Wei Lin
email: linwei@mail.iggcas.ac.cn

Michel Faure

Xian-Hua Li

Wenbin Ji

Arnaud P Cavet

Marchand J Nicolas

Pre-Variscan tectonic setting of the south margin of Armorica: Insights from detrital zircon ages distribution and Hf isotopic composition of the St-Georges-sur-Loire

Keywords: U-Pb-Hf of detrital zircons, Provenance, Cadomian belt, Variscan belt, Armorica microcontinent Palaeozoic volcanism

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Introduction

Detrital zircon U-Pb dating is a powerful tool to assess the provenance of clastic formations (e.g. Fedo et al., 2003;Cawood et al., 2007Cawood et al., , 2012;;Dickinson and Gerhels, 2009).

Combined with in-situ Hf-isotope analysis, this approach can also provide useful information for reconstruction of the tectonic evolution of continental blocks, and discrimination of crust or mantle contributions [START_REF] Griffin | The Hf isotope composition of cratonic mantle: LAM-MC-ICPMS analyses of zircon megacrysts in kimberlites[END_REF]Condie et al., 2009). This method has been widely applied in various orogenic belts, for instance the Variscan-Appalachian orogen

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M A N U S C R I P T [START_REF] Henderson | Gondwanan basement terranes of the Variscan-Appalachian orogen: Baltican, Sahara and West African hafnium isotopic fingerprints in Avalonian, Iberia and Armorican Terranes[END_REF], the Himalaya, and the Alps [START_REF] Gehrels | Detrital zircon geochronology of pre-tertiary strata in the Tibetan-Himalayan orogen[END_REF][START_REF] Cai | Late Triassic paleogeographic reconstruction along the Neo-Tethyan Ocean margins, southern Tibet[END_REF][START_REF] Lin | Detrital zircon age distribution from Devonian and Carboniferous sandstone in the Southern Variscan Fold-and-Thrust belt (Montagne Noire, French Massif Central), and their bearings on the Variscan belt evolution[END_REF][START_REF] Lin | Detrital zircon age patterns from turbidites of the Balagne and Piedmont nappes of Alpine Corsica (France): evidence for an European margin source[END_REF]. The European Variscan belt is well investigated in Iberia (e.g. Martínez [START_REF] Martínez Catalán | U-Pb detrital zircon ages in synorogenic deposits of the NW Iberian Massif (Variscan belt): interplay of Devonian-Carboniferous sedimentation and thrust tectonics[END_REF][START_REF] Martínez Catalán | A rootless suture and the loss of the roots of a mountain chain: the Variscan belt of NW Iberia[END_REF], the Bohemian massif (e.g. [START_REF] Henderson | Gondwanan basement terranes of the Variscan-Appalachian orogen: Baltican, Sahara and West African hafnium isotopic fingerprints in Avalonian, Iberia and Armorican Terranes[END_REF]Linneman et al., 2004Linneman et al., , 2007)), and Corsica [START_REF] Avigad | Cadomian metasediments and Ordovician sandstone from Corsica: detrital zircon U-Pb-Hf constrains on their provenance and paleogeography[END_REF]. In the French Variscan orogen, a few studies deal with detrital zircon age distributions of the French Massif Central, namely in its western part, or Limousin [START_REF] Melleton | Precambrian protoliths and Early Paleozoic magmatism in the French Massif Central: U-Pb data and the North Gondwana connection in the west European Variscan belt[END_REF], and its southern part, in Montagne Noire, where the turbiditic foreland basin is well exposed [START_REF] Lin | Detrital zircon age distribution from Devonian and Carboniferous sandstone in the Southern Variscan Fold-and-Thrust belt (Montagne Noire, French Massif Central), and their bearings on the Variscan belt evolution[END_REF]. In the Armorican Massif, investigations on detrital zircon age distribution have only been carried out in the Central Armorican Domain [START_REF] Ballouard | Multiple crust reworking in the French Armorican Variscan belt: Implication for the genesis of uranium-fertile leucogranites[END_REF], the Early Carboniferous Ancenis Basin, and the Late Carboniferous "coal trough" (Ducassou et al., 2014). This paper aims to provide new data on the age distribution and Hf isotopic composition of the detrital zircons in the matrix of the olistostrome of the S t -Georges sur Loire unit on the southern margin of the Armorica microcontinent, in order to discuss the provenance of the rocks in the unit, and to clarify the tectonic relationships between the different units of the Ligerian Domain during Variscan subduction. The sources of the detrital zircons and their Hf isotopic signatures with respect to the Neoproterozoic Cadomian orogen, and the basement of the Armorican Massif, are also discussed.

Geological outline of the Armorican Massif

The French Armorican Massif experienced poly-orogenic superimposition, namely, the Late Neoproterozoic Cadomian orogeny, and the Late Paleozoic Variscan orogeny (Chantraine et al., 2001;Ballèvre et al., 2009, and references therein). The Armorican Massif is the only place in France that records the structural relationships between the Armorica microcontinent to the north, and the North Gondwana Margin to the south. In the Armorican massif, three domains are separated by ophiolitic sutures, and they correspond to different

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microcontinents with Gondwana affinities (e.g. Faure et al., 2005Faure et al., , 2008;;[START_REF] Ballèvre | Palaeozoic history of the Armorican Massif: Models for the tectonic evolution of the suture zones[END_REF]Fig. 1). From north to south, these domains are: i) the Léon Domain formed by N-directed metamorphic nappes [START_REF] Rolet | Intracontinental Hercynian events in the Armorican Massif[END_REF][START_REF] Melleton | Precambrian protoliths and Early Paleozoic magmatism in the French Massif Central: U-Pb data and the North Gondwana connection in the west European Variscan belt[END_REF]; ii) the North-and-Central

Armorican Domain that consists of deformed and metamorphosed Neoproterozoic rocks related to the ca. 650-540 Ma Cadomian orogeny, and weakly deformed Paleozoic sedimentary cover (e.g. Chantraine et al., 2001); iii) the South Armorican Domain that includes a stack of S-directed metamorphic nappes. In terms of Variscan geodynamics, the Léon, North-and-Central Armorican, and South Armorican domains belong to the Mid-German Crystalline Rise, Armorica, and North Gondwana margin, respectively. All these domains were rifted from Gondwana during the Early Ordovician and subsequently assembled together during the Variscan orogeny.

The Léon domain is not described here as it is not relevant to our study. The Northand-Central Armorican Domain contains an isolated fragment of the Cadomian belt (Fig. 1).

This Neoproterozoic accretionary orogen has been subdivided into several NE-SW trending units that verge to the SE (e. g. Dissler et al., 1988;Chantraine et al., 2001 and references therein). To the NW, the Trégor Unit includes a Paleoproterozoic basement, also known as the Icartian basement, with ca. 2035 ± 35 Ma orthogneiss, and amphibolites, and a calcalkaline volcanic-plutonic complex (Chantraine et al., 2001). These magmatic rocks yielding Ediacaran ages (ca 615 Ma) are interpreted as formed in a magmatic arc. To the SE, S t -Brieuc

Unit is formed by a bimodal volcanic suite dated at ca 588±11 Ma, and a volcanic-clastic series intruded by 590-580 Ma gabbro-dioritic, dioritic or gabbroic plutons. The lower part of the S t -Brieuc Unit is underlain by a 750-650 Ma orthogneiss (Egal et al., 1996;Chantraine et al., 2001). The S t -Brieuc Unit is interpreted as a back-arc basin opened within an Eo-Cadomian arc (Dissler et al., 1988;Chantraine et al., 2001). The Guingamp and S t -Malo Units are characterized by high temperature gneiss, and migmatites developed at the expense of

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Cryogenian to Ediacaran metasediments. The S t -Malo migmatite and the Cancale leucogranite yield zircon U-Pb ages at 541±5 Ma and 555±16 Ma, respectively [START_REF] Peucat | Behaviour of Rb-Sr whole rock and U-Pb zircon systems during partial melting as shown in migmatitic gneisses from the Saint-Malo Massif, NE Brittany, France[END_REF]Egal et al., 1996). Lastly, the southeasternmost Fougères Unit consists of turbidites intruded by Early Cambrian (ca. 540 Ma, [START_REF] Pasteels | Age of the Vire-Carolles granite[END_REF] peraluminous granites, referred to as the Mancellian batholith [START_REF] Graviou | The Cadomian orogeny in the northern Armorican Massif-petrological and geochronological constraints on a geodynamic model[END_REF][START_REF] Guerrot | U-Pb geochronology of the Late Proterozoic Cadomian orogeny in the northern Armorican Massif, France[END_REF]. The Fougères Unit, devoid of metamorphism and ductile deformation, is interpreted as the Cadomian foreland basin filled by eroded material supplied from the Trégor and S t -Brieuc units. Below the Early Ordovician unconformity, the Neoproterozoic rocks that crop out in Central Brittany consist of graywackes, sandstone and mudstone with volcanic intercalations. Their precise age and structure are poorly documented. A recent study combining trace fossils and detrital zircon age investigations were indicative of an Ediacaran-Fortunian age [START_REF] Gougeon | Trace Fossils from the Brioverian (Ediacaran-Fortunian) in Brittany (NW France)[END_REF].

These formations are considered as the southern distal extension of the Fougères Unit.

The Conquet and Nort-sur Erdre faults correspond to the ophiolitic sutures that separate the three domains (Fig. 1). In addition to these major paleogeodynamic boundaries, the Armorican Massif is cut by West-East to NW-SE striking dextral strike-slip faults of the North Armorican Shear Zone, North branch of the South Armorican Shear Zone, and the South Branch of the South Armorican Shear Zone [START_REF] Jégouzo | The South-Armorican Shear Zone[END_REF].

