Véronique Gardien
email: vgardien@univ-lyon1.fr

Jean-Emmanuel Martelat

Philippe-Hervé Leloup

Gweltaz Mahéo

Benoit Bevillard

Pascal Allemand

Patrick Monié

Jean-Louis Paquette

Anne-Sabine Grosjean

Michel Faure

Philippe-Herve Leloup

Grosjean

Cyril Chelle-Michou

Clémentine Fellah

Fast exhumation rate during late orogenic extension: The new timing of the Pilat detachment fault (French Massif Central, Variscan belt)

Keywords: Variscan belt, Pilat shear zone, Velay, lithospheric dripping 40 41 1.Introduction 42

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

12

reactor of Pavia (Italia) together with several monitors of Taylor Creek sanidine at 28.34 ± 268 0.28 Ma [START_REF] Renne | Intercalibration of standards, absolute ages and 874 uncertainties in Ar-40/Ar-39 dating[END_REF]. After irradiation, the samples were loaded in a CO2 laser 269 extraction-purification line connected to a multi-collector mass spectrometer for argon 270 analyses (Argus VI by ThermoFisher at the Montpellier University, France) equipped with 271 four Faraday cups and one CDD multiplier for 36 Ar. Argon isotope intensities were acquired 272 simultaneously on the five detectors in ten runs. Air aliquots from an automated pipette 273 system were analyzed each sample to monitor mass discrimination and detector bias. heating degassing of the micas was done by regularly incrementing the laser power to 275 recover the distribution of argon isotopes in the mineral and to reconstruct its age spectrum.

276

For each spectrum, two to five mica grains were simultaneously degassed depending on 277 their size. Ages reported on the spectra have been obtained after correction with blanks, 278 mass discrimination, radioactive decay of 37 Ar and 39 Ar, irradiation-induced mass 279 interferences and atmospheric contamination. They are reported with two sigma 280 uncertainty and were evaluated using a 40 Ar/ 36 Ar value of atmospheric argon of 298.6 (Lee et 281 al., 2006) and the decay constants of [START_REF] Steiger | Subcomissionon Geochronology-Convetion on use of decay constantrs in 897 geochronology and cosmochronology[END_REF]. Different decay constants 282 have been more recently proposed [START_REF] Min | A test for systematic errors in 40Ar/ 39Ar 862 geochronology through comparison with U/Pb analysis of a 1.1-Ga rhyolite[END_REF][START_REF] Renne | Joint determination of K-40 decay constants and Ar-40*/K-40 for the Fish Canyon sanidine 877 standard, and improved accuracy for Ar-40/Ar-39 geochronology[END_REF] but until now there 283 is no full consensus for their use in 40 Ar/ 39 Ar dating [START_REF] Fleck | 760 Characterization of the rhyolite of Bodie Hills and Ar-40/Ar-39 intercalibration with Ar mineral 761 standards[END_REF]Schaen et al., 2020).

284

The raw data obtained during the acquisition are processed under ArArCalc [START_REF] Koppers | ArArCALC-sofware for 40 AR/ 39 Ar age calculation[END_REF] 285 to calculate the ages of the age spectra and isochron plots. A summary of argon results is 286 given in table 1. Detailed analytical data are given in the Appendix 3 (Supplementary data).

287

The micas collected for dating the rocks were analyzed with a SEM coupled to an EDX at the 288 ENS-Lyon. The chemical composition in mass percentages of biotite and muscovite are 289 comparable to those found in granites. The results of the analyses see Appendix 4 290 (Supplementary data) reveal a homogeneous chemical composition from the core to the 13 edge. The Al2O3 contents vary from 35 to 38%, the K2O varies from 10 to 11% and their Si 292 contents are constant (~6.15). The analyzed biotite grains (PL06 and PL43) have an Al2O3 293 contents which vary from 20 to 23%. Biotite from sample PL43 contain 28% of FeO while 294 biotite from PL06 is poorer in FeO (19%) and richer in MgO (~8%), alkalis (K2O) vary from 8.5 295 to 11%. Their Si / Al ratios are homogeneous in the range of 1.6 to 1.8. The maps of element 296 distributions presented in Appendix 4 (Supplementary data) confirmed that the dated biotite 297 and muscovite are not zoned and do not present traces of alteration. The volcanic layer (sample PL 90) provided translucent homogeneous needle shape 309 zircons grains with high length to width ratios suggesting rapid growth (Fig. 5). Euhedral 310 grains show oscillatory euhedral zoning consistent with a magmatic origin (Fig. 5). Some 311 crystals display rounded gap growth corresponding to former gas bubble footprints (Zr40, 312 Zr48, and Fig. 5). No inherited relict cores have been identified. Such morphology is 313 consistent with an igneous origin of the zircons. Most points are concordant and yield a 314 lower intercept date of 299.3±1.3 Ma.

