Bull. Soc. géol. Fr., 2010, t. 181, n o 4, pp. 363-376 GARIBALDI THER MAL ANO C. MA et LIES al. AND GEO LO GI CAL STRUC TU RES IN THE PRO VENCE BA SIN Thermal anomalies and geological structures in the Provence basin: Implications for hydrothermal circulations at depth CYNTHIA GARIBALDI 1,2,*, LAURENT GUILLOU-FROTTIER 1, JEAN-MARC LARDEAUX 2, DAMIEN BONTÉ 3, SIMON LOPEZ 1, VINCENT BOUCHOT 1 and PATRICK LEDRU 4 Key-words. BHT, Se di men ta ry ba sin, Pro vence ba sin (France), 3D ther mal mo del, Ther mal mo de ling, Fluid flow, Faul ted areas Ab stract. Deep tem per a ture es ti mates pre vi ously made in France show three main pos i tive ther mal anom a lies, one of them be ing cen tred on the Pro vence ba sin (south east France) be tween Mar seille and Montpellier. This study pres ents newly cor rected tem per a ture data and im proved tem per a ture maps in or der to (i) val i date or to in val i date the ther mal anom a lies pre vi ously iden ti fied and (ii) re late deep tem per a tures with ma jor geo log i cal struc tures of the area. Although the ther mal gra dient va ries from place to place, it ave ra ges 31.3 o C/km in the Pro vence ba sin (from 30.6 to 32.5 o C/km in ave rage for France ac cor ding to the cho sen da ta base), but some lo ca tions show gra dients rea ching 36 o C/km. To cha rac te rize ther mal ano ma lous areas, a three-di men sio nal mo del of the tem pe ra tu res was built bet ween the sur face and 6 km depth, al lo wing us to ela bo rate ther mal maps and cross-sec tions. The iden ti fied ther mal ano ma lies are dif fe rent from those ob tai ned by for mer works. New other hot ano ma lous areas (Mont pel lier, Lo dève and Drôme areas) and cold ano ma lous areas (Aix-en-Pro vence and Cé ven nes areas) have been hig hligh ted. At depth, ther mal cross-sec tions show 50 km-scale ano ma lies, which are pa ral lel with the ma jor faults (Cé ven nes, Ni mes, Sa lon-ca vail lon and Moyenne-Du rance faults) whe reas more elon ga ted (roug hly 100 km) ano ma lies are as so cia ted with per pen di cu lar cross-sec tions. On these cross-sec tions each ma jor fault is as so cia ted with a ther mal ano ma ly. In ad di tion, a cold area may overlie a warm one, and vice ver sa. Among dif fe rent pos sible ex pla na tions, these ther mal si gna tu res could cor res - pond to convec tive fluid cir cu la tion wi thin the faults. Simple nu me ri cal mo dels of hy dro ther mal convec tion wi thin fault zo nes ap pear to re pro duce si mi lar am pli tu des and ver ti cal va ria tions of ther mal ano ma lies as those ob ser ved in the Pro - vence ba sin. Anomalies thermiques et structures géologiques du Bassin provençal : implications pour les circulations hydrothermales en profondeur Mots-clés. BHT, Bas sin sé di men taire, Bas sin pro ven çal (France), Mo dèle ther mique 3D, Mo dé li sa tion ther mique, Ecou le ment de flui des, Zo nes fail lées Ré su mé. Les es ti ma tions de tem pé ra tu res pro fon des en France pré cé dem ment réa li sées mon trent trois ano ma lies po si - ti ves prin ci pa les, l une d entre el les étant centrée sur le bas sin pro ven çal (sud-est de la France) entre les vil les de Mar - seille et Mont pel lier. Cette étude pré sente des don nées de tem pé ra ture nou vel le ment cor ri gées et les car tes ther mi ques in ter po lées ré sul tan tes, dans le but de (i) va li der ou in va li der les ano ma lies ther mi ques pré cé dem ment iden ti fiées et (ii) de re lier les tem pé ra tu res pro fon des aux struc tu res géo lo gi ques ma jeu res de la zone d étude. Bien que le gra dient ther mique varie sui vant les ré gions, il est de 31,3 o C en moyenne dans le Bas sin pro ven çal (de 30,6 à 32,5 o C/km en moyenne en France, se lon la base de don nées choisie), mais cer tai nes zo nes mon trent des gra - dients al lant jus qu à 36 o C/km. Dans le but de ca rac té ri ser les zo nes ano ma les, un mo dèle ther mique à trois di men sions a été réa li sé entre la sur face et 6 km de pro fon deur, per met tant d ef fec tuer des sé ries de car tes et de cou pes ther mi ques. Les ano ma lies ther mi ques iden ti fiées sont dif fé ren tes de cel les ob te nues lors des pré cé den tes étu des. De nou vel les ano - ma lies ther mi ques po si ti ves ou zo nes «chau des» (ré gions de Mont pel lier, Lo dève et la Drôme) ain si que des ano ma lies ther mi ques né ga ti ves ou zo nes «froi des» (ré gions d Aix-en-Pro vence et des Cé ven nes) ont pu être mi ses en évi dence. En pro fon deur, les cou pes ther mi ques réa li sées mon trent des ano ma lies de l ordre de 50 km lors qu el les sont pa ral lè les aux fail les ma jeu res (fail les des Cé ven nes, de Nî mes, de Sa lon-ca vail lon et de la Moyenne-Du rance) et un peu plus al - lon gées (en vi ron 100 km) lors qu el les leur sont per pen di cu lai res. Ces cou pes mon trent que chaque faille ma jeure est as - sociée à un si gnal ther mique en pro fon deur. De plus, une zone froide peut sur plom ber une zone chaude, et vice-ver sa au droit d une même faille. Par mi les dif fé - rents scé na rii pos si bles, ces si gna tu res ther mi ques pour raient cor res pondre à de la cir cu la tion convec tive de flui des dans l em prise des fail les. Des mo dè les nu mé ri ques sim ples de convec tion hy dro ther male dans les zo nes fail lées per met tent de re pro duire la va ria tion ver ti cale des ano ma lies avec des am pli tu des si mi lai res à cel les ob ser vées dans le Bas sin pro ven çal. 1. BRGM, 3 avenue Claude Guil le min, BP 36009, 45060 Orléans ce dex 2, France ; c.ga ri bal di@brgm.fr ; l.guil lou-frot tier@brgm.fr ; s.lo pez@brgm.fr ; v.bou chot@brgm.fr 2. Nice Uni ver si ty, 28 avenue Val rose, BP 2135, 06103 Nice ce dex 2, France ; lar deaux@wa na doo.fr 3. Vrije Uni ver si teit, Fa cul teit der Aard-en Le vens we tens chap pen, su baf de ling Tek to niek, de Boe le laan 1085, 1081 HV Amster dam, The Ne ther lands ; dam.bonte@gmail.com 4. AREVA, 27/29 rue Le Pel le tier, 75433 Pa ris ce dex 9, France ; pa trick.le dru@are va.com * Cor res pon ding au thor Ma nus crit dé po sé le 9 mars 2009 ; ac cep té après ré vi sion le 15 fé vrier 2010.
