Malcolm Massuyeau
email: malcolm.massuyeau@wwu.de

Emmanuel Gardés

Grégory Rogerie

Sonja Aulbach

Sebastian Tappe

Emmanuel Le Trong

David Sifré

Fabrice Gaillard

MAGLAB: A computing platform connecting geophysical signatures to melting processes in Earth's mantle

Keywords: Petrological-geophysical modeling, Melt fraction-composition, Upper mantle, CO 2 -H 2 O volatiles, Intraplate magmas, Lithosphere-asthenosphere boundary

Decompression melting of the upper mantle produces magmas and volcanism at the Earth's surface. Experimental petrology demonstrates that the presence of CO 2 and H 2 O enhances peridotite melting anywhere within the upper mantle down to approximately 200-300 km depth. The presence of mantle melts with compositions ranging from carbonate-rich to silicate-rich unavoidably affects the geophysical signals retrieved from Earth's mantle. Geochemical investigations of erupted intraplate magmas along with geophysical surveys allow for constraining the nature and volume of primary melts, and a sound formalism is required to integrate these diverse datasets into a realistic model for the upper mantle including melting processes. Here, we introduce MAGLAB, a model developed to calculate the composition and volume fraction of melts in the upper mantle, together with the corresponding electrical conductivity of partially molten mantle peridotites at realistic pressure-temperature conditions and volatile contents. We use MAGLAB to show how the compositions of intraplate magmas relate to variations in lithosphere thickness. Progressive partial melting of a homogeneous peridotitic mantle source can in theory create the diversity of compositions observed among the spectrum of intraplate magma types, with kimberlite melts beneath thick continental shields, alkaline magmas such as melilitite, nephelinite and basanite beneath thinner continents and relatively old plus thick oceanic lithospheres, and ‗regular' basalts beneath the youngest and thinnest oceanic lithospheres as well as beneath significantly thinned continental lithospheres. MAGLAB calculations support recent experimental findings about the role of H 2 O in the upper mantle on producing primary kimberlitic melts in addition to CO 2 . We demonstrate the robustness of MAGLAB calculations by reproducing the compositions of erupted melts as well as associated mantle electrical conductivities beneath the Society hotspot in the Pacific Ocean. A comparison of our simulations with magnetotelluric surveys at various oceanic settings shows that the heterogeneities in electrical conductivity of Earth's upper mantle are related to variations in volatile content via the presence of small (generally <<1 wt%) and heterogeneously distributed fractions of CO 2 -H 2 O-bearing melts.

Introduction

The flux of heat from Earth's interior generates upwelling limbs of convective cells, such as passive upwelling beneath mid-ocean ridges, or plumes occurring beneath hotspots [START_REF] Ballmer | Spatial and temporal variability in Hawaiian hotspot volcanism induced by small-scale convection[END_REF][START_REF] French | Broad plumes rooted at the base of the Earth's mantle beneath major hotspots[END_REF]. Within these convective cells, the upper mantle is expected to produce partial melts of variable fractions and compositions. Mantle melting is enhanced by the presence of the volatiles CO 2 and H 2 O. The upper mantle volatile contents average around 140 wt ppm CO 2 and 240 wt ppm H 2 O (Le [START_REF] Voyer | Heterogeneity in mantle carbon content from CO 2 -undersaturated basalts[END_REF], but are highly variable with concentrations ranging from some wt ppm to many hundreds of wt ppm as reported in geochemical surveys [START_REF] Marty | The origins and concentrations of water, carbon, nitrogen and noble gases on Earth[END_REF][START_REF] Voyer | Heterogeneity in mantle carbon content from CO 2 -undersaturated basalts[END_REF][START_REF] Hirschmann | Comparative deep Earth volatile cycles: The case for C recycling from exosphere/mantle fractionation of major (H 2 O, C, N) volatiles and from H 2 O/Ce, CO 2 /Ba, and CO 2 /Nb exosphere ratios[END_REF][START_REF] Hauri | Carbon in the Convecting Mantle[END_REF][START_REF] Shimizu | Identifying volatile mantle trend with the water-fluorine-cerium systematics of basaltic glass[END_REF]. Experimental petrology provides numerous constraints on partial melting properties of peridotite in presence of volatiles within the pressure-temperature-composition conditions prevailing in Earth's upper mantle. These studies emphasize the large effect of CO 2 and H 2 O on mantle melting relations, where these volatiles drastically lower the solidus of peridotite to <1000°C [START_REF] Wallace | An experimental determination of primary carbonatite magma composition[END_REF][START_REF] Dasgupta | Melting in the Earth's deep upper mantle caused by carbon dioxide[END_REF][START_REF] Hammouda | Melting in the mantle in the presence of carbon: Review of experiments and discussion on the origin of carbonatites[END_REF][START_REF] Gardés | Unravelling partial melt distribution in the oceanic low velocity zone[END_REF]. CO 2 -H 2 O-assisted melting is thus predicted for most of the upper mantle as long as the oxidized form of carbon (i.e. carbonate) is stable. The depth at which the transition from oxidized to reduced carbon occurs is debated, with options ranging from ~150 km [START_REF] Stagno | The oxidation state of the mantle and the extraction of carbon from Earth's interior[END_REF] to ~250 km [START_REF] Rohrbach | Redox freezing and melting in the Earth's deep mantle resulting from carbon-iron redox coupling[END_REF]. More recent studies [START_REF] Gaillard | The redox geodynamics linking basalts and their mantle sources through space and time[END_REF][START_REF] Eguchi | Redox state of the convective mantle from CO 2trace element systematics of oceanic basalts[END_REF][START_REF] Moussallam | Mantle plumes are oxidised[END_REF] argue that the asthenosphere may be much more oxidized than previously deduced from depleted peridotite samples of the deep cratonic lithosphere [START_REF] Stagno | The oxidation state of the mantle and the extraction of carbon from Earth's interior[END_REF]. Such deep cratonic mantle lithosphere may also have experienced various stages of metasomatism and oxidation over time by infiltrating carbonate-bearing hydrous silicate melts or by the incorporation of subducted carbonatebearing crustal material [START_REF] Yaxley | Redox preconditioning deep cratonic lithosphere for kimberlite genesisevidence from the central Slave Craton[END_REF]. The presence and role of volatile-bearing melts in both oceanic and continental upper mantle have been emphasized based on petrological investigations and geophysical observations. Geochemical studies have deduced their existence by observing characteristic metasomatic overprints of rocks as well as the presence of fluid/melt-derived inclusions in mantle minerals [START_REF] Bodinier | Mechanisms of Mantle Metasomatism: Geochemical Evidence from the Lherz Orogenic Peridotite[END_REF][START_REF] Grégoire | Garnet Lherzolites from the Kaapvaal Craton (South Africa): Trace Element Evidence for a Metasomatic History[END_REF][START_REF] Klein-Bendavid | Fluid inclusions in diamonds from the Diavik mine, Canada and the evolution of diamond-forming fluids[END_REF]O'Reilly and Griffin, 2010;[START_REF] Weiss | High-Mg carbonatitic melts in diamonds, kimberlites and the sub-continental lithosphere[END_REF][START_REF] Tumiati | An Experimental Study on COH-bearing Peridotite up to 3•2GPa and Implications for Crust-Mantle Recycling[END_REF][START_REF] Pilet | Pre-subduction metasomatic enrichment of the oceanic lithosphere induced by plate flexure[END_REF]. Seismic and magnetotelluric surveys have reported geophysical anomalies in the upper mantle, such as reduced seismic shear-wave velocities in the Low-Velocity Zone (LVZ) located between ~50 and 150-200 km depth, and high electrical conductivities at similar depths, both enhanced by the presence of low volumes of melt potentially containing appreciable amounts of CO 2 and H 2 O [START_REF] Eggler | Does CO 2 cause partial melting in the low-velocity layer of the mantle[END_REF][START_REF] Gaillard | Carbonatite Melts and Electrical Conductivity in the Asthenosphere[END_REF][START_REF] Kawakatsu | Seismic Evidence for Sharp Lithosphere-Asthenosphere Boundaries of Oceanic Plates[END_REF][START_REF] Fischer | The Lithosphere-Asthenosphere Boundary[END_REF][START_REF] Hirschmann | Partial melt in the oceanic low velocity zone[END_REF][START_REF] Ni | Electrical conductivity of hydrous basaltic melts: implications for partial melting in the upper mantle[END_REF][START_REF] Schmerr | The Gutenberg Discontinuity: Melt at the Lithosphere-Asthenosphere Boundary[END_REF][START_REF] Naif | Melt-rich channel observed at the lithosphere-asthenosphere boundary[END_REF][START_REF] Sifré | Electrical conductivity during incipient melting in the oceanic low-velocity zone[END_REF][START_REF] Chantel | Experimental evidence supports mantle partial melting in the asthenosphere[END_REF][START_REF] Holtzmann | Questions on the existence, persistence and mechanical effects of a very small melt fraction in the asthenosphere[END_REF][START_REF] Aulbach | Origins of cratonic mantle discontinuities: A view from petrology, geochemistry and thermodynamic models[END_REF][START_REF] Katsura | Electrical conductivity of the oceanic asthenosphere and its interpretation based on laboratory measurements[END_REF][START_REF] Kawakatsu | Seismic and Electrical Signatures of the Lithosphere-Asthenosphere System of the Normal Oceanic Mantle[END_REF]Tharimena et al., 2017a,b;[START_REF] Soltanmohammadi | Transport of Volatile-rich Melt from the Mantle Transition Zone via Compaction Pockets: Implications for Mantle Metasomatism and the Origin of Alkaline Lavas in the Turkish-Iranian Plateau[END_REF]Selway and O'Donnell, 2019;Selway et al., 2019;[START_REF] Rychert | Seismic Imaging of the Base of the Ocean Plates[END_REF][START_REF] Gardés | Unravelling partial melt distribution in the oceanic low velocity zone[END_REF]. Interestingly, reworking, rejuvenation and ultimate loss of deep cratonic lithosphere sections (e.g., North Atlantic craton, North China craton, Tanzania craton) have been suggested to be an expression of intense metasomatic weakening due to repeated passage of volatile-bearing melts [START_REF] Tappe | Craton reactivation on the Labrador Sea margins: 40 Ar/ 39 Ar age and Sr-Nd-Hf-Pb isotope constraints from alkaline and carbonatite intrusives[END_REF][START_REF] Foley | Rejuvenation and erosion of the cratonic lithosphere[END_REF][START_REF] Aulbach | Origins of cratonic mantle discontinuities: A view from petrology, geochemistry and thermodynamic models[END_REF][START_REF] Liu | Thinning and destruction of the lithospheric mantle root beneath the North China Craton: A review[END_REF].