14

The zircon population from the lithic-rich ignimbrite (PL92) is homogeneous, 316 characterized by translucent crystals with potentially corroded and inherited cores (Zr14, Fig. It should be noted that all the studied micas provide well defined 40 Ar/ 39 Ar plateau ages 325 (Table 1 and Fig. 6) for 95 to 100% of the 39 Ar released, except for biotite PL43 (Fig. 6 B andC) 326 for which the plateau age was calculated over 60% of the argon release. The intercept ages 327 in the ( 36 Ar/ 40 Ar) versus ( 40 Ar/ 39 Ar) correlation plot is similar to the plateau ages with 328 atmospheric 40 Ar/ 36 Ar initial ratios. All experiments show Ca-derived 37 Ar close to the 329 detection limit and very low 38 ArCl/ 39 ArK values. The biotite grains selected from the syn-330 kinematic Gouffre d'Enfer granite (PL06) are elongated grains in both foliation planes and 331 shear bands. They yield a plateau age of 303.0 ± 1.6 Ma (Fig. 6A). The white micas selected 332 from the pegmatites (PL 49 and PL51) moderately affected by the shear deformation 333 provided plateau ages of 301.5 ± 1.6 Ma and 302.9 ± 1.6 Ma, respectively (Fig. 6E andF).

334

Muscovite and biotite grains from the post kinematic leucogranite dyke (PL 43) display 335 40 Ar/ 39 Ar ages of 298.5 ± 1.5 Ma and 302.9 ± 1.5 Ma respectively (Fig. 6B andC). The 336 elongated white micas on the brittle normal fault plane (PL48) give an age of 303.9± 1.6 Ma 337 (Fig. 6D). Finally, the muscovite grains from the micaschist from the northern part of the 338 Pilat series (PL94) yielded a much older age of 332.8± 1.7 Ma (Fig. 6G). [START_REF] Caen-Vachette | Age cambrien des rhyolites transformées en leptynites dans la série 714 métamorphique du Pilat (Massif Central français[END_REF] on a leptynite from the Pilat Unit. The youngest population may be 348 interpreted as the emplacement age of the granite. However, assuming that the source of 349 Gouffre d'Enfer granite contains zircons of 530-460 Ma, the partial melting of this rock 350 would had probably dissolved some zircons, while other grains included in minerals that are 351 not involved in the fusion reaction would remain intact. The CL images (Fig. 5) show a very 352 dark border around the old zircons, this border too small to be measured can however be 353 synchronous with the youngest zircon population thus we consider that the oldest zircons 354 are inherited from the source of the granite. The 40Ar/39Ar dating of synkinematic biotite 355 for the same rock yields an age of 303.0±1.6 Ma (Table 2) that can receive two different 356 interpretations. It could correspond to the retention of radiogenic argon at temperature of 357 320-350 °C during the cooling of the granite at relatively fast rates (Harrison et al., 1985). 358 Alternatively, this age could be considered as a crystallization age in agreement with many 359 studies showing that mica ages recorded by deformed rocks are mostly under the control of 360 recrystallization and dissolution/precipitation effects, with a minor influence of volume 361 diffusion processes (Chopin and [START_REF] Maluski | Unconvincing evidence against the blocking temperature concept, a 727 reply[END_REF]Di Vincenzo et al., 2004;[START_REF] Augier | Exhumation, doming and slab 674 retreat in the Betic Cordillera (SE Spain): In situ Ar40/Ar-39 ages and P-T-d-t paths for the 675 Nevado_Filabride complex[END_REF] 362 [START_REF] Villa | Diffusion of Ar in K-feldspar: Present and absent[END_REF][START_REF] Bosse | Petrochronology and hydrochronology of tectono-metamorphic events[END_REF]. However, because the syn-kinematic granite has emplaced in hot surrounding rocks at temperatures above 700°C, it is likely that the meaning 364 of the biotite age at 303 Ma lies between the two interpretations. The closure temperature 365 in the zircon is considered as ~ 900°C [START_REF] Cherniak | Pb diffusion in zircon[END_REF], much higher than those 366 of sialic magmas crystallization. We will thus adopt the peak metamorphic temperature at [START_REF] Gardien | Garnet and Staurolite as relictual phases within the LP facies series of the Pilat unit 768 (French Massif Central) -a record of a polyphase tectonometamorphic reequilibration[END_REF]. The granite and the surrounding micaschists were exhumed to 377 the surface before or slightly before the opening of the St. Etienne basin as they are found as 378 blocks in the basal conglomerates of the St Etienne sedimentary basin. Assuming a depth of 379 18-15 km for the granitic magma emplacement and its final crystallization at 5-7 km in the 380 upper crust as indicated by the presence of retrograde andalusite and pyrophyllite in the 381 micaschists, (stage 3 in the P-T evolution of the Fig 5 in [START_REF] Gardien | Garnet and Staurolite as relictual phases within the LP facies series of the Pilat unit 768 (French Massif Central) -a record of a polyphase tectonometamorphic reequilibration[END_REF] this very rapid cooling 382 is equal to an exhumation rate of ~6 mm/yr. Such result is not incongruous insofar rapid 383 exhumation of deep crustal levels in mountain systems is generally related to extension after 384 thermal softening of a thickened continental lithosphere (Johnston et al., 2000). Pilat series were buried at a depth of 22-25 km and underwent a prograde metamorphism of 464 medium P and T conditions (8-9 kbar, 650°C; [START_REF] Gardien | Garnet and Staurolite as relictual phases within the LP facies series of the Pilat unit 768 (French Massif Central) -a record of a polyphase tectonometamorphic reequilibration[END_REF]. This event occurred before 335 465 Ma in the Pilat Unit (this study) and between 340 Ma and 360 Ma in the Lyonnais series 466 [START_REF] Costa | 40Ar-39Ar chronology of Variscan tectono-732 metamorphic events in an exhumed crustal nappe: The Monts du Lyonnais complex (Massif 733 Central, France)[END_REF] and corresponds to the main nappe stacking event in the eastern part of 467 the French Massif Central. Subsequent evolution under low pressure and high temperature 468 conditions (5-6 kbar, 700-750°C) implies a high thermal gradient of 50°C/km (Gardien et al.,469 1990; [START_REF] Gardien | Garnet and Staurolite as relictual phases within the LP facies series of the Pilat unit 768 (French Massif Central) -a record of a polyphase tectonometamorphic reequilibration[END_REF] which caused the partial melting of the lower part of the series and the 470 formation of migmatites mainly located to the south and below the Pilat series (Fig. 1 and2).