In the SE part of the Armorican Massif, on the two sides of the Nort-sur Erdre fault, the Variscan deformation both affected the southern margin of Armorica, and the northernmost part of the North Gondwana margin. The triangular area located between the north and south branches the South Armorican Shear Zone is also referred to as the Ligerian Domain (Cavet et al., 1970(Cavet et al., , 1978;;[START_REF] Lardeux | Paleozoic of the Ligerian domain[END_REF]Cartier et al., 2001;Cartier and Faure, 2004;[START_REF] Ballèvre | Palaeozoic history of the Armorican Massif: Models for the tectonic evolution of the suture zones[END_REF]Ducassou et al., , 2011Ducassou et al., , 2014;;Figs. 2 and 3). Several lithotectonic units form the Ligerian domain (Figs. 2 and3). Within this domain, the Lanvaux Unit consists of the Neoproterozoic to the Early Ordovician sedimentary and volcanic rocks intruded by the

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Early Ordovician alkaline granites [START_REF] Vidal | L'évolution polyorogénique de Massif Armoricain : apport de la géochronologie et de la géochimie isotopique du strontium[END_REF][START_REF] Ballèvre | Palaeozoic history of the Armorican Massif: Models for the tectonic evolution of the suture zones[END_REF], now deformed as orthogneiss, exposed near Redon and Angers. The S t -Georges-sur-Loire Unit is a clastic unit subdivided into a northern turbiditic sub-unit, and a southern olistostrome sub-unit (cf. details below). The Nort-sur-Erdre fault is the southern boundary of the S t -Georges-sur-Loire Unit and represents the Eo-Variscan suture (Faure et al., 2005(Faure et al., , 2008)). Thus, together with the Lanvaux Unit, the S t -Georges-sur-Loire Unit belongs to the North and Central Armorican Domain (i.e. Armorica). The age of the suture is still disputed; some authors argue for 360 Ma (e.g. Ballèvre et al., 2008[START_REF] Paquette | From opening to subduction of an oceanic domain constrained by LA-ICP-MS U-Pb zircon dating (Variscan belt, southern Armorican Massif, France)[END_REF], whereas others propose a ca 400 Ma age [START_REF] Pin | Variscan oceans: Ages, origins and geodynamic implications inferred from geochemical and radiometric data[END_REF]Faure et al., 2005Faure et al., , 2009)).

South of the Nort-sur-Erdre fault (i.e. the Eo-Variscan suture), several litho-tectonic units occur. Adjacent to the fault, the Late Carboniferous sandstone with coal measures forms the "Sillon Houiller de la Basse-Loire" (Lower Loire coal trough). Early Carboniferous (Tournaisian-Visean) clastic rocks filled the Ancenis Basin. As indicated by the kinematics of the boundary fault and drag folds, the spindle-shaped Ancenis Basin opened as a left-lateral pull apart superimposed upon the Mauges Nappe (Diot and Blaise, 1978). Neoproterozoic metapelite, greywacke, and basalt are the main constituents of the Mauges Nappe. The metamorphic volcanic-sedimentary series is uncomformably overlain by Cambrian conglomerate, sandstone and rhyolitic lava flows, and Ordovician sandstone. The Mauges Nappe overthrusts to the S (SW) an ophiolitic nappe composed of an assemblage of amphibolite, metagabbro, serpentinite (referred to as the Drain Unit), and chloritoid-chloritegarnet metapelite called the Hâvre unit [START_REF] Marchand | Ecaillage d'un ''mélange tectonique'' profond: le complexe cristallophyllien de Champtoceaux (Bretagne Méridionale)[END_REF][START_REF] Ballèvre | Palaeozoic history of the Armorican Massif: Models for the tectonic evolution of the suture zones[END_REF]. A mylonitic metagabbro yields a zircon U-Pb age at 381.8± 2.3 Ma, interpreted as the magmatic crystallization age of this gabbro [START_REF] Paquette | From opening to subduction of an oceanic domain constrained by LA-ICP-MS U-Pb zircon dating (Variscan belt, southern Armorican Massif, France)[END_REF]. This nappe overthrusts the Champtoceaux complex formed by imbricated thrust sheets of high pressure rocks with mafic eclogites, orthogneiss, and paragneiss and locally migmatite. The mafic eclogites are

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commonly retrogressed to garnet amphibolite enclosed in variously melted metapelites and orthogneisses. Monazite from a migmatitic leucosome yields a U-Th-Pb chemical age of 387±6 Ma (Cocherie et al., 2005). The lowermost part of the stack of nappes comprises the Mauves Unit, which consists of paragneiss and micaschists that did not experience the HP metamorphism characteristic of the Champtoceaux complex [START_REF] Marchand | Ecaillage d'un ''mélange tectonique'' profond: le complexe cristallophyllien de Champtoceaux (Bretagne Méridionale)[END_REF][START_REF] Ballèvre | Palaeozoic history of the Armorican Massif: Models for the tectonic evolution of the suture zones[END_REF]. The nappe pile was folded to form an E-W trending upright antiform, the core of which is occupied by late Carboniferous two mica plutons. Most of these leucogranites develop S-C structures coeval with the dextral shearing of the southern branch of the South Armorican Shear Zone (Berthé et al., 1978;[START_REF] Jégouzo | The South-Armorican Shear Zone[END_REF].

The S t -Georges-sur-Loire Unit

North of the Nort-sur-Erdre fault, the southern part of the S t -Georges-sur-Loire Unit is interpreted as a "block-in-matrix" formation, or olistostrome (Dubreuil, 1986;Cartier et al., 2001;Cartier and Faure, 2004; Fig. 4A,B). The main blocks consist of Silurian black chert (Fig. 4G), Late Silurian to Middle Devonian limestone (Fig. 4D), sandstone (Fig. 4C), spilitized mafic lava (Fig. 4H) with porphyritic basalt, pillow basalt, dolerite, gabbro, rhyolite, microgranite, andesite and trachyte (see details in Cartier and Faure, 2004). Geochemical analyses suggest that the mafic rocks were formed either in an active continental margin or in a back-arc basin partly floored by oceanic crust (Carpentier et al., 1982;[START_REF] Cabanis | Identification des séries magmatiques dans les socles métamorphiques sur la base de critères géologiques, pétrographiques et géochimiques. Exemples d'application dans le Massif armoricain[END_REF]Cartier and Faure, 2004). The matrix of the olistostrome commonly consists of pelite, silt or sandstone, and is described as a flysch deposit [START_REF] Lardeux | Paleozoic of the Ligerian domain[END_REF]; Fig. 4A, B, E, andF). Pebbly mudstones, with mm-to cm-sized clasts, are also representative of a gravitydriven, chaotic sedimentation deposited in a tectonically active region. Both the olistostrome and the sandstone-pelite sub-units experienced three phases of ductile deformation (Cartier and Faure, 2004).

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The source of the olistoliths is controversial. A northern origin from the North-and-Central Armorican Domain is ruled out by the lithological and paleontological differences of the Paleozoic successions between the two domains (Dubreuil, 1986;[START_REF] Lardeux | Paleozoic of the Ligerian domain[END_REF]. However, the formations exposed to the South of the Nort-sur-Erdre fault are only represented by metamorphic rocks, except for the Cambrian-Ordovician sedimentary cover of the Mauges Nappe. In particular, the Cambrian rhyolite that overlies the Neoproterozoic micaschist might have supplied blocks to the S t -Georges-sur-Loire Unit. The southern boundary of the Carboniferous Ancenis Basin contains Ordovician to Emsian clastic formations [START_REF] Ballèvre | Palaeozoic history of the Armorican Massif: Models for the tectonic evolution of the suture zones[END_REF](Ducassou et al., , 2011)), but magmatic rocks are absent there. Therefore, following a previous interpretation (Dubreuil, 1986), the possibility of a "missing domain" located between the S t -Georges-sur-Loire Unit and the Mauges Nappe has been proposed (Faure et al., 2008). In this interpretation, a magmatic arc developed upon a Neoproterozoic

Cadomian basement was separated from Armorica by a back-arc basin. During the Variscan tectonics, a part of the back-arc basin, represented by the S t -Georges-sur-Loire Unit, was folded and thrusted to the N or NW upon the Lanvaux Unit. The South Armorican nappe stack was formed by the Mauges Nappe, the ophiolitic nappe, and the Champtoceaux Complex resulted from the North-directed continental subduction of the North Gondwana margin. The reduced lithosphere thickness, below the back-arc basin, played a role in the breakup of the upper plate. This tectonic regime led to the subduction of the magmatic arc, and a great part of the back-arc basin. Consequently, the present S t -Georges-sur-Loire Unit, and the Mauges Nappe are the only remnants of this back-arc-arc system developed along the active margin of the southern Armorica microcontinent.

Petrography of the analyzed samples

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Detrital zircon U-Pb age spectra and isotopic Lu-Hf proved to be an exceedingly useful tool to identify a geological history of sedimentary basins in orogenic belts due to the robustness of zircon to later thermal events and surface processes [START_REF] Gehrels | Detrital zircon provenance of Cambrian to Triassic miogeoclinal and eugeoclinal strata in Nevada[END_REF][START_REF] Bruguier | U-Pb dating on single detrital zircon grains from the Triassic Songpan-Ganze flysch (Central China): provenance and tectonic correlations[END_REF]Fedo et al., 2003). Since the proportion of zircons with different ages does not change drastically during sediment transport, owing to the inherent stability of zircon, they can reveal the history of the source area eroded continental crust and sedimentary regime in an ancient arc-trench system. In order to reveal the pre-Variscan lithological history of the south margin of Armorica block, eight samples from the St-Georges-sur-Loire Unit have been analyzed for zircon dating. Their locations are presented in Fig. 2, and the GPS coordinates are provided in Table 1. Seven samples (13FR12, 13FR18-1, 13FR19, 13FR21, OUT, MB2, RO2) are sandstone or siltstone from the olistostrome matrix. Sample 13FR13 is a rhyolitic block enclosed in the sandstone matrix of the olistostrome. The clastic matrix consists dominantly of rounded quartz grains, although recrystallization developed during the ductile deformation led to a smoothed grain boundary with pressure shadows. Other clasts found in the sandstone are plagioclase and muscovite (Fig. 5). In thin section, quartz grain embayments are indicative of a volcanic or hypovolcanic source (Fig. 5B).

Analytical procedures

Zircon U-Pb dating

Zircons were separated from each sample of ca. 2 kg in weight using standard heavy liquid and magnetic separation techniques. Zircon grains, together with standard 91500 and Temora zircons were cast in an epoxy mount, which were then polished to reveal the grain interiors for analysis. These grains were randomly selected in different sizes to avoid any age bias based on grain size. Zircon structures were documented with transmitted and reflected

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light micrographs, and cathodoluminescence (CL) images were obtained by a CAMECA electron microscope in order to reveal their internal structures.

On the basis of these analyzed photographs, various grains were selected for analysis.