A wide range of magmatic liquids is stable in the upper mantle, ranging from carbonatites with low silica content at high pressures (i.e., great depths), to basanites-basalts with relatively high silica content at low pressures [START_REF] Gudfinnsson | Continuous Gradations among Primary Carbonatitic, Kimberlitic, Melilititic, Basaltic, Picritic, and Komatiitic Melts in Equilibrium with Garnet Lherzolite at 3-8 GPa[END_REF][START_REF] Dasgupta | Carbon-dioxide-rich silicate melt in the Earth's upper mantle[END_REF][START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF]. Indeed, near-solidus melts of peridotite in the presence of CO 2 and H 2 O are typically SiO 2 -poor [START_REF] Foley | The composition of near-solidus melts of peridotite in the presence of CO 2 and H 2 O between 40 and 60 kbar[END_REF], and decreasing pressure and increasing temperature increases the SiO 2 content of peridotite-derived melts [START_REF] Gudfinnsson | Continuous Gradations among Primary Carbonatitic, Kimberlitic, Melilititic, Basaltic, Picritic, and Komatiitic Melts in Equilibrium with Garnet Lherzolite at 3-8 GPa[END_REF][START_REF] Dasgupta | Water follows carbon: CO 2 incites deep silicate melting and dehydration beneath mid-ocean ridges[END_REF][START_REF] Dasgupta | Carbon-dioxide-rich silicate melt in the Earth's upper mantle[END_REF][START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF]. The compositional diversity of mantle-derived melts is evidenced by the variability of intraplate magma compositions observed at the Earth's surface (Fig. 1). Some petrogenetic links have been established between the compositional diversity of mantle-derived magmas from oceanic (e.g., ocean island basalts (OIB)) to continental (e.g., kimberlite) intraplate settings and differences in the pressure of melt extraction from a compositionally similar upwelling mantle source [START_REF] Le Roex | Geochemical correlation between southern African kimberlites and South Atlantic hotspots[END_REF][START_REF] Ringwood | Origin of kimberlites and related magmas[END_REF][START_REF] Gudfinnsson | Continuous Gradations among Primary Carbonatitic, Kimberlitic, Melilititic, Basaltic, Picritic, and Komatiitic Melts in Equilibrium with Garnet Lherzolite at 3-8 GPa[END_REF][START_REF] Tappe | Mantle transition zone input to kimberlite magmatism near a subduction zone: Origin of anomalous Nd-Hf isotope systematics at Lac de Gras, Canada[END_REF][START_REF] Tappe | Geodynamics of kimberlites on a cooling Earth: Clues to plate tectonic evolution and deep volatile cycles[END_REF]. On the other hand, geochemical studies have defined empirical relationships between the composition of basalts and the depth of melt extraction, i.e. the mean extent of melting, which is strongly controlled by lithospheric thickness [START_REF] Ellam | Geophysical evidence from the MELT area for compositional controls on oceanic plates[END_REF][START_REF] Haase | The relationship between the age of the lithosphere and the composition of oceanic magmas: Constraints on partial melting, mantle sources and the thermal structure of the plates[END_REF][START_REF] Prytulak | TiO 2 enrichment in ocean island basalts[END_REF][START_REF] Humphreys | On the composition of ocean island basalts (OIB): The effects of lithospheric thickness variation and mantle metasomatism[END_REF]Dasgupta et al., 2010;[START_REF] Niu | The Origin of Intraplate Ocean Island Basalts (OIB): the Lid Effect and its Geodynamic Implications[END_REF][START_REF] Davies | Lithospheric controls on magma composition along Earth's longest continental hotspot track[END_REF][START_REF] Niu | The petrological control on the lithosphereasthenosphere boundary (LAB) beneath ocean basins[END_REF][START_REF] Guo | Lithosphere thickness controls continental basalt compositions: An illustration using Cenozoic basalts from eastern China[END_REF]. Therefore, first-order variability in primitive basaltic melt compositions appears to relate to lithospheric thickness. However, a unifying model relating melt compositions in diverse tectonic settings, such as oceanic and continental intraplate magmatism, to lithospheric thickness is still lacking. Such a model requires describing chemical and physical properties of mantle melts by interpolating and extrapolating experimental data and comparing them with petrological and geophysical datasets for the terrestrial upper mantle. However, models calculating the compositions and fractions of melts equilibrated with peridotite in the presence of CO 2 ±H 2 O are sparse [START_REF] Dasgupta | Water follows carbon: CO 2 incites deep silicate melting and dehydration beneath mid-ocean ridges[END_REF][START_REF] Dasgupta | Carbon-dioxide-rich silicate melt in the Earth's upper mantle[END_REF][START_REF] Hirschmann | Partial melt in the oceanic low velocity zone[END_REF][START_REF] Ghosh | Phase relations and melting of carbonated peridotite between 10 and 20 GPa: a proxy for alkali-and CO 2 -rich silicate melts in the deep mantle[END_REF][START_REF] Ghiorso | An H 2 O-CO 2 mixed fluid saturation model compatible with rhyolite-MELTS[END_REF][START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF]. Importantly, none of the existing models covers the whole compositional spectrum of mantle-derived melts equilibrated with peridotite within a large pressure-temperature (P-T) window, from carbonatitic to basaltic compositions, or allows for the calculation of both (i) composition and fraction of melt and (ii) corresponding geophysical response of partially molten mantle peridotite.

