Alexandre Cugerone

Bénédicte Cenki

Emilien Oliot

Manuel Muñoz

Structure and texture of Pb-Zn mineralization: example of a multiscale study in the Pyrenees to constrain oreforming processes and critical metals mobility

Introduction

In orogenic basements, the genetic relationship between ore mineralization and host-rock is often difficult to unravel due to complex geometries and the general transposition of structures. Tracking key structural field relationships between mineralization and host-rock is essential to understand their mode of formation and emplacement mechanisms. Moreover, during tectono-metamorphic events, mineralized bodies may have lost their primary features, as well as undergone substantial changes in chemistry and texture making difficult any interpretation based on these techniques. Figure 2.1 shows an overview of possible structural relationships between hostrocks and mineralization in folded and deformed metamorphic terranes. In metallogeny, a syngenetic mineralization is considered synchronous to the deposition of sediments. A mineralization is considered epigenetic if it has emplaced after the sedimentation history (figure 2.1a-b). Veins cross-cutting stratification are typically interpreted as evidences of an epigenetic mineralization. However, the observation of a stratiform or stratabound (sub-concordant to stratification) mineralization in appearance is not sufficient to define an ore-body as syngenetic, due to the possible trapping of mineralization in lithological interface or the presence of transposed structures (for example stratification parallel to tectonic structures). Commonly, characterizing whether it is syngenetic or epigenetic is key to define ore mineralization type and its mode of formation. In deformed metamorphic terranes, these geometrical relationships can be classified as pre-, synor post-deformation structures (figure 2.1c). The structural characterization necessitates a large amount of field structural observations as well as a detailed petrographic examination of the mineral assemblages in the mineralization and the host-rocks as illustrated in Figure 2.1d.

In the world, Pb-Zn mineralizations are mostly associated to the circulation, in the crust, of metal-rich fluids of magmatic and hydrothermal affinities [START_REF] Saini-Eidukat | Zinc-germanium ores of the Tres Marias Mine[END_REF][START_REF] Bodnar | Fluid Inclusions in Hydrothermal Ore Deposits: Treatise on Geochemistry: Second Edition[END_REF][START_REF] Belissont | LA-ICP-MS analyses of minor and trace elements and bulk Ge isotopes in zoned Ge-rich sphalerites from the Noailhac -Saint-Salvy deposit (France): Insights into incorporation mechanisms and ore deposition processes[END_REF][START_REF] Belissont | Distribution and oxidation state of Ge, Cu and Fe in sphalerite by µ-XRF and Kedge µ-XANES: Insights into Ge incorporation, partitioning and isotopic fractionation[END_REF][START_REF] Bauer | Trace element geochemistry of sphalerite in contrasting hydrothermal fluid systems of the Freiberg district, Germany: insights from LA-ICP-MS analysis, near-infrared light microthermometry of sphalerite-hosted fluid inclusions, and sulfur isotope geochemi[END_REF][START_REF] Burisch | The essence of timefertile skarn formation in the Variscan Orogenic Belt[END_REF]. The largest Pb-Zn world resources are located in ancient orogens. As a consequence, they must have experienced deformation and metamorphic events, leading to changes in the primary geometry, mineralization grain size and chemistry [START_REF] Lawrence | Polymetamorphism of the sulphide ores of Broken Hill[END_REF][START_REF] Moore | Geologic setting and genesis of the Red Dog zinc-lead-silver deposit, western Brooks Range, Alaska[END_REF][START_REF] Marshall | Remobilization, syn-tectonic processes and massive sulphide deposits[END_REF][START_REF] Kampunzu | Sediment-hosted Zn-Pb-Cu deposits in the Central African Copperbelt[END_REF]. Some of the largest known Pb-Zn resources are hosted in (meta-)sedimentary terranes and interpreted as syngenetic as sulfide is considered to have form on the seafloor with or without associated volcanic products like volcanogenic massive sulfide (VMS) or sedimentaryexhalative (SEDEX) models, respectively [START_REF] Wilkinson | Sediment-Hosted Zinc-Lead Mineralization: Processes and Perspectives: Processes and Perspectives, Treatise on Geochemistry[END_REF][START_REF] Piercey | Zn-rich Volcanogenic Massive Sulphide (VMS) Deposits: Curent perspectives on Zinc deposits -Irish Association for Economic Geology[END_REF]. Numerous examples of world-class Pb-Zn deposits or districts are currently classified into one of these types such as the Red Dog (USA; [START_REF] Kelley | A special issue devoted to barite and Zn-Pb-Ag deposits in the Red Dog district, Western Brooks Range[END_REF][START_REF] Lange | Geologic Setting, Petrology, and Geochemistry of Stratiform Sphalerite-Galena-Barite Deposits, Red Dog Creek and Drenchwater Creek Areas[END_REF], Mt-Isa inlier (Australia; [START_REF] Gibson | Basin inversion and supercontinent assembly as drivers of sediment-hosted Pb-Zn mineralization in the Mount Isa region, northern Australia[END_REF][START_REF] Huston | Australian Zn-Pb-Ag Ore-forming systems: A review and analysis[END_REF]Perkins and Bell, 1998), Neves Corvo (Portugal;[START_REF] Moura | Metallogenesis at the Neves Corvo VHMS deposit (Portugal): A contribution from the study of fluid inclusions[END_REF][START_REF] Relvas | Hydrothermal alteration and mineralization in the Neves-Corvo volcanic-hosted massive sulfide deposit[END_REF]Tornos et al., 2008), Kidd Creek (Canada;[START_REF] Dewolfe | 3D reconstruction of volcanic and ore-forming environments of a giant VMS system: A case study from the Kidd Creek Mine[END_REF][START_REF] Mercier-Langevin | The Blake River Group of the Abitibi Greenstone Belt and its unique VMS and gold-rich VMS endowment[END_REF] or Xicheng belt (China; [START_REF] Wang | Nature, diversity and temporal-spatial distributions of sediment-hosted Pb-Zn deposits in China[END_REF]. In many of these deposits, even if mineralized bodies are generally sub-concordant to the sedimentary stratification (i.e. these mineralizations are considered stratabound), mineralization emplacement is often controlled by faults and other structural features. In addition, the timing of mineralization is still questioned in many cases [START_REF] Perkins | Stratiform replacement lead-zinc deposits: A comparison between Mount Isa, Hilton, and McArthur River[END_REF][START_REF] Marignac | Remobilisation of base metals and gold by Variscan metamorphic fluids in the south Iberian pyrite belt: Evidence from the Tharsis VMS deposit[END_REF][START_REF] Chauvet | Syn to late tectonic stockwork emplacement within the Spanish section of the Iberian Pyrite Belt: structural, textural, and mineralogical constraints in the Tharsis and La Zarza areas[END_REF][START_REF] Murphy | Structural and stratigraphic controls on mineralization at the George Fisher Zn-Pb-Ag Deposit[END_REF][START_REF] Chauvet | Structural control of ore deposits : the role of preexisting structures on the formation of mineralised vein systems: Minerals[END_REF]Cave et al., 2020a). In the last decades, numerous critical elements that present an affinity with Zn such as germanium (Ge), gallium (Ga) and indium (In) have become more and more valuable for the mining supply chain. They are considered critical by the EU (European Commission, 2020), due to their high supply risk and their economic importance in the optic and electronic industry. In undeformed environment, these critical metals are commonly found in ppm contents associated to sulfides such as sphalerite or chalcopyrite. Nonetheless in orogens, despite the large abundance of zinc ore bodies, critical metals are poorly recovered and the concentration mechanisms of zinc by-products during metamorphism and deformation are still poorly understood. Therefore, understanding the mobility of base and critical elements during the orogenic cycle is essential.