Zircon U-Pb dating for seven sandstones (13FR12, 13FR18-1, 13FR19, 13FR21, OUT, MB2, RO2) and one rhyolite (13FR13) sample was analyzed using a quadrupole ICP-MS (Agilent 7500a) equipped with a 193 nm laser-ablation system (Analyte G2) at the Institute of Geology and Geophysics, Chinese Academy of Sciences in Beijing. U-Th-Pb ratios and absolute abundances were determined relative to the standard zircon. Detailed analytical procedures are described by [START_REF] Xie | In situ simultaneous determination of trace elements, U-Pb and Lu-Hf isotopes in zircon and baddeleyite[END_REF]. The spot diameter is 40 μm in size. Correction of common lead was applied following the method described by [START_REF] Andersen | Correction of common lead in U-Pb analyses that do not report 204Pb[END_REF]. The GLITTER program was used for data processing [START_REF] Van Achterbergh | Appendix 3 data reduction software for LA-ICP-MS[END_REF]. Data plotting was carried out using the Density Plotter program [START_REF] Vermeesch | On the visualisation of detrital age distributions[END_REF]. LA-ICPMS zircon U-Pb analytical data are presented in

Zircon Lu-Hf isotopes

Zircon Lu-Hf isotopic analysis was carried out in situ on a Neptune multi-collector ICP-MS equipped with a Geolas-193 laser ablation system at the Institute of Geology and Geophysics, Chinese Academy of Sciences. Previously analyzed zircon grains for U-Pb isotopes were chosen for Lu-Hf isotopic analyses, with ablation pits of 44 or 60 μm in diameter, ablation time of 26 seconds, repetition rate of 10 Hz, and laser beam energy density of 10 J/cm 2 . The detailed analytical procedures are similar to those described by Wu et al. 2006). Measured 176 Hf/ 177 Hf ratios were normalized to 179 Hf/ 177 Hf = 0.7325. Zircon standards Mud Tank and GJ-1 were analyzed alternately with the unknowns. During the course of this study, we obtained 176 Hf/ 177 Hf ratio of 0.282504 ± 0.000032 (2σ, n=58) and 0.282022 ± 0.000051 (2σ, n=58) for Mud Tank and GJ-1, respectively, in good agreement within errors with the recommended values [START_REF] Woodhead | A preliminary appraisal of seven natural zircon reference materials for in situ Hf isotope determination[END_REF][START_REF] Morel | Hafnium isotope characterization of the GJ-1 zircon reference material by solution and laser-ablation MC-ICPMS[END_REF].

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Zircon U-Pb and Lu-Hf analytical results

Representative CL images of the dated zircons are shown in Fig. 6. All analyzed samples, yield zircon grains with a wide range in size from 50 μm to 200 μm (Fig. 6). Except for a few prismatic crystals, most of the grains possess a rounded shape with abraded crystallographic faces, indicating long fluvial transportation. Most of the grains exhibit a zonal structure, sometimes with an inner core surrounded by recrystallization rims with clear oscillatory zoning.

Lu-Hf isotopes were obtained on dated zircon grains, with analytical spots adjacent to those for U-Pb dating, or in the same growth domain as inferred from CL imagery (Fig. 6). U- 1), is a middle-to fine-grained sandstone. The grain size is around 0.18-0.40 mm and commonly 0.25-0.35mm (Fig. 5A).

Major components are quartz, plagioclase, muscovite, and lithic fragments. In thin section,

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poorly rounded quartz with undulatory extinction represents 75-78% of the detrital component. Plagioclase and muscovite, less than 1%, are rarely observed (Fig. 5A).

In this sample, a total of 100 points on 100 grains were analyzed, and 94 analyses were concordant (Table 2). Concentric zoning is distinctly demonstrated in euhedral zircon grains with 70 to 250 μm in length, rounded or prismatic shape, and length-width ratios of 1:1 to 2.5:1. Th/U ratios range from 0.01 to 2.52. Except one grain, Th/U ratios are higher than 0.1 (Table 2). Combined with the CL images, these compositions and morphometric features of the zircons are indicative of a magmatic origin (Fig. 6). The measured apparent ages range from 3300 Ma to 458 Ma ( of dispersed ages from Mesoarchean to the Neoarchean is also demonstrated (Fig. 7).

Forty dated zircons were chosen for in situ Hf isotope analyses with 176 Hf/ 177 Hf ratios varying from 0.280867 to 0.282355 (Fig. 6; Table 3). All the analyses have εHf (t) values of +6.3 to -23.9 with the two dominant peaks at -4.5 and -9.9, and a subordinate peak at -18.4 (Fig. 8). In sample 13FR12, zircon two-stage model Hf ages (TDM 2 ) range from 1.72 to 3.70

Ga with two clusters around 2225 Ma, and 2820 Ma (Fig. 9; Table 3).

13FR13

Sample 13FR13 is a rhyolitic block in a siltstone matrix at Epiré, and represents the olistostrome sub-unit of the S t -Georges-sur-Loire Unit (Fig. 2, Table 1). In thin section, this sample is rich in plagioclase with grain sizes from 0.1 mm to ~5 mm (Fig. 5B). The major components are polycrystalline aggregates of quartz, plagioclase, and orthoclase phenocrysts.

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Microcrystalline or aphanitic quartz and plagioclase appear as mesostasis. Opaque minerals are also present. Magmatic minerals are still preserved. No secondary plagioclase was observed in the thin section. Concentric zoning is distinct in euhedral zircon grains with 110 to 300 μm in length, prismatic shape, and length-width ratios of 1.5:1 to 4:1(Fig. 6). Th/U ratios range from 0.05 to 1.53. Except for two grains, these zircons have Th/U ratios higher than 0.1 (Table 2).

A total of 90 analyses on 90 grains were made, of which 10 analyses are discordant (Table 2). 80 concordant ages range from 2320 Ma to 445 Ma (Table 2). Around 80 percent of these analyses fall within an age range of 600-450 Ma, and 32 analyses yield a mean 206 Pb/ 238 U age of 479.6 ± 3.3 Ma (Fig. 7; Table 2), which is interpreted as the eruption age of this rhyolite sample (Fig. 7). Precambrian zircons are rare.

Among these 80 concordant ages, 28 "younger" zircons (528-473 Ma) were chosen for in situ Hf isotope determination (Fig. 6). Compared with the highly variable ages of the sandstone or siltstone of the olistostrome matrix, the good concentration of the zircon crystallization ages of these zircons is in agreement with the narrow range of their 176 Hf/ 177 Hf ratios, varying from 0.282134 to 0.282517 (Table 3). All the analyses exhibit εHf (t) values from +2.8 to -12.5 with a peak at -6.2 (Fig. 8). In this sample, the TDM 2 age ranges from 1.25-2.22 Ga with a cluster around 1830 Ma (Fig. 9; Table 3).

13FR18-1

Sample 13FR18-1 was collected from the Olistostrome sub-unit of the S t -Georges-sur-Loire Unit, at Villemoissan (Fig. 2; Table 1), from a lens of coarse sandstone in the siltstone matrix (Fig. 4B). This coarse grained, poorly sorted, and angular or sub-angular sandstone has

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grain sizes around 0.3-1.5 mm with a concentration around 0.3-0.7 mm (Fig. 5C). The major detrital components are polycrystalline quartz, plagioclase, muscovite, and lithic fragments. In thin section, poorly rounded quartz grains represent nearly 70% of the detrital component.

Plagioclase and muscovite are less than 1%, and lithic fragments nearly 30% (Fig. 5C).

Zircons are mostly euhedral to subhedral, transparent and colorless, ranging from 30 to150 μm in length, and possess length to width ratios between 1.1:1 and 2.5:1. Concentric zoning is common in most crystals in CL images (Fig. 6).

Of the 100 analyses conducted on 100 zircons for this sample, 91 are concordant within uncertainties (Table 2). All zircons have Th/U ratios higher than 0.1. Concordant ages range from 2928 Ma to 563 Ma, with one dominant peak at ca. 610 Ma and one subordinate peak at ca. 1920 Ma. Three low backgrounds of dispersed ages fall into the Mesoarchean, Neoarchean, and Neoproterozoic (Fig. 7).

Twenty-eight dated zircons were chosen for in situ Hf isotope analyses among these 91 concordant analyses (Fig. 6; Table 3). The 176 Hf/ 177 Hf ratios vary from 0.280938 to 0.282335.

All the analyses have a εHf (t) range from -20.4 to +1.7 with a peak at -5.5 (Fig. 8). The zircon TDM 2 ranges from 3540 to 1700 Ma with clusters around 2270 Ma, 2710 Ma, and 3430 Ma (Fig. 9; Table 3).

13FR19

Pervasively deformed muddy sandstone, sample 13FR19, is from Roche Ayrault (Fig. 2).

Pressure solution cleavage is well developed in the outcrop and thin section (Figs. 4C and5D).

Fine grain quartz and mica constitute the major components of this sample (Fig. 5D). Zircon grains possess a relatively-round shape, ranging from 30 to 70 μm in size (Fig. 6).

A C C E P T E D M A N U S C R I P T

A total of 69 analyses on 69 grains were obtained (Table 2). Among these analyses, 47 have concordant ages from 3109 Ma to 411 Ma. Two dominant age groups are documented at 720-400 Ma with a peak of ca. 600 Ma, and 3150-1550 Ma with a peak around 1975 Ma (Fig. 7). This sample is the only one to yield detrital zircon ages younger than 450 Ma (411±7 Ma, 411±8 Ma, and 426±6 Ma). Th/U ratios of all zircons from this sample are close to or greater than 0.1.

Because of the small size, only 19 dated zircons were measured for in situ Hf isotope determination from the 47 concordant analyses (Fig. 6; Table 3). The 176 Hf/ 177 Hf ratios vary from 0.281296 to 0.282565. All εHf (t) values range from +2.6 to -20.9 with two dominant peaks at -1.4 and -9.5 (Fig. 8). The TDM 2 model ages vary from 1.31 to 3.20 Ga with clusters around 2305 Ma, and 2870 Ma (Fig. 9; Table 3).

13FR21

To the west of Beaulieu-sur-Layon, the Pierre Bize quarry exposes a schistose-fine grain conglomerate with limestone and volcanic pebbles, which was chosen for detrital zircon analysis (Fig. 4D). A coarse-grained, poorly-sorted sandstone, with angularsubangular shaped, gravel-size clasts has a 0.3-1.5 mm grain size with 0.3-1.1 mm concentration (Fig. 5E). The main detrital components are polycrystalline quartz (~40%), plagioclase (~2%), muscovite (more than 20%), and lithic fragments with carbonate cementation (Fig. 5E).

Zircon grains are mostly euhedral, transparent and colorless, ranging from 70 to 250 μm in length, and with length to width ratios between 1.3:1 and 4:1. A total of 100 analyses of 100 grains from sample 13FR21 were obtained. 94 analyses are concordant within

A C C E P T E D M A N U S C R I P T
uncertainties (Table 2). Combined with CL images, the high Th/U ratio (0.07-2.61) is indicative of magmatic origin (Fig. 6). Concordant ages range from 2690 Ma to 399 Ma, with one dominant peak at ~525 Ma. A few ages, between the Neoarchean and Paleoproterozoic are recorded with a small peak at 2630 Ma (Fig. 7).

Thirty-five dated zircons were chosen for in situ Hf isotope analyses among these 94 concordant analyses (Fig. 6; Table 3). The Hf isotopic compositions reveal 176 Hf/ 177 Hf ratios varying from 0.281953 to 0.282718. εHf (t) values range from+9.6 to -18.7 with two dominant peaks at 2.7 and -3.4 (Fig. 8). More than half of the εHf (t) values of Neoproterozoic to Cambrian zircons are positive (Table 3). The TDM 2 model ages range from 3540 to 1700 Ma with a cluster around 1285 Ma (Fig. 9; Table 3).

