I9 0.8920.03 3.2520.39 1.8920.06 9.2520.17BDX 3609 J9 1.0020.07 2.9820.37 2.0720.22 10.1221.21BDX 3612 I10 1.6420.03 2.8320.37 2.3120.06 8.9620.16BDX 3615 I10 1.0420.02 2.3420.31 1.9220.05 10.4120.14BDX 3620 I9 1.1020.03 2.8320.37 1.9420.06 8.1620.16

Level C (unburntsediments in thecombustion area)

BDX 2793 I8 0.9120.02 2.1820.21 1.6320.03 8.0220.10BDX 2795 I9 0.9020.02 1.9020.24 1.7220.04 8.6920.11BDX 2799 I8 0.8920.02 2.6120.31 1.9020.04 8.2020.13BDX 2801 J8 0.8320.02 2.2920.19 1.5920.04 7.3720.14BDX 2803 H/I8 0.7820.01 1.8520.16 1.6820.02 6.9720.07BDX 3607 I9 0.9520.01 2.1920.18 1.9420.03 8.7920.08BDX 3608 I9 0.9020.01 2.0120.15 1.9820.02 8.5020.07BDX 3610 J9 0.9020.01 1.7020.18 1.7120.03 7.5420.08BDX 3613 I10 1.3920.02 2.0920.18 2.0220.03 7.8020.08BDX 3614 I10 1.0720.01 1.8220.20 1.4820.03 6.4720.09BDX 3616 I10 1.0120.01 2.1320.15 2.1020.02 9.4920.07BDX 3621 I9 0.8320.01 1.4520.12 1.4820.02 6.5120.06

Level C ( . . .outsidecombustion area)

BDX 2796 J/K9 0.7520.01 2.1720.15 1.3720.02 6.6120.07BDX 2804 J8 0.8620.02 2.1620.19 1.5720.03 7.2920.09BDX 3611 J9 0.7720.01 1.7920.13 1.2920.02 6.8720.06BDX 3622 I9 0.7520.01 1.8720.12 1.1920.02 5.7920.05BDX 3942 I10 0.9420.01 1.6320.13 1.7020.02 8.0720.06

Limestonefragments,unaltered

BDX 2941 nd 0.08820.003 0.1920.06 0.18020.010 0.6820.02BDX 3938 K/L14 0.18420.005 0.2620.08 0.28120.011 1.4820.03BDX 4538 nd 0.09020.006 0.2120.04 0.16520.010 0.8420.04

Limestonefragments, altered

BDX 2797 I8 0.12820.006 0.7320.11 0.43020.013 1.3920.04BDX 2802 J8 0.17320.006 0.6420.10 0.38520.011 1.2920.03BDX 3618 I10 0.11020.010 0.8820.11 0.26620.013 1.0820.04BDX 3619 H9 0.10020.010 0.3320.09 0.20220.011 0.9620.03BDX 3623 H9 0.08020.004 0.4020.09 0.19820.011 0.8320.03

The two di�erent values of uranium content are estimated from two groups of g emitters: U(238U) from 234Th and235U; U(226Ra) from 214Pb and 214Bi, in equilibrium with 222Rn. The uncertainty is one counting standard deviation; thesquared calibration errors are to be added to the latter in order to determine the overall uncertainty. The calibrationerrors are:22%% for K, Th and U(226Ra),217% for U(238U) (Bechtel et al., 1997)

NEW METHOD FOR GAMMA DOSE-RATE ESTIMATION 563

K contents) are inversely correlated with the ®negrain CaCO3 content (calcite dilutes the radioactive

minerals).

2.3. Classical approach to environmental dosimetry:

problems of representativeness

These heterogeneities in the radiochemical com-

position of the archaeological deposits raise twoproblems.The ®rst is related to the excavation technique

that has been used: the burnt sediments to be datedby TL were extracted from a horizontal surface andnot a vertical section. The environmental radioac-

tivity could be measured in situ using a dosimeteror a gamma-ray meter introduced into the samelevel C in the nearest stratigraphic section.

However, the sediment in the combustion area ismore radioactive than the sediment from the samelevel C outside this area, as mentioned above. Theradiochemical continuity conditions required for

this in situ measurement are therefore not satis®ed.The second problem is related to the existence of

coarse limestone fragments in the surrounding of

the burnt sediments. Even if direct measurement ofthe environmental dose-rate using a dosimeter or agamma-ray meter was possible on a vertical section,

the distance of a few tens of centimeters betweenthe TL sampling point on the surface and themeasuring point inside the burial medium, wouldinduce an important potential source of uncer-

tainty.To address these problems we develop a new

method for environmental dose-rate determination.

The latter is based upon a reconstruction of thelithologic and radioactive environment of thesample to be dated, as described below.