364 GARIBALDI C. et al. INTRODUCTION The value of the geo ther mal gra di ent may vary from a few o C/km (e.g. Archean shields) to sev eral hun dreds of o C/km (vol ca nic ar eas, rift ing ar eas like in Ice land). The tem per a - ture is known at the sur face and, when sur face dis tur bances (e.g. cli ma tic ef fects) are re moved, al ways in creases with depth, but the amount of in crease de pends on many fac tors. Ther mal re gime on the Earth crust is con trolled by ther mal bound ary con di tions, in ter nal heat pro duc tion, rock ther mal prop er ties, and tec tonic his tory. Ther mal dis tur bances can be due to per tur ba tions of ther mal bound ary con di tions (e.g. el e vated man tle heat flow), con trast in rock ther mal prop er - ties, or pres ence of ac tive struc tural dis con ti nu ities. The mean ther mal gra di ent of an area can be es ti mated from the tem per a tures mea sured on well logs. Bot tom-hole tem per a tures (BHT) mea sured in bore holes af ter drill ing are al tered by the cool ing ef fect of mud cir cu la tion and need to be cor rected. Most of the ex ist ing cor rec tions lead to re li able es ti mates of the for ma tion equi lib rium tem per a - ture within ±10 o C [Goutorbe et al., 2007; Bonté et al., 2010]. Pre vi ous es ti mate of tem per a ture dis tri bu tion at depth in France [Ga ble, 1978; Haenel et al., 1980; Lucazeau et al., 1985; Burrus et Bessis, 1986] high lighted three main pos i tive ther mal anom a lies at 5 km depth (from 180 to 200 o C): the Limagne ba sin of the Mas sif cen tral, the Rhine graben (Al sace) and the Pro vence ba sin (fig. 1), that cor re - spond roughly to zones of con ti nen tal crust thinned dur ing the de vel op ment of the con ti nen tal scale West ern Eu ro pean Ce no zoic Rift Sys tem (ECRIS) [Dèzes et al., 2004]. A crit i - cal anal y sis of the data and in ter po la tion meth ods done by Genter et al. [2003] in the Limagne and Rhine Graben ar eas con firmed the pres ence of high geo ther mal gra di ents that open new per spec tives for de vel op ing En hanced Geo ther - mal Sys tems. This study com ple ments this crit i cal anal y sis for the Pro vence ba sin. Tem per a tures have been cor rected FIG. 1. Tem pe ra tu res es ti ma ted in France at 5 km depth from Hae nel et al. [1980]. FIG. 1. Tem pé ra tu res es ti mées en France à 5 km de pro fon deur d a près Hae nel et al. [1980]. and ex trap o lated us ing two dis tinct meth ods, which use a pa ram e ter un til now un avail able on well logs: the time af ter the end of mud cir cu la tion or shut-in time (SIT). A first set of ex trap o lated tem per a ture maps were made by Haenel et al. [1980] (fig. 1) us ing the cor rec tions of Ga ble [1978], and Lucazeau et al. [1985]. The com par i son be tween these maps and the maps re sult ing from the pres ent study shows dif fer ences which can reach 25 o C at 2 km and am plify with depth [Guillou-Frottier et al., 2010]. The study of the deep tem per a tures of a sed i men tary ba - sin is made through the ob ser va tion of the data of oil ex plo - ra tion bore holes. In the Pro vence ba sin, about 1500 well logs re sult ing from 183 bore holes have been dig i tized to make an in ven tory of the tem per a ture data. A ther mal three-di men sional model has been built and deep tem per a - ture maps from 1 to 5 km depth and ther mal cross-sec tions across dif fer ent types of geo log i cal ar eas can be ex tracted from the model. A pre lim i nary anal y sis of these maps is pre sented. In par tic u lar, sev eral pro cesses of dif fer ent scales, which could pos si bly lead to sig nif i cant ther mal anom a lies, are listed. Be cause of the spe cific fea tures of the iden ti fied anom a lies in the Pro vence ba sin, our anal y sis is fo cused on the pos si ble role of hy dro ther mal con vec tion in faulted zones. GEOLOGICAL SETTING The Pro vence ba sin is a com plex geo log i cal area lo cated be - tween the Mas sif Cen tral to the west, the Digne and Castellane arcs to the east, the Pelvoux mas sif to the north and the Med i ter ra nean sea and its Gulf of Lion to the south (fig. 2). The thick ness of sed i ments, in clud ing Me so zoic de - pos its, can lo cally reach 11 km in the Rhône val ley, im ply - ing that the Pro vence ba sin is the deep est French sed i men tary ba sin. Sev eral hun dred me ters of up per Car - bon if er ous and Perm ian sed i ments are lo cally pres ent be low these Me so zoic se ries. These pri mary for ma tions are lo cal - ized on the west and on the south east ern edges of the ba sin. Nu mer ous Oligocene nor mal faults af fect Cre ta ceous to Eocene com pres sive struc tures. This com plex struc tural pat - tern re sults from the re ac ti va tion of Pyr e nean and Al pine orogenic struc tures by crustal ex ten sion due to the open ing of the Med i ter ra nean sea in re la tion with the ro ta tion of the Corsica-Sar dinia block [Westphal, 1967; Alvarez, 1972; Gattacceca et al., 2007]. The Oligocene ex ten sion and the as so ci ated Neo gene sub si dence are re spon si ble for sed i men - tary fill ings, which can reach over 5 km depth within top o - graphic de pres sions. Plio-Qua ter nary strike-slip de for ma tions are as so ci ated with SW-NE and NW-SE trending faults (fig. 2). The south - east ern base ment of the Mas sif Cen tral is bor dered by the Cevennes fault, which is char ac ter ized by a SW-NE-trending par al lel fault net work stretch ing for about 180 km from the Montagne Noire to Va lence (Rhône Val ley). Ac cord ing to Arthaud and Matte [1975] this was orig i nally a late Hercynian dextral slip-fault zone, which thus ac com mo dated Pyr e nean short en ing of the sed i men tary cover by sinistral slip [-40 Ma; Bodeur, 1976]. Fault seg ments were re ac ti vated as nor mal faults by Oligocene ex ten sion (-30 Ma). Some authors tried to iden tify and quan tify a pos si ble Plio-Qua ter - nary move ment [Bishop and Bousquet, 1989; Lacassin et al., 1998a, b] but none could prove this ac tiv ity. Nu mer ous