RO2

Sample RO2 is a fine-grained siltstone in the clastic matrix of the olistostrome sub-unit, taken from the S t -Georges-sur-Loire Unit near Rochefort-sur-Loire (Figs. 2,4E; Table 1).

This siltstone is fine grained, poorly-sorted, and angular. Its grain size is around 0.1-0.7 mm with a concentration around 0.2-0.4 mm (Fig. 5F). The major detrital components are quartz, muscovite, and sedimentary lithic fragments. In thin section, poorly rounded quartz represents 78% of the detrital component, and muscovite comprises about 20% (Fig. 5F).

Zircon grain size ranges from 40 to 160 μm with length to width ratios between 1:1 and 2:1 (Fig. 6). A total of 185 analyses of 185 grains were obtained for this sample (Table 2).

Among these analyses, 100 concordant ages range from 3300 Ma to 447 Ma with Th/U ratios close to or higher than 0.1 ( background of dispersed ages ranges from 3300 Ma to 2500 Ma (Fig. 7).

Forty dated zircons were measured for Hf isotope determination among these 117 concordant analyses (Fig. 6; Table 3). 176 Hf/ 177 Hf ratios vary from 0.280543 to 0.282664. All the analyses reveal a εHf (t) range from -31.3 to +30.9 with two dominant peaks at +6.5 and -1.7 (Fig. 8). TDM 2 model ages range from 0.63 to 3.95 Ga with clusters around 2970 Ma, and 2255 Ma (Fig. 9; Table 3).

OUT

The sandstone sample OUT was collected to the NW of the S t -Georges-sur-Loire Unit (Fig. 2; Table 1). In the fine-grained, poorly sorted, and angular matrix-supported sandstone, grain size is around 0.1-0.5 mm with a concentration around 0.2-0.4 mm (Fig. 5G). The major detrital components are quartz, muscovite and sedimentary lithic fragments. In thin section, poorly rounded to subangular gravel-size quartz represents 92% of the detrital component, muscovite is less than 1%, and lithic fragmented about 7% (Fig. 5G). As a fine grained sandstone, the zircon grains range from 50 to 250 μm with length to width ratio between 1:1.2 and 2.5:1 (Fig. 6).

A total of 100 analyses from 100 grains were obtained for this sample (Table 2). Among these analyses, 71 are concordant within uncertainties, ranging from 2998 Ma to 299 Ma.

Only one grain is younger than 480 Ma (Fig. 7). The Th/U ratios of almost all zircons are greater than 0.1, except for one grain (Table 2). Two dominant age groups are at 680-490 Ma with a peak of 595 Ma, and 2200-1890 Ma with a peak around 1930 Ma (Fig. 7).

A C C E P T E D M A N U S C R I P T

Seventy-one dated zircons were chosen for in situ Hf isotope analyses among these 71 concordant analyses (Fig. 6; Table 3). The 176 Hf/ 177 Hf ratio varies from 0.280793 to 0.282602. εHf (t) values range from +24.1 to -25.8 with two dominant peaks at -4.0 and -7.8 and also with two subordinate peaks at 7.6 and -16.7 (Fig. 8). The TDM 2 model ages range from 0.98 to 3.62 Ga with clusters around 1200 Ma, 1870 Ma, and 2945 Ma (Fig. 9; Table 3).

MB2

Sample MB2 is a deformed sandstone from the matrix of the olistostrome subunit of the S t -Georges-sur-Loire Unit, Moulin de Beaupreau (Fig. 2; Table 1). In this fine-grained, angular to subangular sandstone, grain size is around 0.1-0.7 mm with a concentration around 0.3-0.5 mm (Fig. 5H). The major detrital components are quartz, muscovite and sedimentary lithic fragments. In thin section, deformed quartz grains represent 78% of the detrital component, muscovite and sedimentary lithic fragments are more than 7%, and 15%, respectively (Fig. 5H). The zircon grains range from 70 to 150 μm with length-to-width ratios between 1:1 and 1.7:1 (Fig. 6).

A total of 100 analyses on 100 grains were carried out (Table 2), and 74 are concordant, ranging in age from 2717 Ma to 280 Ma. The Th/U ratios of all zircons are greater than 0.1 (Table 2). Two dominant age groups are documented at 680-520 Ma with a peak of ca. 615

Ma, and 2230-1855 Ma with a peak around ca. 1940 Ma (Fig. 7). Two grains are younger than 470 Ma (Fig. 7).

Hf isotope determination of seventy-two dated zircons from 74 concordant analyses shows 176 Hf/ 177 Hf ratios vary from 0.280781 to 0.282567 (Fig. 6; Table 3). All the analyses exhibit εHf (t) values from -27.4 to +8.0 with one dominant peak at -5.1. Several subordinate

A C C E P T E D M A N U S C R I P T

peaks can be identified at +6.4, -10.5, -16.2, and -22.9 respectively (Fig. 8). The TDM 2 range from 1.11 to 4.29 Ga with clusters around 1810 Ma, 2300Ma, and 2830 Ma (Fig. 9; Table 3).

Provenance of the detrital zircons in St-Georges-sur-Loire Unit

The S t -Georges-sur-Loire Unit has been interpreted as a remnant back-arc basin deformed during the Variscan orogeny [START_REF] Carpenter | Geochemical and geochronological characteristics of[END_REF][START_REF] Cabanis | Identification des séries magmatiques dans les socles métamorphiques sur la base de critères géologiques, pétrographiques et géochimiques. Exemples d'application dans le Massif armoricain[END_REF]Cartier and Faure, 2004;Fig. 1). Most of the sedimentary and magmatic blocks enclosed in a clastic matrix are interpreted as olistoliths derived from a southern area called the "missing domain", presently exposed as the Variscan Mauges Nappe composed of Cadomian rocks and its Early Paleozoic sedimentary cover (Dubreuil, 1986;[START_REF] Ballèvre | Palaeozoic history of the Armorican Massif: Models for the tectonic evolution of the suture zones[END_REF]Ducassou et al., , 2011Ducassou et al., , 2014)). The "missing domain" is interpreted to have been subducted below Armorica during the Early Devonian (Faure et al., 2008) or the Middle Devonian Variscan collision (Ducassou et al., 2014;[START_REF] Paquette | From opening to subduction of an oceanic domain constrained by LA-ICP-MS U-Pb zircon dating (Variscan belt, southern Armorican Massif, France)[END_REF]. Eight samples have been analyzed for zircon geochronology in the S t -Georges-sur-Loire Unit (Fig. 2); seven samples of them are sandstone or siltstone in the olistostrome matrix, and one is a rhyolitic block as an olistolith. Our new detrital zircon U-Pb ages exhibit age peaks from the Neoarchean to Early Paleozoic at 2650 Ma, 2065Ma, 1910 Ma, 625 Ma, 595 Ma and 490 Ma (Fig. 11A). Statistically, the Neoproterozoic (Cadomian) age cluster is the dominant one that contains nearly half (45.2±2.8%) of all zircon ages (Fig. 11A), similar to the detrital zircon age distribution from the Late Paleozoic sedimentary sequences of the Montagne Noire area of French Massif Central, Corsica and West Avalonia (Ganderia and Notre Dame Subzone) (Fig. 13; [START_REF] Henderson | Gondwanan basement terranes of the Variscan-Appalachian orogen: Baltican, Sahara and West African hafnium isotopic fingerprints in Avalonian, Iberia and Armorican Terranes[END_REF][START_REF] Henderson | A hafnium isotopic record of magmatic arcs and continental growth in the Iapetus Ocean: The contrasting evolution of Ganderia and the peri-Laurentian margin[END_REF][START_REF] Lin | Detrital zircon age distribution from Devonian and Carboniferous sandstone in the Southern Variscan Fold-and-Thrust belt (Montagne Noire, French Massif Central), and their bearings on the Variscan belt evolution[END_REF][START_REF] Avigad | Cadomian metasediments and Ordovician sandstone from Corsica: detrital zircon U-Pb-Hf constrains on their provenance and paleogeography[END_REF]. A secondary Paleoproterozoic age peak (with 27.4±1.7% of measured zircon grains) range from 2100 Ma to 1900 Ma [START_REF] Lin | Detrital zircon age distribution from Devonian and Carboniferous sandstone in the Southern Variscan Fold-and-Thrust belt (Montagne Noire, French Massif Central), and their bearings on the Variscan belt evolution[END_REF]. Nearly 20% of the [START_REF] Matte | The Variscan collage and orogeny (480-290 Ma) and the tectonic definition of the Armorica microplate: a review[END_REF][START_REF] Winchester | Paleozoic Amalgamation of Central Europe: an introduction and synthesis of new results from recent geological and geophysical investigations[END_REF]Linneman et al., 2004Linneman et al., , 2007;;[START_REF] Murphy | Origin of the Rheic Ocean: Rifting along a Neoproterozoic suture?[END_REF]. In the Armorican Massif, Cambrian magmatism is well recorded in the North Armorican Domain (Doré, 1994;[START_REF] Gall | Pétrogenèse des magmas andésitiques et ignimbritiques et leur signification dans l'évolution géodynamique cadomienne. Reconstitution des dynamismes éruptifs d'une province paléovolcanique: l'exemple du graben cambrien du Maine (Est du Massif Armoricain)[END_REF], and in the South Armorican Domain, for example, the protolith of the migmatitic orthogneisses from the Champtoceaux Unit (Cocherie et al., 2005), or the Cambrian rhyolite in the Mauges Nappe [START_REF] Thiéblemont | Le complexe de Cholet-Thouars: un ensemble volcano-plutonique cambrien moyen au sein du bloc précambrien des Mauges[END_REF]. Early Ordovician magmatism is also well preserved in the Armorican Massif [START_REF] Auvray | Rb-Sr dating of the Plouézec volcanics, N Brittany: implications for the age of the red beds ("séries rouges") in the northern Armorican Massif[END_REF][START_REF] Paquette | Absence de tectonique cadomienne dans le complexe de Champtoceaux (Bretagne méridionale)? Comparaison des systèmes Rb-Sr et U-Pb d'un métagranite[END_REF][START_REF] Paquette | From opening to subduction of an oceanic domain constrained by LA-ICP-MS U-Pb zircon dating (Variscan belt, southern Armorican Massif, France)[END_REF][START_REF] Janjou | Notice explicative de la carte géologique de la France (1/50000), feuille de Segré[END_REF][START_REF] Ballèvre | Discovery of an alkaline orthogneiss in the eclogite-bearing Cellier Unit (Champtoceaux Complex, Armorican Massif): a new witness of the Ordovician rifting[END_REF][START_REF] Ballèvre | Geochronology and geochemistry of Ordovician felsic volcanism in the Southern Armorican Massif (Variscan belt, France): implications for the breack up of Gondwana[END_REF][START_REF] Galerne | Magma-sediment mingling in an Ordovician rift basin: The Plouérec-Plourivo half-graben, Armorican Massif, France[END_REF]Diot et al., 2007;Casas and Murphy, 2018), and the French Massif Central (e.g. [START_REF] Alexandrov | Datation U-Pb à la microsonde ionique des zircons de l'unité supérieure de gneiss dans le Sud Limousin, Massif Central[END_REF][START_REF] Melleton | Precambrian protoliths and Early Paleozoic magmatism in the French Massif Central: U-Pb data and the North Gondwana connection in the west European Variscan belt[END_REF][START_REF] Lin | Detrital zircon age distribution from Devonian and Carboniferous sandstone in the Southern Variscan Fold-and-Thrust belt (Montagne Noire, French Massif Central), and their bearings on the Variscan belt evolution[END_REF]. In contrast, Late Paleozoic ages are rarely recorded in the detrital zircon populations (Figs. 7 and 11A; Table 2), but limited zircon grains in sample 13FR19

