Abdeltif Tibari

Lahfid

A Vacherat
email: arnaud.vacherat@upmc.fr

F Mouthereau

R Pik

M Bernet

C Gautheron

E Masini

L Le Pourhiet

B Tibari

A Lahfid

Thermal imprint of rift-related processes in orogens as recorded in the Pyrenees

Thermal imprint of rift-related processes in orogens as recorded in the Pyrenees

Introduction

The steady-state thermal structure of collisional orogenic belts is controlled by upward advection of heat through the coupling between crustal shortening and erosion (Royden, 1993;Stüwe et al., 1994;Willett and Brandon, 2002). However, considering typical thermal relaxation time of several 100 Myrs for thick lithospheres (Jaupart and Mareschal, 2007), transient effects might not be negligible for continental margins that experienced both thermal resetting during thinning and structural inversion over a relatively short period of time [START_REF] Mouthereau | Structure of orogenic belts controlled by lithosphere age[END_REF]. This process might be even more significant for inverted distal margins that have experienced extreme crustal thinning and mantle exhumation [START_REF] Manatschal | New models for evolution of magma-poor rifted margins based on a review of data and concepts from West Iberia and the Alps[END_REF]. The pre-orogenic temperature anomalies caused by crust/subcontinental lithospheric mantle (SCLM) thinning, may therefore significantly impact the thermal history and thermaldependent ductile mechanisms of deformation in orogens, but their magnitude has yet to be constrained. For instance, [START_REF] Mesalles | From submarine continental accretion to arc-continent orogenic evolution: The thermal record in southern Taiwan[END_REF] using low-temperature thermochronological data in southern Taiwan demonstrated that an originally hot distal margin may record cooling only ~20 Myrs after the end of rifting due to the onset of continental accretion.

Here, we focus on the Pyrenees, where geochronological and petrographic constraints indicate that rifting exhumed the SCLM in Albian times (ca. ~110 Ma) [START_REF] Vielzeuf | Crustal splitting and the emplacement of Pyrenean lherzolites and granulites[END_REF][START_REF] Lagabrielle | Submarine reworking of exhumed subcontinental mantle rocks: field evidence from the Lherz peridotites, French Pyrenees[END_REF][START_REF] Jammes | Tectonosedimentary evolution related to extreme crustal thinning ahead of a propagating ocean: Example of the western Pyrenees[END_REF][START_REF] Lagabrielle | Mantle exhumation, crustal denudation, and gravity tectonics during Cretaceous rifting in the Pyrenean realm (SW Europe): Insights from the geological setting of the lherzolite bodies[END_REF][START_REF] Clerc | Exhumation of subcontinental mantle rocks : evidence from ultramafic-bearing clastic deposits nearby the Lherz peridotite body, French Pyrenees[END_REF] while plate convergence initiated at ~83 Ma [START_REF] Rosenbaum | Relative motions of Africa, Iberia and Europe during Alpine orogeny[END_REF]. The Mesozoic Mauléon basin in the north-western Pyrenees (Fig. 1A) is interpreted as a preserved hyper-extended rift system formed during the Late Aptian -Early Albian, above a low-angle detachment system [START_REF] Johnson | Tectono-stratigraphic model for the Massif D'Igountze-Mendibelza, western Pyrenees[END_REF][START_REF] Jammes | Tectonosedimentary evolution related to extreme crustal thinning ahead of a propagating ocean: Example of the western Pyrenees[END_REF][START_REF] Masini | The tectonosedimentary evolution of a hyper-extended rift basin: the example of the Arzacq-Mauléon rift system (Western Pyrenees, SW France)[END_REF]. This is supported by field evidences of breccias of mantle peridotites reworked in syn-/post-rift sediments of Albo-Cenomanian age, or tectonically overlying the granulitic complex of the Labourd-Ursuya Massif [START_REF] Jammes | Tectonosedimentary evolution related to extreme crustal thinning ahead of a propagating ocean: Example of the western Pyrenees[END_REF].

To establish the time-temperature history of the Mauléon basin, we inverse modeled detrital zircon fission-track and (U-Th-Sm)/He thermochronological data collected for this study.

Model results were then compared to thermal patterns predicted from a 1D thermo-kinematic numerical model of the evolution of hyper-extended rift basins that are inverted during collision. Our results reveal that high geothermal gradients, inherited from hyper-extension, are maintained over 30 Myrs after convergence initiated.

Hyper-extension in the Pyrenees and thermal constraints

The Pyrenean belt resulted from the inversion of previously extended domains of the Iberian and European plates from the Late Cretaceous to the Late Oligocene [START_REF] Choukroune | The ECORS Pyrenean deep sismic profile reflection data and the overall structure of an orogenic belt[END_REF] and references therein). The Mauléon basin, located in the western part of the North Pyrenean Zone, consists of folded Mesozoic sedimentary units, thrust northward during the Tertiary along the Saint-Palais Thrust and the North-Pyrenean Frontal Thrust (Fig. 1). The basin is a Late Aptian to Albo-Cenomanian sag basin interpreted as a hyper-extended rift basin formed above a low-angle extensional detachment system, which is identified on the northern flank of the Labourd-Ursuya massif [START_REF] Jammes | Tectonosedimentary evolution related to extreme crustal thinning ahead of a propagating ocean: Example of the western Pyrenees[END_REF] and at the base of the Igountze-Mendibelza massif [START_REF] Johnson | Tectono-stratigraphic model for the Massif D'Igountze-Mendibelza, western Pyrenees[END_REF]. In such a hyper-extended system, middle-lower crustal rocks and the SCLM were exhumed [START_REF] Jammes | Tectonosedimentary evolution related to extreme crustal thinning ahead of a propagating ocean: Example of the western Pyrenees[END_REF][START_REF] Masini | The tectonosedimentary evolution of a hyper-extended rift basin: the example of the Arzacq-Mauléon rift system (Western Pyrenees, SW France)[END_REF], but age constraints on the timing of exhumation are still lacking. The only age associated to this extension phase is obtained in the eastern part of the Mauléon basin, where a gabbroic dyke, intruding the exhumed mantle body of Urdach, is sealed by Cenomanian sediments [START_REF] Jammes | Tectonosedimentary evolution related to extreme crustal thinning ahead of a propagating ocean: Example of the western Pyrenees[END_REF][START_REF] Debroas | Les Brèches d'Urdach, témoins de l'exhumation du manteau pyrénéen dans un escarpement de faille vraconnien-cénomanien inférieur (zone nord-pyrénéenne, Pyrénées-Atlantiques, France)[END_REF], and yields a relative flat Ar-Ar on biotite spectrum in the 105-108 Ma range [START_REF] Masini | The tectonosedimentary evolution of a hyper-extended rift basin: the example of the Arzacq-Mauléon rift system (Western Pyrenees, SW France)[END_REF].

Alkaline magmatism, high-temperature (up to 600°C) low-pressure (HT-LP) metamorphism [START_REF] Montigny | K-Ar study of Cretaceaous magmatism and metamorphism in the Pyrenees: Age and length of rotation of the Iberian Peninsula[END_REF][START_REF] Golberg | High temperature-low pressure Cretaceous metamorphism related to crustal thinning (Eastern North Pyrenean Zone, France)[END_REF], and hydrothermal fluid circulation associated with talc-chlorite mineralization [START_REF] Boulvais | Carbonate alteration associated with talc-chlorite mineralization in the eastern Pyrenees, with emphasis on the St. Barthelemy Massif[END_REF] are observed elsewhere in the North Pyrenean Zone. These constraints indicate a heating episode from 110 Ma to 85 Ma [START_REF] Montigny | K-Ar study of Cretaceaous magmatism and metamorphism in the Pyrenees: Age and length of rotation of the Iberian Peninsula[END_REF]. Raman spectroscopy of carbonaceous material (RSCM) shows that the Albian to Cenomanian series of the Mauléon basin experienced shallow to mid-crustal temperatures of 180 to 295°C [START_REF] Clerc | Thermal control on the modes of crustal thinning leading to mantle exhumation[END_REF]. Determining whether these temperatures reflect thinning processes is not trivial and requires a thermal modeling approach.

An important delay occurred between the onset of plate convergence at ~83 Ma, (chron A34) used in plate reconstructions [START_REF] Rosenbaum | Relative motions of Africa, Iberia and Europe during Alpine orogeny[END_REF] and the exhumation in the belt recorded from ~50 Ma to ~20 Ma, as constrained by low-temperature thermochronological data mainly in the Axial Zone [START_REF] Yelland | Fission track thermotectonics in the Pyrenean orogen[END_REF][START_REF] Yelland | Thermo-tectonics of the Pyrenees and Provence from fission track studies[END_REF][START_REF] Morris | Exhumation of the Pyrenean orogen: implications for sediment discharge[END_REF][START_REF] Fitzgerald | Asymmetric exhumation across the Pyrenean orogen: implications for the tectonic evolution of a collisional orogeny[END_REF][START_REF] Sinclair | Asymmetric growth of the Pyrenees revealed through measurement and modeling of orogenic fluxes[END_REF][START_REF] Jolivet | Thermochronology constraints for the propagation sequence of the south Pyrenean basement thrust system (France-Spaine)[END_REF][START_REF] Maurel | The Meso-Cenozoic thermo-tectonic evolution of the Eastern Pyrenees: an 40 Ar/ 39 Ar fission track and (U-Th)/He thermochronological study of the Canigou and Mont-Louis massifs[END_REF][START_REF] Gunnel | Low long-term erosion rates in high-energy mountain belts: insights from thermo-and biochronology in the Eastern Pyrenees[END_REF][START_REF] Metcalf | Thermochronology of a convergent orogeny: constraints on the timing of thrust faulting and subsequent exhumation of the Maladeta Pluton in the Central Pyrenean Axial Zone[END_REF]. Time-temperature history (burial, heating and cooling) during the initial accretionary stage are therefore largely unknown. It may involve underestimated competing cooling processes such as syn-orogenic thermal relaxation or cooling by underthrusting as suggested recently in Taiwan [START_REF] Mesalles | From submarine continental accretion to arc-continent orogenic evolution: The thermal record in southern Taiwan[END_REF].