Here, we report on a new modeling platform, called MAGLAB (http://calculisto.cnrs-orleans.fr/apps/maglab/), which allows within a single framework to calculate (i) the compositions and fractions of melts equilibrated in the upper mantle as a function of its volatile content (CO 2 and H 2 O), and (ii) corresponding electrical conductivities of partially molten peridotite under upper mantle conditions. MAGLAB covers most of the pressuretemperature-volatile conditions of the terrestrial upper mantle and reproduces the full spectrum of intraplate mantle-derived melts within their domain of stability, i.e. from carbonatitic and kimberlitic through to basanitic and basaltic compositions. This approach allows for simulating electrical conductivity profiles within a constrained petrological framework under relevant mantle conditions. The first part of this contribution presents the structure, formulations, and applicability of MAGLAB (Sections 2 and 3). Melt compositions, melt fractions and electrical conductivities of partially molten peridotite as a function of geodynamic setting are highlighted in Section 4. Based on our results, we demonstrate in Section 5, by using melt SiO 2 content as a first-order discriminant, that lithosphere thickness controls primary melt compositions. A diversity of intraplate magma compositions can be produced as a function of the depth of the lithosphere-asthenosphere boundary (LAB) even if only a single volume of upwelling mantle material is involved. The validity of MAGLAB model outputs for both melt fractions and compositions along with geophysical responses is then illustrated for a well-constrained intraplate setting, the Society hotspot in the Pacific Ocean. Section 5 furthermore shows the excellent match between the range of electrical conductivity simulated by MAGLAB for the Earth's upper mantle with realistic heterogeneities in CO 2 -H 2 O content and the heterogeneities in electrical conductivity of the oceanic upper mantle reported from magnetotelluric surveys.

J o u r n a l P r e -p r o o f

The MAGLAB model

MAGLAB aims at calculating the composition and the fraction of melt in chemical equilibrium with mantle peridotite at a given pressure, temperature and bulk rock CO 2 and H 2 O content. As detailed in following sections, MAGLAB calculates melt compositions in the system SiO 2 -TiO 2 -Al 2 O 3 -FeO-CaO-MgO-Na 2 O-K 2 O-H 2 O-CO 2 , based on the silica activity of the melt (i.e., how ideal is the mixing between silica and other melt components). Silica activity is calculated at given P-T conditions and olivine-orthopyroxene compositions, and three compositional end-members (silicate, carbonate, H 2 O) are mixed in order to determine the melt composition that reproduces this activity best. At a given bulk rock CO 2 and H 2 O content, the melt fraction is obtained by mass balance using the CO 2 and H 2 O concentrations of the melt and volatile partitioning between melt and peridotite. Once melt composition and melt fraction have been determined, MAGLAB calculates the electrical conductivity of corresponding partially molten mantle peridotite.

Calculation of melt composition and fraction at upper mantle conditions

The MAGLAB model first calculates melt composition and melt fraction at given pressure, temperature and bulk rock CO 2 and H 2 O content. The compositions of CO 2 -H 2 Obearing melts in pressure-temperature-bulk rock composition space are calculated according to a thermodynamic model modified after [START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF]. The melt-mantle rock equilibrium is simplified according to the reaction , (1) where Mg 2 SiO 4 is the forsterite component of olivine, Mg 2 Si 2 O 6 is the enstatite component of orthopyroxene, and SiO 2 (melt) is the silica component of melt. Equilibrium implies , or

( ) ( ), (2)
where is the standard state Gibbs free energy of reaction (1), is the activity of component i in phase j, R is the gas constant and T the absolute temperature. At given P and T, is obtained by calculating according to the data of Holland and Powell (2011) (Section 1 of the Supplementary Information). Mineral activities are given by and , where and are the mole fraction of Mg in the M1 site and the M2 site of olivine, respectively, and and are the mole fraction of Mg in the M1 site and the M2 site of orthopyroxene, respectively (see more details about calculations of mineral activities in [START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF]). SiO 2 mixing in melt is not J o u r n a l P r e -p r o o f considered ideal. [START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF] found that the activity coefficient of SiO 2 in the melt, , which describes the deviation from ideal behavior of the mixing between SiO 2 and other components [START_REF] Decapitani | A generalized multicomponent excess function with application to immiscible liquids in the system CaO-SiO2-TiO2[END_REF], is well modeled in the SiO 2 -TiO 2 -Al 2 O 3 -FeO-CaO-MgO-Na 2 O-K 2 O-H 2 O-CO 2 space as:

( ) ( ( ) ) ( ) (( ) ( ) ) ( ) ( ) ( ) ( ) , (3)
where the pressure P is expressed in bar, is the molar fraction of oxide i in melt and the are the Margules parameters, i.e. the interaction parameters between two melt oxides i and j. Noteworthy, Eq. ( 3) is modified from [START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF] by the addition of a pressure-dependent Margules parameter for the interaction SiO 2 -CO 2 . This term was added since it allows for a better reproduction of the progressive transition between carbonate-rich to silicate-rich melts with pressure (see details in Section 3; [START_REF] Stagno | Carbon speciation in the asthenosphere: Experimental measurements of the redox conditions at which carbonate-bearing melts coexist with graphite or diamond in peridotite assemblages[END_REF][START_REF] Dasgupta | Carbon-dioxide-rich silicate melt in the Earth's upper mantle[END_REF][START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF]. The activity of SiO 2 in the melt can then be calculated from Eq. (3) according to (4)

The Margules parameters in Eq. (3) are optimized so that calculated from experimental melt compositions following Eq. (4) best reproduces calculated from experimental P and T following Eq. (2) (Tables S1-S2; more details about the calculations and the optimization procedure can be found in [START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF]). The optimization was done over an extended experimental database covering a large range of pressure, temperature and composition conditions relevant to the upper mantle. It regroups 678 melting experiments at pressures and temperatures ranging from 1 to 14 GPa and 1020 to 1950°C, and bulk rock CO 2 and H 2 O contents from 0 to 10 -20 wt% (Fig. 2A; see also Table S3). This corresponds to 187 more entries than in [START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF]. MAGLAB reproduces experimental data to within ~15% based on the average relative deviation of MAGLAB calculations for the whole database (Fig. 3).

Once the Margules parameters are optimized over the experimental database, MAGLAB can be used to calculate mantle-derived melt compositions at any P and T. First, the activity of SiO 2 in the melt is calculated from Eq.