demonstrate three ages at 411±7 Ma, 411±8 Ma, and 426±6 Ma, respectively. Although these results may not be sufficient to directly prove the existence of the Variscan magmatic arc as previously proposed (Table 2 ;Dubreuil, 1986;Cartier and Faure, 2004;Faure et al., 2008; Nearly 10% of the detrital zircons from the S t -Georges-sur-Loire yield Ediacaran-Early Cambrian ages, around 540 Ma. These ages correspond to that of peraluminous magmatism of the Mancellian granites in the Fougères Unit, and migmatization in the S t -Malo and Guingamp Units (Fig. 1). Both rock types record late Cadomian crustal melting (Egal et al., 1996;Chantraine et al., 2001).

A C C E P T E D M A N U S C
Detrital zircons clustering between 480 and 560 Ma have mostly negative εHf (t) values in agreement with old continental crustal sources. A few positive εHf (t) values is indicative of an addition of juvenile material from a depleted mantle during the Cambrian and Ordovician rifting [START_REF] Kröner | Reassessment of continental growth during the accretionary history of the Central Asian Orogenic Belt[END_REF]Fig. 13). The late-orogenic Cadomian magmatism at 550-540 Ma is typical of crustal reworking (Fig. 9; Table 3). The Early to Middle Cambrian (ca 520 Ma),

A C C E P T E D M A N U S C R I P T

and the Early to Middle Ordovician (490-460 Ma) rifting events might have been associated

with a crustal reworking along with a minor mantle input [START_REF] Auvray | Rb-Sr dating of the Plouézec volcanics, N Brittany: implications for the age of the red beds ("séries rouges") in the northern Armorican Massif[END_REF][START_REF] Paquette | Absence de tectonique cadomienne dans le complexe de Champtoceaux (Bretagne méridionale)? Comparaison des systèmes Rb-Sr et U-Pb d'un métagranite[END_REF]Doré, 1994;[START_REF] Gall | Pétrogenèse des magmas andésitiques et ignimbritiques et leur signification dans l'évolution géodynamique cadomienne. Reconstitution des dynamismes éruptifs d'une province paléovolcanique: l'exemple du graben cambrien du Maine (Est du Massif Armoricain)[END_REF][START_REF] Ballèvre | Discovery of an alkaline orthogneiss in the eclogite-bearing Cellier Unit (Champtoceaux Complex, Armorican Massif): a new witness of the Ordovician rifting[END_REF]Linneman et al., 2004Linneman et al., , 2007;;Cocherie et al., 2005;[START_REF] Murphy | Origin of the Rheic Ocean: Rifting along a Neoproterozoic suture?[END_REF].

Provenance of Neoproterozoic zircons

A main Ediacaran peak, between 625 Ma and 595 Ma, is prominently marked in most samples (Figs. 7 and 11A), indicating that the provenance of the S t -Georges-sur-Loire Unit material may be from a Neoproterozoic basement, such as the Cadomian belt exposed in the S t -Brieuc and Trégor Units of the north Armorican massif (Chantraine et al., 2001). There, a large number of plutons yield Ediacaran ages at ca. 615-570 Ma [START_REF] Adams | Geochronology of the Channel Islands and adjacent French mainland[END_REF][START_REF] Ruffet | 40 Ar-39 Ar dating of a late Proterozoic paleomagnetic pole for the Armorican Massif (France)[END_REF][START_REF] Ruffet | Comparison of 40 Ar-39 Ar conventional and laser dating of biotites from the North Trégor Batholith[END_REF]Dallmeyer et al., 1991;Egal et al., 1996). Thus, eroded plutons and volcanic rocks might have a significant role as sources providing detrital zircons to the S t -Georges-sur-Loire Unit. In the Pierre Bize coarse sandstone (sample 13FR21), the 525 Ma peak suggest a possible source from plutons equivalent to the Thouars microgranite and the Mouclerie granodiorite that crop out in the Mauges Nappe of the S. Armorican Domain (Fig. 1; [START_REF] Thiéblemont | Le complexe de Cholet-Thouars: un ensemble volcano-plutonique cambrien moyen au sein du bloc précambrien des Mauges[END_REF], and the Mauges Nappe represents the only exposure of the "missing domain" at the south S t -Georges-sur-Loire Unit before the Variscan orogeny (Dubreuil, 1986;Cartier and Faure, 2004;Faure et al., 2008). Thus the provenance of the Cadomian zircons of the matrix of the S t -Georges-sur-Loire olistostrome might be supplied from the Neoproterozoic basement of the Mauges Nappe and/or its equivalent, or alternatively, from the Cadomian orogen exposed in the Central-North Armorican Domain (Fig. 13).

Although a northern provenance cannot be ruled out, a southern origin would be in better

A C C E P T E D M A N U S C R I P T
agreement with the sedimentological features of the olistoliths (Dubreuil, 1986;Cartier and Faure, 2004).

7.3. Inherited Neoarchean and Paleoproterozoic zircons from the Icartian basement One peak at 2090-2040 Ma is obtained from samples 13FR12 and 13FR21 (Fig. 11A).

This age group well recorded in the Trégor Unit of the North Armorican Domain characterizes the Icartian basement (Fig. 1; [START_REF] Calvez | Two billion years old relicts in the Hercynian Belt of Western Europe[END_REF], which is an equivalent of the Eburnean basement of the West African Craton [START_REF] Allègre | Nd-Sr isotopic relationship in granitoid rocks and continental crust development: a chemical approach to orogenesis[END_REF].

Similar ages are also discovered from inherited zircons in the Late Carboniferous (320-300

Ma) peraluminous granites [START_REF] Ballouard | Multiple crust reworking in the French Armorican Variscan belt: Implication for the genesis of uranium-fertile leucogranites[END_REF]. The notable peak at ca. 1910 Ma, marked in most samples, indicate a major source from an ancient Icartian continental crust. In the Carboniferous Ancenis Basin deposited on the Mauges Unit, and in the Late Carboniferous coal-bearing basin, a background of dispersed ages ranges from Neoarchean to Paleoproterozoic with three peaks about 2650 Ma, 2065 Ma and 1910 Ma (Fig. 11B; Ducassou et al., 2014). Thus, these grains might either be reworked in the vicinity of the S t -Georges-sur-Loire Unit, or directly supplied from a northern Icartian source.

Recycled zircons from Archean-Paleoproterozoic magmatic and metamorphic sources are documented in the Iberian massif [START_REF] Fernández-Suárez | News ideas on the Proterozoic-Early Palaeozoic evolution of NW Iberia: insights from U-Pb detrital zircon ages[END_REF][START_REF] Andersen | Correction of common lead in U-Pb analyses that do not report 204Pb[END_REF][START_REF] Fernández-Suárez | Constraints on the provenance of the uppermost allochtonous terrane of the NW Iberian Massif: inferences from detrital zircon U-Pb age[END_REF][START_REF] Martínez Catalán | Provenance constraints from detrital zircon U-Pb ages in the NW Iberian Massif: implications from Palaeozoic plate configuration and Variscan evolution[END_REF], 2008, 2009), the French Massif Central [START_REF] Lin | Detrital zircon age distribution from Devonian and Carboniferous sandstone in the Southern Variscan Fold-and-Thrust belt (Montagne Noire, French Massif Central), and their bearings on the Variscan belt evolution[END_REF], Cadomian metasedimentary rocks in Corsica [START_REF] Avigad | Cadomian metasediments and Ordovician sandstone from Corsica: detrital zircon U-Pb-Hf constrains on their provenance and paleogeography[END_REF], and Central European Variscan Massifs [START_REF] Friedl | Deducing the ancestry of terranes: SHRIMP evidence for South America-derived Gondwana fragments in central Europe[END_REF]Linneman et al., 2004). relatively wide variation from -12 to +4, with a peak at -5 (Fig. 10A). Hf crustal model ages (TDM 2 ) range from 3.5 to 1.0 Ga, with peaks at ~1.28, 1.98, 2.20, and 2.86 Ga (Fig. 10B). The Hf isotopic composition for detrital zircons clustering between 480 and 650 Ma demonstrate a relatively large range of εHf (t) values from -25 to +10 (Fig. 12B). Despite two anomalous εHf (t) values higher than the depleted mantle line, only a few points reach the depleted mantle line, and points with εHf (t) value lower than -20 are also rare (Figs. 10A and12A). Combined with the calculated TDM 2 ages for most of the Phanerozoic zircons that range from 1.2 Ga to 3.0 Ga (Figs. 10B and12A), these results are comparable with the previous geochemical studies on the mafic complexes that range in age from ca. 400 Ma to 330 Ma, which are characterized by high εNd values related to the lithosphere of the Rheic Ocean [START_REF] Murphy | Highly depleted oceanic lithosphere in the Rheic Ocean: implications for Paleozoic reconstructions[END_REF][START_REF] Murphy | Highly depleted isotopic compositions evident in Iapetus and Rheic Ocean basalts: implications for crustal generation and preservation[END_REF].

Conclusion

Detrital zircon ages of the clastic matrix in the S 2 and3. [START_REF] Lin | Detrital zircon age distribution from Devonian and Carboniferous sandstone in the Southern Variscan Fold-and-Thrust belt (Montagne Noire, French Massif Central), and their bearings on the Variscan belt evolution[END_REF], Cadomian metasediments and Ordovician sandstone of Corsica [START_REF] Avigad | Cadomian metasediments and Ordovician sandstone from Corsica: detrital zircon U-Pb-Hf constrains on their provenance and paleogeography[END_REF], and West Avalonia [START_REF] Henderson | Gondwanan basement terranes of the Variscan-Appalachian orogen: Baltican, Sahara and West African hafnium isotopic fingerprints in Avalonian, Iberia and Armorican Terranes[END_REF][START_REF] Henderson | A hafnium isotopic record of magmatic arcs and continental growth in the Iapetus Ocean: The contrasting evolution of Ganderia and the peri-Laurentian margin[END_REF]. Table 1: Summary of the analyzed samples from the olistostrome of the sub-unit of the S t -Georges-sur-Loire Unit.