Relationship between the PSZ and the St Etienne Basin

471

This partially melted zone gradually becomes toward the south the Velay Dome which 472 consists of migmatites and granites themselves formed at the expense of metapelites and 473 orthogneiss [START_REF] Downes | Sr, Nd and Pb isotopic evidence for 740 the lower crustal origin of Hercynian granodiorites and monzogranites[END_REF][START_REF] Ledru | 818 The Velay dome 2422 (French Massif Central): melt generation and granite emplacement 819 during orogenic evolution[END_REF][START_REF] Barbey | Multiphase melting, magma emplacement and 677 P-T time path in late-collisional context: The Velay example (Massif Central France)[END_REF] during a high 474 temperature ~ 850 °C and low pressure 4-5 kbar metamorphic stage [START_REF] Montel | Thermobarometry and granite genesis: 859 the Hercynian low-P, high T Velay anatectic dome (French Massif Central)[END_REF] 475 [START_REF] Barbey | Cordierite growth 680 textures and conditions of genesis and emplacement of crustal granitic magmas: The Velay 681 granite complex (Massif Central, France)[END_REF][START_REF] Barbey | Multiphase melting, magma emplacement and 677 P-T time path in late-collisional context: The Velay example (Massif Central France)[END_REF]. The crystallization of these magmas is dated between 310 and 476 300 Ma [START_REF] Barbey | Multiphase melting, magma emplacement and 677 P-T time path in late-collisional context: The Velay example (Massif Central France)[END_REF][START_REF] Chelle-Michou | Pre-Cadomian to late Variscan odyssey of the 721[END_REF].

477

The peraluminous Gouffre d'Enfer granite (sample PL06) was produced by the 478 melting of pelitic protoliths [START_REF] Vitel | Le granite du Gouffre d'Enfer (Massif Central français) Pétrologie d'un marqueur 911 tectonique Varsique[END_REF] and is thought to represent an extension of the 479 Velay dome [START_REF] Gay | Age radiométrique des granites allongés et 786 en feuillets minces syntectoniques dans les Monts du Lyonnais (Massif Central français). 787[END_REF][START_REF] Vitel | Le granite du Gouffre d'Enfer (Massif Central français) Pétrologie d'un marqueur 911 tectonique Varsique[END_REF]. The 302 Ma age of this syn tectonic granite (U-Pb

Results

523

The results show that when a 2 km thick or wide layer of magma is intruded at 18 km depth 524 at a temperature of 750°C, the magma layer (footwall) crystallizes and cools in less than 500 525 ky when the crust is not thinned (Fig. 8A). A second case has been tested in which the crust 526 is thinned by pure shear. In this case too, the thermal anomaly produced by the magma is 527 relaxed in less than 500 ky (Fig. 8A). The modelling shows that in both cases (with or without 528 shearing and with or without exhumation) the extremely rapid cooling of a granitic sill is 529 achievable. However, the key point we can learn from the results is that because of the tightness of the isotherms the thermal field is dominated by the strain effect rather than by 531 the intrusion effect. Thus, the strain effect maintains the crust in hot thermal regime well tested [START_REF] Montel | Thermobarometry and granite genesis: 859 the Hercynian low-P, high T Velay anatectic dome (French Massif Central)[END_REF][START_REF] Gardien | Metamorphism during late 780 orogenic extension: insights from the French Variscan belt[END_REF][START_REF] Ledru | 818 The Velay dome 2422 (French Massif Central): melt generation and granite emplacement 819 during orogenic evolution[END_REF][START_REF] Laurent | Protacted, coeval crust and mantle melting during Variscan late orogenic 813 evolution: zircon U/Pb dating in the eastern French Massif Central[END_REF].