In the Pyrenean Axial Zone (PAZ, France and Spain), which has mainly recorded the Variscan orogeny, we have studied stratabound and cross-cutting vein mineralizations. These Pb-Zn ores are hosted in metasedimentary sequences that recorded metamorphism from low (< 350°C) to medium grade (> 550°C) as well as associated deformation phases. The PAZ is an ideal case study to unravel the structural control on ore genesis and revisit the mode of formation of mineralized veins.

In this chapter, we will complete the recent model of Cugerone et al. (2018b) with additional data on the structural framework of Pb-Zn mineralization in the PAZ. Here, we will study the stratabound Horcall and Crabioules deposits belonging to the Bossost and Lys-Caillaouas massifs, respectively, and the vein deposits of the Arre-Anglas district in the Pierrefitte massif (figure 2.2b). Together with those already described in the Bossost massif (Cugerone et al., 2018a(Cugerone et al., , 2018b[START_REF] Cugerone | Behavior of critical metals in metamorphosed Pb-Zn ore deposits : example from the Pyrenean Axial Zone[END_REF], we highlight the structural control on the formation and transposition of several types of Pb-Zn mineralization in orogenic basement. In the final section, we will describe the micron-scale relationships between sulfide texture and critical metals such as germanium (Ge) in order to constrain general ore-forming processes and critical metals mobility in an orogenic context.

Geological overview of the Pyrenean Axial Zone

Structural setting

The Pyrenean Axial Zone (PAZ), made up of Paleozoic basement, materialized the antiformal crustal nappe stack of the Pyrenean mountain belt that results from the collision between the Iberian and Eurasian plates during the Pyrenean-Alpine orogeny (from late to Cretaceous-Miocene, figure 2.2a). The PAZ is composed of Paleozoic metasedimentary rocks intruded by Ordovician and Carboniferous granitoids. It is limited to the north and the south by the North and South Pyrenean zones, respectively, that are mainly composed of Mesozoic and Cenozoic rocks (figure 2.2b).

Nonetheless, most of the pervasive deformation and metamorphism recorded in the PAZ is not Pyrenean-Alpine in age, but Variscan (i.e. Carboniferous-to early-Permian). The deeper structural level, commonly named the Infrastructure, is composed of high-grade rocks and is structurally positioned below the Suprastructure, which on the other hand represents the upper crustal level, mostly composed of low-grade and moderately deformed metamorphic rocks [START_REF] Kleinsmiede | Geology of the Valle de Aran[END_REF][START_REF] Zwart | The Geology of the Central Pyrenees[END_REF][START_REF] Carreras | The Variscan Orogeny: Extent, Timescale and the Formation of the European Crust[END_REF][START_REF] Denèle | Timing of granite emplacement, crustal flow and gneiss dome formation in the Variscan segment of the Pyrenees[END_REF].

On the field throughout these two major domains, the main foliation S1 is generally E-W-trending, parallel to and transposing the S0 stratification, also being axial plane of kilometric recumbent folds that reflect an early crustal thickening event called D1 [START_REF] Garcia-Sansegundo | Stratigraphy and structure of the southeastern Garona Dome[END_REF][START_REF] Vilà | LPHT metamorphism in a late orogenic transpressional setting, Albera Massif, NE Iberia: Implications for the geodynamic evolution of the Variscan Pyrenees[END_REF]Cugerone et al., 2018b and Cochelin et al., chapter 1 of this volume). The D1 deformation phase is commonly associated to MT-MP (medium temperature -medium pressure) regional metamorphism characterized by a staurolite-garnet peak assemblage (580°C and 5.5 kbar; de Hoÿm de [START_REF] De Hoÿm De Marien | Two-stage Variscan metamorphism in the Canigou massif: Evidence for crustal thickening in the Pyrenees[END_REF][START_REF] Mezger | Polymetamorphism and ductile deformation of staurolite-cordierite schist of the Bossòst dome: indication for Variscan extension in the Axial Zone of the central Pyrenees[END_REF].