Figure captions

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ACCEPTED MANUSCRIPT

  of the Hf isotopes Hf isotopic data show the predominance of crustal vs. mantle-derived sources in felsic to intermediate magmatism. As indicated by Condie et al. (2009), 75-80% of juvenile continental crust had been extracted from the mantle during the Archean and the Paleoproterozoic. Detrital zircon εHf (t) values in the S t -Georges-sur-Loire Unit record a

Fig. 1 .Fig. 2 .

 12 Fig. 1. Tectonic map of the Armorican Massif (modified from Faure et al., 2005).A: Location of the S t -Georges-sur-Loire Unit and suture zones in the French Variscan belt.

Fig. 3 .

 3 Fig.3. Schematic cross section of the Ligerian domain (located in Fig.2). Diamond:

Fig. 4 .

 4 Fig.4. Field photos and photomicrographs of the olistostrome sub-unit of the S t -Georges-sur-

Fig. 7 .

 7 Fig. 7. Probability diagrams of U-Pb ages of the detrital zircons from the olistostrome subunit of the S t -Georges-sur-Loire. See Fig. 2 for sample locations, andTable 2 for zircon ages.

Fig. 13 .

 13 Fig. 13. Synthetic and comparison of the cumulative probability plots of detrital zircon U-Pb ages from the olistostrome sub-unit of the S t -Georges-sur-Loire Unit (this study), Ancenis

Fig. 14 .

 14 Fig. 14. Schematic model of the Silurian-Early Devonian (ca. 440-400 Ma) oceanic

  In the S t -Georges-sur-Loire block-in-matrix unit, detrital zircon ages spectra and their Hf isotopic composition predominantly indicate Early Paleozoic and Neoproterozoic populations.  The analyzed zircon grains are preferentially derived from oa southern source, but at northern one cannot be discarded  Most of the grains record negative Hf isotopic values indicating that crustal melting played a major role in the Neoproterozoic and Paleozoic evolution of Armorica microcontinent.

Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13

 2345678910111213 Figure2

Figure 14

 14 Figure14

Table 2

 2

. Uncertainties on individual analyses in data tables are reported at a 1σ level. Analyses that are >15% discordant (by comparison of 206 Pb/ 238 U and 207 Pb-206 Pb ages) are excluded (Table 2). Zircon ages younger than 1000 Ma were based on 206 Pb/ 238 U ratios, and ages older than 1000 Ma were based on 207 Pb/ 206 Pb ratios.

Table 2

 2

). Two major age groups occur at 760-450 Ma and 2210-1560 Ma, and one subordinate group at 2850-2500 Ma (Fig. 7). Two dominant age peaks are around 1865 Ma and 595 Ma, with a subordinate age peak at ca. 2050 Ma. A low background

Table 2

 2 peak of ca. 590 Ma, and 2200-1900 Ma with two peaks around 2130 Ma and 1910 Ma. A low

). Two dominant age groups occur at 720-460 Ma with a

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  Unit. However, this age peak is not documented in our study, as well as in the late Ancenis and Coal basins. On the contrary, the Neoproterozoic age population corresponds well to the

	Cadomian orogeny exposed on both sides of the S t -Georges-sur-Loire Unit. A southern
	provenance, from the Mauges Nappe and the "missing domain" is in better agreement with
	sedimentological data (e.g. Dubreuil, 1986; Cartier et al., 2001), however a northern one
	supplied by the Cadomian belt of the North-Central Armorican domain cannot be ruled out. Most of the grains record negative Hf isotopic values, indicating that crustal melting played a major role in the evolution of the Armorica microcontinent. Positive εHf (t) values are related to the Neoproterozoic Cadomian orogeny in which subduction-related juvenile magma are M A N U S C R I P T recognized.
	A C C E P T E D	t -Georges-sur-Loire olistostrome
	display predominant Neoproterozoic to Early Paleozoic (625-490 Ma) populations. These
	zircons are related to Cambrian aborted rifting at ca. 525 Ma, and Early Ordovician rifting
	around 480-470 Ma that separated the Armorica microcontinent from Gondwana. Poorly
	constrained Silurian to Early Devonian magmatic rocks that yield a whole rock Rb-Sr age at
	ca. 400±24 Ma (Carpenter et al., 1982) are found as olistoliths in the S t -Georges-sur-Loire

Table 2

 2

	for zircon ages.

Table 2 :

 2 Detrital Zircon U-Pb analytical data. Discordance (%) is calculated as (1) 100%*( 207 Pb/ 206 Pb age-206 Pb/ 238 U age)/( 207 Pb/ 206 Pb age), if the 206 Pb/ 238 U age is older than 1000 Ma; (2) 100%*( 207 Pb/ 235 U age-206 Pb/ 238 U age)/( 206 Pb/ 238 U age), if the

206 Pb/ 238 U age is younger than 1000 Ma.

Table 3 :

 3

LA-ICP-MS zircon Lu-Hf isotopic data. Age is the same from Table

2

T(DM) and T(DM2) are one-stage and two-stage Hf model ages, respectively.

176 Hf/ 177 Hf (CHUR, t) = 0.282772-0.0332*(EXP(0.01867*Age/1000)-1).

176

Hf/ 177 Hf (DM, t) = 0.28325-0.0384*(EXP(0.01867*Age/1000)-1). TDM1= (1/0.01867)*LN(1+ (( 176 Hf/ 177 Hf-0.28325)/( 176 Lu/ 177 Hf-0.0384))). TDM2= Age/1000+(1/0.01867)*LN(1+ ( 176 Hf/ 177 Hf(σ, t)-176 Hf/ 177 Hf(DM, t))/(0.015-0.0384)).

Table 2 . LA-ICPMA Zircon U-Pb analytical data

 2

							Isotopic ratios					Ages (Ma)
	Sample#sp ot	Th (ppm)	U (ppm)	Th/ U	207 Pb/ 206 Pb	± 1σ	207 Pb/ 23 5 U	± 1σ	206 Pb/ 23 8 U	± 1σ	207 Pb/ 206 Pb	± 1σ	207 Pb/ 23 5 U	± 1σ	206 Pb/ 23 8 U	± σ	Disconcorda nce
	13FR12
	13FR12#01	148	196	0.7 6	0.12772	0.002 45	6.3155 0	0.115 45	0.3588 0	0.005 27	2067	15	2021	16	1976		4.61%
	13FR12#02	211	440	0.4 8	0.05647	0.003 03	0.6607 3	0.033 89	0.0849 0	0.001 78	471	76	515	21	525		-1.90%
	13FR12#03	250	285	0.8 8	0.05868	0.002 60	0.8283 1	0.035 07	0.1024 3	0.001 90	555	60	613	19	629		-2.54%
	13FR12#04	138	795	0.1 7	0.17388	0.001 84	12.107 62	0.124 94	0.5052 7	0.006 12	2595	9	2613	10	2636		-1.56%
	13FR12#05	210	216	0.9 7	0.06366	0.003 50	0.9815 4	0.051 42	0.1118 8	0.002 51	730	73	694	26	684		1.46%
	13FR12#06	172	236	0.7 3	0.06973	0.003 51	1.0561 2	0.050 36	0.1098 9	0.002 39	920	62	732	25	672		8.93%
	13FR12#07	54	271	0.2 0	0.06969	0.002 24	1.5418 4	0.047 14	0.1605 2	0.002 60	919	37	947	19	960		-1.35%
	13FR12#08	144	297	0.4 9	0.13628	0.002 27	7.7512 1	0.123 98	0.4126 9	0.005 77	2180	12	2203	14	2227		-2.11%
	13FR12#09	157	187	0.8 4	0.05992	0.003 40	0.8337 7	0.045 08	0.1009 6	0.002 25	601	78	616	25	620		-0.65%
	13FR12#10	79	177	0.4 5	0.12964	0.002 58	7.2340 1	0.138 39	0.4048 8	0.006 16	2093	15	2141	17	2191		-4.47%
	13FR12#11	144	167	0.8 6	0.11373	0.002 85	5.2902 3	0.126 20	0.3375 0	0.005 62	1860	21	1867	20	1875		-0.80%
	13FR12#12	111	232	0.4 8	0.11458	0.002 33	5.3299 8	0.103 28	0.3375 0	0.004 98	1873	16	1874	17	1875		-0.11%
	13FR12#13	80	102	0.7 8	0.11319	0.003 47	5.4972 7	0.161 00	0.3523 7	0.006 77	1851	27	1900	25	1946		-4.88%
	13FR12#14	102	108	0.9 4	0.11413	0.003 28	5.0950 2	0.139 04	0.3239 1	0.005 88	1866	25	1835	23	1809		3.15%

Table 3 . LA-MC-ICPMS zircon Lu-Hf isotopic data

 3

	Sample#spot	t (Ma)	176 Yb/ 177 Hf 176 Lu/ 177 Hf 176 Hf/ 177 Hf	2σ	176 Hf/ 177 Hfi εHf(t)	2σ	TDM1	2σ	TDM 2	2σ
	13FR12
	13FR12#02		0.058483	0.002305	0.282355 0.000017 0.282332	-4.30 0.61	1311.6	24.97	1738.36	38.51
	13FR12#03		0.021926	0.001011	0.282244 0.000020 0.282233	-5.51 0.70	1421.5	27.47	1895.25	43.89
	13FR12#09		0.017693	0.000783	0.282107 0.000014 0.282098	-10.47	0.50	1602.9	19.60	2199.98	31.51
	13FR12#11	1860 0.017425	0.000751	0.281487 0.000014 0.281460	-4.89 0.51	2451.8	19.45	2812.20	31.29
	13FR12#12	1873 0.013933	0.000547	0.281469 0.000015 0.281449	-4.97 0.54	2463.0	20.37	2827.38	32.95
	13FR12#13	1851 0.017211	0.000688	0.281315 0.000019 0.281291	-11.10	0.68	2679.7	25.70	3186.53	41.41
	13FR12#14	1866 0.017989	0.000725	0.281587 0.000016 0.281562	-1.14 0.56	2312.9	21.61	2585.58	34.80
	13FR12#15	1868 0.018340	0.000725	0.281457 0.000015 0.281432	-5.72 0.55	2489.9	21.00	2869.26	33.81
	13FR12#17		0.040271	0.001534	0.282324 0.000015 0.282308	-4.13 0.54	1328.6	21.45	1763.97	33.80
	13FR12#18		0.012470	0.000473	0.282108 0.000015 0.282102	-10.95	0.53	1589.5	20.67	2208.72	33.51
	13FR12#20	2659 0.012327	0.000485	0.281083 0.000012 0.281058	-0.59 0.44	2976.9	16.40	3174.15	26.57
	13FR12#21		0.016534	0.000742	0.281809 0.000017 0.281801	-21.23	0.59	2011.1	22.98	2864.76	36.98
	13FR12#22		0.008194	0.000322	0.282154 0.000018 0.282150	-8.25 0.65	1519.8	25.22	2073.63	41.04
	13FR12#23		0.032691	0.001382	0.282041 0.000020 0.282027	-14.39	0.70	1721.0	27.56	2397.83	43.60
	13FR12#24		0.020878	0.000852	0.282154 0.000017 0.282144	-8.50 0.58	1541.3	22.88	2088.72	36.72
	13FR12#29	1895 0.018377	0.000714	0.281323 0.000014 0.281297	-9.87 0.51	2671.3	19.58	3145.21	31.53
	13FR12#33		0.020792	0.000858	0.281791 0.000016 0.281782	-22.85	0.56	2041.8	21.90	2933.06	35.14