THER MAL ANO MA LIES AND GEO LO GI CAL STRUC TU RES IN THE PRO VENCE BA SIN 365 The N-S Sa lon-cavaillon fault zone is the least ex - pressed at the sur face. It is about 20 km length. It is mainly iden ti fied from dis con ti nu ities in ma jor E-W struc tural axes (Pyr e nean-provençal folds re ac ti vated in the Neo gene) and is af fected by post-mio cene move ments [Peulvast et al., 1999]. The morpho-struc tural pat terns show an extensional or strike-slip Mio cene or post-mio cene ac tiv ity along some seg ments of this fault zone, prob a bly fol lowed by lo cal ized flex ural move ments and sub si dence to the west (Carpentras ba sin) [Peulvast et al., 1999]. THERMAL THREE-DIMENSIONAL MODEL OF THE PROVENCE BASIN FIG. 2. Struc tu ral scheme of the Pro vence ba sin with ma jor se ries and faults. FIG. 2. Sché ma struc tu ral du Bas sin pro ven çal avec les sé ries et fail les ma jeu res. com ments have been made in re sponse to the pa per of Lacassin et al. [1998a] but these can not to tally ex clude the hy poth e sis of a Plio-Qua ter nary ac tiv ity [Ambert et al., 1998; Mattauer, 1998; Sébrier et al., 1998]. Bishop and Bousquet [1998] do not ex clude a pos si ble ver ti cal move - ment and Séranne et al. [2002] con firm that the mor phol ogy of the Cévennes area is in great part due to a pre-qua ter nary her i tage and that the re cent ver ti cal de for ma tion is nec es - sar ily weak. The SW-NE-trending Nimes fault zone (over 120 km length) is one of the most im por tant of the Ba sin [Combes, 1984; Grellet et al., 1993; Schlupp et al., 2001]. This fault bounds the Vistrenque graben to the NW and forms at depth a low-an gle crustal ramp [25 o ; Séranne et al., 1995; Benedicto et al., 1996]. It is con sid ered ac tive by sev eral au thors [Combes et al., 1993; Baroux, 2000] and is as so ci - ated with few seis mic events but paleoseismic events pos si - bly oc curred with earth quakes of mag ni tudes of 6.5 [Combes et al., 1993]. A post-messinian ac tiv ity was ev i - denced by Schlupp et al. [2001]. Its ac tiv ity is how ever still un der de bate [e.g. Mattauer, 2002]. The SW-NE-trending Moyenne-Du rance fault zone is about 70 km length and is the most ac tive struc ture of the ba sin [Combes et al., 1993; Cush ing et al., 2008; Baroux, 2000] as ev i denced by its his toric seis mic ac tiv ity (one ev - ery cen tury since 1509 with mag ni tudes be tween 5.0 and 5.5) [Volant et al., 2003], even though its pres ent seis mic ity is very low. This fault de lim its west ern Pro vence char ac ter - ized by a sed i men tary cover of about 6-10 km thick ness and east ern Pro vence where the sed i men tary cover is 2-3 km thick ness. This sys tem is con sti tuted by sev eral fault seg - ments [Cush ing and Bellier, 2003]. Presentation of temperature data set Bot tom-hole tem per a tures (BHT) from oil ex plo ra tion are the most com mon tem per a ture mea sure ments. Raw BHT data are known to be out of ther mal equi lib rium, es pe cially be cause of the cool ing ef fect of mud cir cu la tion, which can how ever be cor rected to ob tain the equi lib rium tem per a ture [Bonté et al., 2010]. Drill stem tests (DST) are rare but in - valu able be cause they are di rectly mea sured on the flu ids con tained by the drilled rock. They do not need to be cor - rected be cause they are not dis turbed by the drill ing op er a - tion. From the 183 drill-holes that are avail able over the Pro vence ba sin, 103 of them show as so ci ated well logs that con tain BHT or DST data. Over all, 203 BHT and 10 DST have been com piled. Choice of correction method In or der to con strain the subsurface ther mal re gime of the Pro vence ba sin we used all the DST and the BHT mea sure - ments. From these nu mer ous data, thanks to ad e quate cor - rec tions, we can ob tain val ues with a small un cer tainty (lower than 10%). There are two main types of BHT s cor rec tion meth ods: an a lyt i cal and sta tis ti cal meth ods. The rec om mended method for cor rect ing BHT de pends on the in for ma tion avail able (BHT mea sure ment, time since cir cu la tion or SIT, depth) [Deming, 1989]. The ap pli ca tion of an a lyt i cal meth - ods re quires the SIT and at least two tem per a ture mea sure - ments at the same depth [Goutorbe et al., 2007]. Sta tis ti cal meth ods are ap pli ca ble to a greater num ber of data be cause they only re quire the depth of mea sure ment. Among the sev eral an a lyt i cal meth ods, the In stant Cyl - in der Source method (ICS) de scribes tran sient heat prop a - ga tion from a cy lin dri cal source; this method has been im proved to be ef fi cient when the SIT is in di cated on well logs [Goutorbe et al., 2007]. So we chose to ap ply the ICS cor rec tion when this pa ram e ter was avail able. Un for tu - nately, this was the case for only 10 BHT mea sure ments, and we thus had to ap ply a sta tis ti cal cor rec tion method on all re main ing BHT data. In the 1970 s the AAPG (Amer i can As so ci a tion of Pe tro leum Ge ol o gists) Geo ther mal Sur vey of North Amer ica (GSNA) pro duced a mas sive da ta base (over 20,000 BHT from over 10,000 bore holes in the US, Can ada, and Mex ico). The AAPG sta tis ti cal cor rec tion method [Har - ri son et al., 1983] is based on the cal i bra tion of BHT data of the AAPG dataset in Oklahoma us ing DST mea sure ments and is adapted to data on which the SIT is un avail able. In this work, 193 tem per a ture data have been cor rected with
366 GARIBALDI C. et al. this method. By com par ing DST (10 data), BHT cor rected with ICS cor rec tion (10 data) and those cor rected with AAPG method (193 data), we ob tained a bulk av er age dif - fer ence of 3.7 o C which is very low for tem per a tures of sev - eral hun dreds of de grees (see some de tails in fig ure 5 of Bonté et al. [2010]). Kriging interpolation and thermal three-dimensional model The or di nary kriging method as sumes that the es ti mated vari able is sta tion ary. As the tem per a ture con tin u ously in - creases with depth, we used the kriging with trend-es ti - mated method. By def i ni tion, re sid ual tem per a tures, which are cal cu lated at each depth, cor re spond to the dif fer - ence be tween cor rected tem per a ture data and tem per a ture com puted with the mean ther mal gra di ent of the area. Kriging is an es ti ma tion pro ce dure used in geostatistics to in ter po late data points that are de pend ent on each other. As far as tem per a tures are con cerned, it seems quite nat u ral to con sider that a spa tial de pend ence ap plies: for a given hor i zon tal length scale, there is no rea son to con sider that tem per a ture var ies. Pa ram e ters gov ern ing spa tial dis tri bu - tion of field data al low con struct ing an em pir i cal variogram, which leads to a model of the spa tial struc ture of the as so ci - ated phe nom e non. If pa ram e ters of the em pir i cal variogram are well cho sen, then the variogram is used to op ti mize the in ter po la tion. The em pir i cal variogram at an ap prox i mate dis tance of h (equa tion 1) cor re sponds to the half mean square of the dif fer ences be tween mea sured val ues inter-dis tant of h and is de fined as [Journel and Huijbregts, 1978; Cressie, 1993]: 1 ( h) 2 N ( h) i 1 z( x ) z( x h) i N( h) where z(x i ) de notes the mea sured value at the lo ca tion x i, z(x i + h) the mea sured value at the lo ca tion x i + h, h the dis - tance be tween x i + h and, and N(h) the set of pairs of ob ser - va tion i. As tem per a tures data are dis trib uted in a three-di men - sional space, the ex per i men tal variogram is com posed of a hor i zon tal variogram and a ver ti cal one (fig. 3). The em pir i cal variogram can not be com puted at ev ery lag dis