Sampling and methods

Strategy

Determining thermal histories of crustal rocks is classically done using multiple lowtemperature thermochronometers on bedrock samples, but, in the Pyrenees, published bedrock low-temperature data are only consistent with episodes of collision-related cooling. To gain resolution on syn-to post-rift time-temperature history, a direct approach relies on examining syn-rift basins that recorded both extension and compression in the North Pyrenean Zone. In this aspect, the Mauléon basin is suitable as it experienced temperatures in the 110-295°C range (Fig. 1A). Its time-temperature evolution may therefore be resolved by combining zircon fission-track (ZFT) and (U-Th-Sm)/He (ZHe) thermochronology, which have their Partial Annealing Zone and Partial Retention Zone (PRZ) between 160-270°C and 140-220°C, respectively (e.g. [START_REF] Brandon | Late Cenozoic exhumation of the Cascadia accretionary wedge in the Olympic Mountains, northwest Washington State[END_REF][START_REF] Guenthner | Helium diffusion in natural zircon: Radiation damage, anisotropy, and the interpretation of zircon (U-Th)/He thermochronology[END_REF]. When zircons reside in these temperature intervals, the resulting ages are highly dependent on their timetemperature histories and diffusion kinetics. Recently published helium diffusion models reveal that apparent (U-Th-Sm)/He ages are controlled by the amount of α-recoil damage, which is proportional to the effective U concentration [eU] [START_REF] Flowers | Apatite (U-Th)/He thermochronometry using a radiation damage accumulation and annealing model[END_REF][START_REF] Gautheron | Effect of alpha-damage annealing on apatite (U-Th)/He thermochronology[END_REF][START_REF] Guenthner | Helium diffusion in natural zircon: Radiation damage, anisotropy, and the interpretation of zircon (U-Th)/He thermochronology[END_REF]. Following these models, the thermal history explaining these ZHe age and eU correlations can be deduced from inverse modeling.

The dataset consists of five detrital sandstone samples from deep-water turbidites of the western part of the Mauléon basin, deposited at 101 ± 4 Ma in Albo-Cenomanian (Su-1, Ar-2, Lu-1, Ch-1, and Mi-1, Fig. 1A,B). Two basement samples from a granitic intrusion (Itx-1) and gneiss (Lag-1) were collected (Fig. 1) to complete these data with apatite (AHe) and ZHe analyses, and to add independent constraints on collision-related cooling. Lu-1 was analysed with Raman Spectroscopy following the protocol developed by [START_REF] Lahfid | Evolution of the Raman spectrum of carbonaceous low-grade metasediments of the Glarus Alps (Switzerland)[END_REF]. Samples were prepared at CRPG (Nancy, France). They were crushed and zircon and apatite grains were separated for low-temperature thermochronological analyses using standard heavyliquid and magnetic separation from the 61-280 μm fraction.

Zircon Fission track analysis

Zircon grains were handpicked for fission track dating and analysed at the thermochronology laboratory of ISTerre (Université Joseph Fourier, Grenoble). We used standard ZFT preparation procedures as described by [START_REF] Bernet | Fission-track analysis of detrital zircon[END_REF]. Grains were mounted in a teflon sheet, polished to expose internal surfaces and etched with NaOH-KOH at 228°C between 8 and 13 hrs. Irradiation was performed in the FRM II Research Reactor at the Technische Universität München (Germany) with CN1 dosimeter glasses and Fish Canyon Tuff age standards. Mica detectors used for external detector method [START_REF] Gleadow | Fission track dating of zircon: improved etching techniques[END_REF] and standards were then etched in 48% HF at 21°C for 18 min. Counting was carried out on a Olympus BH2 optical microscope using FTStage 4.04 system of [START_REF] Dumitru | A new computer-automated microscope stage system for fission-track analysis[END_REF]. Individual fission-track ages were obtained using zeta factors following approach of [START_REF] Hurford | The zeta calibration of fission-track dating[END_REF].

Zircon (U-Th-Sm)/He analysis

For (U-Th-Sm)/He dating, we handpicked 5 to 10 zircon grains per bedrock sample and between 60 and 110 zircon grains per detrital sample. Detrital zircons were mounted in epoxy and polished for future U/Pb analyses. Among those zircons, we retrieved from the epoxy mounts between 20 and 35 zircons per detrital samples for (U-Th-Sm)/He analysis, chosen so as to represent the main peaks individualized in the U/Pb age distributions. All theses detrital zircons were measured as single grains. Additionally, 4 to 5 replicates of 5 to 10 zircon grains were analysed in bedrock samples (Itx-1 and Lag-1). Zircon grains (prismatic to roundshaped, 0 to 2 pyramids, with an equivalent spherical radius ranging from 35 to 60 µm) were then measured, and loaded in Pt capsules for He extraction at CRPG. They were outgassed at 1500°C for 20 min, and analyzed for He concentrations with a VG603 noble gas mass spectrometer [START_REF] Pik | Stability of the Upper Nile drainage network (Ethiopia) deduced from (U-Th)/He thermochronometry: implications for uplift and erosion of the Afar plume dome[END_REF][START_REF] Godard | Late Cenozoic evolution of the central Longmen Shan, eastern Tibet: Insight from (U-Th)/He thermochronometry[END_REF]. After total helium extraction, Pt capsules containing zircon grains were retrieved for U, Th, and Sm content measurements at SARM (Nancy, France). Pt capsules were opened, and loaded in Pt crucibles along with ultra-pure LiBO 2 and ultra-pure B(OH) 3 for 2 hrs at 990°C in an automatic tunnel oven. Then, the Pt crucibles were digested 12 hrs into acid. The preparation was then analysed using an inductively coupled plasma mass spectrometer. The overall precision of He ages determined with this procedure is within 5-6% (1σ). Zircon grains whose He and/or U concentrations are too close from the blank (e.g. for He content less than 1.10 -13 moles and for U concentration in the solution less than 100 ppb after blank correction) were not considered for this study.

Zircon ages were corrected for α-ejection (F T ) following [START_REF] Ketcham | Accounting for long alpha-particle stopping distances in (U-Th-Sm)/He geochronology: Refinement of the baseline case[END_REF] (Table DR2,DR3). To account for the abrasion of the detrital zircon single grains, we consider that we deleted ~20 µm (the mean stopping distance [START_REF] Ketcham | Accounting for long alpha-particle stopping distances in (U-Th-Sm)/He geochronology: Refinement of the baseline case[END_REF]) and the half of the mean width of our zircon grains (~45 µm). Following [START_REF] Reiners | Wildfire thermochronology and the fate and transport of apatite in hillslope and fluvial environements[END_REF], we corrected F T considering an abrasion of 45 µm for each detrital grain.

Apatite (U-Th-Sm)/He analysis

Apatites were prismatic, with 0 to 2 pyramids, and with an equivalent spherical radius ranging from 60 to 160 µm. We performed AHe analyses at Paris-Sud University (Orsay, France) on bedrock samples (Lag-1 and Itx-1, Fig. 1) following the procedure described by [START_REF] Fillon | Oligocene-Miocene burial and exhumation of the Southern Pyrenean foreland quantified by low-temperature thermochronology[END_REF]. Four single grain replicates were analyzed for Itx-1 and Lag-1 with 8% precision (1σ).

AHe ages were corrected for α-ejection following [START_REF] Ketcham | Accounting for long alpha-particle stopping distances in (U-Th-Sm)/He geochronology: Refinement of the baseline case[END_REF] and apatites with outlier Th/U ratios were excluded (Table DR4).

Results

ZFT analyses performed on samples Su-1, Ar-2, Ch-1, and Mi-1 yielded 23 to 63 dated grains per sample (Table DR1). Each sample with an identical depositional age shows a similar age distribution. We therefore only present age component distributions for the combined samples (n=171) (Fig. 2A). Most of the grains (97%) are older than the depositional age, indicating very minor resetting after deposition.

We decomposed our age distribution into age components using DensityPlotter [START_REF] Vermeesch | RadialPlotter: A Java application for fission track, luminescence and other radial plots[END_REF][START_REF] Vermeesch | On the visualization of detrital age distributions[END_REF]. The software represents distribution of ages using KDE (Kernel Density Estimation), which is determined by stacks of Gaussian curves on top of each measurement, whose standard deviation is determined by the local probability density. Deconvolution for combined data returned three age components (errors are given as ±2σ): two majors at 134 ± at 1005 ± 886 Ma (4%) characterized by a too important error to be statistically meaningful (Fig. 2A).

ZHe analyses were carried out on the same Su-1, Ar-2, Ch-1 samples and on Lu-1. Ten to 27 grains were dated per sample (Table DR2) and show similar ages and eU distributions. The age distribution from the combined data ranges from 36 Ma to 131 Ma (n=75, Fig. 2B) and yields four age peaks at 39 ± 4 (16%), 50 ± 3 (38%), 68 ± 4 (33%), and 116 ± 7 Ma (13%).