546

The mechanism classically invoked for such context is the removal of the orogenic root by 547 delamination or rollback [START_REF] Laurent | Protacted, coeval crust and mantle melting during Variscan late orogenic 813 evolution: zircon U/Pb dating in the eastern French Massif Central[END_REF], inducing a rapid rise of the asthenosphere 548 and a significant heating of the orogenic crust. Consequently, the magmatism is produced by [START_REF] Montel | Thermobarometry and granite genesis: 859 the Hercynian low-P, high T Velay anatectic dome (French Massif Central)[END_REF][START_REF] Ledru | The massif central : structure. Pre-Mesoz[END_REF]Bé Mézème et 568 al., 2005;[START_REF] Faure | The South Millevaches 754 Middle Carboniferous crustal melting and its place in the french Variscan Belt[END_REF][START_REF] Barbey | Multiphase melting, magma emplacement and 677 P-T time path in late-collisional context: The Velay example (Massif Central France)[END_REF], to the point of forming plutons like the 569 Tournon granite, the Margueride granite, the Civrieux granite, all dated between 335 and 570 320 Ma (Laurent et al., 2017 and ref therein). Hence, anatectic domes such as the Velay 571 dome could have developed earlier in the Variscan belt history, especially because extension 572 was already active since the Moscovian. Thus, as such dome appears during the late 573 Carboniferous (Gzhelian), removal of the lithospheric mantle remains, therefore, the most 574 plausible cause of the sudden Pilat/Velay uplift. The Velay a poly-diapir dome corresponds to 575 a multistage emplacement of granites superimposed on extensional structures (Laurent et 576 al., 2017]. During this process, the dome was shifted horizontally southward (Lagarde et al. 577 1994; [START_REF] Ledru | 818 The Velay dome 2422 (French Massif Central): melt generation and granite emplacement 819 during orogenic evolution[END_REF] carrying during its migration rafts of metamorphic units mainly 25 affected by northward normal fault [START_REF] Gardien | Découverte d'éclogites dans la synforme de Maclas : extension 774 de l'unité supérieure des gneiss à l'Est du Massif Central[END_REF]Gardien, 1993;Chelle-579 Michou et al., 2017). Thus, granites forming the dome intruded the main detachment fault 580 whose ~35 km amplitude (Fig 1A) [START_REF] Malavieille | Collapse of the thickened 834 Variscan crust in the french Massif central: Mont Pilât extensional shear zone and St Etienne 835 upper Carboniferous basin[END_REF] and 10 to 30° angle towards the 581 North can accommodate the rise of the dome from 20 km depth. regime reached during its evolution (Zwart, 1967;[START_REF] Letterrier | Aspects chimiques des interactions entre les magmas basiques et leur encaissant 824 pélitique dans le plutonisme[END_REF][START_REF] Cuney | Metallogenesis in the French part of the Variscan orogen. Part I: U preconcentrations in 736 pre-Variscan and Variscan formations: A comparison with Sn, W and Au[END_REF] 586 Bussien et al., 2008;[START_REF] Von Raumer | Durbachites-Vaugnerites -a 913 geodynamic marker in the central European Variscan orogen[END_REF], Laurent et al., 2017). However, among these 587 plutons very few have the characteristics of domes (i.e., concentric shape of foliations, 588 horizontal structures at the roof progressively tilted to the vertical at its margin, detachment 589 faults bordering the pluton and responsible for is exhumation). The Velay massif has a dome 590 feature [START_REF] Burg | Structures and way upcriteria in migmatites, with application to 708 the Velay dome (French Massif Central)[END_REF][START_REF] Lagarde | Deformation localization with laterally 803 expanding anatectic granites: Hercynian granites of the Velay, French Massif Central[END_REF][START_REF] Ledru | 818 The Velay dome 2422 (French Massif Central): melt generation and granite emplacement 819 during orogenic evolution[END_REF] reflecting 591 gravitational instabilities that develop at the base of the orogenic crust coeval to the late 592 extensional evolution of the belt (Van den Driesche and Brun, 1992;[START_REF] Gardien | Metamorphism during late 780 orogenic extension: insights from the French Variscan belt[END_REF] 593 [START_REF] Ledru | 818 The Velay dome 2422 (French Massif Central): melt generation and granite emplacement 819 during orogenic evolution[END_REF]. The mechanisms invoked for the development of this domes consistently 594 imply lithospheric tear [START_REF] Ledru | 818 The Velay dome 2422 (French Massif Central): melt generation and granite emplacement 819 during orogenic evolution[END_REF][START_REF] Laurent | Protacted, coeval crust and mantle melting during Variscan late orogenic 813 evolution: zircon U/Pb dating in the eastern French Massif Central[END_REF]. Whether it is slab break-off 595 or slab retreat remains an open question. Both mechanisms require that the lithosphere 596 shears horizontally or vertically in its thickness over a large distance. Moreover, the strong 597 coupling between the crust and the lithospheric mantle causing the tearing of the slab 598 affects a wide area in the overriding domain. For example, the tearing of the Indian 599 lithosphere is referred for the formation of MCC North of the Shyok Suture Zone (SSZ) over 600 more than 150 km in the South Karakorum and south Tibet [START_REF] Rolland | Tectono-metamorphic evolution of the 889 Karakorum Metamorphic complex (Dassu-Askole area, NE Pakistan): exhumation of 890 mid-crustal HT-MP gneisses in a convergent context[END_REF]. In the 601 punctual removal of the lithospheric mantle such as dripping.