tance h due to vari a tion in the es ti ma tion. The em pir - i cal variogram is thus ap prox i mated by model func tion en - sur ing va lid ity [Chiles and Delfiner, 1999]. The the o ret i cal model is then su per im posed to the an a lyt i cal one to de fine a cor re la tion law be tween the data [Kitanidis, 1997]. Our ex - per i men tal variogram can not be sim ply fit ted by a sin gle model, so we chose to use a pluri-model of variogram, say a com bi na tion of sev eral the o ret i cal mod els, whose pa ram e - ters en able to sim u late the ex per i men tal variogram. The best fit is reached when two Gaussi an mod els are su per im - posed. Pa ram e ters of both Gaussi an mod els (nug get ef fect, sill and range) are in di cated in cap tion of fig ure 3. We used the Isatis geostatistics soft ware from Geovariances. The di men sions of the three-di men sional model are guided by the space dis tri bu tion of the data and are in di cated in fig ure 4. In or der to op ti mize the pre ci sion of the model, we chose a grid spac ing of 2 km in the hor i - zon tal plane and of 50 m in the ver ti cal one. The kriging was car ried out with the unique neigh bour hood method in i 2 (1) or der to guar an tee the spa tial con ti nu ity of the kriging es ti - ma tor. This ap proach is well adapted for a re gional sam ple as all data points are taken into ac count (al though their weight de creases with dis tance) to es ti mate each un known point by a lin ear com bi na tion. Thermal mapping and cross-sections The 3D ther mal model cov ers the en tire area, but for leg i bil - ity, we ex tracted 2D cross-sec tions of the 3D model, ei ther at a given depth or along a ver ti cal plane. We thus ob tained i) ther mal maps (hor i zon tal cross-sec tions) ev ery kilo metre be tween 1 km and 5 km depth, and ii) ver ti cal ther mal cross-sec tions across geo log i cal ar eas or along ma jor faults. For ex am ple, we show in fig ure 5 two iso-depth maps FIG. 3. Expe ri men tal va rio grams (das hed) and mo dels of va rio grams (so - lid). Ver ti cal (top) and ho ri zon tal (bot tom) va rio grams. Nug get ef fect of 25 o C 2, sill of 187 o C 2 (sum of the nug get ef fect and of the two Gaus sian mo dels of 62 and 100 o C 2 ), ho ri zon tal range of 23 km and ver ti cal range of 500 m. The num ber of cou ples of points for each dis tance class is in di ca ted over green dots. FIG. 3. Va rio gram mes ex pé ri men taux (ti rets) et mo dè les de va rio gram mes (li gnes plei nes). Va rio gram mes ver ti cal (en haut) et ho ri zon tal (en bas). Effet de pé pite de 25 o C 2, pa lier de 187 o C 2 (somme de l ef fet de pé pite et des pa liers des mo dè les gaus siens de 62 et 100 o C 2 ), portée de 23 km à l ho ri zon tale et de 500 m à la ver ti cale. Le nombre de cou ples de points cor res pon dant à chaque classe de dis tance est in di qué sur les points.
THER MAL ANO MA LIES AND GEO LO GI CAL STRUC TU RES IN THE PRO VENCE BA SIN 367 to gether with the as so ci ated stan dard de vi a tions. In fig ure 6, three ver ti cal cross-sec tions are il lus trated (two along two ma jor faults and one across the four main faults). These ther mal cross-sec tions were ob tained us ing the Isatis soft - ware and al low the ob ser va tion of tem per a ture vari a tions with depth (fig. 6) in the ver ti cal plane. SPATIAL VARIATIONS OF TEMPERATURES Thermal anomalous areas of the Provence basin and their variations with depth In France, the av er age ther mal gra di ent as in ferred from heat flow study in France [Lucazeau and Vasseur, 1989] is 32.5 o C/km. With an up dated da ta base of tem per a ture data col lected in pe tro leum bore holes, Bonté et al. [2010] ob - tained the value of 30.6 o C/km. In the Pro vence ba sin, a sim - i lar value of 31.3 o C/km is ob tained, with a cor re la tion co ef fi cient R of 0.93, when a sur face tem per a ture of 14 o C is im posed [Bessemoulin, 1969]. How ever, tem per a ture data points show a great dis par ity, and vari a tions reach 70 o C at z = 3.5 km (fig. 7). The ther mal maps (fig. 5) al low lo cal iz - ing the dis par ity of the data ob served on the di a gram. At 1 km and 3 km depth, tem per a tures range be tween 35-75 o C and 95-135 o C, re spec tively. Er rors in duced by the in ter po la tion range be tween 7 o C and 10 o C, ex cept be tween Carpentras and Gap where there is no data (S.D. = 14 o C) (fig. 5), which is small for tem per a ture val ues of this or der. The ma jor cold and hot ther mal anom a lies show shape vari a tions and spa tial evo lu tion with depth (fig. 5). The hot anom aly cen tred on Montpellier (anom aly 1, fig. 5) de - creases in in ten sity be tween 1 km and 2.5 km depth and then in creases with a con stant north ward evo lu tion to reach the Rhône val ley area fol low ing the Nimes fault ori en ta tion. That of the Drôme area (anom aly 2, fig. 5) in ten si fies with depth with a west ward evo lu tion from 1 km to 3.5 km depth and a south ward evo lu tion while reach ing 5 km depth. The warm anom aly of Lodeve (anom aly 3, fig. 5) dis ap pears at 2 km depth. With re gard to cold anom a lies, that of Aix-en-Pro vence (anom aly 4, fig. 5) pro gres sively dis ap pears on the east to con cen trate west ward. The cold anom aly of the Cevennes (anom aly 5, fig. 5), first with a south west-north east elon ga - tion par al lel to the ma jor fault, dis ap pears to the north with depth to con cen trate south ward along the fault. The large-scale ther mal cross-sec tions par al lel and per - pen dic u lar to the ma jor faults (Cevennes, Nimes, Sa lon- Cavaillon and Moyenne Du rance faults) al low the ob ser va - tion of ther mal vari a tions with depth with the ma jor faults of the Pro vence ba sin. In this pa per we chose to show an ex - am ple of one per pen dic u lar cross-sec tion (fig. 6, sec tion 2) and two par al lel ones (fig. 6, sec tions 1 and 3). These cross-sec tions rep re sent vari a tions of tem per a ture with depth (T) and vari a tions of re sid ual tem per a tures with depth ( T) (see sec tion 3.3). It must be em pha sized that on per - pen dic u lar cross-sec tions, each ma jor fault is al ways as so ci - ated to a warm or a cold ther mal anom aly at a given depth. Thermal potential of the Vistrenque graben Nimes fault area: a striking example to link temperature variations and geology FIG. 4. Avai lable tem pe ra ture data lo ca tion on the geo lo gi cal map cen - tred on the Pro vence ba sin (A) and their dis tri bu tion in the 3D mo del box used (B). FIG. 4. Lo ca li sa tion des don nées de tem pé ra ture dis po ni bles sur la carte géo lo gique centrée sur le Bas sin pro ven çal (A) et leur ré par ti tion dans l es pace au sein du mo dèle 3D (B). The tem per a ture vari a tions cited above are also lo cally observed. The Oligocene Aquitanian Vistrenque graben, where a tem per a ture of 180 o C is cal cu lated at 5 km