A D2 deformation event related to magmatism and metamorphic dome formation is reflected by the local presence of an E-W-trending vertical S2 cleavage, which is axial planar of upright to m-scale isoclinal folds. This second deformation phase D2 occurred in relation to HT-LP (high temperature -low pressure) regional metamorphism characterized by cordierite superimposed assemblages (575-600°C and 3 kbar; [START_REF] Mezger | Polymetamorphism and ductile deformation of staurolite-cordierite schist of the Bossòst dome: indication for Variscan extension in the Axial Zone of the central Pyrenees[END_REF]. A late D3 transcurrent deformation is reported in the PAZ and localized in regional E-W-trending shear zones and faults [START_REF] Carreras | Zooming on Northern Cap de Creus shear zones[END_REF][START_REF] Mezger | Transpressional tectonic setting during the main Variscan deformation: Evidence from four structural levels in the Bossòst and Aston-Hospitalet mantled gneiss domes, central Axial Zone[END_REF][START_REF] Mezger | Evolution of the Central Pyrenean Mérens fault controlled by near collision of two gneiss domes[END_REF]. It is important to note that the emplacement of metamorphic domes in the PAZ belong to a continuous dynamic process during the Variscan orogenic cycle and that may overlap in time within different structural levels of the crust (Rey et al., 2011(Rey et al., , 2017)).

Pyrenean Pb-Zn mineralizations

In the Pyrenees, about one hundred Pb-Zn deposits were mined during the 20th century, constituting the second largest Pb-Zn district in France with ~ 400,000 t Zn and ~ 180,000 t Pb extracted (Cugerone et al., 2018b). Most of the Pb-Zn deposits are located in the central and western part of the PAZ and hosted in the Bossost and the Pierrefitte massif (figure 2.2b). They appear as either stratabound or crosscutting veins hosted in Cambrian-Ordovician, Devonian or Carboniferous metasedimentary rocks [START_REF] Bois | Les minéralisations de Zn (Pb) de l'anticlinorium de Pierrefitte: un exemple de gisements hydrothermaux et sédimentaires associés au volcanisme dans le Paléozoïque des Pyrénées centrales[END_REF][START_REF] Pouit | Arrens Zn ( Pb ), Ba Devonian deposit , Pyrénées , France : an exhalative-sedimentary-type deposit similar to Meggen[END_REF][START_REF] Pesquera | The arditurri Pb-Zn-F-Ba deposit (Cinco Villas massif, Basque Pyrenees): A deformed and metamorphosed stratiform deposit[END_REF][START_REF] Pujals | Las mineralizaciones de sulfuros en el Cambro-Ordovicico de la Val d'Aran[END_REF]Cugerone et al., 2018b). Cross-cutting veins are also reported in Carboniferous magmatic rocks [START_REF] Castroviejo Bolibar | Estructura y metalogenia del campo filoniano de Cierco (Pb-Zn-Ag)[END_REF][START_REF] Johnson | Cierco Pb-Zn-Ag Vein Deposits: Isotopic and Fluid Inclusion Evidence for Formation during the Mesozoic Extension in the Pyrenees of Spain[END_REF][START_REF] Fanlo | Geochemical patterns of a sheared fluorite vein, Parzan, Spanish central Pyrenees[END_REF]. Lead-zinc mineralization is essentially composed of sphalerite (ZnS), and galena (PbS) in a gangue of quartz, calcite and rare barite (BaSO4).

The Bossost massif is located in the central part of the PAZ and hosts about twenty Pb-Zn deposits. This massif is composed of Cambro-Silurians rocks and present a metamorphic core in the southern part (figure 2.3). Located in its eastern part close to a kilometric recumbent F1 fold hinge, the Bentaillou deposit was the largest Pb-Zn mine of the Bossost massif, made of stratabound bodies oriented subparallel to S1 foliation transposing S0 stratification (Garcia-Sansegundo and Alonso, 1989 ; Cugerone et al., 2018b) (figure 2.2b-c). Similar stratabound bodies are reported in the southern part of the Bossost massif, in the Victoria-Margalida-Solitaria district (figure 2.2b-c). Nonetheless, in these deposits, stratabound mineralizations exhibit isoclinal E-W F2 folds and are considered syn or slightly post-metamorphism. In the northern part of the Bossost massif, cross-cutting vein mineralization is dominant and observed in the Argut-dessus, Pale Bidau and Pale de Rase deposits. They mostly appear vertical and parallel to S2 cleavage (figure 2.2b-c; Cugerone et al., 2018a).

The Pierrefitte massif is located at the western part of the PAZ and hosts the Pierrefitte Pb-Zn district. At the Pierrefitte mine, Pb-Zn mineralizations are mostly composed of stratabound veins hosted in Ordovician and Devonian rocks, oriented parallel to (S0-)S1 foliation and hosted in metric D1 Variscan low-dipping thrusts. At the western edge of the Pierrefitte massif (figure 2.2b), some vein systems are reported such as in the Arre-Anglas district [START_REF] Reyx | Relations entre tectonique, métamorphisme de contact et concentrations metalliques dans le secteur des anciennes mines d'Arre et Anglas (Hautes-Pyrénées -Pyrénées atlantiques[END_REF]Cugerone et al., 2018b).

Structures of the studied Pb-Zn mineralizations

The Pb-Zn deposits studied in this chapter share significant similarities with those already described in the Bossost massif in terms of structures and mineralization types. The Horcall and Crabioules are hosted in the central part of the PAZ, at the eastern tip of the Bossost massifs and the northern termination of the Lys-Caillaouas dome, respectively. These deposits are all located in the Suprastructure of the PAZ. In the Horcall and Crabioules deposits, S0 stratification, S1 foliation and S2 cleavage generally trend between N090E and N110E with various plunge direction and dipping angles. Moreover, in this study, additional informations on the Arre-Anglas district are presented to better constrain the regional framework of the Pb-Zn vein emplacement close and structurally below the regional Eaux-Chaudes thrust.