3. PRINCIPLE OF THE ANNUAL gg DOSE-

RATE ESTIMATION USING A

RECONSTRUCTION METHOD

The archaeological deposits overlying the TLsamples of Grotte XVI were removed during exca-vation. The g contribution of the upper depositswas therefore irreversibly missing. In order to deter-

mine the total g dose-rate at the TL sampling point,we reconstruct by computation the missing upperenvironment of the TL samples (i.e. the relative lo-

cation, the shape and the size of the limestone frag-ments embedded in sand) using maps, photographsor even numerical records from previous exca-

vations.Two types of material contribute to the total g ir-

radiation at this TL sampling site: the sediment

(sand) and the limestone fragments. Hence, theannual g dose-rate, Dg, belongs to the intervalde®ned by the in®nite sediment matrix dose-rate,Dg sed , and the in®nite limestone matrix dose-rate,

Dg limestone as:

Dg � p :Dg limestone � �1ÿ p� :Dg sed �1�where p represents the e�ective limestone content of

the soil (or the deposits) surrounding the TL

samples. Furthermore, Dg limestone and Dg sed can be

estimated from their respective K, U and Th con-

tents, using the dose-rate data compiled by Nambi

and Aitken (1986) or, more recently, by Liritzis andKokkoris (1992) [appendix (1)]. The parameter p

must be determined using the available archaeologi-

cal maps or other ®eld documents, taking into

account the absorption properties of g rays by the

soil.

For this purpose, a decomposition of the space

surrounding the TL samples, within a 50 cm radius

sphere, is suggested (Fig. 2). A ®nite number of

volume elements is obtained. Each contributes to

the total g dose-rate and ®nally Dg can be formu-

lated according to relation (2):

Dg �Xi

Dgi �2�

where Dgi is the i-th element contribution to the g

Fig. 2. Decomposition of the space surrounding the TLsample for estimation of the environmental dose-rate.Figure 2(a): Spherical volume elements centred on the TLsampling point. Figure 2(b): Horizontal plane (P) showingthe intersection of the volume elements with limestone

fragments.

P. GUIBERT et al.564

dose-rate. Within each volume element, Dgi is thesum of g contributions from the limestone and the

sediment, according to relation (3):

Dgi � wi : �xi :Dg limestone � �1ÿ xi� :Dg sed� �3�xi, the mass fraction of limestone in the i-th volumeelement, can be evaluated from the excavationdocuments as described below. The parameter wi is

a weighting coe�cient (awi=1) which depends onthe speci®c geometry of the i-th element and on theg radiation absorption by the soil. The e�ectivelimestone content p, de®ned in relation (1), is ®nally

given by:

p �Xi

wi : xi: �4�

In order to evaluate the wi coe�cients, spherical

volume elements, contiguous and centred on the TLsampling point, are de®ned (Fig. 2). With suchspherical geometry, wi depends only on g radiation

absorption. In other words, the wi coe�cients referonly to the g dose transmission through the spheri-cal volume of soil between the TL sample and the

i-th volume.

4. TRANSMISSION OF gg DOSE IN SOIL

4.1. Basic relations

The basic formula for the computation of the wi

coe�cients de®ned above relates the volume el-ement, dt, to the g dose-rate, Dg, according to (5):

d 4Dg � dt4pr2

:E : men�E� : exp�ÿmatt�E�rr� : n�E�dE�5�

where r is the distance between the TL sample andthe volume element, E is the photon energy, men(E)is the mass energy transfer coe�cient of the irra-diated sample, matt(E) is the mass attenuation coe�-

cient of the soil, r is the speci®c mass of the soiland n(E) dE is the number of photons whose ener-gies range from E to E + dE. Using a spherical de-

composition of the space, relation (5) becomes:

d2Dg � E : men�E� : exp�ÿmatt�E�rr� : n�E�dE dr �6�where dr is the thickness of volume elements(dt = 4pr2dr). It should be stressed that, if absorp-

tion of g-rays in the soil [expressed by the exponen-tial term in relation (6)] did not occur, any volumeelement would have the same weight in the total gdose-rate. However, relation (6) allows us to com-pute the screening e�ect of the soil to g radiation ina spherical geometry. Thus, the g annual dose-rate

transmission factors through a sphere of radius r,f(r), centred on the TL sampling point, can be com-puted according to relation (7):

f�r� �RE : men�E� : exp�ÿmatt�E�rr� : n�E�dER

E : men�E� : n�E�dE: �7�

For speci®c values of r, deduced from the space de-composition, the weighting coe�cients, wi [relation

(3)] are related to the dose transmission factors by asimple proportion:

wi � K : f�ri� �8�with i being the index of volume element, ri itsradius, and K a normalisation factor so thatSwi=1.

Relations (5)±(7) include a term, n(E)dE, whichrepresents the g photons distribution according totheir energies. Computation of wi requires that the

g-ray spectrum be known; the latter is generatedusing the computation described in the followingsection.

4.2. Computation of the gamma spectrum

Computation of the radioactive medium g spectra

was carried out in our laboratory for an in®niteand homogeneous soil. Note that this kind of com-putation has also been run in the ®eld of environ-mental dosimetry by other authors (Valladas, 1982:

Evans et al., 1982; Aitken et al., 1985; FaõÈ n et al.,1985). The principle of such computation is the fol-lowing. Within the energy range 10 keV (Bi X-rays,

L-series), 2615 keV (208Tl g-ray, daughter of 232Th),photoelectric absorption and Compton scatteringwere the only e�ects taken into account in our com-

putation. The production of pairs (electron±posi-tron) has been neglected here because of its lowcontribution. A simpli®ed g spectrum is thenobtained by superposition of a primary radiation

emitted by natural nuclides and a secondary radi-ation originating from Compton single and multiplescattering.