depth (fig. 6), is lim ited west ward by the Nimes fault which af fects the base ment [Benedicto et al., 1996]. This hemi-graben is filled by sed i ments, which can lo cally reach a thick ness of 6 km. Be cause of the usu ally in su lat ing ef fect of sed i ments [Lucazeau and Le Douaran, 1985], high tem per a tures in the Vistrenque graben may be ex pected. If this is a gen eral rule, we should ob serve a cor re la tion be tween ar eas with a thick sed i men tary pile and zones with high tem per a tures. How - ever, fig ure 8a shows that it is not the case and thus that it is not the only cause for cre at ing hot anom a lies. The in crease of tem per a ture with depth can in deed be due to nu mer ous pro cesses that can in ter act at dif fer ent scales, from the shal - low crust to crustal- and lithospheric-scales. For ex am ple, if the Moho dis con ti nu ity is con sid ered as an iso therm dur ing a deep thermo-me chan i cal per tur ba tion (e.g. crustal thin ning) and if this event is not too re cent (i.e. not youn ger than the dif fu sive time-scale of 10 Ma), then this can also be a cause of high tem per a tures in subsurface. Al though the warm anom a lies could par tially be due to the as so ci a tion of the crustal thin ning as so ci ated with the Moho dis con ti nu ity depth de crease, this can only ex plain tem per a - ture vari a tions at the hor i zon tal scale of the thin ning mech a - nism (sev eral hun dreds of kilo metres) but not those we ob serve at many places sep a rated by a few tens of kilo - metres. Fig ure 8b il lus trates there is no di rect cor re la tion
368 GARIBALDI C. et al. be tween Moho depth vari a tions and the cal cu lated tem per a - tures. How ever, ex plain ing the de tails of how hot or cold anom a lies are es tab lished is not as sim ple as these sim ple cor re la tion tests. Ther mal evo lu tion of a sed i men tary ba sin should in deed ac count for tran sient tectono-ther mal pro - cesses af fect ing the ba sin dur ing tens to hun dreds of m.y. (e.g. ero sion and sed i men ta tion pe ri ods, tran sient crustal thin ning ep i sodes, de crease of crustal heat pro duc - tion, and pos si ble tran sient and spa tial man tle heat flow FIG. 5. Ther mal maps of the Pro vence ba sin at 1 km and 3 km depth and lo ca tion of bo re ho les (black points) with maps of the kri ging es ti ma ted va riance. The prin ci pal ano ma lous areas are those of: 1) Mont pel lier, 2) the Drôme, 3) Lo deve, 4) Aix-en-Pro vence and 5) the Ce ven nes. FIG. 5. Car tes ther mi ques du Bas sin pro ven çal à 1 km et 3 km de pro fon deur et lo ca li sa tion des fo ra ges (points noirs) avec car tes des er reurs d in ter po - la tion. Les ano ma lies prin ci pa les sont cel les de : 1) Mont pel lier, 2) La Drôme, 3) Lo dève, 4) Aix-en-Pro vence et 5) Les Cé ven nes.
THER MAL ANO MA LIES AND GEO LO GI CAL STRUC TU RES IN THE PRO VENCE BA SIN 369 vari a tions). As an ex am ple, van Wees et al. [2009] pre - sented a proba bil is tic model based on in ver sion of ba sin sub si dence his to ries and in cor po rat ing dis tinct tec tonic sce nar ios, in clud ing a per ma nent de crease of bulk crustal heat pro duc tion dur ing crustal ex ten sion. At lithospheric scale, it turns out that thin ning of pre vi ously thick ened litho sphere tends to en hance tec tonic heat flow. In and around the Vistrenque graben area, the el e vated heat flow val ues, greater than 100 mw.m -2, have been sug gested by Lucazeau and Vasseur [1989], to il lus trate a lo cal man tle heat flow in crease (50-60 mw.m -2 ). It is thus not clear whether the Vistrenque graben ther mal anom aly would be to tally ex plained by subsurface ge ol ogy or by deep crustal and lithospheric pro cesses, even if en hanced heat flow val - ues are not nec es sar ily cor re lated with high tem per a tures [Guillou-Frottier et al., 2010]. A com plete tran sient ther mal model of the Pro vence ba sin would in deed help to sep a rate dis tinct pro cesses ex plain ing ther mal anom a lies, but our main ob jec tive in this study is to iden tify and char ac ter ize ther mal anom a lies, which may be ex plained by sev eral in - de pend ent phe nom ena. Going back to the Vistrenque graben anom aly, it must be noted that nu mer ous an ti thetic faults are as so ci ated with the bor der ing Nimes fault, thus rep re sent ing hydraulical con duc tive struc tures. Al though free con vec tion in fault zones is the o ret i cally one of the pos si ble mech a nism for heat trans - fer in the Earth crust [Norton and Knapp, 1977; Rühaak, 2009], few data are avail able (see how ever Bonnaveira et al. [1999]). Fluid cir cu la tion is en hanced by the pres ence of per - me able faults, de pend ing on the frac ture ap er ture and thus on stress re gime. Along the Nimes fault, ther mal map ping (fig. 5) shows a north east ward mi gra tion of the warm anom aly with depth. The same ob ser va tion can be made along the Cevennes fault. If the heat can be trans ported along a con duc tive fault, this trans fer can be done by cir cu lat ing flu ids. This phe nom e - non may ex plain tem per a ture vari a tions of sev eral tens of de - grees that we ob serve on ther mal maps. This ob ser va tion can be made on ther mal cross-sec tions along the Nimes fault (fig. 6) in which we can see the hot ther mal anom aly as so ci ated to the Vistrenque graben (sec tion 3). Vari a tions of T and T in the ther mal cross-sec tion show a ther mal sig na ture of which the shape is sim i lar to those of the o ret i cal and nu mer i cal mod el - ing sim u la tions of fluid con vec tive cir cu la tion within a fault made by Zhao et al. [2004] and Bächler et al. [2003]. In or der to test this pos si ble sce nario, some sim ple mod els of con vec - tive fluid cir cu la tion within faults are pre sented be low. FIG. 6. Ther mal cross-sec tions and their lo ca tion on the geo lo gi cal map where avai lable tem pe ra tu res data are re pre sen ted (black dots): along the Ce ven - nes fault (1), across the ma jor faults (2) and along the Ni mes fault cros sing the Vis trenque gra ben (3). T is the dif fe rence bet ween cal cu la ted tem pe ra tu res T and gra dient tem pe ra tu res. Das hed li nes em pha size ther mal un du la tions at depth and cor res pond to the 160 o C iso therms. FIG. 6. Cou pes ther mi ques et leur lo ca li sa tion sur la carte géo lo gique où les don nées de tem pé ra ture dis po ni bles sont re pré sen tées (points noirs) : le long de la faille des Cé ven nes (1), à tra vers les fail les ma jeu res (2) et le long de la faille de Nî mes tra ver sant le gra ben de Vis trenque (3). T est la dif fé - rence entre les tem pé ra tu res cal cu lées T et les tem pé ra tu res cor res pon dent à un gra dient moyen. Les li gnes en ti rets met tent en évi dence les on du la tions ther mi ques en pro fon deur et cor res pon dent aux iso ther mes 160 o C.