Horcall and Crabioules stratabound mineralizations

The Horcall Pb-Zn deposit is located at the eastern tip of the Bossost massif, south-east of the Bentaillou deposit (figure 2.3a). The mineralization appears stratabound with a decimetric to metric thickness and is hosted in low-grade Cambro-Ordovician schist (Orla schist; Garcia-Sansegundo and Alonso, 1989). At the north of the Horcall deposit (figure 2.4a), a succession of kilometric recumbent F1 folds are visible, subsequently affected by F2 upright folds. At Horcall, Pb-Zn bodies are generally parallel to sub-horizontal S0-S1 foliation trending N090-100E, but some remobilizations appear in the fold hinge of N100-110E upright folds, interpreted as F2 folds and represent the thicker mineralized bodies (figure 2.4b-c). The Crabioules Pb-Zn deposit is located in Ordovician low-grade calc-schist rocks (figure 2.5a). S1 foliation is generally parallel to the stratification and trends N090-110E with a general regular dip of 30-40°S. Decimetric to metric veins are mostly parallel to S0-S1 (figure 2.5b). Close to the various gallery entrances, mineralization is thicker with a pluri-metric extend. In the stratabound veins, clasts of calc-schist appear (figure 2.5c). Nonetheless, stratabound bodies with constant dip are not observed everywhere. The presence of extensional pull-apart features with a sinistral movement top to the south-east is observed locally where the S0-S1 foliation is dipping steeper (40-50°S) (figure 2.5d). These structures are in the direct continuity of the widespread general stratabound mineralization and are frequently surrounded by a high density of fractures sealed with quartz. In the two deposits, the mineralogy of the stratabound mineralization is mostly composed of coarse polygonal grains of sphalerite (up to few hundreds of µm; 80% vol.), with minor galena, magnetite, pyrrhotite, arsenopyrite and chalcopyrite. At microscopic scale, dark-red sphalerite grains at Horcall are observed in pressure shadows of garnet parallel to S1 foliation, interpreted as syn-D1 kinematic (figure 2.4d-e). ) with minor galena, and a gangue of quartz and calcite. At microscopic scale, sphalerite grain size is highly heterogeneous with small grain-size (<100 µm) domains and coarse millimetric (>100 µm) grains. At sample and thick section scale, the relationship between these small grain domains and coarse sphalerite grains evidences dextral simple shear with a similar trend than S2 cleavage in the hostrock.

A novel interest in base metal mineralizations: the presence of critical metals

Once we have gained a robust understanding of the regional structural framework for mineralization emplacement, the textural relationships between mineralization and host-rock needs to be examined as it is key to understand the genesis of mineralization responsible for the concentration of valuable critical metals with Zn affinity, such as germanium (Ge), indium (In) and gallium (Ga). These critical metals can be either found in the crystallographic lattice of sulfides like sphalerite (ZnS) and chalcopyrite (CuFeS2), with contents up to a few thousands of ppm, or more rarely in highly-concentrated micrometer-sized minerals, with content up to a few tens of percent (e.g. brunogeierite, Fe2GeO4 that contains about 29 wt% of Ge). Sulfide dynamic recrystallisation is a primary driver of the mobility and concentration of critical metals [START_REF] Cugerone | Redistribution of germanium during dynamic recrystallization of sphalerite[END_REF][START_REF] Cugerone | Behavior of critical metals in metamorphosed Pb-Zn ore deposits : example from the Pyrenean Axial Zone[END_REF]. Therefore, after a detailed structural and petrological investigations, the textural analysis at microscopic scale is essential to characterize the degree of deformation of sulfides.

In massive sphalerite (as in other sulfide phases), the geometry of grain boundaries reflecting the degree of deformation or recrystallisation is difficult to observe under the microscope (transmitted or reflected light) without etching the thin section surface (hypochlorous acid HClO for sphalerite). The use of electron back-scattering diffraction (EBSD) technique enables the visualization of grain boundaries and additionally allows the characterization of crystallographic orientation of grains which is essential to unravel internal deformation mechanisms.

Coupled to EBSD textural analyses, in-situ chemical mapping techniques are used to characterize the distribution of critical metals, either in the sphalerite crystal lattice or in highly enriched minerals for which the critical metals are major elements. Laser-induced breakdown spectroscopy (LIBS) mapping is an innovative technique to map a large portion of thin section, as well as detect a large spectrum of elements at low detection limit (about 10 ppm for Ge) and low spatial resolution (about 13 µm).

Sphalerite textures observed for the four studied deposits are shown in the Figure 2.7. At Crabioules and Horcall, stratabound sphalerite crystals exhibit homogeneous coarse polygonal grains (> 100 µm) with dark-red to orange colors under the optical microscope and present no pronounced color zonation (figure 2.7a-b). Germanium and other critical metals are relatively depleted (below ~ 10 ppm Ge) in the sphalerite lattice and highly concentrated critical metal accessory minerals are absent.

In the Arre-Anglas vein mineralization, sphalerite generally appears with heterogeneous grain size (figure 2.7) as shown on the EBSD granulometric map (figure 2.7e). Coarse sphalerite crystals (> 100 µm) are mantled by fine recrystallized sphalerite grains (<100 µm) following S2 cleavage (figure 2.7e). This significant textural heterogeneity associated to internal ductile deformation of the coarse grain [START_REF] Cugerone | Redistribution of germanium during dynamic recrystallization of sphalerite[END_REF] matches the large variability observed in sphalerite chemistry (figure 2.7f). In coarse "parent" grains, Ge may reach up to 600 ppm whereas in recrystallized sphalerite, concentrations are only up to few tens of ppm Ge. Highly concentrated critical metal accessory minerals like Ge-minerals (oxides, sulfides with Ge contents up to 25 wt.%) are present, located at grain boundaries within recrystallized sphalerite domains or close to twin boundary of coarse "parent" crystals. ppm Ge) and in Ge-minerals (up to 25 wt.% Ge).