(2) at P and T of interest, assuming a pressure-dependent activity ratio for the upper mantle estimated from experimental data (Fig. S1; see details in Section 2 of the Supplementary Information). Then, the method consists in finding the composition for which the SiO 2 activity calculated from Eq. ( 4) matches the SiO 2 activity calculated from Eq. ( 2) (see Fig. S2). However, J o u r n a l P r e -p r o o f instead of searching for a solution in the whole SiO 2 -TiO 2 -Al 2 O 3 -FeO-CaO-MgO-Na 2 O-K 2 O-H 2 O-CO 2 compositional space, we designed MAGLAB to work in the space of three endmembers: silicate , carbonate and H 2 O . The melt composition is thus calculated as a linear combination of the three end-members, i.e.

, where the coefficients , and are optimized for minimizing the difference between and (with , and being all positive and such that

). The use of these three end-members reduces the degrees of freedom but their compositions were defined in a way that their combination covers most of the compositional range of both experimental and natural melts (Figs 2B-S3). This procedure allows for reproducing a wide range of natural volatile-bearing melts produced in equilibrium with peridotite, from carbonatites to kimberlites to basanites and basalts. Strongly alkaline magmas and intrusive carbonatites, as well as some kimberlites and basalts, may require additional differentiation processes or the involvement of other lithologies such as eclogite, pyroxenite or hornblendite, which are not treated by the present model [START_REF] Hirschmann | Alkalic magmas generated by partial melting of garnet pyroxenite[END_REF][START_REF] Sobolev | The Amount of Recycled Crust in Sources of Mantle-Derived Melts[END_REF][START_REF] Pilet | Metasomatized Lithosphere and the Origin of Alkaline Lavas[END_REF][START_REF] Doucelance | Geochemical constraints on depth of origin of oceanic carbonatites: The Cape Verde case[END_REF]Baudouin et al., 2016;[START_REF] Tappe | Sources and mobility of carbonate melts beneath cratons, with implications for deep carbon cycling, metasomatism and riftinitiation[END_REF][START_REF] Weidendorfer | A common origin of carbonatite magmas[END_REF][START_REF] Lu | Lithospheric memory of subduction in mantle pyroxenite xenoliths from rift-related basalts[END_REF]. Note that the compositions of the silicate and carbonate melt end-members are not constant but vary as a function of pressure (Fig. S4 and Table S4). Moreover, the pure H 2 O endmember allows water content to vary independently from CO 2 content, contrary to the model of [START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF]. Details on calculations and compositions of the melt endmembers are provided in Section 3 of the Supplementary Information.

In addition to melt composition, melt fraction can also be determined using volatile partitioning. CO 2 is treated as highly incompatible, i.e. entirely residing in the melt (e.g. [START_REF] Dasgupta | Carbon-dioxide-rich silicate melt in the Earth's upper mantle[END_REF]. The H 2 O content of the melt is constrained using partition coefficients for nominally anhydrous minerals/hydrous silicate melt systems from [START_REF] Hirschmann | Dehydration melting of nominally anhydrous mantle: The primacy of partitioning[END_REF] and [START_REF] Novella | The distribution of H 2 O between silicate melt and nominally anhydrous peridotite and the onset of hydrous melting in the deep upper mantle[END_REF]. Note that H 2 O solubility does not significantly differ between CO 2 -poor basaltic melts and CO 2 -rich, low-SiO 2 melts [START_REF] Dasgupta | Carbon-dioxide-rich silicate melt in the Earth's upper mantle[END_REF][START_REF] Moussallam | H 2 O-CO 2 solubility in low SiO 2melts and the unique mode of kimberlite degassing and emplacement[END_REF]. Thus, the mass fraction of melt, , can be calculated either from CO 2 partitioning , ( 5 2014) (see details in Section 4 of the Supplementary Information). Hence, two different melt fractions can be obtained when varying and independently following Eqs. ( 5) and ( 6), which should converge to an identical value. The optimizations of melt composition and melt fraction are thus performed concomitantly in such a way that ( ) ( ) (8) is minimized (see details about the optimization procedure in Section 5 of the Supplementary Information).

For some pressure-temperature-bulk rock composition conditions, melt composition cannot be unequivocally predicted and MAGLAB yields two distinct solutions, carbonate-rich and silicate-rich. This numerical feature, which relies on the Margules formalism used to calculate in Eq. ( 2), occurs mainly at low P-T conditions and for H 2 O-poor peridotite systems. It is indicative of the non-ideality in the mixing between silicate and carbonate components at these conditions, which ultimately results in immiscibility [START_REF] Dasgupta | Carbon-dioxide-rich silicate melt in the Earth's upper mantle[END_REF][START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF]. However, we expect only one liquid to be stabilized because immiscibility is not reported in most of the experimental studies of melting in peridotitic compositions (Martin and Schmidt, 2013;[START_REF] Hammouda | Melting in the mantle in the presence of carbon: Review of experiments and discussion on the origin of carbonatites[END_REF]. Since silicate-rich melts are favored at high T and low P and, conversely, carbonate-rich melts are favored at low T and high P, we use a pressure-dependent formulation to determine, at a given P, the most probable stable melt composition between these two distinct compositional solutions as a function of T (Fig. S5).

J o u r n a l P r e -p r o o f

Calculation of the electrical conductivity for model mantle peridotite

The second part of MAGLAB calculates the bulk electrical properties of mantle rocks with melt composition and melt fraction equilibrated at P, T and bulk rock CO 2 and H 2 O content. As volatile-bearing melts interconnect in mantle rocks at any melt fraction [START_REF] Gardés | Unravelling partial melt distribution in the oceanic low velocity zone[END_REF], the bulk electrical conductivity of partially molten mantle peridotite is a combination of the conductivity of the rock and the conductivity of the melt weighted by melt fraction.

The electrical conductivity of melt is calculated following the model of [START_REF] Sifré | Electrical conductivity during incipient melting in the oceanic low-velocity zone[END_REF][START_REF] Sifré | Effects of temperature, pressure and chemical compositions on the electrical conductivity of carbonated melts and its relationship with viscosity[END_REF] for CO 2 -and H 2 O-bearing melts

( ( ) ) ( ( )
), (9

)
where P is the pressure (bar), and and are the pre-exponential factor (S m -1 ) and the activation energy (J mol -1 ), respectively, for the two Arrhenius laws describing the contributions of the hydrous silicate component (

) and the carbonate component ( )

( ) with ( ) , (10) and ( ) with ( ) . (11)
This law is valid for from 0 to ~50 wt% and from 0 to ~10 wt%.

The electrical conductivity of the solid rock is assumed to be controlled by the conductivity of olivine. We use the model of [START_REF] Gardés | Toward a unified hydrous olivine electrical conductivity law[END_REF] which provides conductivity as a function of temperature and H 2 O content

( ) ( ) ( ) ( ( )
). ( 12)

, the mass fraction of water in olivine in wt%, is given by , (13) where is the partition coefficient of H 2 O between olivine and melt (see Section 4 of the Supplementary Information).