370 GARIBALDI C. et al. FIG. 7. Maxi mal, mi ni mal and mean mea su red tem pe ra ture data in the Pro vence ba sin vs. depth +/-500 m. A dif fe rence of 70 o C bet ween mi ni mal and maxi mal tem pe ra tu res is rea ched at 3.5 km depth. FIG. 7. Tem pé ra tu res me su rées maxi ma les, mi ni ma les et moyen nes du Bas sin pro ven çal en fonc tion de la pro fon deur à +/-500 m. Une dif fé rence de 70 o C entre tem pé ra tu res mi ni male et maxi male est at teinte à 3,5 km de pro fon deur. ON THERMAL ANOMALIES GENERATED BY HYDROTHERMAL CONVECTION IN FAULTS Previous approaches and results As men tioned above, few tem per a ture data around per me - able faults have been pub lished. Most stud ies deal ing with free ther mal con vec tion in faults cor re spond to mod el ling stud ies ded i cated to the un der stand ing of hy dro dy nam ics in - volved in ore gen e sis around fault zones [e.g. Matthaï et al., 2004; Yang et al., 2004; Harcouët-Menou et al., 2009] or re lated to geo ther mal sys tems within sed i men tary bas ins [e.g. Le Carlier et al., 1994; Royer and Flores, 1994; Bächler et al., 2003; Wisian and Blackwell, 2004; Simms and Garven, 2004]. Bächler et al. [2003] have stud ied the Lan dau geo ther mal anom aly (Ger many) where two pre dom - i nant faults of high per me abil ity are pres ent. Nu mer ous tem per a ture data show that tem per a ture un du la tions at 1 km depth along one of the faults have am pli tudes reach ing 12 o C. At 500 m be low the sur face, sim i lar un du la tions of some what smaller am pli tudes ( 8 o C) are ob served. The au - thors re pro duced these un du la tions at fixed depths with a tran sient 3D nu mer i cal model sim u lat ing ther mal con vec - tion in a fault sys tem. Fol low ing a sim i lar al though sim - pler ap proach, steady-state mod els of 2D hy dro ther mal con vec tion within a per me able ver ti cal fault zone have been per formed with a par tic u lar ob jec tive. In all nu mer i cal mod els of ther mal con vec tion within fault zones, ther mal ups (or downs) are ver ti cally con tin u - ous, say a warm anom aly at depth in duces a warm one at the subsurface, even if am pli tude is de creased (as in the nat u ral case pre sented above). In the Pro vence ba sin, one has to ex - plain how cold anom a lies at depth can change to warm anom a lies a few kilo metres above (e.g. SW of Montpellier; fig. 5) or warm to cold (e.g. NE of Cevennes fault area; fig. 5). Note that a sim i lar ob ser va tion has been made in the south west ern part of the Aquitanian ba sin be tween 1000 and 3000 m depths [Bonté et al., 2010]. This ir reg u lar depth vari a tion of in ten sity of ther mal anom a lies can also be seen in ver ti cal cross-sec tions of fig ure 6. It is ex pected that par - tic u lar con vec tive pat terns could in deed ex plain spa tial vari - a tion and in ten sity changes of warm and cold anom a lies. To keep the nu mer i cal ap proach sim ple (steady-state and 2D) while ver ti cal fea tures are in ves ti gated, per me abil ity of crustal units has been as signed a depth-de pend ence vari a - tion, as it seems to be the rule for crustal rocks [Manning and Ingebritsen, 1999]. It must be noted that the ory of hy dro ther mal con vec tion does not con sider the pos si ble (and more re al is tic) spa tial vari a tion of per me abil ity. Con se quently, the use of a per me - abil ity thresh old value, or the anal y sis of a crit i cal Ray leigh num ber, be comes here use less and our study there fore re - quires a nu mer i cal ap proach. Numerical model Heat equa tion is cou pled with Darcy s law through the use of the Comsol Multiphysics soft ware. Be fore tack ling our cho sen sce nario, pre vi ous pub lished mod els of tran sient hy - dro ther mal con vec tion com ing from dis tinct nu mer i cal codes have been suc cess fully re pro duced [Royer et Flores, 1994; Rabinowicz et al., 1998; Gerdes et al., 1998; Wisian and Blackwell, 2004]. For each of these bench mark cases, tem per a ture field, fluid ve loc i ties, and con vec tive pat terns were com pa ra ble [see also Eldursi et al., 2009]. Fig ure 9a shows two sim i lar cases as those pre sented by Rabinowicz et al. [1998], where con vec tive pat terns and sur face heat flow val ues are re pro duced. In our model, in ad di tion to the depth-de pend ence of per me abil ity, fluid den sity and fluid vis cos ity are tem per a - ture-de pend ent. Bound ary con di tions for fluid flow cor re - spond to im per me able lat eral and bot tom bound aries, while a con stant pres sure is im posed at the sur face. A fixed tem - per a ture (0 o C) is im posed at the sur face, and a fixed heat flux of 100 mw/m 2 is im posed at the base of the model (depth of 5 km). Lat eral bound aries are ther mally in su lat - ing. The fault zone (width w) is in serted within a weakly per me able host rock (10-17 or 10-16 m 2 at the sur face) in or - der to fo cus on fluid cir cu la tion within the fault zone. Models are thus per pen dic u lar to the fault zone plane (fig. 9b). Permeabilities of the host rocks (k e ) and of the fault zone (k f ) fol low depth-de pend ence laws given by: z ke ke exp 0 1500 (2) z k f k f exp (3) 0 where k f0 is var ied from 10-14 m 2 to 2 10-12 m 2, and where k e0 = 10-17 or 10-16 m 2. These math e mat i cal laws al low test ing of a large range of rea son able depth-de pend ent per me abil ity func tions. Fig ure 9c shows sev eral of these laws for host rocks and for the fault zone. When = 1.5 km, per me abil ity de creases by 3 or ders of mag ni tude within the 10 first kilo metres, as it is de scribed by Man ning and Ingebritsen s ex po nen tial law [1999]. Some ex treme case