603

The geochronological data and more precisely the argon ages provide arguments in 604 favour of this localized delamination of the mantle under the Velay. Indeed, the similarity of 605 the micas ages of samples coming from the footwall of the PSZ and from the PSZ itself can be 606 due to a reset of Ar ages even away from the deformation zone due to fluid ingress (Villa,607 2014) and metamorphic recrystallization. However, the absence of zonation and 608 retromorphosis on the dated micas grains (see appendix 2) does not argue in favour of 609 resetting the Ar-Ar system in connection with fluid circulation. An explanation for the 610 velocity and synchronism of exhumation on either side of the PSZ is that the lithospheric 611 rebound linked to the mantle dripping provoke the sudden upward of the whole system, 3.

623

The effect of sedimentation rate on the thermal state of the upper crust has been tested.

624

Two very small sedimentation rates of 0.005 mm/yr and 0.002 mm/yr, respectively, have been applied (Fig. 8B). The results show that sedimentation has a clear cooling effect on the 626 base of the basin and therefore on the roof of the footwall. Indeed, the base of the basin is samples together with the radio-chronological available ages in black (this study) and in red (Costa, 935 1990). 936 937 geotherm each 50ky; left) without thinning of the crust. The thermal anomaly is less than 0.5 Myr; 979 right) with a pure shear thinning of the crust (strain rate of 4. 10 -12 s -1 ), the thermal anomaly is also 980 less than 0.5 Myr. What is dominant on the thermal field is the strain effect more than the intrusion. 981 (B): Thermal evolution of the upper crust with sedimentation effects. The sedimentation has a clear 982 cooling effect by bringing cold sediment at the top of the basin. Left) The base of the basin is at a 983 temperature of 60°C after a sedimentation of 5000m at a velocity of 5. 10 -3 m/yr during 1 Myr and 984 right) at a temperature of 40°C after a sedimentation of 2000m at a velocity of 1.10 -3 m/yr during 1 985

Myr. These temperatures are incompatible with coal formation comprises between 150°C and 200°C. 986

Tables captions

  d'Enfer syntectonic granite (Sample PL06) contains poorly translucent zircons 301 with varied shapes (elongated or rounded). They are composed of inherited relict cores 302 surrounded by oscillatory zoned rims of magmatic origin (Fig. 5; Photo Zr PL06). There is no 303 textural evidence for metamorphic zircon overgrowth. Dating the zircon rims provides two 304 main populations of concordant U-Pb dates at ca. 528 Ma and 301.8±3.1 Ma (lower 305 intercept, n = 14, Fig. 5) respectively. An intermediate group of concordant dates at ca. 470 306 Ma has also been measured and most likely represents an Ordovician inherited component 307 in the source of the granite.

  308

  by thick euhedral oscillatory zoning rims. A wide range of concordant dates 318 are obtained from 850 to 310 Ma as expected for a volcano clastic rock. For such rock type, 319 the emplacement age is constrained by the youngest zircon population defining a lower 320 intercept date of 310.5±3.4 Ma (n = 7). All the youngest dates were obtained on euhedral 321 grains showing oscillatory without any inherited relict cores (grains Zr31, Zr45 and Zr48, Fig.

  ages on Gouffre d'Enfer Granite (sample PL06) yield two distinct populations at 343 530-460 Ma and at 302±3 Ma (

367 750 -

 750 700°C which was recorded by the surrounding metamorphic rocks as the zircon growth 368 temperature. Considering the uncertainties on the ages obtained from the two dating 369 systems, the radiometric data of both chronometers are overlapping. Thus, the cooling 370 between 700°C and 355°C could have occurred either in 2 My or instantaneously. Both 371 hypotheses however indicate that the Gouffre d'Enfer leucogranite experienced a quasi-372 instantaneous cooling at an average rate of 150 °C/My or more. 373 The micaschists of the Pilat Unit underwent a low pressure-high temperature (5-6 374 kbar, 700 °C) metamorphic stage coeval with the development of the PSZ and the 375 emplacement of the syn-kinematic Gouffre d'Enfer granite (stage 2 in the P-T evolution of 376 the Fig. 5 in