Following [START_REF] Sifré | Electrical conductivity during incipient melting in the oceanic low-velocity zone[END_REF], the mixing model for calculating the bulk conductivity of partially molten mantle peridotite is taken as a combination of an Hashin-Shtrikman upper bound (HS+) mixing model and a tube mixing model (e.g. [START_REF] Schmeling | Numerical models on the influence of partial melt on elastic, anelastic and electrical properties of rocks. Part II electrical conductivity[END_REF] J o u r n a l P r e -p r o o f

(( ( ) ) ) ( (
) ), (14) where the volume fraction of melt is given by

( ) ( ( )
)

. ( 15)

Olivine density is taken as 3.34 (average of values given for olivine in both spinel and garnet peridotite in Table 1a of [START_REF] Lee | Compositional variation of density and seismic velocities in natural peridotites at STP conditions: Implications for seismic imaging of compositional J o u r n a l P r e -p r o o f Journal Pre-proof heterogeneities in the upper mantle[END_REF]). Following [START_REF] Sifré | Electrical conductivity during incipient melting in the oceanic low-velocity zone[END_REF], melt density is calculated as

( ) , (16) with , and .
J o u r n a l P r e -p r o o f

MAGLAB: comparison with previous models

In contrast to models developed for dry and hydrous silicate magmatic systems (e.g., MELTS family: [START_REF] Ghiorso | Chemical mass transfer in magmatic processes IV. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid-solid equilibria in magmatic systems at elevated temperatures and pressures[END_REF], [START_REF] Ghiorso | The pMELTS: A revision of MELTS for improved calculation of phase relations and major element partitioning related to partial melting of the mantle to 3 GPa[END_REF], [START_REF] Gualda | Rhyolite-MELTS: a Modified Calibration of MELTS Optimized for Silica-rich, Fluid-bearing Magmatic Systems[END_REF]; COMAGMAT: [START_REF] Ariskin | Phase equilibria modeling in igneous petrology: use of COMAGMAT model for simulating fractionation of ferro-basaltic magmas and the genesis of high-alumina basalt[END_REF]; PerpleX: Connolly ( 2005)), only a few models allow for calculating the composition and fraction of melts derived from peridotite melting in the presence of CO 2 and H 2 O, and their range of applicability is limited, especially in terms of composition and pressure. The model of [START_REF] Ghiorso | An H 2 O-CO 2 mixed fluid saturation model compatible with rhyolite-MELTS[END_REF] addresses silicate melts with limited dissolved CO 2 and H 2 O components and is not relevant to investigating carbonate-rich melts with CO 2 content >~10 wt% or P > 3 GPa. Calculation of melt composition is limited to CO 2 , H 2 O and SiO 2 oxides in the model of [START_REF] Dasgupta | Carbon-dioxide-rich silicate melt in the Earth's upper mantle[END_REF], CO 2 and H 2 O in the model of [START_REF] Hirschmann | Partial melt in the oceanic low velocity zone[END_REF], and to CO 2 only in the models of [START_REF] Dasgupta | Water follows carbon: CO 2 incites deep silicate melting and dehydration beneath mid-ocean ridges[END_REF] and [START_REF] Ghosh | Phase relations and melting of carbonated peridotite between 10 and 20 GPa: a proxy for alkali-and CO 2 -rich silicate melts in the deep mantle[END_REF]. Furthermore, the pressure range of application is ≤5 GPa for the models of [START_REF] Dasgupta | Water follows carbon: CO 2 incites deep silicate melting and dehydration beneath mid-ocean ridges[END_REF][START_REF] Dasgupta | Carbon-dioxide-rich silicate melt in the Earth's upper mantle[END_REF], [START_REF] Hirschmann | Partial melt in the oceanic low velocity zone[END_REF] and [START_REF] Ghiorso | An H 2 O-CO 2 mixed fluid saturation model compatible with rhyolite-MELTS[END_REF], and >10 GPa for the model of [START_REF] Ghosh | Phase relations and melting of carbonated peridotite between 10 and 20 GPa: a proxy for alkali-and CO 2 -rich silicate melts in the deep mantle[END_REF]. Thus, none of these models allows calculations at pressures between 5 and 10 GPa. The model of [START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF] does not allow varying bulk rock CO 2 and H 2 O contents independently. To date, MAGLAB is the model simulating the widest ranges of temperature and pressure, from ~900 to 1700°C and from ~2 to 10 GPa (i.e., from ~60 to 300 km depth). It allows composition calculations in SiO 2 -TiO 2 -Al 2 O 3 -FeO-CaO-MgO-Na 2 O-K 2 O-H 2 O-CO 2 space where, notably, CO 2 and H 2 O are independent variables.

A key feature of mantle-relevant melting is the abrupt transition from carbonatitic melts (<15 wt% SiO 2 ) to silicate-rich melts (>30 wt% SiO 2 ), as illustrated by experimental data at e.g. 3 and 5 GPa where the transition occurs at ~1350°C and ~1450°C respectively (Fig. 4A-B). At 3 and 5 GPa, both [START_REF] Dasgupta | Water follows carbon: CO 2 incites deep silicate melting and dehydration beneath mid-ocean ridges[END_REF] and [START_REF] Dasgupta | Carbon-dioxide-rich silicate melt in the Earth's upper mantle[END_REF] do not reproduce this abrupt transition. At 5 GPa, the model of [START_REF] Dasgupta | Carbon-dioxide-rich silicate melt in the Earth's upper mantle[END_REF] yields an almost linear positive evolution of the SiO 2 content with increasing temperature corresponding to a near ideal system. At 3 GPa, the model of [START_REF] Dasgupta | Water follows carbon: CO 2 incites deep silicate melting and dehydration beneath mid-ocean ridges[END_REF] fails to predict the formation of carbonatite melts at low temperatures (Fig. 4A). On the other hand, MAGLAB captures this chemical shift at 3 and 5 GPa, as does the model of [START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF] (Fig. 4A-B). In contrast, MAGLAB produces a smoother transition from carbonaterich melts to silicate-rich melts at higher pressures, as observed experimentally at e.g. 7 and 10 GPa, which is not well captured in the model of [START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF] (Fig. 4C-D).

Thus, MAGLAB fairly well reproduces the wide range of mantle-relevant, CO 2 ±H 2 Obearing melts. It applies to pressures and temperatures covering most of Earth's upper mantle regions subject to (CO 2 +H 2 O)-assisted melting [START_REF] Wallace | An experimental determination of primary carbonatite magma composition[END_REF][START_REF] Foley | The composition of near-solidus melts of peridotite in the presence of CO 2 and H 2 O between 40 and 60 kbar[END_REF] which, away from ridges, starts at depths >~60 km beneath mature to old oceanic lithosphere (Fig. 5). Moreover, in addition to melt composition, MAGLAB also allows the calculation of melt fraction and corresponding bulk rock electrical conductivity. It should be noted, however, that MAGLAB calculations are valid as long as oxygen fugacity stabilizes carbonates as important carbon species, i.e. in upper mantle regions, estimated between ~60 km and ~300 km depth [START_REF] Wallace | An experimental determination of primary carbonatite magma composition[END_REF][START_REF] Hirschmann | Partial melt in the oceanic low velocity zone[END_REF][START_REF] Rohrbach | Redox freezing and melting in the Earth's deep mantle resulting from carbon-iron redox coupling[END_REF][START_REF] Stagno | The oxidation state of the mantle and the extraction of carbon from Earth's interior[END_REF][START_REF] Gaillard | The redox geodynamics linking basalts and their mantle sources through space and time[END_REF][START_REF] Yaxley | Redox preconditioning deep cratonic lithosphere for kimberlite genesisevidence from the central Slave Craton[END_REF][START_REF] Dasgupta | Volatile-bearing partial melts beneath oceans and continentswhere, how much, and of what compositions[END_REF][START_REF] Eguchi | Redox state of the convective mantle from CO 2trace element systematics of oceanic basalts[END_REF][START_REF] Moussallam | Mantle plumes are oxidised[END_REF][START_REF] Gardés | Unravelling partial melt distribution in the oceanic low velocity zone[END_REF]. Furthermore, calculations are not possible at zero bulk rock CO 2 content and in a set of extreme P-T-volatile content conditions, e.g. at low P <5 GPa in very hot mantle with potential temperature T P >1500-1600°C, or even at higher pressures for bulk rock CO 2 -H 2 O contents >0.1-0.2 wt% and with H 2 O/CO 2 molar ratio >10-20 (see details in Section 6 of the J o u r n a l P r e -p r o o f