Most of these detrital ZHe grain ages (87%) are younger than the depositional age, suggesting that they have been, at least, partially reset by post-deposition burial. We will test the timing and amount of burial and exhumation through numerical inversion of the data in the next section.

ZHe analyses on two bedrock samples from the Labourd-Ursuya massif (Lag-1 and Itx-1)

give ages ranging from 51 ± 5 to 74 ± 7 Ma, and from 61 ± 6 to 86 ± 9 Ma, respectively (Table DR3). AHe single grain analyses performed on the same samples yield ages ranging from 42 ± 3 to 49 ± 4 Ma and from 35 ± 3 to 43 ± 4 Ma for Lag-1 and Itx-1, respectively (Table DR4).

Thermal modeling of partially reset ages

It has been demonstrated that α-recoil damages associated to U and Th decay, and their respective concentration (eU) could affect He diffusion in apatites [START_REF] Shuster | The influence of natural radiation damage on helium diffusion kinetics in apatite[END_REF][START_REF] Flowers | Apatite (U-Th)/He thermochronometry using a radiation damage accumulation and annealing model[END_REF][START_REF] Gautheron | Effect of alpha-damage annealing on apatite (U-Th)/He thermochronology[END_REF]. For high eU concentrations, the amount of αrecoil damages increases with He retentivity and closure temperature. [START_REF] Guenthner | Helium diffusion in natural zircon: Radiation damage, anisotropy, and the interpretation of zircon (U-Th)/He thermochronology[END_REF] highlighted the same trend in zircons but only for relatively low concentrations of eU. For very high eU concentrations, the He retentivity rapidly decreases. These authors hypothesized that for very high eU content, the amount of α-recoil damage is high enough so that damaged areas in the crystal are interconnected and form through-going fast diffusion pathways for He. [START_REF] Guenthner | Helium diffusion in natural zircon: Radiation damage, anisotropy, and the interpretation of zircon (U-Th)/He thermochronology[END_REF] showed that the evolution of He retentivity in zircons, which depends on the eU content, controls both variations of the closure temperature and individual annealing behaviors. This effect can lead to large ZHe age distributions, under a given timetemperature path. The non-random distribution of our ZHe age-eU dataset is supported by their statistical distribution in Figure 3 (see caption for details concerning the density function used) and suggests such a control. Originating from a dense zone of young ZHe ages and low-eU grains two opposite trends can be identified as ZHe-eU groups. A first group A (red area) consists in young ZHe ages (from 36 to 65 Ma) associated with a large eU distribution (from 400 to 4000 ppm). The group B (blue area) corresponds to older ZHe age (from 65 to 131 Ma) associated with low eU values only (from 0 to 1100 ppm).

Following [START_REF] Guenthner | Helium diffusion in natural zircon: Radiation damage, anisotropy, and the interpretation of zircon (U-Th)/He thermochronology[END_REF], the oldest ages could correspond to zircon grains that have been less resetted due to a higher closure temperature (~220°C). Such zircons require a longer residence time in the PRZ to be reset. In contrast, the young ZHe grain ages that display eU>1100 ppm would correspond to a lower closure temperature of <140°C.

To determine the time-temperature paths of these zircon grains, we used the HeFTy soft [START_REF] Ketcham | Forward and inverse modeling of low-temperature thermochronometry data[END_REF] that includes the kinetic model of [START_REF] Guenthner | Helium diffusion in natural zircon: Radiation damage, anisotropy, and the interpretation of zircon (U-Th)/He thermochronology[END_REF]. The limited number of grains (seven) that can be input in the HeFTy inverse modeling procedure do not allows direct inversion of the entire dataset and requires to identify representative individual ZHe age-eU pairs within the two groups observed in Figure 3. These two trends which originate in the red high density zone of Figure 3 can be easily and robustly described by a couple of representative samples. In order to describe the entire range of age-eU distribution, seven representative samples have been taken along the A and B groups and used for distinct sets of inversion. Various tests demonstrated that the use of representative samples is not an issue in this inversion procedure.

Because the A and B groups have been potentially controlled by distinct closure temperatures linked to the amount of radiation damage accumulated in the zircon grains [START_REF] Guenthner | Helium diffusion in natural zircon: Radiation damage, anisotropy, and the interpretation of zircon (U-Th)/He thermochronology[END_REF]) it is crucial to take into account the ZFT data obtained for these zircons in the inversion modeling. The ZFT data also exhibit two distinct populations characterized by peak ages at P1 (~134 Ma) and P2 (~236 Ma) that represent two independent cooling histories prior to deposition (at ~100 Ma). At that time, the amount of accumulated damages was therefore significantly higher for the P2 population and could have triggered differential He diffusion when the sediments have been subsequently buried and re-heated. It is however not possible to directly relate one ZFT population with one ZHe ages group. Consequently both P1 and P2 ZFT populations have been used alternatively as input parameters for the inversion modeling.

Four sets of inversion models have therefore been tested (Fig. 4), corresponding to the various correlations between eU and ZHe ages that reproduce the data (Fig. 4B). We infer that all Albo-Cenomanian ZHe detrital data are obtained by the combination of these two timetemperature models (Fig. 4).

These models show a consistent post-100 Ma thermal history. In particular, time-temperature paths of our zircon grains are consistent with heating to temperatures of ~180°C soon after ~100 Ma at an average heating rate of ~5°C/Myr. Several of these pathways show a nearly isothermal stage established at ~80 Ma which lasted maximum ~30 Myr. This heating/isothermal stage was followed by a relatively rapid cooling stage from 50 Ma to present (~3°C/Myr). This cooling path is not very precisely described by the inverse modeling because of the lack of additionnal lower temperature thermochronometers.

1D thermo-kinematic modeling of rift-to-collision evolution

The results of modeling (Fig. 4) show that the Albo-Cenomanian zircon grains were heated to a temperature of ~180°C during the post-breakup evolution of the Mauléon basin. To constrain the geothermal gradient associated with this heating episode, a few Myrs only after deposition of the sampled Albo-Cenomanian rocks (see Figure 4A Cretaceous history, and Lahontan 1bis, Lacq 301, and Nassiet 1 for the Late Cretaceous to the Late Eocene deposits (Fig. 5B). Estimates of minimum and maximum thicknesses at time of deposition of the studied samples from 105 to 70 Ma are indicated in Figure 1B. We estimate that a mean sediment thickness of ~2 km was deposited above the studied samples during this period of time (Fig. 5A). A temperature of 180°C at ~2 km depth, as suggested from the ZHe data, allows to define a geothermal gradient as high as ~80°C/km (assuming a surface temperature of 20°C).

To examine the tectonic conditions that led to the observed cooling history, we consider two different end-member thinning processes (Figs. 6A, B, and7) that are thought to embody most of the fundamental characteristics of rifted margins as summarized by [START_REF] Huismans | Depth-dependent extension, two-stage breakup and cratonic underplating at rifted margins[END_REF]. A stepwise tectonic evolution from 130 Ma to 0 Ma of a lithosphere section below the Mauléon basin involves thinning through a rifting phase from the Early Barremian (130 Ma) until the Late Cenomanian (95 Ma) with a breakup occurring at 110 Ma. This is followed by inversion and underthrusting of the thinned lithosphere from 83 Ma until the Early Eocene (50 Ma) that marks the onset of crustal thickening and thrust-related exhumation. In order to test these two hypotheses, we adopt a 1D forward thermo-kinematic modeling approach. The thermochronological modeling showed that the Albo-Cenomanian series in the Mauléon basin were heated to a temperature of ~180°C, which was maintained during ~30 Myrs (Fig. 4). We therefore attempt to retrieve from the model the time-depth evolution of the 180°C isotherm by varying thinning factors for crust and mantle.

The thickness of the Mauléon sedimentary layers at time of deposition of Albo-Cenomanian is constrained by the subsidence history of the Mauléon basin defined in Figure 5A. We consider an initial thickness of 2 km of sediments above the continental crust that increases to a final thickness of 6 km. The current Moho depth is estimated to 32 km in the region of the Mauléon basin (Daignieres et al., 1982;Jammes et al., 2010;Chevrot et al., in revision) leading to consider a final thickness of continental basement of 28 km. We hypothesize that the thickness of the continental basement was the same before the onset of rifting. At the initial and final stages we consider that the lithosphere is in equilibrium stage and adopt a typical thickness value for a Phanerozoic continental lithosphere of 130 km (e.g., Poudjom Djomani et al., 2001) (Fig. 6).

In model A, the crust is thinned until breakup occurs (Fig. 6A). After crustal breakup, the SCLM is thinned and exhumed at the base of the Mauléon basin, according to variable amount of thinning factors β A ranging from 4, 10 and higher (SCLM breakup). In model B, the SCLM is thinned until its breakup, leading to the rise of hot asthenosphere below the continental crust (Fig. 6B). Similarly to model A, model B is run for the same variable amount of thinning factor β B for the continental crust. We also test the impact of the thickening of the SCLM (model A) or the crust (model B), after convergence initiated at 83 Ma, on the thermal evolution of Mauléon basin. This was performed by taking into account the accumulation of syn-orogenic sediments under local isostatic conditions.