Discussion and conclusions

Macro-structural observations of Pb-Zn vein mineralizations in the PAZ at regional scale highlight two main types of ore bodies: (i) Stratabound mineralizations which are mostly parallel to the (S0-)S1 foliation. These Pb-Zn mineralizations were previously interpreted as SEDEX and syngenetic with ages ranging from Ordovician to Devonian [START_REF] Bois | Les minéralisations de Zn (Pb) de l'anticlinorium de Pierrefitte: un exemple de gisements hydrothermaux et sédimentaires associés au volcanisme dans le Paléozoïque des Pyrénées centrales[END_REF][START_REF] Pouit | Arrens Zn ( Pb ), Ba Devonian deposit , Pyrénées , France : an exhalative-sedimentary-type deposit similar to Meggen[END_REF]. However, our detailed structural study indicates that their emplacement is associated to the Variscan orogeny. The source and the exact timing of emplacement of these mineralizations are still unclear but may be related to late-orogenic fluid-assisted metamorphism and deformation (Cugerone et al., 2018b[START_REF] Cugerone | Redistribution of germanium during dynamic recrystallization of sphalerite[END_REF][START_REF] Cugerone | Behavior of critical metals in metamorphosed Pb-Zn ore deposits : example from the Pyrenean Axial Zone[END_REF]; (ii) Vein mineralizations are generally parallel to S2 cleavage and probably syn-to late orogenic deformation. They frequently exhibit pull-apart-type structures, and the timing may be related to Late-Variscan or even Mesozoic tectonics. Similar veins are reported in various locations in the Pyrenees [START_REF] Johnson | Cierco Pb-Zn-Ag Vein Deposits: Isotopic and Fluid Inclusion Evidence for Formation during the Mesozoic Extension in the Pyrenees of Spain[END_REF][START_REF] Fanlo | Geochemical patterns of a sheared fluorite vein, Parzan, Spanish central Pyrenees[END_REF][START_REF] Subias | The Yenefrito Pb-Zn mine (Spanish Central Pyrenees ): an example of superimposed metallogenetic events[END_REF][START_REF] Munoz | Mesozoic veintype Pb-Zn mineralization in the Pyrenees: Lead isotopic and fluid inclusion evidence from the Les Argentières and Lacore deposits[END_REF]. The in-situ mineralogical, textural and chemical characterizations of Pyrenean Pb-Zn mineralizations show that vein mineralizations are the main host for critical metals and exhibit complex sulfide dynamic recrystallization features (coarse parent grains surrounded by small recrystallized crystals).

This study highlights the importance of performing a detailed multi-scale geology framework before interpretating Pb-Zn mineralizations geneses. Describing simple stratiform or stratabound veins, without an associated coherent regional structural study, is not sufficient to interpret mineralization genesis. In the Pyrenees, evidences of orogenic mineralizations are often poorly exposed due to general transposition of stratification and deformation structures. It may explain the previous controversies on their geneses. This study delivers some important keys to target specific textural locations and structures at regional or deposit-scale, which may be relevant in other terranes where the question between syngenetic and epigenetic genesis is still not resolved.

The remobilization of Ge during dynamic recrystallization of sphalerite can be explained as follow [START_REF] Cugerone | Redistribution of germanium during dynamic recrystallization of sphalerite[END_REF][START_REF] Cugerone | Behavior of critical metals in metamorphosed Pb-Zn ore deposits : example from the Pyrenean Axial Zone[END_REF]: Pb-Zn veins were naturally deformed at low metamorphic grade (<400 °C) promoting the sphalerite dynamic recrystallization and inducing a vertical late cleavage plane (parallel to S2 cleavage affecting the host-rock). During sphalerite recrystallization, the germanium hosted in undeformed millimetric crystals, is spatially remobilized, leached into the chemical system and redistributed in newly formed small Ge-minerals (oxides, sulfide), mostly hosted at grain boundaries of the recrystallized sphalerite grains. A simple mass balance calculation shows that this redistribution occurs at sample scale in a closed system [START_REF] Cugerone | Behavior of critical metals in metamorphosed Pb-Zn ore deposits : example from the Pyrenean Axial Zone[END_REF].

One major consequence of this work is to reconsider exploration strategies for critical metals. The exploration of critical metals may not only focus on coarse and undeformed mineral host, but also on domains with smaller and potentially recrystallized grains. In addition, when focusing on bulk chemical analyses, this information might be lost. Germanium and other critical metals may have been remobilized and concentrated in accessory minerals during fluid-assisted tectonometamorphic events that lead to the dynamic recrystallization of sulfides.

These ideas may have large implications when considering other metamorphosed base-metal deposits located in orogens, such as sediment or volcanic hosted massive sulfide deposit (SEDEX, VHMS) or deformed carbonate-hosted deposits [START_REF] Ye | Trace and minor elements in sphalerite from base metal deposits in South China: A LA-ICPMS study[END_REF][START_REF] Belissont | Germanium crystal chemistry in Cu-bearing sulfides from micro-XRF mapping and micro-XANES spectroscopy: Minerals[END_REF][START_REF] Wei | Distribution and occurrence of Ge and related trace elements in sphalerite from the Lehong carbonate-hosted Zn-Pb deposit , northeastern Yunnan , China : Insights from SEM and LA-ICP-MS studies[END_REF]Cave et al., 2020b). Further investigations on critical metal remobilization are required to understand the processes of concentration of these valuable critical metal resources, especially in orogens. The integration of various complementary methods at different scales, from the regional field scale to in-situ chemical analyses in thin section, is necessary in order to fully understand how base and critical metals ore deposits form.

Figure 2 . 1 .

 21 Figure 2.1. Differences between syngenetic and epigenetic mineralization. a-b) Basic sketches showing fundamental difference between a syngenetic and an epigenetic mineralization (modified from Jébrak and Marcoux, 2008). c) Few generic examples to unravel ore-body geometry on the field. d. Typical example of complex geometries hosting an ore-body (linked to poly-phase deformation). Some relevant examples are represented to understand relationships between mineralization and structures. These relationships are key to understand their genetic origin and guide ore exploration. e-f) Typical examples of stratabound and vein mineralizations (from the Liat and Anglas deposits).