MAGLAB simulations of oceanic and cratonic mantle

We used MAGLAB to calculate melt composition, melt fraction and associated electrical conductivity of the upper mantle in oceanic and cratonic settings, with focus on three main parameters: lithospheric thickness, mantle potential temperature (T P ), and mantle CO 2 -H 2 O content. It should be noticed that the following results correspond to equilibrium melt fractions and compositions, and thus do not consider dynamic phenomena such as melt migration, melt accumulation and depletion processes. The position of the base of the lithosphere, i.e. LAB depth, can be approximately located within the thermal boundary layer where a time-dependent thermal transition from the conductive to fully convecting upper mantle occurs [START_REF] Parsons | Mantle Convection and the Thermal Structure of the Plates[END_REF][START_REF] Mckenzie | The Volume and Composition of Melt Generated by Extension of the Lithosphere[END_REF][START_REF] Jaupart | The thermal structure and thickness of continental roots[END_REF][START_REF] Mckenzie | Thermal structure of oceanic and continental lithosphere[END_REF][START_REF] An | Temperature, lithosphere-asthenosphere boundary, and heat flux beneath the Antarctic Plate inferred from seismic velocities[END_REF][START_REF] Priestley | A Lithosphere-Asthenosphere Boundary-a Global Model Derived from Multimode Surface-Wave Tomography and J o u r n a l P r e -p r o o f Journal Pre-proof Petrology[END_REF]. It is hereafter defined at the base of this thermal boundary layer [START_REF] Jaupart | The thermal structure and thickness of continental roots[END_REF][START_REF] An | Temperature, lithosphere-asthenosphere boundary, and heat flux beneath the Antarctic Plate inferred from seismic velocities[END_REF] as the depth where mantle temperature is lowered by 10°C from the temperature of the adiabatic geotherm. Although we acknowledge that our definition for identifying the base of the lithosphere is somewhat simplistic in comparison with the complex and diffuse nature of the lithosphere-asthenosphere transition, this method provides a reasonable estimation of the lithospheric thickness, with the advantage of being consistent when applied to different tectonic settings. Fig. 5 reports MAGLAB simulations for an ambient oceanic upper mantle with average volatile content, i.e. 140 wt ppm CO 2 -240 wt ppm H 2 O (Le [START_REF] Voyer | Heterogeneity in mantle carbon content from CO 2 -undersaturated basalts[END_REF], and a potential temperature T P of 1350°C (thermal model G13R1350 from [START_REF] Grose | Comprehensive plate models for the thermal evolution of oceanic lithosphere[END_REF]). The most striking result is the contrast in melt composition and melt fraction between the asthenosphere and the lithosphere.

In the asthenosphere, from high to low pressure, both melt SiO 2 content and melt fraction increase while melt CO 2 content and bulk electrical conductivity decrease. The evolution of melt composition is consistent with the increase in silica activity with decreasing pressure [START_REF] Carmichael | Silica activity in igneous rocks[END_REF][START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF], as well as with the systematic complementarity of melt CO 2 content and melt SiO 2 content observed experimentally (e.g. [START_REF] Gudfinnsson | Continuous Gradations among Primary Carbonatitic, Kimberlitic, Melilititic, Basaltic, Picritic, and Komatiitic Melts in Equilibrium with Garnet Lherzolite at 3-8 GPa[END_REF][START_REF] Dasgupta | Water follows carbon: CO 2 incites deep silicate melting and dehydration beneath mid-ocean ridges[END_REF][START_REF] Dasgupta | Carbon-dioxide-rich silicate melt in the Earth's upper mantle[END_REF][START_REF] Ghosh | Phase relations and melting of carbonated peridotite between 10 and 20 GPa: a proxy for alkali-and CO 2 -rich silicate melts in the deep mantle[END_REF]. At around 300 km depth, a fraction of ~0.05 wt% (0.06 vol.%) of carbonatitic melt is produced, with SiO 2 , CO 2 and H 2 O contents of ~11, 31 and 4 wt%, respectively, and mantle electrical conductivity is about 10 -0.9 S m -1 . At 80 km depth beneath ridges to young lithospheres (<~10 Ma), a fraction of 0.24 wt% (0.30 vol%) of silicate-rich melt is produced, with SiO 2 , CO 2 and H 2 O contents of ~42, 6 and 2 wt%, respectively, and is ~10 -1.4 S m -1 . Noteworthy, for constant volatile content in the source, variations reported in mantle electrical conductivity are buffered by the opposite effects of melt composition and melt fraction: for example, volatile contents increase , but smaller melt fractions decrease it.

The evolution strongly differs beneath mature to old lithospheres (>~50 Ma), where both melt SiO 2 content and melt fraction drop while melt CO 2 content rises in the lithosphere. These abrupt changes in melt composition and melt fraction from asthenosphere to lithosphere are a direct consequence of the abrupt change in temperature (Fig. 4), and may be accompanied by a slight increase in bulk electrical conductivity (e.g., near LAB depth at 120-125 km in an ambient oceanic upper mantle with average volatile content; see profile -Ambient‖ in Fig. 6F). At 80 km depth in 70 Ma oceanic lithosphere, a fraction of 0.03 wt% (0.05 vol%) of carbonatitic melt is produced, with SiO 2 , CO 2 and H 2 O contents of ~2, 42 and 2.5 wt%, respectively, and is about 10 -1.45 S m -1 . Note that melting stops when crossing the CO 2 -H 2 O-bearing peridotite solidus above 60-70 km depth beneath mature to old J o u r n a l P r e -p r o o f lithospheres (P <~2 GPa and T <~930-1100°C; grey areas in Fig. 5, see also Fig. 2). Then, mantle electrical conductivity is mainly controlled by olivine, with values <10 -2 S m -1 [START_REF] Gardés | Toward a unified hydrous olivine electrical conductivity law[END_REF].

The base of mature to old lithospheres thus corresponds to a region where melt fraction is maximum. At the vicinity of the LAB beneath >~50 Ma lithospheres, i.e. at 120-125 km depth, a fraction of 0.14 wt% (0.17 vol%) of silicate-rich melt is present, with SiO 2 , CO 2 and H 2 O contents of ~35, 10 and 3 wt%, respectively, and mantle electrical conductivity is about 10 -1.2 S m -1 .

Melt composition, melt fraction and mantle electrical conductivity profiles in 70 Ma oceanic lithosphere for various T P and volatile contents are reported in Figs 6 and7, respectively. In Fig. 6, we report calculations for a mantle with average volatile content and various T P of 1300, 1350, 1400 and 1450°C (G13R1300, G13R1350, G13R1400 and G13R1450 models from Grose and Afonso ( 2013)), corresponding to cold, ambient, hot, and hotspot settings, respectively. Near the LAB, at ~115-125 km depth, MAGLAB yields melt compositions ranging from ~7 to 40 wt% SiO 2 , 37 to 5 wt% CO 2 , and 4 to 3 wt% H 2 O from cold mantle (~1350°C at LAB depth) to hotspot-like mantle (~1500°C at LAB depth), respectively (Fig. 6A-D). Melt fraction ranges between 0.04 and 0.26 wt% (0.05-0.32 vol%) within the same temperature interval (Fig. 6E), while slightly increases from 10 -1.15 to 10 -1.06 S m -1 approximately (Fig. 6F). Note that most of the variations in composition and melt fraction occurs between cold and ambient settings since, e.g., the range of SiO 2 content reduces to 35-40 wt% from ambient to hotspot settings. The electrical conductivity remains, however, rather constant because the large variation in melt composition, changing from silicate-rich in hotspot settings to carbonatitic in cold settings, is compensated by a large decrease in melt fraction.