THER MAL ANO MA LIES AND GEO LO GI CAL STRUC TU RES IN THE PRO VENCE BA SIN 371 where equals 10 km and where k f0 is large were also tested in or der to ap proach a con stant and large per me abil - ity fault zone. In the con stant per me abil ity mod els of Bächler et al. [2003], on set of con vec tion needed fault per - me abil ity greater than 5 10-13 m 2. In our model where per - me abil ity strongly de creases with depth, sig nif i cant tem per a ture dis tur bances are thus ex pected for rel a tively high sur face (k f0 ) permeabilities. Preliminary results Fig ure 9d-9f shows dif fer ent cases where sur face per me - abil ity val ues (k f0 ) are var ied. Fault zone width equals 1 km and per me abil ity of the host rocks is low (k e0 = 10-17 m 2 ). When per me abil ity does not vary much with depth (fig. 9d, case with = 20 km), iso therms are sig nif i cantly up lifted and fluid ve loc i ties are large. When is de creased, the ef fi - cient per me able zone is less thick, fluid ve loc ity strongly de creases and iso therms re main flat (fig. 9d, case with = 1 km). Note that al though stream lines (in black) are sim i lar for the three cases in fig ure 9d, the max i mum fluid ve loc ity is more than 100 times greater when iso therms are up lifted, say around 3.5 10-9 m.s -1, in ac cor dance with Bächler et al. s re sults [2003]. Fig ure 9e and 9f il lus trate the role of the de creas ing trend of per me abil ity ( ) when sur face per me abil ity (k f0 ) is high (10-12 and 2 10-12 m 2, re spec tively). Fig ure 9e shows an ex treme case where the bulk fault zone is highly per me - able (from 10-12 m 2 at the sur face to 6 10-13 m 2 at 5 km depth). Due to large per me abil ity, fluid ve loc ity reaches large val ues and iso therms are sig nif i cantly dis torted. It must be noted that con vec tive pat terns ex hibit some de coup - ling at 4 km depth, where one con vec tive cell sep a rates from the over ly ing small as pect ra tio (width/height) cir cu la - tion. When a de creas ing trend of per me abil ity is en hanced (i.e. when is de creased, thus ap proach ing the Man ning and Ingebritsen s law), the same de coup ling is ob served but FIG. 8. Moho depth (A) [data of Te sau ro et al., 2008] and se di ment thick ness (B) of the Pro vence ba sin with cal cu la ted tem pe ra tu res at 3 km depth. FIG. 8. Pro fon deur du Moho (A) [don nées de Te sau ro et al., 2008] et épais seur des sé di ments (B) dans le Bas sin pro ven çal avec les tem pé ra tu res cal cu - lées à 3 km de pro fon deur.
372 GARIBALDI C. et al. at shal lower depth (around 3.5 km depth in fig ure 9f where = 3 km). In fig ure 9f, the thick white iso therms em pha size the in verted ther mal anom a lies cre ated by advection of cold fluid at mid-depth and advection of hot fluid com ing from the bot tom of the fault zone. Note that lat eral ther mal anom - a lies of about 18 o C are ob tained. Fig ure 10 shows the case of a wider fault zone (w = 2 km), where depth-de creas ing trend equals 1.5 km, al low ing to re pro duce 3 or ders of mag ni tude of per me abil - ity de crease from the sur face to 10 km depth. Two cases for per me abil ity of the host rocks are shown (k e0 = 10-17 and 10-16 m 2 ). For each k eo value, three dif fer ent con vec tive pat - terns are shown. De spite in put pa ram e ters be ing iden ti cal in the three ex per i ments of each case, var i ous com put ing pro - ce dures (see be low) pro vide dis tinct steady-state con vec tive pat terns. In the top case, where host rock per me abil ity is low, in di vid ual con vec tive lay ers de velop, cre at ing four, six and eight con vec tive cells within the per me able fault zone. In the left case, the de coup ling depth (in ter face be tween top con vec tive cells and bot tom con vec tive cells) is in creased when com pared with fig ure 9f, since is lower. For each ex per i ment, ther mal un du la tions of more than 10 o C are ob tained. Be cause host rock per me abil ity is low, the fault zone ap pears as a closed sys tem, as em pha sized by flat and reg u larly spaced iso therms in host rocks. In the bot tom case of fig ure 10, where host rock per me abil ity is larger, con vec - tive pat terns ex hibit more com pli cated fea tures since ad ja - cent rocks re cord more eas ily dis tur bances from the fluid ve loc ity and tem per a ture fields in the fault zone. It fol lows that a wide range of con vec tive pat terns can be ob tained. In par tic u lar, two and three small as pect ra tio (width/height) cells are il lus trated. In the mid dle case, al ter na tion of ther - mal ups and downs of more than 10 o C can be ob served in a sin gle ver ti cal pro file. FIG. 9. Nu me ri cal ex pe ri ments of hy dro ther mal convec tion wi thin a per meable fault zone. a) ben - chmark tests re pro du cing convec tive pat terns (top: iso therms in co lour and stream li nes in black) and sur face heat flow va ria tions (bot tom) ob tai ned by Ra bi no wicz et al. [1998] with si mi lar in put pa ra me - ters; b) sketch of nu me ri cal set-up and boun da ry condi tions; c) il lus tra tion of depth-de pen dence laws of per mea bi li ty tes ted in the mo dels; d) case where k f0 =5 10-13 m 2, with va rying. Co lou red bar scale cor res ponds to per mea bi li ty va lues, white li nes are iso therms se pa ra ted by 25 o C, and black li nes re pre - sent stream li nes of convec tive cir cu la tion; e) case where k f0 = 10-12 m 2, and =10 km; f) case of a high sur face per mea bi li ty and a more rea lis tic depth-de - pen dence of per mea bi li ty. In ca ses d-e-f, fault zone width equals 1 km and host rock per mea bi li ty at the sur face equals 10-17 m 2. FIG. 9. Mo dè les nu mé ri ques de convec tion hy dro - ther male dans une zone faillée per méable. a) tests de ca li bra tion re pro dui sant les fi gu res convec ti ves (en haut : iso ther mes en cou leur, et li gnes de cou - rant en noir) et les va ria tions de flux de cha leur en sur face (en bas) ob te nus par Ra bi no wicz et al. [1998] avec des pa ra mè tres sem bla bles ; b) re pré - sen ta tion de la mise en oeuvre nu mé rique et des condi tions aux li mi tes ; c) il lus tra tion des lois de dé pen dance de la per méa bi li té avec la pro fon deur tes tées dans les mo dè les ; d) cas pour le quel k f0 = 5 10 13 m 2, avec va riable. L é chelle de cou - leurs re pré sente les va leurs de per méa bi li té, les li - gnes blan ches cor res pon dent aux iso ther mes es pa cés de 25 o C et les li gnes noi res re pré sen tent les li gnes de cou rant de la cir cu la tion convec tive ; e) cas pour le quel k f0 = 10-12 m 2, et = 10 km ; f) cas où la per - méa bi li té en sur face est forte, et où la dé pen dance de la per méa bi li té avec la pro fon deur est plus réa - liste. Dans les cas d-e-f, la lar geur de la zone faillée est de 1 km et la per méa bi li té de l en cais sant à la sur face vaut 10-17 m 2.