For both scenarios, the role of transient diffusive heat relaxation and advection related to basin subsidence history, isostasy and rock uplift is quantified. It accounts for realistic diffusivity and heat production distribution. To simulate the effect of a high thermal conductivity layer represented by the Triassic evaporites, the basin rests above a 1 km-thick Triassic salt layer, which thickness is kept constant during the simulation. Although fluid circulations may play a key role during extension by maintaining high temperatures below the basin and favoring heat transfers, we kept the model as simple as possible so as to depend on a minimum of unknown parameters, as the basin evolved from extensional to compressional tectonic settings.

Model results show that the depth of the 180°C isotherm is controlled to first order by the amount of thinning of the SCLM (Fig. 7). This effect is most significant for model A (SCLM exhumation) in which the depth of the 180°C isotherms is seen to vary between 1 and 5 km as a function of the amount of thinning. In the model B, this is less apparent because the asthenosphere is kept closer to the surface (from 7 km depth to surface depending on the β considered) during all the experiment.

Prior to crustal breakup at 110 Ma, model A and B show very different thermal responses to rifting. An upward deflection of isotherms is observed for the model B, while model A indicates a cooling phase before heating. Thermal evolution in model B reflects the upward advection of the base of the lithosphere during thinning, which is maximum when the SCLM breakup is achieved. In model A, a delay is observed between the onset of crustal and SCLM breakup. This reflects the loss of the radiogenic heat source caused by crustal breakup, which is not instantaneously compensated by advection of heat caused by SCLM thinning.

During the inversion phase, the 180°C isotherms are maintained to the same depth from 95 to 50 Ma for both models (red and black curves on figure 7) corresponding to a limited linear increase of heat with respect to the base of the Mauléon basin. When we account for the thickening of the SCLM or the crust below the basin during the underthrusting phase, the 180°C isotherms remain flat from 83 Ma to 50 Ma for both models A and B. The progressive deepening of the 180°C isotherms after 50 Ma reflects the primary effect of thermal relaxation and the deepening of the SCLM, relative to the heat advection due to erosion.

Discussion

Comparison between thermochronological data and thermo-kinematic modeling

In this study, we focus on the thermal history of the Mauléon basin from Albo-Cenomanian times until today. However, because our ZFT ages are only slightly reset (10%) with no significant influence on age populations, we can assume that P1 (~134 Ma) and P2 (~236 Ma) reflect two cooling events that occurred prior to deposition. The P1 cooling event appears to be consistent with extension recorded in the Early Cretaceous at ca. 145-132 Ma [START_REF] Vergés | Peri-Tethys Memoire 6, Pery-Tethyan Rift/Wrench Basins and Passive Margins[END_REF]. Zircons cooled between 150 Ma and 100 Ma (P1) from mid-crustal to surface temperatures may reflect denudation in the footwall of a rolling-hinge normal fault (Axen and Baertley, 1997). The P2 event is also coherent with a magmatic [START_REF] Rossi | Datation U/Pb sur zircons des dolerites tholéiitiques pyrénéennes (ophites) à la limite Trias-Jurassique et relations avec les tufs volcaniques dits "infra-liasiques" nord-pyrénées[END_REF] and/or exhumational event during the Triassic, as recognized in Albian sediments in the southern Pyrenees [START_REF] Filleaudeau | Thermo-tectonic evolution of the southcentral Pyrenees from rifting to orogeny: insights from detrital zircon U/Pb and (U-Th)/He thermochronometry[END_REF].

On the other hand, ZHe age data show a complex and large distribution from 36 to 131 Ma with most of them younger than depositional age. This is typical of partial resetting and, for a given duration of thermal event, its amplitude could have been controlled by various factors including: (i) the size of the grains, (ii) the initial age distribution of grains, (iii) the position in the PRZ during re-heating, (iv) the residence time above the PRZ and the amount of αrecoil damages accumulated before re-heating [START_REF] Guenthner | Helium diffusion in natural zircon: Radiation damage, anisotropy, and the interpretation of zircon (U-Th)/He thermochronology[END_REF]. Inversion of ZHe data with thermochronological models (Fig. 4) suggests that zircon grains have been heated to temperatures up to ~180°C soon after deposition ~100 Ma ago (Fig. 4A,B). This is consistent with our thermo-kinematic models A and B showing that the basin was already hot at the end of the rifting phase (95 Ma), due to upward deflection of the 180°C isotherm reaching the depth of the Albo-Cenomanian series at 2 km for =10 or higher (Fig. 7). After this heating phase, both our thermochronological models P1-A and P2-B require that zircon grains were maintained at this temperature of 180°C through a nearly isothermal stage until 50 Ma. This period corresponds to the inversion phase of the thermo-kinematic models, where the 180°C isotherm depth remains constant from 95 Ma to 50 Ma.

The youngest ZHe population from 60 to 40 Ma is associated to the largest eU concentration distribution (from ~0 to 4000 ppm, Fig. 3) and corresponds to the lower limit of the He-PRZ (closure temperature lower or equal to 140°C, [START_REF] Guenthner | Helium diffusion in natural zircon: Radiation damage, anisotropy, and the interpretation of zircon (U-Th)/He thermochronology[END_REF]. These youngest ages are directly related to the main episode of cooling that affected the Mauléon basin since the Eocene. This is consistent with our thermo-kinematic models that indicate a progressive cooling driven by mantle subduction and thermal relaxation during the orogenic phase (Fig. 6). This directly led to the compensation of the hot thermal anomaly previously emplaced, as plate collision and crustal thickening initiated at 50 Ma. In the absence of very-lowtemperature thermochronological constraints, the results of the inversion models (Fig. 4A) do not lead to precise t-T scenario concerning this late phase of cooling. Whether such cooling through the He-PRZ of zircons was mostly achieved early (50 -40 Ma) and driven by thermal relaxation or whether part of this cooling occurred later in the Pyrenean orogenesis (40 -25 Ma) and was driven by exhumation is not precisely expressed in the models. However thermo-kinematic models conducted in this study clearly demonstrate that thermal relaxation during exhumation, following transient upward deflection of isotherms, represent a significant cooling process that must be taken into account in the interpretation of thermochronological data in this range of temperature. In the Pyrenean belt this is particularly true for the North Pyrenean Zone which experienced large-scale hyper-extension related high geothermal gradients.

Our simple approach did not allow the evaluation of the role of the fluids effect in the Mauléon basin, but the good agreement between model and data suggests its role might be minor at least from a thermal perspective. However, fluid flow and serpentinization of the exhumed mantle in such settings may be prominent processes allowing the localization of deformation during extension.

Implications for the evolution of the Pyrenees

After deposition, Albo-Cenomanian zircon grains were heated to a temperature of ~180°C during the post-breakup evolution of the Mauléon basin. At this time, the basin was presumably floored by the exhumed mantle as shown by geological evidences summarized in [START_REF] Jammes | Tectonosedimentary evolution related to extreme crustal thinning ahead of a propagating ocean: Example of the western Pyrenees[END_REF]: reworked granulites and mantle peridotites in Albian sediments, and tectonic relationship with SCLM exhumation. These geological data best support a model A hyper-extended rift basin (Fig. 6A) even if both models A and B rift basins reproduce the thermal history of the basin (Fig. 6A,B). This heating phase was characterized by a geothermal gradient as high as ~80°C/km consistent with RSCM temperatures (180°C to 295°C) and HT-LP metamorphism of pre-Cenomanian sedimentary units (Fig. 1).

Heating in the basin ceased rapidly from ~80 Ma on. This stage was followed by a rather isothermal period that initiated coevally with the onset of plate convergence at 83 Ma. Both temperature and geothermal gradient were then kept at a high level for 30 Myrs, until 50 Ma when cooling/exhumation started associated with mountain building. The persistence of high surface thermal flow and geothermal gradients 18 Myrs after sea-floor spreading has been reported in present-day rifted margins of the Gulf of Aden [START_REF] Lucazeau | Heat-flow and hydrothermal circulation at the oceancontinent transition of the eastern gulf of Aden[END_REF][START_REF] Rolandone | New heat-flow measurements in Oman and the thermal state of the Arabian Shield and Platform[END_REF]. In the case of the Mauléon basin, the temperature structure acquired during the rift phase prevailed at the earliest stage of continental accretion. This is in marked contrast with thermal evolution reported, e.g., in Taiwan [START_REF] Mesalles | From submarine continental accretion to arc-continent orogenic evolution: The thermal record in southern Taiwan[END_REF] where rapid underthrusting of the lower plate (50-80 mm/yr) at onset of continental accretion led to downward deflection of isotherms. This cooling phase is not detected in the early accretionary prism stage of the Pyrenees. We interpret this difference as a consequence of limited lateral heat advection induced by a much slower plate convergence of only 3-4 mm/yr [START_REF] Mouthereau | Placing limits to shortening evolution in the Pyrenees: role of margin architecture and implications for the Iberia/Europe convergence[END_REF].

Our result reveals that onset of shortening in the Mauléon basin occurred in an abnormally hot basin. Due to the absence of significant nappe stacking in the region, we argue that ductile shortening documented in the inverted rifted basin results from high temperatures inherited from rifting rather than syn-convergence burial. It is characterized by axial-planar and crenulation cleavages in folded Albian to Cenomanian units of the Mauléon basin that reveal ambient temperatures of 100-200°C [START_REF] Choukroune | Structure et evolution tectonique de la Zone Nord-Pyrénéenne[END_REF], consistent with our models.