The primary radiation is made of g photons, pro-duced by radionuclide decays, which did not inter-act with matter during their transport from the

volume element-source to the absorbing sample tobe dated. If n0 is the number of photons of E0

energy emitted per time and soil volume unit, a

total ¯uence for primary radiation, F0 (number ofphotons per time and surface unit) is given by re-lation (9):

F0 � n0matt�E0�r �9�

with matt(E0) being the mass attenuation coe�cient

of medium at the photon energy E0 and r itsspeci®c mass. Note that the ratio n0/r is the numberof photons emitted per time and mass unit which is

proportional to the parent nuclide mass concen-tration.The primary radiation photons can interact with

the emitting medium according to Compton scatter-ing. It leads to a ``®rst generation'' Compton radi-ation photons whose energies, E, are smaller than(or at most equal to) primary E0 energies. A limited

NEW METHOD FOR GAMMA DOSE-RATE ESTIMATION 565

fraction of these interactions give rise to photon

energies ranging from E to E + dE. Let the ¯uence

of these photons be F1(E):

F1�E� �Z

F0�E0� : mc�E0�matt�E�

:F�E0;E� : dE0: �10�

In relation (10), F(E0, E) is the probability that a

Compton interaction of a photon with an initial

energy ranging from E0 to E0+dE0, produces a sec-

ondary photon of energy E; this probability was

modelled using Klein and Nishina's formula

(Evans, 1968); mc(E0) and matt(E) are, respectively,

the Compton mass attenuation (in soil) coe�cient

for E0 energy photons and the total mass attenu-

ation (in soil) coe�cient for E energy photons.

The ``®rst generation'' of Compton photons mayinteract again according to a second Compton scat-

tering that produces a ``second generation''Compton radiation, etc. Finally, the total ¯uence ofphotons having an energy E, n(E), is the sum of the

primary radiation and the secondary Compton radi-ation composed of ``multiple generation'' of pho-tons:

n�E� �Xk�0

Fk�E�: �11�

Di�erent procedures have been proposed in the lit-erature for calculation of the in®nite matrix g spec-

tra: an iterative calculation of the multiplegenerations of Compton photons has been pre-sented by FaõÈ n et al. (1985). Valladas et al. (1982)have published a Monte-Carlo type computation.

In our laboratory the g spectra were obtained usinga calculation the principle of which derives fromthe Compton multiple generation iterative pro-

cedure. To summarize this technical aspect, the con-vergence limit of Compton series was found out,like the limit of geometric series; consequently, the

computation of Compton spectral componentsrequires only one run instead of numerous iter-ations of the multiple generation process.

Figure 3 shows the g spectra obtained in our lab-oratory; the chemical composition of the mediumthat has been used in each computation is reportedin the corresponding caption. The total and

Compton mass attenuation coe�cients were evalu-ated using Storm and Israel's (1970) tables. At thisstage of computation, the following simplifying ap-

proximations have been made: a secular equilibriumof the U-series has been assumed, a simpli®ed g-raylist for U and Th has been used (restricted to the

most intense gamma lines that emit up to 90% ofthe total photon energy). Their e�ect on the g-dosetransmission factors and on the g dose-rate will be

discussed below.

4.3. Gamma dose transmission factors

In Fig. 4 and Table 2 we report the g dose trans-

mission factors obtained for a distance r, betweenthe TL sample and the irradiation source, rangingfrom 0 to 50 cm in a medium of density 2 and a

dose absorbing material similar to quartz (SiO2).The rapid decrease of the g dose-rate transmissionis noticeable within a 5±10 cm distance between the

TL sample and the irradiating source. The separatecomputations of transmission factors for K, U andTh spectra, show the dependence of di�erential

absorption of photons on the g energy distribution:the lower the g photon energy, the more rapid thedecrease of the g dose-rate transmission factors withdistance.

Fig. 3. Gamma spectra of K, U and Th (and daughters inequilibrium) in an in®nite and homogeneous soil as com-puted in our laboratory (CRPAA, Bordeaux). Resolutionof calculation is 10 keV. Soil composition is as follows:H = 1.12% (H2O= 10%), C = 0.60%, O = 52.54%,Na = 2.23%, Mg = 3.02%, Al = 5.29%, Si = 28.02%,

K= 1.66%, Ca = 2.00% and Fe = 3.50%.

P. GUIBERT et al.566

4.4. Evaluation of the error on the g dose trans-mission factors

We use a simpli®ed list of g-rays when calculating

in®nite medium spectra of the U and Th series in

order to reduce the computation time. For instance,

the U-series spectrum of more than 500 lines is

restricted to the 40 most intense lines since they

emit up to 90% of the total g energy of the U-

series. The average photon energy (or energy per

emitted photon) is an important parameter on

which depend the g dose transmission factors. The

most important relative di�erence in the trans-

mission factors, by only a few percent, is obtained

with 40K (photon energy of 1461 keV) and U-series

emissions (average energy per photon of 750 keV).