Acknowledgments

Brendan Murphy and Michel Ballèvre are deeply acknowledged for their constructive scientific and formal remarks to improve an early draft of this paper. Prof. Mark Allen is thanked for his help to polish the English of the final version. This work is supported by the National Nature Science Foundation of China (91855212, 91755205, and 41472193) and the National Key R&D Program of China (Grant Numbers 2016YFC0600401, 2016YFC0600102).

A C C E P T E D M A N U S C R I P T


Martin Heusse Ab -

Annie Gravey

A Routing and Resource Preservation Strategy for Traffic Engineering in Communication Networks

This paper presents a method for dynamic load balancing in data networks. When multiple routes are available, it determines their load shares as a function of a composite metric that takes into account the paths' length and load. A general resource preservation mechanism is also presented that complements the proposed random routing strategy when the network is heavily loaded. We compare our approach with trunk reservation in the particular case of fully meshed networks and evaluate its performance in any network, where an equivalent mechanism is missing. We validate our approach by means of simulation and provide insights on the routing solutions that it obtains.

Introduction

This paper details a load sharing strategy that aims at providing a better network utilization than current routing approaches. The core of the present proposition is to send the load not only on the best path at the moment, but rather to spread it on all comparable paths with probabilities computed based on the quality of each path. The probabilities represent the relative quality of a path with respect to the others.

Although load balancing is generally recognized as desirable to use efficiently the communication equipments, it appears as a challenging task in many respects. First it has to be adapted to the network capabilities in terms of flow management. Protocols like MPLS [START_REF] Swallow | MPLS advantages for traffic engineering[END_REF] address this issue. They bring to packet switched networks management capabilities that were available only in connection oriented networks (or with ATM, for instance). Second, from the performance viewpoint, load balancing must be stable in the sense that the path set of each flow across the network should not vary significantly over short periods of time. Furthermore, network resources should be preserved so that the network keeps accepting flows possibly at the cost of the load balancing accuracy.

This paper describes a load balancing proposal that takes into account these objectives. For convenience, it is denominated hereafter as Random Shaped Routing (RSR). It is a dynamic routing strategy that can be used to enhance routing protocols like PNNI or applied to the routing of MPLS label switched paths (LSP). RSR is not based on a centralized multi-commodity flow routing computation (see [START_REF] Ben-Amer | Routing strategies for IP networks[END_REF][START_REF] Fortz | Internet traffic engineering by optimizing OSPF weights[END_REF]) and consequently leads to less optimal routing patterns, especially for demands with bandwidth constraints of the same order of magnitude as the transport infrastructure. Rather, it is adaptive in the sense that it is able to track continuously the load variations. Although it stems from a different approach, RSR takes over in data networks the same task as DAR (Dynamic Alternative Routing [START_REF] Gibbens | Dynamic routing in fully connected networks[END_REF]) does in telephone networks and we show that the resulting routing is comparable in this particular case.

The paper is organized as follows. Section 2 gives an overview of RSR. Section 3 gives insights on the routing obtained by RSR, comparing it with other strategies proposed for traffic engineering in data networks. Similarly to DAR, the present routing proposition requires a specific mechanism to deal with high load conditions, so a variation of the trunk reservation principles is proposed in Section 2.2. Simulation results obtained with RSR in the context of a fully meshed network are provided in Section 4. Section 5 gives an overview of implementation issues related to the computation of the routing tables used by RSR and concludes the paper.

Splitting the load

Computing path costs and path selection principles

We propose to use a composite path metric that reflects the load on the links and the path length for the estimation of the each path's quality. In this scope, load balancing consists in finding a tradeoff between resource conservation and load distribution. Actually, a network is likely to accept more connections if none of its parts are congested, but ensuring this should not lead to a global routing solution too far from optimal (when the network gets congested because much of the traffic is sent on "long" paths). In fact, optimality criteria for the routing solution are numerous, one of them being the usage of as little resources as possible (as in the multi-commodity flow problem), or maximizing a concave decreasing function of the edges loads as in [START_REF] Mo | Fair end-to-end window-based congestion control[END_REF]. In practice, RSR is strongly focused on preserving network resources while accepting as much load as possible. We consider the path metric:

M = r exp(B × h)
where r is the available bandwidth on the path, and h its number of hops (links crossed). B is a parameter that sets the relative weight of bandwidth against length for the path's quality computation. This metric is derived from utility U = log(M ) proposed in [START_REF] Oueslati-Boulahia | An approach to routing elastic flows[END_REF] specifically for the routing of elastic flows (see also [START_REF] Ma | Routing traffic with quality of service guarantees in integrated service networks[END_REF]). In the remainder of this paper, we take B = 1, as it corresponds to a satisfactory compromise also chosen in [START_REF] Oueslati-Boulahia | An approach to routing elastic flows[END_REF].

Path selection

Once the path metrics are computed, the routing decision consists generally in choosing the best one, but it is also possible to split evenly the load on equivalent paths. This can be achieved by randomly selecting the paths with probabilities proportional to their estimated quality. Therefore, routing randomly according to M, paths with equal length and bandwidth receive the same amount of traffic, and the emphasis is strongly put on the shorter paths. With random routing, the load is readily split on all available paths, even before the routing protocol takes into account the changes in the link loads caused by the presence of a new traffic. This is very valuable when a large number of connections enter the network at the same time, which occurs for instance when a component of the network goes down and the traffics that were using it are redistributed on the network. Variations of DAR (Dynamic Alternative Routing) [START_REF] Gibbens | Dynamic Routing in Circuit Switched Telecommunication Networks: The Dynamic Alternative Routing Strategy[END_REF] in fully meshed networks propose in the same manner to send traffic on alternate routes in proportions inversely proportional to the load that they already carry, but only if the direct one is saturated. We consider here that no route can be distinguished from the other ones, and in particular that no route can be identified as the "direct" one in contrast with the "alternate" ones for a given flow.

Random path selection in RSR follows a very simple principle. It incrementally builds the path, starting from the node of origin of the connection request. Then one of its neighbors is randomly selected and the same operation is reiterated from node to node. The probability of choosing a next hop n at the router a for a flow bound to d is :

P n = M ad n i∈N (a) M ad i
where N (a) are the neighbors of a, and M ad i designates the metric associated with the best path from a to d starting with link a -i.

It can be noted that this incremental path construction is well suited for hop by hop dynamic routing. But it can also be used in the context of source routing, in which case the first node performs all the computation. This is the case for the simulations displayed in this paper. Such an approach requires that the adequate routing information be available at the source node, which is the case when a link state routing protocol is used.

Random routing on a subset of the paths

Random routing leads to a traffic distribution on the network very different from the one obtained with best path routing when using the same metric.

For instance, we consider the simple network shown in figure 1 composed of three similar links of bandwidth r, loaded by a set of connections from S to D. Using a single best path, route b does not receive any S-D traffic until the load on a reaches l a = r (1 -e -1 ). Then the routing starts to oscillate between the two paths. Using random routing, route b would receive its share of traffic from the beginning. In the case of a burst in the connection demands between S and D, this insures to balance the load before the routing algorithm takes into account the impact of the traffic on the link loads. But this behavior may be problematic in some cases, as it leads to the routing of a great proportion of the connections on sub-optimal paths. This can lead to an early congestion of the network, particularly when alternate paths are numerous like in fullymeshed networks [START_REF] Gibbens | Dynamic routing in fully connected networks[END_REF]. Fortunately, it is straightforward to address this issue.

The path selection presented in 2.1.1 is slightly modified in order to have RSR to not use all feasible paths. No connection is routed on a path whose metric is under a given threshold (α times the metric of the best path, 0 < α < 1). The primary effect of this procedure is to limit the number of connections sent on saturated or long paths. For α = 1, RSR degenerates to best path routing, and for α = 0, plain randomized routing is used. If N (a) is the set of neighbors of a that are the starting points of paths complying to this condition:

P n =        M ad n -α×M ad max i∈N (a) M ad i -α×M ad max if n ∈ N (a) 0 otherwise.
In particular, for α > exp(-3/2) (provided that B = 1) two routes sharing the same bottleneck both receive traffic only if their lengths differ by less than 2. Of course, if the shortest one becomes notably more loaded (if the bottleneck is not any more shared by the two routes) then the traffic is split. This setting also guarantees that the incremental routing of a connection be cycle-free, so it appears as a good lowest bound for this parameter (provided that the administrative metric of any link is greater than 1) [START_REF] Heusse | A new routing policy for load balancing in communication networks[END_REF].

Adapting trunk reservation to non fully meshed networks

Trunk reservation was proposed in the context of fully meshed networks, to address an intrinsic flaw of the dynamic routing algorithms in high load conditions. These algorithms were shown to oscillate between the global optimum which is that all nodes are using direct routes -and the local optimum when all consider that their direct routes are full and they seek overflow paths [START_REF] Key | Distributed dynamic routing schemes[END_REF].

Trunk reservation consists in rejecting (overflow) calls that attempt to use a two-link route when the number of available circuits on one of its parts is below a given threshold. In this way, already highly loaded links keep accepting connections that follow a direct route, to the detriment of more resource consuming ones, and the global optimum is privileged. The order of magnitude of the threshold r s is of 5% of the link bandwidth and the routing performance is rather insensitive to this parameter.

Applying trunk reservation in non-fully meshed networks in a straightforward manner is not satisfactory, mainly because the notions of direct and overflow calls can not be directly transposed to the general case. It appears that an initialization phase -or statical configuration -be required to indicate which routes should be protected and which ones should be privileged for each nodes pair.