Fission track analyses on the Labourd-Ursuya Massif yield two ages at 42.2 ± 2.4 Ma and 48.3 ± 2.3 Ma on apatites, and an age at 81.8 ± 3.1 Ma on zircons [START_REF] Yelland | Thermo-tectonics of the Pyrenees and Provence from fission track studies[END_REF]. Thus, ZFT and ZHe ages from the Labourd-Ursuya Massif indicate initial cooling from probably deeper crustal temperatures at 80-50 Ma, showing a different thermal history from the Mauléon basin. AFT and AHe ages (ranging from 49 ± 4 Ma and 35 ± 3 Ma) in the Western Pyrenees suggest that cooling/thermal relaxation of high temperatures after 50 Ma occurred synchronously with the North Pyrenean massifs in the Eastern and Central Pyrenees [START_REF] Morris | Exhumation of the Pyrenean orogen: implications for sediment discharge[END_REF][START_REF] Fitzgerald | Asymmetric exhumation across the Pyrenean orogen: implications for the tectonic evolution of a collisional orogeny[END_REF][START_REF] Yelland | Thermo-tectonics of the Pyrenees and Provence from fission track studies[END_REF], as a result of crustal thickening and erosion. The thermal relaxation observed after 50 Ma in the Mauléon basin therefore appears related to a major and regional exhumational phase in the Pyrenees. Because erosion is one of the main agent in orogenic belts bringing heat closer to the surface it may seem counterintuitive that thermal relaxation occurred during the main exhumational phase.

Processes other than erosion may therefore explain the thermal relaxation. Heat advection recorded in the Mauléon basin remained limited first because only 2 km of basin sediments were eroded since 50 Ma. In addition, our thermo-kinematic experiments (Fig. 6) show that the emplacement the Mauléon basin onto a thicker and colder foreland lithosphere compensates heating due to exhumation.

Conclusions

This study demonstrates that the analysis of low-temperature thermochronological constraints performed on pre-/syn-rift sediments preserved in mountain belts is effective in resolving the long-term post-rift and syn-convergence thermal evolution of rifted margins and hyperextended rift basins. When combined with thermal-kinematic models of rift-to-collision evolution, our data allowed to test hypotheses on the thinning processes between crust and the lithospheric mantle that cause the reconstructed time-temperature history.

Our low-temperature thermochronological data show that the sediment succession of the Mauléon basin recorded a phase of heating following breakup in the Albo-Cenomanian as a result of extreme extension. The Albo-Cenomanian sandstones reached temperatures of 180°C at only ~2 km depth, corresponding to a geothermal gradient of ~80°C/km.

Using this approach we demonstrate that the thermal structure of the Mauléon basin is consistent with extreme thinning, although the relative thermal effect of breakup of the SCLM and crustal breakup can hardly be differentiated. The temperature anomaly inherited from extreme thinning lasted 30 Myrs, from ~80 Ma to ~50 Ma. This inherited thermal anomaly explains ductile shortening identified in the inverted basin. It provides a mechanism for explaining the observations of abnormally high temperatures (relative to inferred burial), synconvergence MT or HT metamorphism and ductile deformation in post-rift sediments. On the other hand, these tectono-metamorphic characteristics are diagnostic of highly extended rift basin inverted relatively soon after its emplacement. Thermal relaxation of the rift-related heat anomaly occurred during the main stage of the orogenic development, when the hyperextended rift basin was thrusted over the colder and thicker European plate ~50 Myrs ago.

The Pyrenees give us a vivid example of how high temperatures inherited from the rifting can affect the thermal structure of the early stages of the collision, and how these temperatures are relaxed during the late stage of orogenic processes.

Figure Captions

  combinations using ZFT populations (P1, P2) and ZHe ages groups (A, B). Models are characterized by: (i) different pre-deposition histories constrained by the P1 and P2 ZFT characteristics (134 ± 15 Ma / 240 ± 40°C and 236 ± 20 Ma / 240 ± 40°C respectively), (ii) identical depositional age at 110 Ma, (iii) a free post-depositional time-temperature history inverted for 7 representative ZHe ages of groups A and B independently. To reproduce the partial reset signature of the ZHe data, we constrained the software to search post-deposition time-temperature paths from shallow to mid-crustal temperatures, corresponding to a range from 20°C and 200°C.The inversion consisted of randomly testing 300,000 time-temperature paths for each model. The P1-A model returned 439 acceptable and 180 good solutions. The P1-B model returned only 70 acceptable and no good solutions. The P2-A model only returned 35 acceptable and no good solutions. The P2-B model returned 405 acceptable and 62 good solutions. The best time-temperature path of each model corresponds to a ZHe age-eU correlation, which is compared to the data in Figure 4B. The P1-A model better fits the group A than the P2-A model, which fails to reproduce the data with eU > 2000 ppm. The P2-B model is in better agreement with the group B than the P1-B model. Models P1-A and P2-B return the best

  ), we first need to determine the thickness of the entire pile of sediments in the Mauléon basin. The complete burial history shown in Figure 5A was resolved by combining well data from different boreholes, including boreholes in the Arzacq basin, North of the Mauléon basin (for instance Lacq 301, Brunet (1984)), and wells drilled in the Mauléon basin. They are from South to North: Ainhice 1, Chéraute 1, Uhart-Mixe 1 and Saint-Palais 1 for the Triassic to Late

Figure 1 :

 1 Figure 1: A) Geologic map of the study area. Red stars and circles depict the position of studied samples and samples from which RSCM temperatures were obtained (Clerc and Lagabrielle 2014, including one new estimate from this study (Lu-1), respectively. The extent of cleavage domain is shown as red dashed area. B) Synthetic lithostratigraphy of mesocenozoic successions of the Mauléon basin and layer thickness inferred from borehole data (Fig. 5B). C) Geological cross-section of the western part of the Mauléon basin, including the location of samples and the extent of cleavage domain, same as shown in A. Note that the ductile deformation domain is observed at the base of the basin. NPFT: North Pyrenean Frontal Thrust, SPT: Saint-Palais Thrust, GRH: Grand-Rieu High.

Figure 2 :

 2 Figure 2: Results of thermochronological analyses and decomposition of statistically representative age component of Albo-Cenomanian detrital samples. A) ZFT results from Su-

Figure 3 :

 3 Figure 3: The statistical distribution of our ZHe age-eU data (blue empty squares) is resolved from a 2D Kernel probability density function using a Parzen window approach (Matlab code available on request). Low eU content from 0 to 1100 ppm correspond to a large distribution of ZHe ages from 65 Ma to 131 Ma (group B in blue). These oldest ages are associated to a closure temperature of ~220°C. By contrast, high eU content (>1100 ppm) only show young ZHe ages from 36 Ma to 65 Ma (group A in red), corresponding to lower closure temperatures (<140°C).

Figure 4 :

 4 Figure 4: A) Time-temperature histories extracted from HeFTy inverse modeling constrained by ZFT data, ZHe age-eU pairs, and depositional ages, for each model (P1-A, P1-B, P2-A and P2-B). B) ZHe age-eU statistical distribution of Albo-Cenomanian detrital zircon grains. We compare the ZHe age-eU correlation corresponding to the best time-temperature path of each model with the data.

Figure 5 :

 5 Figure 5: A) Total decompacted thickness of sediments in the Mauléon basin, as obtained by combining seven boreholes within or close to the Mauléon basin for maximum, minimum and weighted averaged (red curve) estimations. Temporal influence intervals resolved from each borehole is shown in grey. Vertical dashed lines represent the period of heating highlighted in model of Figure 4 and the horizontal dashed lines correspond to the thickness of sediments deposited during this period. A mean value of 2 km of sediments was deposited between 105 and 70 Ma. B) Map showing the location of the different boreholes.

Figure 6 :

 6 Figure 6: 1D thermal-kinematic models tested for the Mauléon basin. A) Model A: crustal breakup at 110 Ma and SCLM is thinned and exhumed to the base of the basin until 95 Ma. Dashed red lines on model A correspond to tests considering SCLM thickening from onset of convergence at 83 Ma to mature collision and exhumation after 50 Ma. B) Model B: SCLM breakup occurs at 110 Ma and the continental crust thins until 95 Ma, lying in contact with the asthenophere. Tested thinning factors β A and β B are 4, 10, and ∞ (breakup) in both models.

Figure 7 :

 7 Figure 7: Comparison of the Mauléon basin burial history with the depth of the 180°C isotherm predicted from 1D rift-to-collision thermal models (A and B) shown in Figures 6A and 6B, respectively. Depth evolution of the Albo-Cenomanian deposits (grey) is distinguished from the Meso-Cenozoic successions (green) and water (blue). Depth of the

Figure 1 Figure 2 Figure 3

 123 Figure 1

Figure 4 Figure 5 Figure 6

 456 Figure 4

Figure 7

 7 Figure7

Table A1 .

 A1 Thermal and mechanical parameters considered for each type of rock in the model

		Sedimentary cover		Basement
		Deposits Triassic salt	Continental crust	SCLM	Asthenosphere
	Thermal conductivity k W/(m.K)	2.25	6.5	2.25	3.3	3.3
	Heat capacity Cp m²/(m.s²)	900	840	900	750	750
	Heat production H µW/m 3	0.9	0	0.6	0.009	0.009
	Density ρ kg/m 3	2500	2170	2800	3300	3300

Acknowledgments

This study was supported by French National Research Agency (ANR Project PYRAMID).

We thank G. Manatschal and R.S. Huismans for constructive discussions. We also thank the staff of the different laboratories (CRPG, SARM, ISTerre, IDES) for welcoming us and for their precious help during data acquisition. Comments by two anonymous reviewers have been helpful in clarifying some points of the manuscript. This is CRPG contribution number 2344.