We therefore suggest that using a complete list,

with an average energy of 740 keV for U-series

(instead of 750 keV), would not signi®cantly a�ect

our results. Finally, the g dose-rate at a given

sampling point, Dg, is estimated by a linear combi-

nation of in®nite matrix g dose-rates of all lithologic

components of the environment (i.e. limestone frag-

ments and sand) according to relation (1). These

are determined from their K, U and Th contents,

using annual dose-rate tables. The simpli®cation of

U and Th emission spectra does not a�ect the in®-

nite matrix g dose-rate estimation, but gives rise to

only a weak dependence of the g dose transmission

factors (the parameters of this linear combination).

It should be stressed that the uranium enrichment

of the archaeological deposit has been taken into

account for the in®nite matrix g dose-rate evaluationbut not for the computation of the g dose-rate trans-mission factors; this U ingress does not induce an im-

portant change in the g spectrum and produces a

similar e�ect on the transmission factor to that

induced by the simpli®cation of the U and Th series

emission spectra. A more accurate computation of

the g dose transmission factors is to be carried out in

the near future; it requires the consideration of two

sets of emitting nuclides, separately: on one hand, the

set from 238U to 234U and from 235U to 231 Th, and

on the other hand, the set from 230Th to 206 Pb and

from 231Pa to 207Pb.

The values of the g dose transmission factors may

be a�ected by the existence of spatial heterogeneities

in the g-ray absorption. However, within the natural

g emission energy range, higher than 100±150 keV,

the strongly predominant e�ect is the Compton scat-

tering, the probability of which is proportional to the

Z/M ratio (atomic number/mass number) of the

emitting medium. Since its components, limestone

and sand, have nearly constant Z/M ratios and den-

sities, we assumed that the Compton absorption

properties were isotropic. In the low energy region

(less than 100±150 keV), photoelectric absorption

strongly a�ects the dose absorption and the g attenu-ation; the existence of discontinuities implies spatial

anisotropies of the low energy part of g spectra. Thiskind of e�ect should a�ect the values of the g dose

transmission factors, although the energy of the gphotons is low and their contribution to the dose is

minor. The signi®cance of this e�ect remains to be

investigated. Nevertheless, the homogeneity of the

emitting medium with the few centimeters around the

TL samples should make the e�ect of this anisotropy

small. This homogeneity condition is satis®ed for the

burn sediments from the Mousterian ®res at Grotte

XVI.

Within the energy range considered, the systematic

relative uncertainties in the mass attenuation and the

mass energy absorption coe�cients are approxi-

mately23% (Storm and Israel, 1970). According to

relation (7), the systematic uncertainties in the mass

Fig. 4. Gamma dose-rate transmission factor, f(r), in amedium of density 2 calculated for K, U and Th, separ-ately, vs the distance between the TL sample and thespherical radioactive source (K: solid diamonds, U: open

diamonds, Th: solid triangles).

Table 2. K, U and Th g dose transmission factors, f(r),calculated for di�erent distances (r) between the sourceand the absorber in a spherical geometry. Dose absorberis silica (SiO2); see caption of Fig. 3 for the soil compo-

sition

r(cm) K U Th

0 1.000 1.000 1.0001 0.877 0.858 0.8562 0.775 0.739 0.7383 0.687 0.642 0.6434 0.611 0.561 0.5665 0.544 0.493 0.5026 0.486 0.435 0.4498 0.389 0.342 0.36410 0.312 0.272 0.29912 0.252 0.217 0.24815 0.183 0.155 0.18820 0.108 0.089 0.11925 0.065 0.052 0.07530 0.040 0.031 0.04935 0.024 0.020 0.03340 0.014 0.012 0.02345 0.007 0.007 0.01450 0.003 0.003 0.007

NEW METHOD FOR GAMMA DOSE-RATE ESTIMATION 567

energy absorption coe�cients are compensated bythe ratio of integrals. However, the uncertainties on

the mass attenuation coe�cients a�ect the absorp-tion term, exp(ÿmatt(E)rr), and thus the g dose trans-mission factors. In order to evaluate the likely error,

it should be stressed that the error on exp(ÿmrr) var-ies as: eÿx(eÿaxÿ1), where x is mrr and a, the relativeerror on m (a = 0.03, i.e. 3%). The largest error on

the absorption term occurs when x11, and thus, theerror on exp(ÿmrr) is around 0.01; it tends to zerowhen the absorption is small (x10) or strong [exp(ÿmrr)10]. This ®rst analysis gives the maximisederror evaluation on the g dose transmission factors:20.01, in the worst case, knowing this error tends tozero when the g dose transmission factors also tend

to zero, for ``long'' sample-source distances. The lar-gest error on the dose-rate Dg due to uncertainties onm is proportional to the di�erence between the two

in®nite matrix g dose rates (i.e. Dg sedÿDg limestone).At Grotte XVI, the subsequent uncertainty on Dg islower than 0.005 Gy/ka, which is one order of magni-

tude below the other experimental uncertainties onthe Dg determination, such as for instance the dis-persion in K, U, Th contents within the analysed

sediment samples.