385

  The 40Ar/39Ar biotite age of the Gouffre d'Enfer granite is like the biotite age of 386 302.9±1.5 obtained on the post kinematic leucogranite dyke (PL 43) coming from the footwall of the fault. Muscovite 40Ar/39Ar ages of 301.5±1.6 Ma and 302.9±1.6 Ma obtained 388 on pegmatititic synkinematic granites (samples PL 49 and PL51 from the PSZ) and of 389 303.9±1.6 Ma of the lineation of a brittle fault plane (PL48) are statistically similar to the age 390 of the biotite. They are considered to narrowly date their crystallization according to the 391 references cited above showing that white mica ages in crustal scale shear zones are better 392 interpretable to record their (re) crystallization at temperatures up to 550°C. Therefore, 393 these 40Ar/39Ar ages on syn-and post-kinematic biotite and muscovite that crystallized at 394 different crustal levels suggest that the rocks of the Pilat fault footwall were exhumed to the 395 upper crust during a relatively short-lived tectonic event. Muscovite from the post kinematic 396 leucogranite dyke PL 43 gives an age at 298.5±1.5 Ma younger than the biotite age from the 397 same body. This age inversion with respect to the generally assumed closure temperatures 398 of both micas suggests that muscovite could record a crystallization age related to the late 399 infiltration of fluids in the leucogranite along fractures. 400 The PSZ bordering the northern part to the Velay dome and the granite sills emanating from 401 it (as for example the Gouffre d'Enfer granite) corresponds to the footwall of an extensional 402 fault system allowing the exhumation of the Velay dome. The exhumation of the dome 403 created a relief that was eroded, resulting in coarse-grained clastic sedimentation preserved 404 as boulders in the conglomeratic and brecciated formations at the base of the sedimentary 405 sequence filling the Late Carboniferous basin.

  406

407

  The basin corresponding to the hangingwall of the fault was filled by sediments 408 comprising very coarse conglomerates and sandstones, including migmatite and granite 409 from the Velay dome and micaschists from the Pilat Unit. The nature of the clasts and their 410 imbrication (Fig. 7) indicate a southern origin confirming that the main relief bordering the the volcano clastic block (PL92) is compatible with the age Westphalian -Middle 413 Pennsylvanian of the Grand Croix conglomeratic series in which the sample PL92 was taken. 414 This new dating highlights that magmatism in the lower crust responsible for the formation 415 of the granite-migmatite Velay dome and the associated surface volcanism are synchronous 416 with the basin formation whose initiation occurred as early as 310 Ma. The new age confirms 417 that some basins across the French Massif Central could have started to open as early as the 418 Middle Pennsylvanian as for example the Decazeville and the Bosmoreau basins [Bruguier et 419 al., 2003] located along the Sillon Houiller and the Argentat fault respectively (Fig. 1B). 420 The sedimentary series that have filled the St Etienne basin ended with a fine-grained 421 volcano-detrital sequence alternating with coal layers. The ash sample (PL90) taken at the 422 summit of the series gives a U-Pb age of 299.3±1.3 Ma consistent with the Autunian-Middle 423 Cisuralian age of the surrounding sandstone and shale sediments of the Ricamary site. This 424 age agrees with 297 Ma K-Ar illite age (Bruguier et al., 2003) obtained for the sedimentation 425 in the Carboniferous Bosmoreau basin along the Argentat Fault (Fig. 1B). The St. Etienne coal 426 Basin correspond to an intracontinental rift that opened during Carboniferous time. 427 Whatever the global tectonic context, intracontinental rifting is often synonymous with 428 volcanic activity characterized by the formation of volcanoes in the grabben of the rift, very 429 often related to the astheospheric rise at the base of the thinned crust. Our 430 geochronological data show that the St. Etienne basin begins to open with such magmatic 431 activity as evidenced by the presence of the ignimbrite (PL92) dated at 310 Ma. Between 305 432 Ma and 300 Ma, extension and magmatic activity were active as indicated by both the 433 emplacement of the syntectonic granite (PL06) from the PSZ and the deposit of the cinerite 434 (PL90) sampled at the top of the sedimentary series of the St Etienne basin. Finally, the chronological data available before this study were 323 Ma for the Gouffre d'enfer syn 436 tectonic granite (Gay et al.), 313 Ma for an orthogneiss sill in the PSZ and 290 Ma for an 437 undeformed granite (Pl4, Fig. 1) cut off by the St Chamond fault (Costa 1990) suggest a long-438 lasting activity of the PSZ. This evolution over 20 Ma would therefore comprise two stages, i) 439 an early ductile and deep stage related to the motion of a low angle normal fault (the PSZ) 440 and the exhumation of the Velay granite, ii) a second more surficial stage corresponding to 441 the opening of the Carboniferous basin associated with the development of a second-high 442 angle normal fault connecting in depth to the former ductile fault (Fig. 5d Malavieille et al., 443 1990). This second fault correspond to the St. Chamont fault which intersects the USG 444 gneiss to the east and surrounded by the Carboniferous basin and the Pilat series to the 445 West (Fig. 1). Our geochronological data are in conflict with such a scheme. Indeed, we have 446 demonstrated the synchronism between the ductile and fragile deformation and thus the 447 opening of the Carboniferous Basin. The St. Chamond fault which limits the basin to the 448 southwest and intersecting the USG gneisses to the east is therefore contemporary with the 449 PSZ further suggesting a single deformation step and potentially a single extensive structure. 450 However, in the absence of a detailed structural study on the fault of St. Chamond, we 451 cannot exclude that the latter is a second fragile and more recent fault superimposed on the 452 PSZ. This could explain the presence of a sheet of coal caught between micachists and 453 controlled by vertical faults bearing horizontal striations showing that these are strike-slip 454 planes (Mattauer and Matte, 1998). Finally, the ages obtained from the PSZ and those of the 455 Carboniferous St Etienne basin suggest that the opening of the basin is coeval with the 456 development of the PSZ contrary to what Mattauer and Matte (1998) proposed.