Appendix

The code of our 1D thermo-kinematic model solves the transient heat advection diffusion equation (A1), including heat production in one dimension: (A1) Density, ρ, heat capacity, Cp, heat production H and the heat conductivity, k, are given constant values for each rock type and are listed in Table A1. The solution is obtained using a standard implicit in time centered finite difference scheme at each time step. However, in order to allow for advection of the 1330°C isotherm, or to allow for erosion and sedimentation, the model domain is remeshed at every time step.

The material advection parameter is treated independently of the mesh using pre-computed level-set functions that define the limit between each material phase (sediment, basement crustal rocks, mantle rocks), excluding artificial diffusion of material properties with time.

In the models, we assume that velocity, vz, in the rock column can be interpolated linearly between each petrologic interface. Beneath the lowest interface, velocity is constant and equal to the velocity of that interface. This ensures that the 1330°C isotherm imposed at the base of the model is not tight to rock uplift and allows for thermal relaxation to occur. Similarly, to enable effects of rock uplift or sedimentation, the 20°C isotherm is imposed at the surface of the Earth, but velocity at the surface is equal to that of the shallowest rock interface. Initial conditions are obtained by solving the heat diffusion equation (A2) at steady state using defined material properties:

(A2) This avoids artificial thermal re-equilibration, which would relate to ill-defined initial geothermal gradients that would not be consistent with the material properties and particularly heat production distribution.


Gérald Oster
email: oster@loria.fr

Hala Skaf-Molli

Pascal Molli
email: molli@loria.fr

Hala Naja-Jazzar

SUPPORTING COLLABORATIVE WRITING OF XML DOCUMENTS

Keywords: CSCW, Collaborative Writing, XML, Change Control

Data management is a key issue in cooperative systems. Anyone who uses more than one computer or collaborates with other people is aware of the problems posed by having multiple copies of shared documents. Most existing synchronization tools are specific to a particular type of shared data i.e. text files, calendars, XML files. Therefore, user should use several tools to maintain their different copies up-to-date. This is not an easy task. To address this issue, we defined a generic synchronization framework based on the operational transformation approach. This framework allows to synchronise text files, calendars, XML files by using the same tool. The main objective of this paper is to present this framework and how it is used to support cooperative writing of XML document. An implementation is illustrated through the revision control system called So6, which is a part of a distributed collaborative technology called LibreSource.

INTRODUCTION

Cooperative writing is becoming increasingly common; often compulsory in academic and corporate work. Even the World Wide Web or simply the Web becomes a global read-write information space where multiple authors are interacting, in contrast of the traditional model of one author publishing to many readers. People involved in cooperative writing can work across space, time and organizational boundaries with links strengthened by webs of communication technologies. In spite of this need for collaboration, it is surprising to see how poorly computer systems support group activities. Very often, people just send the shared document by mail and use a turn taking strategy to avoid conflicting updates. This is a serious bottleneck for productive work since people cannot work in parallel. A good cooperative editor should allow anyone1 to write any shared data at any time. The existing popular alternatives to the mail approach are Wikis and tools such as CVS/Subversion.

Wiki is a kind of cooperative writing environment.

It allows anyone to write at any time not any type of data, but just a Wiki page. A special markup language that offers a simplified alternative to HTML is used to write wiki pages. In case of concurrent modification, Wikis apply the last writer wins rule. Consequently, modifications done by some users may not appear in the last visible page. This is a kind of lost updates.

Our requirements to improve a cooperative editor should be refined as: a good cooperative editor should allow anyone to write any shared data at any time without lost updates.

The existing tools such as CVS [START_REF] Berliner | CVS II: Parallelizing Software Development[END_REF]) avoid lost updates. However, CVS was originally designed to support cooperative software development. It considers only text files containing code sources such as C files, JAVA files for merging. In this context, when conflicting changes are performed, conflicts appear inside merged files. A special syntax is used to clearly help the programmers to locate the problem. Thus, CVS allows anyone to write any text files at any time without lost updates.

We want to build a cooperative editor that allows anyone to write any kind of data, not only text files, but also XML files, CAD files, calendar files at any time without lost updates. A generic synchronizer that enables to merge any data type without lost update is required. We propose to build a generic and a safe synchronisation framework. This framework allows to synchronise text files, calendars, XML files by using the same tool while ensuring that conflict resolution will not introduce lost updates.

In previous work, we described how we use the operational transformation approach (OT) as a theoretical foundation to build such a generic and safe synchronizer [START_REF] Molli | Using the Transformational Approach to Build a Safe and Generic Data Synchronizer[END_REF]. We defined also the specific transformation functions to synchronise linear structure such as text files.

This paper will focus on the transformation functions for XML data and their implementation in an open source collaborative technology called Libre-Source. Our final objective is to build a library for blocks of text, strings, trees, graphs. Anyone can use these functions, add new functions or modify exiting ones according to their needs. The paper is structured as follows. The next section will introduce the operational transformation approach which serves as a theoretical foundation for our generic synchronisation framework called So6. The section 3 will present the architecture and the algorithms used in So6. The Section 4 will define the XML transformation functions and will demonstrate the use of these functions through an example. The section 5 will discuss related work. The last section will conclude and point some future work.

BACKGROUND

This section describes the Operational transformation approach (OT) that is the theoretical foundation of the generic and safe synchroniser So6. OT [START_REF] Ellis | Concurrency Control in Groupware Systems[END_REF] is an optimistic replication model used in real-time group editors domain. OT considers n sites, each site owns a copy of shared data. When a site performs an update, it generates a corresponding operation, which is first executed locally then broadcasted to other sites. Every operation is processed in four steps: (a) generated on one site, (b) broadcasted to other sites, (c) received by other sites, (d) executed on other sites.

The execution context of a received operation op i may be different from its generation context. In this case, the integration of op i by other sites may lead to inconsistencies between replicas.

For instance, we consider two sites site 1 and site 2 working on a shared data of type string of characters initially equal to the string e f ect. We consider that a string of characters can be modified with the operation ins(p, c) for inserting a character c at posi-tion p in the string. We assume the position of the first character in a string is 0. user 1 and user 2 generate and execute two concurrent operations respectively op 1 = ins(2, f ) and op 2 = ins(5, s). When op 1 is received and executed on site 2 , it produces the expected string "effects". But, when op 2 is received on site 1 , since it does not take into account that op 1 has been executed before it, its execution leads to the state "effecst". Finally, the copies of site 1 and site 2 do not converge.

In the operational transformation (OT) approach, before being executed, received operations are transformed regarding concurrent operations that were already executed on the local copy. This transformation is performed by calling transformation functions.

Definition A transformation function T takes two concurrent operations. These two operations namely op 1 and op 2 , must be defined on a same state S. The function computes a new operation op ′ 1 equivalent to op 1 -i.e. has the same effects -but defined on the state S ′ = S ⊙ op 2 . S ′ is the state resulting from the execution of op 2 on state S.

Using OT approach, our previous example is now executed as follows. When op 2 is received on site 1 , op 2 needs to be transformed regarding op 1 . The integration algorithm calls the transformation function

T (op 2 = ins(5, s), op1 = ins(2, f )) = ins(6, s) = op ′ 2 .
The insertion position of op 2 is incremented since op 1 has inserted an f before s in state e f ect. After the execution of op ′ 2 , the state of site 1 becomes e f f ects. On the contrary, when op 1 is received on site 2 , the transformation does not modify op 1 's parameters since f is inserted before s. Thus, op 1 is executed as-is and the state of site 2 is e f f ects. On our scenario, OT approach has ensured that both copies converge to the same value.

The OT approach distinguishes two main components. An integration algorithm. This algorithm is in charge of reception, diffusion and execution of operations. When necessary, it calls transformation functions. This algorithm does not depend on type of replicated data. A set of transformation functions. These functions can merge concurrent modifications in serializing two concurrent operations. These functions are specific to a particular type of replicated data such as string of characters, XML documents, calendars or file system.

The main criterion in OT approach is Convergence.

Convergence As every optimistic replication algorithms, OT approach tries to ensure eventual consistency i.e. when no updates occurs for a long period of time, eventually all updates will propagate through the system and all the copies will converge towards a same value. In other words, when the system is idle (no operations in pipes), all copies are identical.

To ensure this criterion, it has been proved [START_REF] Suleiman | Concurrent Operations in a Distributed and Mobile Collaborative Environment[END_REF] that the underlying transformation functions must satisfy two properties:

Definition The T P 1 property defines a state equivalence. The state generated by the execution of op 1 followed by T (op 2 , op 1 ) must be the same as the state generated by the execution of op 2 followed by

T (op 1 , op 2 ): op 1 •T (op 2 , op 1 ) ≡ op 2 •T (op 1 , op 2 )
Definition The T P 2 property ensures that the transformation of an operation regarding a sequence of concurrent operations does not depend on the order in which operations of this sequence were transformed:

T (op 3 , op 1 •T (op 2 , op 1 ))=T (op 3 , op 2 •T (op 1 , op 2 ))
Therefore, the operational transformation approach could be used to design a reconciliation framework able to reconciliate divergent copies of any type of data. In order to build such a framework, the following task have to be completed. First, an integration algorithm must be chosen ; regarding this algorithm, T P 2 property may be required on underlying transformation functions. Second, operations which could be performed on shared data types must be defined. Finally, the required transformation functions for all combination of operations have to be provided. In the next sections, we are going to describe our framework.