4.5. Intercomparison of g dose rate computations

To check the validity of our computation, ourresults were compared with those published byAitken et al. (1985). These authors have calculated

the variation of the g dose rate below the ground sur-face assumed to be plane and horizontal. They used adi�erent computation code and obtained a good

agreement between their numerical and experimentalapproaches. The g dose-rate relative values obtainedin our laboratory as a function of depth for the same

semi-in®nite medium, are reported in Fig. 5 and arecompared with the data of Aitken et al. (1985). The

data sets match fairly well which proves the validityof the g dose-rate computations in the case of a sim-pler plane discontinuity. We will therefore assume

that the computation is valid for the ``random'' geo-metry of ``lumpy'' (Schwarcz, 1994) archaeologicalsites.

5. ENVIRONMENTAL DOSE-RATE

DETERMINATION AND TL AGE

ESTIMATION AT GROTTE XVI

5.1. Practical aspects concerning the reconstructionof the environment at Grotte XVI

The deposits overlying the TL samples weregraphically reconstructed using the information

recorded in ®eld documents. Because the distancebetween the TL sampling point and the nearestcoarse limestone fragment was greater than 5 cm,

the space was decomposed into 10 spherical volumeelements of 5 cm thickness (Fig. 2), with an internalradius ranging from 0 to 45 cm and an external

radius ranging from 5 to 50 cm. Ten horizontalplanes were built at relative heights of 2.5, 7.5 . . . ,47.5 cm from the TL sampling point. Within each

plane, the intersection of the volume elements withthe limestone fragments was identi®ed (Fig. 2).Then, the fraction of space ®lled by limestone ineach volume element was graphically determined.

This volume content was equated to the mass con-tent, since densities of sand (silicate grains) andlimestone are very similar.

If a better spatial resolution is required, the thick-ness of the volume elements can be reduced, down to1 cm, a lower limit which is greater than the range of

secondary electrons produced by g interactions,around 2 mm. Furthermore, it is not essential tokeep thickness constant for all shells [appendix (2)].

5.2. Estimation of the environmental dose-rate atGrotte XVI using the reconstruction method

For a given TL sampling point within the burntsediments, the average radioelement content of thenearest sediments was taken into account in order to

evaluate the in®nite matrix g dose-rate of pure sedi-ment, Dg sed [relation (1)]. The in®nite matrix g dose-rate of pure limestone, Dg limestone, was estimated

from the average radiochemical content of the buriedlimestone fragments (Dg limestone=0.11620.021 Gy/ka). The water content of the deposit was estimated

at 824%. In Table 3, we report the K, U and Thcontents of the average sediment (sand), the e�ectiveconcentration of limestone fragments around the TL

sampling point [p in [1]] and the result of the g dose-rate evaluation. These data show that the limestonecontribution to the total g dose-rate is rather lowaround the Mousterian ®res of Grotte XVI: their

Fig. 5. Gamma dose-rate relative variations with depthbelow ground surface in a semi-in®nite medium (reference100%, in®nite soil g dose-rate); comparison between thecomputation performed in our laboratory (K: solid dia-monds, U: open diamonds, Th: solid triangles) and the

computation of Aitken et al. (1985) (solid line).

P. GUIBERT et al.568

e�ective mass concentration ranges between 0.7 and

15.0%.

The uncertainty on the Dg values (Table 3) can

be attributed to two main sources, in decreasing

order of signi®cance: the dispersion in K, U and Th

contents within the analysed sediment and the error

on the estimated water content. These two sources

of uncertainty yield a probable error ranging from

0.04 to 0.07 Gy/ka depending on the sample. These

uncertainties are noticeably greater than the one

expected from the simpli®cations and the uncertain-

ties on the g dose transmission factors computation,

but they are smaller than the wide variation range

of environmental dose rate at Grotte XVI.

In order to check the sensitivity of our reconstruc-

tion method to di�erent parameters, other

approaches for g dose-rate determination have been

carried out. For instance, a simpli®ed procedure has

been performed assuming a ``simple mixing'' of all

components (limestone and sand) within a 15 cm

radius sphere (Table 4). The g dose-rate [Dg(mix)]

was estimated using the K, U and Th average con-

tents of the limestone fragments and the sediment

within this sphere which, in this case, is assumed to

be homogeneous. The mass content of limestone

fragments within this sphere is reported in Table 4

(% limestone rE15 cm). The deviation between this

concentration and the e�ective concentration varies

from ÿ4.5% (BDX 2794) to +13% (BDX 2800). It

represents the relative error on the g dose-rate deter-

mination when applying a ``simple mixing'' approxi-

mation within a 15 cm radius sphere, from which

originates nearly 75% of the total g irradiation. As

shown in Table 4, the g dose-rate is very sensitive to

the relative location of the limestone fragments

within this 15 cm radius sphere. If the limestone frag-

ments are close to the TL sample: a minimum value

of Dg is obtained, Dg(close); if the limestone frag-

ments are located as far as possible from the TL

sample: Dg is maximum, Dg(far). Both Dg values were

estimated using the reconstruction method, assuming

a constant limestone content in the 15 cm radius

sphere.