  457 4.3. Thermal evolution of the crust 458 4.3.1. Petrological constraints from isotopic systems with different closure temperatures. This technique requires the 461 knowledge of the thermal gradient associated with the studied context and be ensured that 462 it remains stable during the exhumation of the rocks. During the continental collision, the 463

  scheme. The latent heat of crystallization, L, is computed at each time step. The latent heat

  522

  532 allowing it to flow easily. These results allow us addressing the question of whether the Pilat 533 Shear Zone is a response to the formation of the Velay dome or is consequence. In other 534 words, either the partial melting of the continental crust responsible for the Velay formation 535 has favoured the extensive regime or this extension has induced partial melting of the 536 continental crust by adiabatic decompression. Our numerical modelling is more in 537 agreement with the second hypothesis corresponding to a dominant passive rifting model. 538To supports this model, we also can invoke the under platting of mantle derived magmas, 539 the so called vaugnerites[START_REF] Laurent | Protacted, coeval crust and mantle melting during Variscan late orogenic 813 evolution: zircon U/Pb dating in the eastern French Massif Central[END_REF] whose intrusion contemporaneous with the 540 Velay dome formation would have increased the gravitational forces associated with the 541 delamination of the lithosphere under the Velay dome.

  regime associated with the extensional tectonic in the Pilat Unit 544 showing a widespread melting of the rocks and the formation of anatectic granites has been 545

  549 decompression-induced melting of the previously thickened crust and the asthenospheric 550 mantle. This lasting high heat flux after delamination and a very low-density lower crust and 551 mantle maintain the internal part of the Variscan Belt at relatively elevated altitudes with 552 respect to the thickness of the lithosphere. Hence, some authors (Becq-Giraudon et al., 553 1996) relying on sedimentary structures and paleontological data suggested that at the 554 period of the extensional tectonics in the Pilat Unit and the opening of the St Etienne Coal 555 Basin the elevation of this part of the belt could have been ~ 4000 mrates of the Pilat metamorphic Unit and the Velay dome require 558 geological factors including not only a heat source to provide the partial melting of the lower 559 to middle orogenic crust but also driving forces allowing a rock uplift. In that case, the 560 presence of melt in the crust would induce the localisation of strain within shear zones, the 561 latter being a suitable structural geometry able to exhume the deep melted crust. These 562 conditions are present in a scenario involving the removal of part of the lower lithosphere 563 beneath the Velay dome. 564 Paragneiss and orthogneiss are the dominant constituents of the nappes pile formed 565 during the continental collision at ~345 Ma. They are known to be partially molten during 566 the Carboniferous (345-315 Ma) as evidenced by the formation of migmatites at medium 567 pressure-high temperature conditions

  resulting from partial melting of the continental crust and 584 the lithospheric mantle are abundant in the Variscan chain testifying of the high thermal 585

  612including the footwall and the hangingwall of the PSZ. This rebound has the effect of 613 canceling the diachronism of the exhumation between the foot wall and the hanging wall 614 because it is much faster than the exhumation velocity of the Velay along the sedimentation on the hanging wall of the fault has also been tested. As 618 it concerns the upper crust, only the first five kilometers of the crust have been modelled (fig 619 8B). At the beginning of the experiment, however, the model was limited to the uppermost 620 2.5 km of the crust. The velocity field is kept constant and equal to the sedimentation rate 621 except for the first point at the surface for which velocity is nil. The thermal parameters used 622 in the model are given in Table

  627 at a temperature of 60 °C after sedimentation of 5000 m at a velocity of 5.10-3 m/yr during 1 628 My while it is only at 40 °C after sedimentation of 2000 m at a velocity of 2.10-3 m/yr during 629 1 My. The results show that sedimentation has a clear cooling effect at the base of the basin 630 and therefore at the roof of the footwall. Indeed, the base of the basin is at a temperature of 631 60 °C after sedimentation of 5000 m at a velocity of 5.10 -3 m/yr during 1 My while it is only 632 at 40 °C after sedimentation of 2000 m at a velocity of 2.10 -3 m/yr during 1 My. The 633 modelling shows that the supply of cold material (sediments) on top of the crust prevents 634 the heat diffusion throughout the basin. Thus, a cold thermal gradient prevail in the upper 635 crust (hanging wall) during extension eventually preventing the resetting of the geo 636 chronometers during extensional. The northern part of the Pilat metamorphic series located 637 just below the St. Chamond fault (fig.1) where the basin opened and the sediments were 638 deposited, have preserved the 40Ar/39 Ar age of ~335 Ma that could be assigned to the 639 stacking nappes stacking event during the continental collision 640 In addition, these results show that independently of the rate of sedimentation, the 641 temperature at the base of the basin remains low precluding thermal degradation of the 642 organic matter (120-200°C). Thus, according to the model, the temperatures obtained during 643 the sedimentation would prevent the formation of coal. It suggests that the formation of the 644 coal layers is not in relation with the formation of the PSZ and the exhumation of Velay. The 645 history of the maturation of the organic matter should therefore be the subject of a specific 646 and detailed study in relation to the history of sedimentation in the basin.