THE SO6 FRAMEWORK

So6 framework is based on SOCT4 integration algorithm [START_REF] Vidot | Copies Convergence in a Distributed Real-Time Collaborative Environment[END_REF]. Originally, SOCT4 has been designed for real-time group editors, we adapted it for asynchronous interaction [START_REF] Molli | Using the Transformational Approach to Build a Safe and Generic Data Synchronizer[END_REF]. SOCT4 integration algorithm requires only T P 1 property on transformation functions. It is based on a continuous global order of operations. Shared data are replicated on different sites (workspaces). Each operation generated in a local site is sent with a unique global timestamp to other sites. An operation from a site with a given timestamp can be sent to other sites only if all its preceding operations based on the timestamp order have been received and executed. By this way, SOCT4 ensures that concurrent operations will not be transformed following different transformation paths. This leverages the need for transfor-mation functions to satisfy T P 2 property. Moreover, this mechanism looks like the Copy-Modify-Merge paradigm which is widely used in version control management systems such as CVS. Regarding this paradigm, a user can publish her modifications only if she had read all previously published modifications.

The So6 framework has two main components: a central timestamper also called So6 queues, and So6 workspaces which are connected to a timestamper.

So6 Queue

A So6 queue Q is a timestamper that stores a sequence of operations. An operation is timed when a user sends it to the queue. A queue maintains a timestamp lastTicket equals to the last delivered timestamp. When a user creates a queue, the timestamp lastTicket is initialized to zero and the sequence of operations is empty.

The publish procedure assigns a new timestamp to the operation op and stores it in Q.

int publish (Operation op) { lastTicket ++ Q[ lastTicket ] = op return lastTicket }

So6 Workspace

Each user owns a So6 workspace in which a user can work insulated. The workspace stores all the documents shared by the user. This workspace is generally connected to a So6 queue. When a user modifies a document, she generates corresponding operations.

Workspace has the following data structure:

A timestamp siteTicket. It memorises the timestamp of the last operation published to or retrieved from the So6 queue.

Two states currentState and re f erenceState. They are used to compute the sequence of operations that have been made locally. currentState is the state on which the user works. re f erenceState is the state resulting from the execution of all the operations integrated by the site.

A sequence of operations Hg. It stores all the operations integrated by the site. This sequence contains all operations published by the site, and those retrieved from the timestamper. The operations are ordered according to their timestamps. If the sequence of the operations Hg are executed on an empty state, then it always computes the state re f erenceState.

Inside a workspace, the following procedures are defined:

A Commit procedure. During this procedure, the system detects local operations generated since last commit. Then, it sends each operation to the So6 queue in order to be timed and stored. The update procedure calls two other subprocedures computeDifference and merge. The first one uses a differentiation algorithm to compute the sequence of operations that have been executed on the state state1 to obtain the state state2. For instance, in the case of an XML document, any XML differentiation algorithm can be used. For our prototype, we used XyDiff [START_REF] Cobena | Detecting changes in XML documents[END_REF]. The merge procedure integrates two sequences of concurrent operations using the set of T transformation functions. This procedure relies on the SOCT4 integration mechanism. Each remote[i] operation must be transformed to an operation opr regarding the whole sequence of local operations. Then, this operation can be executed on the current state currentState of the site. The original operation remote[i] is executed on the state re f erenceState.

XML DOCUMENTS SUPPORT

In the previous section, we presented our generic framework for reconciliating divergent copies of data. In this section, we describe how this framework could be instantiated to support collaboration over XML documents. In [START_REF] Molli | Using the Transformational Approach to Build a Safe and Generic Data Synchronizer[END_REF], we instantiated our framework to reconciliate a file system and also text documents.

As usual, we model the XML document as a nodelabelled ordered tree, and each XML element, be it leaf or non-leaf, corresponds to a node of that tree. Since we suppose the tree is ordered, the children of every node are ordered i.e. there is a first child, a second child, etc. Therefore, each node is uniquely identified by its path. This path is defined as the sequence of child number starting from the root. The path of the root node is denoted []. For instance, the XML document presented in Figure 1 is mapped to the tree depicted by Figure 2. And, the path [0, 1, 0] leads to the leaf labelled with the value The abstract is.... We assume that the tree representation of an XML document can be changed by the following two operations: -, () *+ sect1

<?xml version="1.0" encoding="UTF-8"?> < article > <sect1> < title >Abstract</ title > <para>The abstract is ... </para> </sect1> <sect1> < title >Introduction</ title > <para>Optimistic replication ... </para> </sect1> </ article >
[0,0]

x x q q q q q q q q q q q [0,1] /.

-, () *+ sect1

[1,0] [1,1] @ @ /.
-, () *+ title [0,0,0] /.

-, () *+ para [0,1,0] /.

-, () *+ title [1,0,0] /.

-, () *+ para • addNode(parent, n, val) adds a new node as a child of the node identified by the path parent. This node is added as nth child and its value -or label -is val. • delNode(parent, n) deletes the nth child of the node identified by the path parent.

We consider that performing a move operation on a node of the tree is equivalent to first delete this node from its old location, then add this node to its new location.

In order to work with paths of nodes, we define the following functions. The function length(p) returns the length of the path p, i.e. the number of nodes in this path. The predicate childO f (p 1 , p 2 ) is true if the node identified by the path p 1 is a descendant of the node identified by the path p 2 . The function getPos(p, n) returns the (n + 1)th value of the path p, i.e. getPos([3, 2, 1, 4], 2) = 1. The function incPos(p, n) computes a new path by incrementing the (n + 1)th value of the path p, i.e. incPos ([3, 2, 1, 4], 2) = [3, 2, 2, 4]. In the same manner, the function decPos(p, n) computes a new path by decrementing the (n + 1)th value of the path p, i.e. decPos ([3, 2, 1, 4], 2) = [3, 2, 0, 4]. Finally, we define the function codeIn f (val 1 , val 2 ) which allows to compare two values val 1 et val 2 . It is always possible to define such a function. For example, for text nodes, codeIn f () is defined on the lexicographical order between the values, i.e. codeIn f (Abstract, Introduction) = true.

As we explained in section 2, a transformation function computes the result of the integration of two concurrent operations. So, for one XML tree, we have to consider all possible combination of operations defined on that XML tree. Thus, we have to defined transformation functions for each couple of operations : (addNode(), addNode()), (delNode(), delNode()), (addNode(), delNode()) and (delNode(), addNode()). Due to space limitations, we are going to describe in details only the transformation function T (addNode(), addNode()).

Figure 4 indicates the complete definition of the transformation function T for two concur- This function transforms op 1 = addNode(p 1 , n 1 , v 1 ) regarding op 2 = addNode(p 2 , n 2 , v 2 ). The main idea of this function is to compare the insertion position of two concurrent addition of nodes in the XML tree. It has to consider the following cases :

T (addNode(p 1 , n 1 , v 1 ), addNode(p 2 , n 2 , v 2 ) = if ( p 1 = p 2 ) then if (n 1 < n 2 ) then addNode(p 1 , n 1 , v 1 ) elsif (n 2 < n 1 ) then addNode(p 1 , n 1 +1, v 1 ) elsif (codeIn f (v 1 , v 2 )) then addNode(p 1 , n 1 , v 1 ) elsif (codeIn f (v 2 , v 1 )) then addNode(p 1 , n 1 +1, v 1 ) else Id() endif elsif (childO f (p 1 ,p 2 )) then if (n 2 ≤ getPos(p 1 , length(p 2 ))) then addNode(incPos(p 1 ,length(p 2 )), n 1 , v 1 ) else addNode(p 1 , n 1 , v 1 ) endif else addNode(p 1 , n 1 , v 1 ) endif
• If the two additions operate on the same parent node, then T compares their insertion positions.

-If op 1 inserts a child at a position after the insertion position of op 2 then the insertion position of op 1 has to be shifted one position to right. Therefore, its insertion position is incremented. -If op 1 inserts a child before the insertion position of op 2 , then the insertion position of op 1 remains the same. -If op 1 and op 2 try to insert at the same position, T must decide the serialisation order. In the above definition, the decision of T is based on the codeIn f () function, which compares the lexicographic value of nodes. If lexicographic values are equals, then op 1 and op 2 try to insert the same node at the same position, consequently, the function disables effect of op 1 by transforming it into an identity operation. Of course, this is an arbitrary choice,other solutions are possible such as the insertion of both nodes.

• If the two additions operate on different parent nodes, then the previous execution of op 2 might move the parent node of op 1 . This situation occurs when the parent node of op 1 is a child of the parent node of op 2 .

To illustrate, consider the initial XML tree given in the figure 4 and two concurrent operations op 2 = addNode([], 1, X) and op 1 =

[0]

| | y y y y y y The execution of the operation op 2 moves the parent node on which the operation op 1 has to be executed. In other words, the transformation of the operation op 1 regarding of the operation op 2 must give the operation

[1] 4 4 i i i i i i [2] @ @ | | y y y y y y 4 4 i i i i i i [3,0] Figure 4: Initial tree [0] | | z z z z z z z [1] [2] h h h 4 4 h h h [3] @ @ Ð Ð Ñ Ñ Ñ Ñ Ñ Ñ Ñ 2
op ′ 1 = addNode([2 + 1], 1,Y ).
To compute this operation, T has to compare and may update the position in the path of op 1 . This is achieved by using getPos() and incPos() functions. The resulting tree is depicted in figure 5.