Some remarks can be deduced from the data

reported in Table 4:

(i) The relative location of limestone fragments can

induce signi®cant variations in the g dose-rate

when the limestone concentration is high

(samples BDX 2800, 3606 and 3612);

Table 3. Gamma dose-rate estimate obtained after reconstruction of the upper g irradiating environment of the TL datedburnt sediments (Dg sup). The average radiochemical composition of each TL sample and its nearest sediments isreported; U*

U and U*Ra are the average values through time of U(238U) and U(226Ra) respectively, assuming that the

enrichment in uranium occurred around 1429 ka before present (Guibert et al., 1997). Dg sed is the g dose-rate in an in-®nite pure sediment. ``E�ective % of limestone'' is the e�ective limestone concentration in a 50 cm radius sphere, p in [1]

TL sample(nearestsediments) K (%) U*

U (ppm) U*Ra (ppm) Th (ppm) Dg sed (Gy/ka)E�ective % of

limestone Dg sup (Gy/ka)

BDX 2794 (sediments BDX 2793, 2795, 2799, 2801, 2803)0.8620.05 1.7520.11 1.6420.14 7.8520.61 0.74220.048 4.5 0.71420.060

BDX 2800 (sediments BDX 2793, 2795, 2799, 2801, 2803)0.8620.05 1.7520.11 1.6420.14 7.8520.61 0.74220.048 15.0 0.64820.041

BDX 3606 (sediments BDX 3607, 3608, 3610, 3611, 3621)0.8720.06 1.7020.23 1.6620.29 7.6420.69 0.73620.065 10.7 0.67020.058

BDX 3609 (sediments BDX 3607, 3608, 3610, 3611, 3621)0.8720.06 1.7020.23 1.6620.29 7.6420.69 0.73620.065 0.7 0.73120.065

BDX 3612 (sediments BDX 3613, 3614, 3942)1.1320.19 1.7420.20 1.7220.25 7.4520.70 0.79220.073 6.2 0.75120.068

BDX 3615 (sediments BDX 3616, 3942)0.9820.04 1.9020.18 1.9020.23 8.7820.71 0.84120.057 2.4 0.82320.056

Table 4. Gamma dose-rate estimate of the upper environment using di�erent procedures: (1) the reconstruction method(Dg sup) and, (2) a ``simple mixing'' procedure Dg(mix) as detailed in the text. Dg(mix) has been estimated using the K,U and Th average contents of the limestone fragments and the sediment lying within a 15 cm radius sphere which, inthis case, is assumed to be homogeneous. The ``limestone % (rE15 cm)'' is the real fraction of limestone within the15 cm radius sphere. Dg(close) and Dg(far) are estimated using the reconstruction method and assuming a constant lime-stone content but di�erent limestone fragment positions within this 15 cm radius sphere: the fragments are close to the

TL sample, Dg (close), or far from the TL sample, Dg(far)

TL samplereferences

E�ective % oflimestone Dg sup (Gy/ka)

Limestone %(rE 15 cm) Dg (mix) (Gy/ka)

Dg (close)(Gy/ka) Dg(far) (Gy/ka)

2794 4.5 0.714 0.0 0.742 0.714 0.7142800 15.0 0.648 28.0 0.534 0.483 0.6483606 10.7 0.670 15.6 0.639 0.504 0.6923609 0.7 0.731 0.0 0.736 0.731 0.7313612 6.2 0.751 14.0 0.698 0.547 0.7513615 2.4 0.823 0.0 0.841 0.823 0.823

NEW METHOD FOR GAMMA DOSE-RATE ESTIMATION 569

(ii) the results of the simple mixing procedure arein good agreement (discrepancy lower than10%) with those obtained by the reconstruction

technique, except for a high limestone concen-tration sample, BDX 2800;

(iii) the simple mixing procedure within a 15 cm

radius sphere cannot be used in any situationand we recommend to check its suitabilityaccording to the di�erence in radioactivitybetween the irradiating materials, the internal

radioactivity of the samples to be dated and,®nally, the degree of accuracy required for dat-ing. For that purpose, the data reported in

Table 2 could be useful.

The cosmic dose-rate has been estimated usingPrescott and Hutton's relations (1994). The depth

of Grotte XVI below the surface of the calcareousplateau (Massif du Conte) being approx. 40 m, thecosmic dose-rate was estimated at 0.012 Gy/ka.

However, the Mousterian ®res receive a direct cos-mic irradiation through the cave entrance whichwill also contribute to the environmental dose-rate.Thus, 0.012 Gy/ka is to be seen as a minimum esti-

mate. The cosmic dose-rate within the well-knownGrotte Vaufrey (Grotte XV) was estimated at0.0320.01 Gy/ka by Huxtable and Aitken (1988).

The context of both caves being similar, we use thelatter estimate which gives, on a qualitative point ofview, a better representation of the situation in the

main chamber of Grotte XVI.