THER MAL ANO MA LIES AND GEO LO GI CAL STRUC TU RES IN THE PRO VENCE BA SIN 373 and con firmed by oth ers [e.g. Wang, 1999; Tournier et al., 2000; Zhao et al., 2004] dis tinct con vec tive pat terns can be ob tained at a given Ray leigh num ber through nu mer i cal ex - per i ments where box size dif fers or where ini tial sta ble re - gime dif fers. The main re sults in our fig ures 9 and 10 deal with (i) the pos si ble hor i zon tal tem per a ture anom a lies ex - ceed ing 10 o C; (ii) the pos si ble ver ti cal in ver sion (e.g. from cold to hot) of ther mal anom a lies with depth. How - ever, it must also be noted that over ly ing lay ers of con vec - tive cells, and thus al ter na tion of ther mal ups and downs, seem to be fa voured when host rocks per me abil ity is low (fig. 10). FIG. 10. Case of a wi der per meable zone (2 km) with a depth-de pen dence of per mea bi li ty close to the Man ning and Inge brit sen s law ( = 1.5 km). Top: host rock per mea bi li ty at the sur face equals 10-17 m 2 while it is 10-16 m 2 for fi gu res at bot tom. Although se ve ral conver gent stable convec - tive pat terns can be ob tai ned ac cor ding to the cho sen nu me ri cal pro ce dure (see text), la te ral tem pe ra ture ano ma lies of at least 10 o C can be ob tai ned in each case. FIG. 10. Cas d une zone per méable plus large (2 km) avec une dé pen - dance de la per méa bi li té avec la pro fon deur proche de celle de la loi de Man ning et Inge brit sen ( = 1.5 km). En haut, la per méa bi li té de l en cais - sant en sur face vaut 10-17 m 2 et elle vaut 10 16 m 2 pour les fi gu res du bas. Bien que plu sieurs com por te ments convec tifs sta bles conver gents puis sent être ob te nus se lon la pro cé dure nu mé rique choisie (cf. texte), des ano ma - lies ther mi ques d au moins ± 10 o C sont ob ser vées dans tous les cas. For each row of fig ure 10, the dis tinct con vec tive pat - terns cor re spond to dif fer ent nu mer i cal pro ce dures to reach the steady-state so lu tion. Left cases were ob tained with a fixed value for (1.5 km) and by in creas ing reg u larly the k f0 pa ram e ter, from 10-15 to 2 10-12 m 2 : the steady-state so - lu tion for a given k f0 value is in ferred from the so lu tion com puted with the pre vi ously lower k f0 value. For mid dle cases, the vari able (in cre ment) pa ram e ter is, whereas per - me abil ity k f0 is fixed at 2 10-12 m 2. This pro ce dure en sures the achieve ment of a nu mer i cally sta ble so lu tion but the fi - nal so lu tion implicitely de pends on pre vi ous ones. In the right cases, so lu tion is com puted with no in cre ment in any pa ram e ter. Steady-state so lu tion is di rectly com puted, im - ply ing pos si ble nu mer i cal di ver gence and the pos si ble need of finer nu mer i cal meshes, which in fact was not needed here. The pos si bil ity to get sev eral so lu tions for a given set of pa ram e ters may be ex plained by non lin ear dy nam ics of con vec tive sys tems. As al ready noted by Quintard [1984] Summary These sim ple re sults of hy dro ther mal con vec tion within per me able zones dem on strate that ther mal anom a lies of more than 10 o C can eas ily de velop as soon as a fault zone is suf fi ciently wide and per me able at the sur face. Up lifted iso - therms de velop in per me able zones of con stant per me abil ity through the en tire ver ti cal do main, and since sin gle con vec - tive cells of small width/height ra tios are pro moted. How - ever, when depth-de pend ence of per me abil ity is ac counted for, lo cal Ray leigh num bers (which would be de fined with a lo cal rep re sen ta tive per me abil ity) dif fer from the top to the bot tom of the fault zone, and sta ble con vec tive wave lengths must adapt. Ap par ently, both hor i zon tal and ver ti cal con - vec tive strat i fi ca tion can de velop. In other words, the ac - count of depth-de pend ence of per me abil ity im plies that sev eral lay ers of con vec tive cells may jux ta pose each other. When the de creas ing trend of per me abil ity re sem bles Man - ning and Ingebritsen s law, i.e. for = 1.5 km, and when high sur face per me abil ity val ues are con sid ered, then fluid ve loc ity be tween 10-9 and 10-8 m.s -1 are eas ily reached, al - low ing tem per a ture anom a lies of more than 10 o C to de - velop within a sin gle ver ti cal pro file. DISCUSSION AND CONCLUSION Our work fo cused on the ther mal po ten tial of the Pro vence ba sin and the re la tion be tween tem per a tures, geo log i cal struc tures and fluid cir cu la tion along fault zones. We first in ter po late the tem per a tures in three di men sions, which en - abled us to make ther mal maps be tween 1 km and 5 km depth. The pre ci sion of these maps was greatly in creased com pared to the pre vi ously es tab lished ones and they en - able to con firm a re gional ther mal anom aly cen tred on the Pro vence ba sin, but from which the shape, the in ter nal struc ture and the tem per a tures are dif fer ent. We also high - lighted new warm and cold ther mal anom a lies that were not in di cated on the pre-ex is tent ther mal maps. With re gard to the po ten tially in ter est ing geo ther mal ar - eas, tem per a tures of 125 o C at 3.5 km depth and 185 o C at 5 km depth are reached in the Vistrenque graben area. Tem - per a tures of 155 o C at 3.5 km depth are also reached in the Drôme area. The warm anom a lies do not show di rect spa tial cor re la - tion with the Moho dis con ti nu ity depth vari a tions, even if large-scale trends are con sid ered. These anom a lous ar eas should be thus in ter preted to gether with a smaller scale phe - nom e non. For ex am ple, they could be ex plained by in su lat - ing sed i ments (e.g. Vistrenque graben) more or less as so ci ated with fluid cir cu la tion within faults as would