In the same way, we wrote transformation functions for couples of operations delNode -delNode, addNode -delNode. In these cases, there is a critical point to consider: what to do when an operation removes a subtree while another concurrent one appends a node to this subtree? This is clearly a case of conflict. The solution we choose is to remove the subtree even if in this case the concurrent changes performed on this subtree are lost. This solution allows to ensure data convergence. To avoid this lost update, we assume that the system should provide an undo feature in order to restore lost changes if the convergent state is not suitable for users. This undo feature is subject to many research efforts [START_REF] Sun | Undo as Concurrent Inverse in Group Editors[END_REF].

Writing correct transformation functions regarding the T P 1 property is not an easy task. The safety of the operational transformation approach relies on the correctness of transformation functions. If transformation functions do not verify T P 1 then the integration algorithm cannot ensure convergence of copies. Proving T P 1 property is error prone, time consuming and part of an iterative process. It is nearly impossible to do this by hand. In order to achieve this task, we used our VOTE environment [START_REF] Imine | Formal Design and Verification of Operational Transformation Algorithms for Copies Convergence[END_REF] which is based on an automatic theorem prover. The input of this environment is exactly the definition of the transformation functions given in this paper. Describing our environment for verifying correctness of transformation functions is out of the scope of this pa-per, a more detailed description is available in [START_REF] Imine | Formal Design and Verification of Operational Transformation Algorithms for Copies Convergence[END_REF][START_REF] Imine | Proving Correctness of Transformation Functions in Real-Time Groupware[END_REF]. In the following, we present a scenario illustrating how the So6 framework is working. It considers two users who are cooperating in the writing of an XML document. They are working in their own workspace respectively called site 1 and site 2 . Each workspace contains a copy of the shared XML document. At the beginning, both copies are identical.

The different steps of this scenario are summarized as follows:

site 1 site 2 op 1 op 3 op 2 commit (send op 3 ) update (compute op ′ 3 , op ′ 1 , op ′ 2 ) commit (send op ′ 1 , op ′ 2 ) update (exec. op ′ 1 , op ′ 2 )
Users work concurrently to edit the document. The first user produces operations op 1 and op 2 while the second produces the operation op 3 . The states of the copies of the document including these modifications are depicted by the Figure 6. After that, the second user commits their modifications i.e. the operation op 3 is sent to the timestamper. Later, the first user updates their workspace in order to integrate modifications published by the second user. During the update, the transformed operations op ′ 3 , op ′ 1 , op ′ 2 are calculated. At this step, only the operation op ′ 3 is locally executed. Then, the first user commits his modifications. During this step, op ′ 1 and op ′ 2 are sent to the timestamper. When the second user calls the update procedure op ′ 1 and op ′ 2 are executed as-is on the local copy of the workspace site 2 (remember that this user does not perform new operation). At the end of the execution, both copies of the document converge towards a unique value.

RELATED WORK

Configuration Management (CM) tools [START_REF] Berliner | CVS II: Parallelizing Software Development[END_REF] are widely used for asynchronous collaborative editing. Users work in parallel, produce data divergence and reconciliate later using the Copy-Modify-Merge paradigm. Reconciliation is performed by tight cooperation between version manager and merge tools. When a reconciliation is required, i.e. usually when a user updates their workspace, version manager provides required versions to merge tools [START_REF] Munson | A flexible object merging framework[END_REF]. Merge is performed locally in the workspace of the user. Merge tools extract from different versions concurrent logs of operations using differentiation algorithms [START_REF] Chawathe | Meaningful change detection in structured data[END_REF]. These differentiation algorithms are specific to data types. Finally, concurrent operations are merged using ad-hoc algorithms specific to data types. An XML merge tool such as DeltaXML [START_REF] Fontaine | Merging XML files: A new approach providing intelligent merge of XML data sets[END_REF] or XyDiff [START_REF] Cobena | Detecting changes in XML documents[END_REF] can be used in conjunction with CM tools for supporting collaboration on XML data. However, in this approach, several merge tools are used: one for file systems, another one fro text files and another one fro XML files. Each merge tool has its own merge algorithm. They might not be consistent together if they do not apply the same strategy. For example, in CVS, the merge tool used for text files relies allows compensation contrary to the merge tool used at the file system level. Thus, whatever are the changes performed on a text file, they will always be merged into the new file version ; even conflicting changes are put in the text file -they are delimited with special markups -. After the merging, a user can compensate what has been performed by the merge tool by editing the content of the text file. Whereas the merge tool used at the file system level does not apply this principle, in the case it detects a conflict, the reconciliation process is stopped and the user is asked to solve the conflict. The operational transformation (OT) model is more general, more uniform and safer than the model used in CM tools. In the OT approach, the merge algorithm is shared by all transformation functions. It ensures convergence if underlying transformation functions ensure the T P 1 property. By this way, we can extend the reconciliation engine by adding new transformation functions without violating consistency. Some propositions have been done in the OT model to work with XML data. [START_REF] Davis | Generalizing Operational Transformation to the Standard General Markup Language[END_REF] defined some transformation functions for SGML. These functions present some similarities with our transformations for XML. However, Davis and al functions do not verify the T P 1 property. Thus, using these transformation functions in our framework will not ensure convergence of copies of shared data.

In [START_REF] Shen | Flexible Merging for Asynchronous Collaborative Systems[END_REF], Shen et al. proposed a framework similar to our So6 framework. The main difference is when a conflict occurs between two concurrent operations, the operation coming from the repository is cancelled, and the local operation is preserved. Firstly, this choice is not acceptable since cancelling an operation means losing some previously published work. Secondly, the authors do not provide any information concerning the editing of a tree structure such as an XML document. In parallel to our work, Ignat et al. [START_REF] Ignat | Supporting Customised Collaboration over Shared Document Repositories[END_REF] extended the Shen et al.'s approach to a tree structured document. The main idea is to distribute the log of operations through the tree. Thus, each node is associated with a log containing the operations performed on its content, insertion and deletion of child nodes. Using this model, they are able to use transformation functions defined for a linear structure such as the one proposed for a string of characters by Ressel et al. [START_REF] Ressel | An Integrating, Transformation-Oriented Approach to Concurrency Control and Undo in Group Editors[END_REF]. Their proposition constitues an alternative to our approach.

IceCube [START_REF] Kermarrec | The IceCube Approach to the Reconciliation of Divergent Replicas[END_REF]) is a generic approach for reconciliating divergent copies of documents. It handles reconciliation as a constraints optimisation problem: the one of executing an optimal combination of concurrent changes. IceCube uses semantic constraints between operations that the reconciliation algorithm has to preserve. Basically, Ice-Cube explores all possible combinations of concurrent operations and reject all combinations violating constraints. This approach is interesting because, Ice-Cube is looking for the combinations of concurrent operations that minimize conflicts of reconciliation. Maybe, on this point, the operational transformation approach will not find the optimal reconciliation. On the other hand, IceCube has some intrinsic drawbacks: Combinatorial explosion can occur during the first stage of reconciliation.

The Harmony project [START_REF] Foster | Exploiting Schemas in Data Synchronization[END_REF]) is a generic framework for reconciliating divergent copies. In this framework, the reconciliation process exploits schema of the structures being synchronized to achieve a better accuracy. This framework relies on a state-based approach which means three copies of the document -the two divergent copies and the com-mon ancestor document -are required for reconciliation. As most state-based synchronizer, the goal of the reconciliation engine is to make divergent copies more similar. In other words, convergence of copies is not achieved in all cases, but changes performed by a user will never be backed up. Indeed, in case conflicting changes are detected between two copies, the conflicts are marked but the copies remain divergent. On the contrary, our framework will always ensure convergence of copies. Simply, in a case of conflicting changes, these changes will be transformed to be integrated as conflicting changes in the copies. This allows every participant to solve later the conflict. We think sharing conflicts is useful, because sometimes the user who gets the conflict is not the user who has the knowledge to solve it.

CONCLUSION

We have presented the SO6 framework for supporting cooperative writing over documents. This framework relies on a theoretical model called operational transformation approach. Our framework is generic in the sense it could be instantiated to manage multiple types of document. In order to illustrate these feature, we explained how to enable cooperative writing of XML documents. This framework and the presented transformation functions are integrated in the SO6 revision management tool included in the LibreSource (http://www.libresource.org/) collaborative platform. This tool is able to reconciliate copies of a file system containing text documents and XML documents.

If our framework ensures convergence, the convergence state may violate the DTD. For example suppose two users add concurrently a "title" element in an XML document. From the point of view of an ordered tree, two title nodes can appear under the root. However, from the point of view of the DTD, only one title is allowed. Finally, the SO6 framework is able to compute a convergence state, but this state may violate the DTD. This is clearly an open issue for the So6 framework and for XML merge tools.

  merge(Operation[] remotes, Operation [] locals ) { for ( int i=0; i<remotes.length ; i++) { Operation opr = remotes[ i ] int ticket = remotes[ i ]. ticket for ( int j=0; j<locals . length ; j++) { Operation opl = locals [ j ] locals [ j ] = T(opl , opr) opr = T(opr, opl } execute (remotes[ i ], referenceState ) Hg[ ticket ] = remotes[ i ] execute (opr , currentState ) siteTicket = ticket } }

Figure 1 :

 1 Figure 1: An example of XML document.

Figure 2 :

 2 Figure 2: Mapping document of Fig. ?? to an ordered tree

Figure 3 :

 3 Figure 3: Transformation function for addNode-addNode

Figure 5 :

 5 Figure 5: Concurrent additions on different parents

Figure 6 :

 6 Figure 6: Collaborative Editing Scenario

Any user providing that he has the right permissions to do so.