5.3. Determination of the environment dose-rate com-

bining in situ measurements and the reconstructionmethod

Reconstruction of the upper irradiating hemi-sphere of the TL samples enables us to reconstruct50% of the real irradiating volume. By contrast, the

contribution of the lower hemisphere to the total gdose-rate cannot be estimated by the reconstructionmethod since the underlying deposits have been

excavated. However, in Grotte XVI the location ofthe burnt sediment, BDX 3606, enables us to esti-mate the g contribution of the lower deposits to thetotal g dose-rate using in situ measurements.

A TL dosimeter and a gamma-ray meter were setat the TL sampling point of this burnt sediments, onthe horizontal surface of the combustion area. Three

di�erent sources of g radiations have been identi®ed:the g radiation originating from the bed-rock roofand walls, Dg rock, the g radiation from the deposits

underlying the TL sample and not yet excavated Dg

inf, and the cosmic radiation, Dcosmic. We assume thathalf the space around the measurement point isformed by the bed-rock limestone and the other half

by the lower deposit. Consequently, the g dose ratededuced from the dosimeter and the gamma-raymeter, Dg surface, can be written as follows:

Dg surface � 1

2Dg inf � 1

2Dg rock �Dcosmic �12�

neglecting the absorption of g-rays from the lime-stone bed-rock by the air. The bed-rock in®nitematrix g dose-rate, Dg rock, is known from low back-ground gamma spectrometry analyses; the missing

information is given by

1

2Dg inf �Dcosmic � Dg surface ÿ 1

2Dg rock: �13�

As the g contribution of the excavated upper depos-its, Dg sup, has already been calculated using thereconstruction method, the environmental dose-rate,

Denv, is now fully determined:

Denv � Dg surface ÿ 1

2Dg rock � 1

2Dg sup: �14�

The experimental results and the ®nal value of the en-vironmental dose-rate, Denv, for sample BDX 3606,

are reported in Table 5. The bed-rock g dose-rate, Dg

rock, was estimated using the average value of theanalytical measurements performed on the unalteredlimestone fragments BDX 2941, 3938 and 4538 (see

Table 1).

5.4. Total annual dose-rate determination and TL

dating of burnt sediments

Table 6 shows the b equivalent dose, the alpha,beta, environmental and total dose-rates of sedi-ments that have been su�ciently heated in the past.The TL ages and associated uncertainties are

Table 5. Environmental dose-rate determination of the burnt sediment BDX 3606 from Grotte XVI, combining in situmeasurements and the reconstruction method

Contributions to the total g dose-rate Method Dose-rate (Gy/ka)

In situ super®cial measurement (Dgsurf)TL dosimetry (CaSO4:Tm) 0.40420.020Gamma-ray (NE102A) 0.42220.021

Arithmetic mean 0.41320.020In®nite bed-rock g dose-rate (Dgrock)

KUTh analyses 0.10020.020g dose-rate from upper environment (Dgsup)

Analyses and reconstruction 0.67020.050Environmental dose-rate (Dg env)

Denv=Dg surfÿ1/2 Dgrock+1/2 Dgsup 0.70020.050

P. GUIBERT et al.570

reported in Table 7. The statistical, systematic and

®nal global standard deviations are detailed. The

statistical errors are due mainly to glow-curve dis-

persion and counting statistics of g spectrometry.

The systematic errors include the calibration uncer-

tainties of the radioactive sources used for TL

measurements, the calibration uncertainties in the gspectrometry, the error on the estimated water con-

tent and the uncertainties in the environmental

dose-rate determination.

The arithmetic mean of the 6 TL ages is 64.7 ka,

assuming that the Mousterian ®res are contempor-

ary (i.e. the age di�erences are smaller than the stat-

istical error on the age measurements). The

standard deviation is 4.2 ka. It represents the real

dispersion of the results (or estimated TL ages) and

is similar in magnitude, to the statistical uncertain-

ties which range from 2.7 to 4.2 ka. The grouping

of the TL ages is satisfactory and there is no evi-

dence for anomalies. This tends to support the pro-

cedures which have been implemented for the TL

dating of the Mousterian ®res from Grotte XVI

including the reconstruction technique.

We think that the development of this technique

and its application to Grotte XVI sediments lead to

a more representative determination of g dose-rate

than any other classical or usual method. In prac-

tice the consequences on dating precision are signi®-

cant but quantitatively limited to a low percentage

according to the predominant contribution of the

internal radioactivity (a + b) of the dated sedi-

ments. However, on the fundamental side, the

development of the reconstruction technique was

essential to quantify the in¯uence of the limestone

fragments around the mousterian ®res of Grotte

XVI on g dose-rate.

5.5. Conclusions

In karstic areas, the heterogeneity of archaeologi-cal deposits often enhances di�culties when apply-ing paleodosimetric dating methods such as TL,OSL and ESR. The main problem is the spatial

representativeness of the annual g dose-rate deter-mination when using standard procedures such asTL dosimetry or gamma-ray measurement. To solve

this problem, a new method based upon the recon-struction of the radioactive environment of thesamples to be dated has been developed. This

method is complex, but consistent with the complexnature of most palaeolithic sites in southwesternFrance.