In Fig. 7, mantle CO 2 and H 2 O contents are varied around their average contents in an ambient mantle: 50 -80, 140 -240 and 420 -720 wt ppm CO 2wt ppm H 2 O, corresponding to depleted, average, and enriched mantle source, respectively. Near LAB depth, depleted to enriched sources produce silicate-rich melts with an almost constant melt SiO 2 content of around 35 wt%, a slightly variable melt CO 2 content ranging from 11 to 8 wt%, and a more variable melt H 2 O content spanning the range 1-6 wt%, respectively (Fig. 7B-D). On the other hand, melt fraction dramatically increases from about 0.04 to 0.54 wt% (~0.05-0.68 vol%) from depleted to enriched sources, respectively, illustrating the strong dependence of melt fraction on volatile content (Fig. 7E). As a consequence, contrary to temperature variations, the large increase in melt fraction together with variations in melt volatile content from depleted to enriched volatile content induce a large variation in electrical conductivity, from 10 -1.54 to 10 -0.76 S m -1 (Fig. 7F).

Importantly, at any of the temperature and bulk rock volatile content simulated, no transitional melts with intermediate compositions between silicate-rich and carbonatitic melt, i.e. carbonated silicate melts with SiO 2 content within the range 15-35 wt%, are obtained near the LAB in oceanic mantle. In contrast, the asthenosphere beneath extremely thick continental lithosphere, such as in undisturbed cratonic regions, can give rise to melts with low to intermediate SiO 2 contents at realistic pressure-temperature-volatile content conditions (Fig. 8B). We performed MAGLAB calculations along a typical cratonic geotherm, with T P = 1350°C and considering various bulk rock volatile contents as previously described (see details about geotherm in Figs 8A-S6 and their caption). Near the LAB, at ~210 km depth, while depleted to average mantle sources produce carbonatitic melts with <~15 wt% SiO 2 , >~30 wt% CO 2 and <~5 wt% H 2 O, enriched sources produce kimberlitic melt with intermediate SiO 2 and CO 2 contents of ~22 and ~18 wt%, respectively, and an H 2 O content of J o u r n a l P r e -p r o o f about 9 wt% (Fig. 8B-D). Noteworthy, similar kimberlitic, transitional melts are calculated in the case of a CO 2 -average and H 2 O-enriched mantle (i.e., with 140 wt ppm CO 2 -720 wt ppm H 2 O; Fig. 8B). As with oceanic mantle, melt fraction at LAB depth beneath cratonic settings largely increases from depleted to enriched sources, from ~0.01 to 0.24 wt% (0.02-0.31 vol%), which, coupled with variations in melt volatile content, induces a large increase in electrical conductivity, from about 10 -1.4 to 10 -0.5 S m -1 (Fig. 8E-F).

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Discussion

Linking the diversity of mantle-sourced intraplate magmatism to lithosphere thickness

The composition of intraplate magmas generally relates to the tectonic setting in which they were produced, with mid-ocean ridge basalts (MORB) sampled around oceanic ridges, OIBs mainly erupted over ocean floors away from plate boundaries, and kimberlites quasi-exclusively observed on continental shields, mainly on-craton. These systematics indicate that geodynamic context exerts a primary control on the compositional spectrum of intraplate magmatism. One of the main features varying between different tectonic settings is lithosphere thickness, being thin near oceanic ridges and thick beneath most cratons. It is therefore reasonable to assume that variations in lithosphere thickness may generate variations in primitive melt composition, without invoking large compositional variations in the mantle sources [START_REF] Le Roex | Geochemical correlation between southern African kimberlites and South Atlantic hotspots[END_REF][START_REF] Ringwood | Origin of kimberlites and related magmas[END_REF][START_REF] Gudfinnsson | Continuous Gradations among Primary Carbonatitic, Kimberlitic, Melilititic, Basaltic, Picritic, and Komatiitic Melts in Equilibrium with Garnet Lherzolite at 3-8 GPa[END_REF][START_REF] Tappe | Mantle transition zone input to kimberlite magmatism near a subduction zone: Origin of anomalous Nd-Hf isotope systematics at Lac de Gras, Canada[END_REF][START_REF] Tappe | Melt evolution beneath a rifted craton edge: 40Ar/39Ar geochronology and Sr-Nd-Hf-Pb isotope systematics of primitive alkaline basalts and lamprophyres from the SW Baltic Shield[END_REF][START_REF] Tappe | Geodynamics of kimberlites on a cooling Earth: Clues to plate tectonic evolution and deep volatile cycles[END_REF][START_REF] Grose | Chemical Disequilibria, Lithospheric Thickness, and the Source of Ocean Island Basalts[END_REF][START_REF] Baudouin | Phlogopite-Olivine Nephelinites Erupted During Early Stage Rifting, North Tanzanian Divergence[END_REF]. A critical effect of lithosphere thickness on the composition of mantle-derived intraplate alkaline basalts and basalts (i.e., melts with >40 wt% SiO 2 ) has been outlined in previous geochemical studies: with increasing lithospheric thickness, the final equilibrium pressure before melt extraction increases, lowering the degree of melting and thus lowering melt SiO 2 and Al 2 O 3 contents, while increasing MgO and FeO contents [START_REF] Haase | The relationship between the age of the lithosphere and the composition of oceanic magmas: Constraints on partial melting, mantle sources and the thermal structure of the plates[END_REF][START_REF] Humphreys | On the composition of ocean island basalts (OIB): The effects of lithospheric thickness variation and mantle metasomatism[END_REF]Dasgupta et al., 2010;[START_REF] Niu | The Origin of Intraplate Ocean Island Basalts (OIB): the Lid Effect and its Geodynamic Implications[END_REF][START_REF] Davies | Lithospheric controls on magma composition along Earth's longest continental hotspot track[END_REF]Zhang et al., 2017;[START_REF] Guo | Lithosphere thickness controls continental basalt compositions: An illustration using Cenozoic basalts from eastern China[END_REF]. Furthermore, a natural example for the continuum of melt composition ranging from kimberlitic to OIB-type alkaline basaltic was described in [START_REF] Tappe | Craton reactivation on the Labrador Sea margins: 40 Ar/ 39 Ar age and Sr-Nd-Hf-Pb isotope constraints from alkaline and carbonatite intrusives[END_REF], where changes in magma composition through time are explained as a function of significant lithosphere thinning of a single cratonic block. Excluded from this concept are lamproites and other highly potassic magma types, as well as intrusive carbonatites, because these intraplate magmas have typically experienced variable contributions from strongly metasomatized nonperidotitic components of the mantle lithosphere, or they can be highly differentiated in nature [START_REF] Becker | Geochemistry of South African On-and Offcraton, Group I and Group II Kimberlites: Petrogenesis and Source Region Evolution[END_REF][START_REF] Pilet | Metasomatized Lithosphere and the Origin of Alkaline Lavas[END_REF][START_REF] Doucelance | Geochemical constraints on depth of origin of oceanic carbonatites: The Cape Verde case[END_REF][START_REF] Weidendorfer | A common origin of carbonatite magmas[END_REF][START_REF] Tappe | Sources and mobility of carbonate melts beneath cratons, with implications for deep carbon cycling, metasomatism and riftinitiation[END_REF].