Figure 1

 1 Figure captions 927

Figure 2 :Figure 3 :Figure 6 :Figure 7 :

 2367 Figure 2: Northwest-Southeast oriented sections (located in Fig 1C) across the St Etienne coal basin, 938

Table 2 )

 2 . The two age populations were obtained on distinct 344 crystals; thus, two interpretations are possible: i) It may be considered that the oldest ages 345 may correspond to inherited zircons from surrounding rocks or ii) to the granite source rock,

	346
	347	this age being close to the Cambrian age of 545±14 Ma (Rb-Sr method) obtained by Caen-

Table 1 :

 1 987 Synthesis of the Ar-Ar ages obtained on the Pilat samples. 988

Table 2 :

 2 Synthesis of the ages obtained on the Pilat samples. 989

Table 3 :

 3 Thermal data used in the numerical simulation. 990

Acknowledgements 671 This research project was funded by the program SYSTER INSU.

Supplementary Data 992


Keywords: deep learning, protein structure prediction, geometric learning, end-to-end architectures, protein language models

est destinée au dépôt

Deep learning entering the post-protein structure prediction era : new horizons for structural biology

Sergei Grudinin

To cite this version: sergei.grudinin@univ-grenoble-alpes.fr

The potential of deep learning has been recognized in structural bioinformatics for already some time, and became indisputable after the CASP13 (Critical Assessment of Structure Prediction) community-wide experiment in 2018. In CASP14, held in 2020, deep learning has boosted the field to unexpected levels reaching near-experimental accuracy. Its results demonstrate dramatic improvement in computing the three-dimensional structure of proteins from amino acid sequence, with many models rivalling experimental structures. This success comes from advances transferred from several machine-learning areas, including computer vision and natural language processing. At the same time, the community has developed methods specifically designed to deal with protein sequences and structures, and their representations. Novel emerging approaches include (i) geometric learning, i.e. learning on non-regular representations such as graphs, 3D Voronoi tessellations, and point clouds; (ii) pre-trained protein language models leveraging attention; (iii) equivariant architectures preserving the symmetry of 3D space; (iv) use of big data, e.g. large meta-genome databases; (v) combining protein representations; (vi) and finally truly end-to-end architectures, i.e. single differentiable models starting from a sequence and returning a 3D structure. These observations suggest that deep learning approaches will also be effective for a range of related structural biology applications that will be discussed in this lecture.

  Sergei Grudinin. Deep learning entering the post-protein structure prediction era : new horizons for structural biology. Acta Crystallographica Section A : Foundations and Advances [2014-..], 2021, A77 (C473), 10.1107/S0108767321092138. hal-03874684 MS-73-2 Microsymposium Acta Cryst. (2021), A77, C473 Deep learning entering the post-protein structure prediction era : new horizons for structural biology Sergei Grudinin Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK, 38000 Grenoble, France;


The delayed damage model has been introduced by Allix and Deü [START_REF] Allix | Delayed-damage modelling for fracture prediction of laminated composites under dynamic loading[END_REF] as a way to overcome spurious mesh dependency in failure analysis involving damage and dynamic loading. The damage rate is bounded through a time scale which, combined with the wave speed, introduces implicitly a length scale. In this work, the delayed damage model is analyzed through numerical experiments on three different loading cases of a bar: a slow loading leading to a dynamic failure, pulses, and impact. We observe and discuss the load level needed for failure (and the dependence of this load level with respect to the loading rate), as well as the dissipation and extent of the fully damaged zone at failure [START_REF] Zghal | Analysis of the delayed damage model for three onedimensional loading scenarii[END_REF]. Observations lead to the following conclusions:

• First, the delayed damage model has no regularization effect for a dynamic failure initiating from rest.

• Second, for pulse loadings, the loading rate has no influence on the minimal load level needed for failure (even though the delayed damage model is a timedependent model), and beyond this minimal load level for failure, the extent of the fully damage zone rises, proportionally to the length scale.

• Third, regarding the impact, the velocity needed to reach failure depends only the time-independent parameters of the models, and not the ones linked to the delayed damage.

Illustration of the weakness of the delayed damage model for dynamic loading

	18th European Mechanics of Materials Conference (EMMC18)
	April 4 -6, 2022, Oxford, UK

Jihed Zghal 1 and Nicolas Moës