Figure 2

 2 Figure 2.2. a) Location of the Pyrenean Axial Zone (PAZ) in the western part of the Variscan belt. b) Simplified geological map of the central and western part of the PAZ. Lithology and Pb-Zn deposits are emphasized. Location of the Figure 2.3 is noted. c) 3D structural sketch of the Bossost massif with representation of Pb-Zn deposits.

Figure 2 . 3 .

 23 Figure 2.3. The Bossost and north of the Lys-Caillaouas massifs. a) Lithological map and the location of the main Pb-Zn deposits. Lithologies are based on geological map of BRGM (France; BRGM[START_REF] Brgm | Pic de Mauberme[END_REF]Barrère et al., 1984;Clin et al., 1989) and IGME(Spain, Aran Valley;García-Sansegundo et al., 2013) b) Cross-section at the east of the Bossost massif. c. Structural map with foliation trajectories of S0-S1, S2 and related F2 folds.

Figure 2 . 4 .Figure 2 . 5 .

 2425 Figure 2.4. Horcall mine (abbreviations: Grt: garnet; Ms: muscovite; Sp: sphalerite). a) Panoramic sketch of the surrounding rocks at Horcall showing recumbent folds (F1). b) Stratabound Pb-Zn mineralization sub-parallel to S0-S1 foliation in Cambrian schist. c) Stratabound Pb-Zn mineralization remobilized and thicker in F2 folds. d) Microphotograph of sphalerite in shadow pressure of garnet (reflected light). e) Microphotograph of stratabound sphalerite replacing garnet (plane polarized light).

Figure 2 . 6 .

 26 Figure 2.6. Arre-Anglas mining district. a) Structural 3D model of the Arre-Anglas district. (b-c) Outcrop photograph of the Anglas and Arre veins, respectively. These veins are mostly composed of light-brown sphalerite and are oriented parallel to S2 cleavage. Sphalerite is also imprinted by a cleavage, probably S2. d) Pull apart features in schist, filled with calcite, quartz and light-brown sphalerite.

Figure 2 . 7 .

 27 Figure 2.7. Examples of textural and chemical features of the Pyrenean sphalerite (ZnS; thick section-100 µm) (abbreviations: Qz: quartz; Sp: sphalerite) observed in plane polarized light. (a-b) Stratabound sphalerite from the Horcall and Crabioules deposits. Grain boundaries are represented in white. c) Thick section scale scan of Arre vein sphalerite. A cleavage (probably S2) is observed and imprint light and dark domains (color zoning) in sphalerite d) Zoom on Arre sphalerite with color zoning. e) EBSD grain size map in the same area as (d). Blue and light-brown colors correspond to small and coarse sphalerite grain fraction, respectively. f) LIBS map showing Ge concentrations in sphalerite (low and middle concentrations up to 600 ppm Ge) and in Ge-minerals (up to 25 wt.% Ge).

Version proof


Emma Lagracie

Lisl Weynans

Yves Coudière

Comparison of Two Formulations for Computing Body Surface Potential Maps

In order to establish a link between the activation map and the body surface signals, we want to compute body potentials from activation maps and a frontlike approximation of the activation of the heart. To do so, two formulations that map the extracardiac potential from the transmembrane voltage naturally emerge from the bidomain model. Either the extracellular/extracardiac potential solves a Laplace equation with discontinuous conductivity coefficient and ionic current as a source (Source Formulation F1); or the quasi-stationary electrical balance between the intra-and extracellular fields (Balance Formulation F2). In this work, we compare F1 and F2, to determine which formulation is the most relevant to use.

We compute reference activation map ψ, transmembrane voltage v and body surface map u with a bidomain 2D code. We design two alternative shapes ṽ for a frontlike approximation of v. Afterwards, two extracellular / extracardiac potentials are computed from the activation time ψ and ṽ, using the two different formulations. Then the extracardiac potentials solutions of F1 and F2 are compared respectively to the solution of the bidomain u.

Results show that the Balance Formulation F2 is robust to the input data (ṽ and ψ). On the contrary, the Source Formulation F1 is very unstable and generates very large errors on the body surface map.

Introduction

In the framework of ECGi, we would like to reconstruct activation maps of the heart directly from torso potentials, available thanks to multi-electrode vests for example. To this end, we need to express a direct problem given the activation time ψ(x). In particular, we want to deduce the extracellular and extracardiac potential u directly from ψ. We choose to model the transmembrane voltage as an activation front with a predefined shape as in [START_REF] Franzone | Mathematical modeling of the excitation process in myocardial tissue: Influence of fiber rotation on wavefront propagation and potential field[END_REF][START_REF] Van Dam | Non-invasive imaging of cardiac activation and recovery[END_REF][START_REF] Ravon | Impact of the endocardium in a parameter optimization to solve the inverse problem of electrocardiography[END_REF]. In this context, the approximate transmembrane voltage writes ṽ(x, t) = V (tψ(x)). Even if its shape is uncertain, this representation of the transmembrane voltage captures the global behaviour of the depolarisation front.

Then, the extracellular and extracardiac potential is expressed as a solution of a partial differential equation with a source term that depends on V , ψ, and the formulation of the operator [ṽ -→ u]. This operator is derived from the bidomain equations that follow. In a heart (Ω H ) embedded in a torso (Ω T ) geometry, the bidomain model is given by div(σ

i ∇u i ) = ∂ t v + I ion (v) in Ω H , div(σ e ∇u) = -∂ t v -I ion (v) in Ω H , div(σ T ∇u) = 0 in Ω T , σ i ∇(u + v) • n = 0 on ∂Ω H , σ T ∇u • n = 0 on ∂Ω T , (1)
with

u i ∈ H 1 (Ω H ), u ∈ H 1 (Ω H ∪ Ω T )
the intracellular and extracellular / extracardiac potentials respectively, v = u iu ∈ Ω H the transmembrane voltage, and σ i , σ e , σ T the conductivities respectively in the cardiac intracellular medium, cardiac extracellular medium and torso medium. They are scaled to use nondimensionnal terms. The ionic current, I ion is a non-linear (often cubic) function of v and other variables that depend on the ionic model chosen. Equivalently, the volumic equations in the heart can write

div(σ i ∇(u + v)) = ∂ t v + I ion (v) in Ω H , div((σ i + σ e )∇u) = -div(σ i ∇v) in Ω H . (2)
This version is more widely used in the literature. In these two equivalent formulations of the bidomain we see two equations modelling the dependency between u and v:

-div (σ e ∇u) = ∂ t v + f (v) in Ω H , -div (σ T ∇u) = 0 in Ω T ; (F1) and -div (σ e ∇u) -div (σ i ∇(u + v)) = 0 in Ω H , -div (σ T ∇u) = 0 in Ω T . (F2)
Thus, (F1) and (F2) can be seen as two independent problems which data is v and that define two mappings of [ṽ -→ u], taking v = ṽ. Either u solves a Laplace equation with discontinuous conductivity coefficients (heart and torso) and a nonlinear source (Source Formulation (F1)), or it solves the quasi-stationary electrical balance between the intra and extracellular fields (Balance Formulation (F2)). Commonly, the potential u is computed from the Balance Formulation (F2). Anyway, we may also use (F1), that has the advantage of not including any coupling on the heart boundary, and which differential operator is naturally shaped for the coupled heart/torso problem. Note that if v solves the complete bidomain equations, the two formulations are equivalent. However, as soon as v differs from the bidomain solution, (F1) and (F2) are no longer equivalent. In this study, we compare the solutions of the two formulations (u 1 for (F1) and u 2 for (F2)) evaluated in ṽ(x, t) = V (tψ(x)), with the bidomain solution (denoted by the index ref ). We also investigate the robustness of those two formulations to small variations in the transmembrane voltage and the activation time.

Method

Reference solution and activation map

Let (u ref , v ref ) be the couple solution of the bidomain with the Mitchell-Shaeffer [START_REF] Mitchell | A two-current model for the dynamics of cardiac membrane[END_REF] model for the ionic potential, given by

∂ t v = 1 τ in hv 2 (1 -v) - v τ out , ∂ t h =        1 -h τ open is v < v gate , -v τ close otherwise. (3)
Concerning the numerical schemes, the 2D Discrete Duality Finite Volume (DDFV) [START_REF] Delcourte | Discrete-duality finite volume method for second order elliptic problems[END_REF] scheme was used for the space discretization and an order 2 Semi-implicit Backward Discretization scheme (SBDF2) for the temporal discretization. Thus, in the bidomain code, the term

∂ t v + f (v) is approached by 1 dt 1.5v n -2v n-1 + 0.5v n-2 + 2f (v n-1 , h n-1 ) -f (v n-2 , h n-2 ), (4)
for a time step dt > 0. Two 2D meshes were used, an artificial mesh of a circular heart in a circular torso, and a 2D slice of a segmentation of a patient's ventricle and torso.

The activation map of the heart was computed as a piecewise affine function given by its values ψ i at each node x i of the mesh (example Figure 3). The time ψ i (x i ) is defined as the fist time at which t -→ v(x i ) crosses a threshold. This threshold is set at 0.5, as in the Mitchell-Shaeffer model v takes values between 0 and 0.95. To find ψ i at each x i , the functions t -→ v(x i ) are interpolated by cubic splines.

Numerical resolution of the two approached formulations

The equations (F1) and (F2) being static, we used again a 2D DDFV spatial scheme for the resolution and the discretization. Two predefined shapes V were designed. The first one is a Heaviside front, smoothed such that the righthand sides (RHS) of the two formulations ∂ t ṽ + f (ṽ) and -div(σ i ∇ṽ) are L 2 regular. The second one is the front obtained by solving the 0D Mitchell-Shaeffer problem, with a C ∞ initial stimulation. For the formulation (F2), the RHS is computed by applying a DDFV scheme to the chosen form of ṽ. For the source formulation (F1), the temporal derivative term is either explicitly given, ∂ t ṽ = V ′ , either derived numerically as in (4). In the Source Formulation (F1), the ionic term is a cubic function of v.

Choice and computation of the front V

In the first case, V is a smoothed Heaviside function depending on a front duration parameter ε, specifically, ṽ = v ε (x, t) = Hε (tψ(x)). To fulfill the constraint of a H 1 regularity for the solution of (F1), we imposed Hε (x) = 0 for x < -ε, Hε (x) = 0.94 for x > ε and Hε (x) = g in between (|x| ≤ ε), with g(x) = 0.94 -1 4ε 3 x 3 + 3 4ε x + 1 2 . Both v ε and its temporal derivative are then analytically known.

For the 0D Mitchell-Shaeffer front (MS0D), the Mitchell-Shaeffer model was solved in 0D, using classical python integration tools, on a time range of 330 ms (AP duration). Then, a cubic spline interpolation from python scipy library was used to compute a model for ṽ callable at all times. The time scale was translated to center ṽ on the activation time.

Computation of the ionic term

In the Mitchell-Shaeffer model, for an ideal propagation, h = 1 on the activation front. Then the Mistchell-Shaeffer fonction

f MS becomes f MS (v) = v 2 (1-v) τin -v
τout , with τ in = 0.3 and τ out = 6 as in the original paper [START_REF] Mitchell | A two-current model for the dynamics of cardiac membrane[END_REF]. Denoting f ref (v) the bidomain ionic term, we compared f MS to a cubic polynomial interpolation of

v ref -→ f ref (v ref ) denoted f int .
Several random points x k of the heart mesh were selected, and a least-square minimization was realised to find v(x k ) -→ f int (v(x k )) under the constraint that 0 and 0.94 are zeros of the function. This means that two coefficients were left to find: the dominant coefficient and the third root. For all points x k , the interpolated coefficients found were close to each other. Thus we took their mean value for designing the function f int (v). As illustrated on one mesh point in Figure 1

f (v) f ref (v) f int (v) f MS (v)

Results

Verification of the resolution of the two formulations

To verify the resolution, we substituted v ref in both formulations. For the formulation (F1), the RHS is computed with (4). u 1 and u 2 are expected to match exactly the reference u ref . In practice, the differences are ≈ 10 -13 due to numerical errors. However, the result u 1 is very sensitive to small errors in the RHS. For instance, if we replace formula (4) by another discretization scheme of same order, the errors

∥u1-uref∥ L 2 (Ω T ) ∥uref∥ L 2 (Ω T )
jump to an order 10 -2 or even 10 -1 , as presented in Tables 1 and2 for the circular mesh. Table 1. Relative L 2 (Ω T ) errors for the solution of (F1) when changing f in (4).