For example, when considering the network appearing in figure 2, the application of trunk reservation is straightforward for the traffic between S 2 and D. In this case S 2 would not be allowed to send its traffic toward D on route b if the available bandwidth is below r s . Between S 1 and D, there is no natural path, and the less demanded ones should actually be preferred. In fact, it is possible to use different trunk reservation parameters for different flows, e.g. giving in our example a greater priority on link S 2 -D to the traffic between S 2 and D over the one between S 1 and D. However, finding the best (hierarchical) trunk reservation parameters is to our knowledge an open issue.

As it appears that trunk reservation should depend on the length of a route, and the existence of other more direct ones or not, the proposed mechanism is the following. A minimum r min is assigned to the available bandwidth used and distributed by the routing algorithm (or "advertised by the links") when the actual number of free circuits is below this level.

In the context of this article, connections are definitively discarded and lost after two unsuccessful routing attempts.

Comparison with other routing strategies

Overview

The most commonly envisaged approach for routing protocols that can adapt to the links loading is most probably the Widest Shortest (WS) one. It is the routing strategy retained for QOSPF and recommended by PNNI. It is also proposed for traffic engineering with MPLS in [START_REF] Awduche | Requirements for traffic engineering over MPLS[END_REF]. With WS, a connection is sent on the shortest path that can handle it and, if more than one solution exists, on the path displaying the most available bandwidth. This approach stands as a good reference because it is actually used and does not require important changes in the routing protocols to be implemented.

Load balancing has also been a concern during the design of OSPF (version 2) [START_REF] Moy | OSPF version 2[END_REF], and ECMP (Equal Cost Multi-Paths) consists in using all the paths with equal administrative costs through a network. This mechanism does not rely on any load measurement.

Contrasting with WS on the complexity ground, MPLS-OMP [START_REF] Villamizar | MPLS-OMP[END_REF] is aimed at the dynamic routing and load balancing of flows through a network. MPLS-OMP decreases the load on the most loaded links of the network, by gradually sending traffic on suboptimal -alternate -paths (roughly determined on the basis of their administrative metrics). Simulations reported in [START_REF] Villamizar | MPLS-OMP[END_REF] show the good behavior of this approach in realistic conditions, although the complexity of the load adjustment strategy makes it hard to implement. OMP also adapts well to varying traffic patterns, but its gradual moves from one equilibrium to another make it intrinsically less responsive than our proposal.

Cisco's EIGRP also uses of a composite path metric for load balancing. But EIGRP is based on a shortest paths computations, and it is in fact recommended to not use a dynamic metric, or at least one that only marginally depends on dynamic measurements. There is also no resource preservation associated to it.

Experimental results

In order to compare random shaped routing (RSR) to WS, our simulations focus on the source routing of fixed rate connections through a network whose links feature limited transport capacities. Source routing is used under the assumption that the exact and immediate state of each link is available at the source. This would not be true in more realistic conditions (because it takes time to broadcast the routing information in a In the case of two distinct paths that share at least a common first link, the measure used for the computation of the selection probability of this first link is the best one.

Competing flows

The context here is the one of a data network, loosely connected. Experiments take place in the 13 nodes network shown in figure 3, with links featuring a capacity of 20 simultaneous connections (except for the links on the path 2 -10 -6: 80, and 4 -2: 40). The traffic is a Poisson process of intensity 50 triggering the creation of an average number of 5 connections lasting one time unit each with random source and destination nodes. The measures are averaged over 20 runs of 100 time units.

Table 1 shows the number of connections successfully routed through the network for various routing settings. The first observation is that without trunk reservation, the results are similar with RSR and WS. Also, it appears that not restricting the routing to the best path does not have any impact on the network's throughput. Secondly, using the resource preservation principles described in section 2.2 improves the network throughput significantly. The next paragraph details a particular case where RSR intrinsically outperforms WS.

Single flow

On the network shown in figure 4, we focus on the routing of a single commodity flow from node 1 to 8. The four available paths between 1 and 8 are depicted as a, b, c and d in figure 4. Under light load, and all links capacities being equal, the optimal routing is to use the direct route c. But if the traffic grows and c gets saturated, a part of the traffic must be sent on the two alternate routes a and d. Unfortunately, the WS strategy is not able to shift from the first load distribution to the second one, as it first saturates the direct route and then sends overflow traffic on route b through 1 -2 -3 -5 -4 -6 -7 -8. This strategy needs an adequate bootstrapping to reach the optimal routing, which can be the pre-existence of a traffic on link 4 -5 that causes it to be avoided from the beginning. On the contrary, RSR shifts gracefully from using only the direct route to using the two alternate routes as the load increases, up to a point where the direct route is totally neglected when the network capacity is reached.

Figure 5 illustrates these remarks: for a traffic from 1 to 8 that exceeds the capacity of the network (90 connections per time unit lasting 1 time unit for a link capacity of 40), the uni-directional links 4 -5 and 5 -4 (routes c and b) are fully loaded with the WS approach, but not used by RSR, which sends all the connections over the two secondary routes a and d. This lowers the overall network usage generated by the flows between 1 and 8, and in particular links 4 -5 and 5 -4 remain available to other traffics.

In this case, no trunk reservation of any type was used (α = 0.4 and r min = 0). It would cause in both cases a part of the traffic to be rejected instead of saturating alternate routes.

Comparison with DAR in a fully meshed network

The aim of the experiments carried out in this section is to test the RSR approach in a well-known context. Here RSR is not meant to lead to major improvements, as the usual approaches are satisfactory. This is rather a validation, having in mind the portability of RSR to other contexts.

DAR is a simple decentralized routing scheme, that was originally designed for the British Telecom trunk network [START_REF] Stacey | Dynamic alternative routing in the British Telecom trunk network[END_REF]. It assumes a fully interconnected network, and uses only local information for taking routing decisions. When a call establishment request reaches a switch, it always tries to select the direct route to the destination. If this link is saturated, the call request attempts to reach the destination via the default alternate switch known for this destination. If this two-link route is also busy, the call request is lost and a new default switch is chosen at random. Trunk reservation then consists in rejecting (overflow) calls that are attempting to use a two-link route when the number of available circuits is below a given threshold r s .

Traffic discarding procedure

With the policy described in section 2.2, and in the particular case of fully meshed networks, connection dropping always occurs when a connection is sent on a path that cannot handle it. Three operating points are remarkable:

• connection dropping appears when the direct route is full, but it is nevertheless eligible because the available bandwidths r alt on all alternate routes are low enough.

i.e. r alt < r min × e -1 /α.

• all connections are lost when the direct route is full, and no alternate route are eligible. This means that r alt < r min × e -1 × α for all alternate paths.

• connection dropping also happens when an alternate route has no free circuit, but it is nevertheless used by the routing algorithm. This may occur when the bandwidth on the direct route r direct is such that r direct < r min /(e 1 × α). One can note that for α > e -1 this last case is avoided.

So it appears that this policy correspond to a behavior very similar to "normal" trunk reservation, with a gradually increasing connection dropping probability when the load on the links passes the point where a link is saturated and the other link loads are such that the first point above be valid.

Simulations confirm this remark, and RSR compares successfully to DAR with trunk reservation when applied in a 6 nodes fully meshed network (figure 7) under high load.

The number of lost connections is plotted in figure 6, for a "bandwidth" of 40 connections per link and a Poisson traffic of intensity 45 (each connection lasting 30 time units). The traffic gets concentrated in both cases to the direct routes, and RSR benefits from the a priori random distribution of the load on alternate routes, which explains its slightly better performance (on average, after stabilization, DAR looses 0.5 more connections per time unit). For DAR, a trunk reservation of 6 connections was used, α = 0.4 and r min = 3.

Conclusion

Implementation issues

RSR may be used for either hop-by-hop routing or source routing. Moreover, in the hop by hop case, RSR allows to greatly diminish the risk of loops while routing a connection as stated in [START_REF] Heusse | A new routing policy for load balancing in communication networks[END_REF].

In the simulations presented above, the routing computation is based on the true state of the network at the moment when a connection establishment request appears at its source node. However this computation is really based on past information as a delay is introduced by the routing protocols. In this respect, RSR presents two valuable features. First, a priori load balancing allows to distribute the load on the network before the routing protocols take into account the impact of this new traffic. Moreover, the load is distributed in a way that tends to maintain identical the traffic proportions associated to the different routes over time. Second, the two variables (available bandwidth and path length) required by RSR to compute its estimate of the route state can be gathered by most advanced routing algorithms.

The biggest concern with the load-adapting routing algorithms like the one presented here is their stability when the typical period of variations in the load are of the same order of magnitude as the algorithm convergence time. Although stability is an intrinsic feature of RSR, common damping techniques such as an hysteresis in the routing shifts should be considered. Agent-based routing [START_REF] Heusse | Adaptive routing and load balancing of ephemeral connections[END_REF] could also be considered as it was designed to keep track of more than one routing solution at a time in a dynamic environment.

Conclusion and future work

The approach presented in this paper is a simple and versatile routing policy that is designed to dynamically balance the load in communication networks. It does not require major implementation changes in the current routing protocols. Moreover, this approach is tunable and strongly focused on an efficient network usage through its adaptation of the trunk reservation principles. It gives results very similar to plain trunk reservation in fully meshed networks (Section 4), although it has been designed specifically for data networks, where it can significantly improve the network throughput and utilization efficiency (Section 3).

This work opens several new directions of future research. First, a stronger justification of the load routing proportions, which may lead to other metrics propositions can be studied. Second, the possible re-packing strategies that this approach can spawn are numerous. The most straightforward would be to discard and re-route connections residing on paths that are not any more considered as valid by the routing protocol. This should be done based on the acceptance parameters of the routing algorithm. In this way we will obtain a re-optimization method whose potential benefits are not known yet, but it

Figure 1 .

 1 Figure 1. Route b is neglected when the routing policy selects the shortest path.

Figure 2 .

 2 Figure 2. A problematic case for trunk reservation

Figure 4 .

 4 Figure 3. 13 nodes test network

Figure 5 .

 5 Figure 5. Load on links 4 -5 and 5 -4 for a high demand between nodes 1 and 8

Figure 6 .Figure 7 .

 67 Figure 6. Number of lost connection establishment attempts per time unit for DAR and RSR

Table 1

 1

	number of successfully routed connections for various routing algorithms
	routing algorithm	av. num. of successful connections std. deviation
	WS	170.

responds to critical needs in the field of traffic engineering.

It would also be of great interest to investigate the application of RSR in other domains, like for example the routing of elastic flows, possibly with different performance estimates. Routing connections bulks is also a promising research domain, where the granularity of the flow splitting can be discussed with respect to the routing performance obtained.

This work has been partially supported by France Telecom R&D.