The reconstruction method requires determi-nation of the K, U and Th contents of all lithologiccomponents of the g irradiating environment of theTL samples (i.e. limestone fragments and sand at

Grotte XVI). The relative positions of the variouslithologic components, their shape and size, enablethe determination of g dose-rate by a reconstruction

using spherical shells. The contribution of each shellto the total g dose-rate is obtained by computationof the g dose transmission factors; this operation

takes into account the elementary composition ofthe burial irradiating medium and the irradiatedsample.Even though the reconstruction of the environ-

ment is complex, it provides a more reliable esti-mation of the total g dose-rate when compared with

Table 6. Beta equivalent dose and contributions to the total dose-rate (alpha, beta and environmental dose-rates).Uncertainty is one standard deviation

TL sampleBeta equivalentdose, b ED (Gy)

Alpha dose-ratekDa (Gy/ka)

Beta dose-rateDb (Gy/ka)

Internal dose-rate kDa+Db

(Gy/ka)

Environmentaldose-rate Denv

(Gy/ka)Total dose-rate

D(Gy/ka)

BDX 2794 173.628.7 0.70720.075 1.28020.048 1.98720.102 0.74420.060 2.73120.130BDX 2800 186.2212.0 0.95420.105 1.46120.054 2.41520.133 0.67820.050 3.09320.153BDX 3606 171.929.9 0.54520.055 1.21320.055 1.75820.093 0.70020.050 2.45820.118BDX 3609 158.2211.7 0.61420.097 1.31420.093 1.92820.160 0.76120.070 2.68920.183BDX 3612 227.3214.5 0.75320.074 1.86120.075 2.61420.124 0.78120.070 3.39520.158BDX 3615 197.4213.2 0.63720.075 1.37220.055 2.00920.106 0.85320.060 2.86220.137

Table 7. TL dating of burnt sediments from the Mousterian combustion structure of Grotte XVI. Total uncertainty, onestandard deviation, results from the quadratic sum of statistical and systematical uncertainties. The weighted average (bythe reciprocal of the square of statistical standard deviation) is reported, assuming that all these TL samples are contem-

porary

TL sample references No. TL age21s (ka)Statistical uncertainty

(ka)Systematic uncertainty

(ka)

BDX 2794 273 63.623.8 2.73 2.53BDX 2800 279 60.223.9 2.94 2.43BDX 3606 415 69.924.6 3.33 3.00BDX 3609 418 58.825.2 4.20 2.92BDX 3612 421 66.924.5 3.40 2.87BDX 3615 424 69.024.8 3.74 2.95

Weighted average 64.623.1 1.30 2.70

NEW METHOD FOR GAMMA DOSE-RATE ESTIMATION 571

in situ or laboratory classical approaches, oreven with simpli®ed determination relying on the

average radiochemical composition of the depositlying within a sphere of arbitrary radius (15,20, . . .30 cm?) centred on the TL dated sample,

specially in the case of signi®cant gamma gradients.The dosimetric problems raised by the presence

of heterogeneities in archaeological deposits from

caves or rockshelters are not easy to solve.However, a chronological reevaluation of palaeo-lithic reference sites is now underway. Application

of paleodosimetric dating methods in complex kars-tic environment, as performed in Grotte XVI, isone methodological approach required to contributeto this reevaluation.

AcknowledgementsÐThis research was ®nancially sup-ported by the following organisations: Society and HumanSciences Department of CNRS, University of BordeauxIII, Michel de Montaigne, ``Conseil Re gional d'Aquitaine''and ``Service Re gional de l'Arche ologie'' (DirectionRe gionale des A�aires Culturelles d'Aquitaine). This worktook place within the research activities of the ``Groupede Recherche`` (GDR CNRS 1033): ``Me thodesnucle aires en arche ologie'' and the CNRS program``Pale oenvironnement, e volution des Hominide s'' (PL 97-18). Field studies and ®eld documents interpretation wereperformed in close collaboration with Dr J Ph. Rigaud(Institut de Pre histoire et de Ge ologie du Quartinaire,UMR CNRS 9933, Talence) in charge of the archaeologi-cal research at Grotte XVI. We are grateful to CatherineMouysset-Paya, research student, and to Claude Ney andPierre Selva, CNRS engineers, for their helpful partici-pation. Special thanks to Re my Chapoulie, Univ. Bx III,for his suggestions regarding this manuscript.

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APPENDIX

1. The discrepancy in U-series g dose-rate betweenNambi and Aitken's data (1986) and Liritzis andKokkoris' (1992) which has been pointed out byOlley et al. (1996), is due to an erroneous conversionof dose rate per oxide content of parent element intodose rate per atomic content. The detailed list of U-series emissions reported in Liritzis and Kokkoris'paper gives a total g dose-rate of 11.1 Gy/ka.ppmU(instead of the published value of 11.1 Gy/ka.ppmUO3).

2. In the case of an irregularly thick shell decompo-sition, the weighting coe�cients of the i-th volume el-ement contribution to g dose-rate, wi, must includeits thickness, Dri as:

wi � K : f�ri� :Dri: �A1�

P. GUIBERT et al.572