Ionic term

∥u1-uref∥ L 2 (Ω T ) ∥uref∥ L 2 (Ω T ) f ref (v ref ) (reference) 1.5E-13 f int (v ref (t n )) 8.1E-01 f MS (h(t n ), v ref (t n ))
4.4E-02 These results anticipated mediocre performances for (F1) Table 2. Relative L 2 (Ω T ) errors for the solution of (F1) when changing ∂ t v in (4).

Discrete derivative scheme

∥u1-uref∥ L 2 (Ω T ) ∥uref∥ L 2 (Ω T ) SBDF2 (reference) 1.5E-13 Euler centered 2.5E-02 Explicit Euler 4.3E-01
in case of a pre-shaped front, the source term being very 4) (line 2 of Table 1).

∂ t v = ∂ t v ref and f (v) = f int (v ref (t n )) in (
sensitive to small variations, and relying on a balance between the transmembrane voltage time derivative and the ionic term. Figure 2 illustrates this observation. In the following, v is substituted by ṽ = v ε or the MS0D front. The relative differences between u 1 and u ref and u 2 and u ref are presented in Figure 4. Accordingly to the previous results, (F1) generates huge errors, thus cannot be used in computations. On the contrary, (F2) seems robust and generates less than 10% of difference for all the tested ṽ. For parameter ε between 0.5 and 5 for v ε , the errors are lower than the ones obtained with the MS0D model. We can also notice that there exist an optimal ε 0 parameter that minimizes the difference

Analysis of the effects of the formulation

||u2-uref|| L 1 (∂Ω T ×(0,T )) ||uref|| L 1 (∂Ω T ×(0,T ))
. Anyway, if we look at the difference in space only, ε 0 slightly depends on time.

First sensitivity analysis

Focusing on (F2), a white noise perturbation w was added to the RHS of the equation. Four noisy trans-

1 -u ref || L 1 (∂ΩT ×(0,T )) ||u ref || L 1 (∂ΩT ×(0,T )) ||u 2 -u ref || L 1 (∂ΩT ×(0,T )) ||u ref || L 1 (∂ΩT ×(0,T )) ||ṽ -v ref || L 2 (ΩH)×L 1 (0,T ) ||v ref || L 2 (ΩH)×L 1 (0,T )
Figure 4. Relative differences between u 1 (red), u 2 (blue) and u ref respectively, and ṽ and v ref (black). ṽ may be the MS0D model (horizontal dashed lines), or v ε with varying duration parameter ε (points).

membrane voltages were designed: ṽ

= v ref + w(x), ṽ = v ε + w(x), ṽ = H ε (t -ψ(x) + w(x)) and ṽ = H ε (t -ψ(x) + w 0 )
, where w 0 is a scalar. The last case represent a displacement of the whole activation front line, as it would be if the initial activation site were uncertain.

For the % of noise on the activation time, a reference amplitude was needed. Denoting p the position of the stimulation site, we allow p + ∆p to be located in all septum.

Then ∆t = ∆p c with c the mean speed of the activation front in the septum. Surprisingly, the chart Figure 5 shows

0.0 0.1 0.2 0.3 0.4 0.5 2 % noise w ṽ = v ref + w v ε + w v ε (ψ + w) v ε (ψ + w 0 I) 0.0 0.5 1.0 Error on u 2 (∂Ω T , t 1 )
4 % noise w no significant difference between the solutions of (F2) with ṽ = v ref + w and ṽ = v ε + w, confirming again the validity of using (F2) in future computations. Moreover, the formulation does not appear to be very sensitive to small noise in the stimulation site. In this case, the errors are significantly inferior to raw gaussian noise on the activation time.

Discussion and Conclusion

Our results point out clearly that the Source Formulation (F1) cannot be used for propagating u from v. Even with very accurate entries, the body surface potential map is no longer preserved. This emphasizes the underlying equilibrium existing between the ionic term and v. On the contrary, the Balance Formulation allows to correctly recover body surface potentials even with a simple preshaped transmembrane potential or with noise. It would be interesting to push further this study in 3D. Moreover, a real sensitivity analysis of u 2 as function of ψ would be very useful. In future work, we could also study the sensitivity of formulation (F2) to heterogeneities in the heart conductivity.

  the f int function fits better the reference curve f ref (v ref ) than f MS and was thus chosen for the following.

Figure 1 .

 1 Figure 1. Comparison between f MS in green and f int in red, as functions of v. The stars are the reference values f ref (v) obtained by the bidomain propagation.

Figure 2 .

 2 Figure 2. Bidomain solution u ref on the left, and u 1 solution of (F1) on the right for∂ t v = ∂ t v ref and f (v) = f int (v ref (t n )) in (4) (line 2 of Table1).

Figure 3 .

 3 Figure 3. Activation times computed from the bidomain propagation.

  ||u

Figure 5 .

 5 Figure 5. Relative difference between u 2 and u ref on the torso at time t = 35 ms for 5000 realisations of white noise w. ε = 2.5.

Acknowledgments

This study received financial support from the French Government as part of the "Investments of the Future" program managed by the National Research Agency (ANR), Grant reference ANR-10-IAHU-04.