Here, we use MAGLAB to simulate the effect of varying lithosphere thickness on primitive melt composition by calculating volatile-bearing melt compositions in equilibrium with peridotite near the LAB and comparing them with corresponding erupted magmas. We performed MAGLAB simulations by varying LAB depth as a function of the tectonic setting (see P-T conditions in Fig. S7), and considering a single homogeneous mantle source with 140 wt ppm CO 2 and 240 wt ppm H 2 O on average (Le [START_REF] Voyer | Heterogeneity in mantle carbon content from CO 2 -undersaturated basalts[END_REF]. Using the SiO 2 content as a relevant proxy for the compositional variability of intraplate magmatism in Fig. 9, the composition of erupted basaltic magmas such as MORBs and OIBs with SiO 2 >45 wt% are well reproduced by MAGLAB beneath the thinnest and youngest oceanic lithospheres with LAB depths <60 km. Primitive alkaline magmas such as melilitites, nephelinites, basanites and silica-poor OIBs with 35-45 wt% SiO 2 are reproduced by MAGLAB beneath the thickest oceanic lithospheres away from modern spreading centers, as well as beneath young or rejuvenated continents with LAB depths ranging from around 60 to 125 km (Fig. 9). Interestingly, rare occurrences of alnoitic CO 2 -rich intrusions with SiO 2 ~36 wt% have been reported at the surface of the ~120-km-thick lithosphere of the Ontong Java Plateau [START_REF] Neal | An unmetasomatized source for the Malaitan alnöite (Solomon Islands): petrogenesis involving zone refining, megacryst fractionation, and assimilation of oceanic lithosphere[END_REF][START_REF] Simonetti | In-situ chemical, U-Pb dating, and Hf isotope investigation of megacrystic zircons, Malaita (Solomon Islands): Evidence for multi-stage alkaline magmatic activity beneath the Ontong Java Plateau[END_REF][START_REF] Smart | K-rich hydrous mantle lithosphere beneath the Ontong Java Plateau: Significance for the genesis of oceanic basalts and Archean continents[END_REF], and this SiO 2 content is well reproduced in our MAGLAB calculations at such LAB depth (i.e., ~35 wt% SiO 2 ; Figs 5B, J o u r n a l P r e -p r o o f 9). In addition, MAGLAB predicts mantle-derived melts with a SiO 2 content of ~40 wt% beneath ~90-km-thick lithosphere, similar to the petit-spot magmas erupted directly from the asthenospheric source located beneath the flexed sections of the oceanic lithosphere prior to entering subduction zones [START_REF] Hirano | Volcanism in Response to Plate Flexure[END_REF][START_REF] Matsuno | Upper mantle electrical resistivity structure beneath the central Mariana subduction system[END_REF][START_REF] Machida | Petit-spot as definitive evidence for partial melting in the asthenosphere caused by CO 2[END_REF][START_REF] Sato | Direct ascent to the surface of asthenospheric magma in a region of convex lithospheric flexure[END_REF]. Generation of kimberlites also fits well into this hypothesis, with primary melts with 15-35 wt% SiO 2 being produced at >120 to ~200 km depth beneath continental shields including cratons (Fig. 9; [START_REF] Gudfinnsson | Continuous Gradations among Primary Carbonatitic, Kimberlitic, Melilititic, Basaltic, Picritic, and Komatiitic Melts in Equilibrium with Garnet Lherzolite at 3-8 GPa[END_REF][START_REF] Brey | Influence of water and fluorine on melting of carbonated peridotite at 6 and 10 GPa[END_REF][START_REF] Foley | The composition of near-solidus melts of peridotite in the presence of CO 2 and H 2 O between 40 and 60 kbar[END_REF][START_REF] Stamm | Asthenospheric kimberlites: Volatile contents and bulk compositions at 7 GPa[END_REF][START_REF] Tappe | Sources and mobility of carbonate melts beneath cratons, with implications for deep carbon cycling, metasomatism and riftinitiation[END_REF][START_REF] Giuliani | Kimberlites: From Deep Earth to Diamond Mines[END_REF][START_REF] Sun | Slab-mantle interaction, carbon transport, and kimberlite generation in the deep upper mantle[END_REF]. Such carbonated silicate melt compositions can be equilibrated beneath typical LAB depths of undisturbed cratons (i.e., 180-250 km) in warmer thermal conditions, with T P >~1350-1400°C, equivalent to the peripheries of modern mantle plumes or Early Proterozoic and Archean ambient upper mantle conditions [START_REF] Korenaga | Urey ratio and the structure and evolution of Earth's mantle[END_REF][START_REF] Davies | Effect of plate bending on the Urey ratio and the thermal evolution of the mantle[END_REF][START_REF] Ganne | Primary magmas and mantle temperatures through time[END_REF][START_REF] Aulbach | Eclogites as Palaeodynamic Archives: Evidence for Warm (not hot) and Depleted (but heterogeneous and evolving) Archaean Ambient Mantle[END_REF]Sun and Dasgupta, 2020; see also Fig. 6B). However, many kimberlite occurrences at the Earth's surface were emplaced between 50-250 Ma [START_REF] Tappe | Geodynamics of kimberlites on a cooling Earth: Clues to plate tectonic evolution and deep volatile cycles[END_REF], a period for which the Earth's mantle presented a thermal regime similar to present-day (difference in T P <40-50°C; [START_REF] Korenaga | Urey ratio and the structure and evolution of Earth's mantle[END_REF][START_REF] Davies | Effect of plate bending on the Urey ratio and the thermal evolution of the mantle[END_REF][START_REF] Ganne | Primary magmas and mantle temperatures through time[END_REF][START_REF] Aulbach | Eclogites as Palaeodynamic Archives: Evidence for Warm (not hot) and Depleted (but heterogeneous and evolving) Archaean Ambient Mantle[END_REF]. Furthermore, genetic connections between kimberlite magma generation and mantle plumes are still debated (see for example [START_REF] Tappe | The tungsten-182 record of kimberlites above the African superplume: Exploring links to the core-mantle boundary[END_REF]. Alternatively, primary transitional carbonated silicate melts can also be produced beneath such undisturbed cratons with higher H 2 O content in the bulk peridotite (e.g., carbonatitic melts equilibrated near the LAB at 210 km depth in a mantle source with 140 wt ppm CO 2 -240 wt ppm H 2 O versus kimberlitic melts equilibrated in a mantle source with 140 wt ppm CO 2 -720 wt ppm H 2 O; see Section 4 and Fig. 8B), as is supported by the experimental work of [START_REF] Stamm | Asthenospheric kimberlites: Volatile contents and bulk compositions at 7 GPa[END_REF]. Therefore, our simulations indicate that presence of kimberlitic melts beneath undisturbed cratons may be related to greater H 2 O enrichment in the mantle source. Similarly, either excess temperatures or H 2 O enrichments in the mantle source would explain generation of basalts with >45 wt% SiO 2 beneath strongly disturbed cratons with drastically thinned lithospheres (~60-100 km) within our scenario (e.g., East African rift, Wyoming, North China; see Aulbach, 2019, and references therein).

The empirical observation that variations in lithosphere thickness primarily govern the compositional diversity of primitive mantle-derived magmatism [START_REF] Gudfinnsson | Continuous Gradations among Primary Carbonatitic, Kimberlitic, Melilititic, Basaltic, Picritic, and Komatiitic Melts in Equilibrium with Garnet Lherzolite at 3-8 GPa[END_REF][START_REF] Tappe | Craton reactivation on the Labrador Sea margins: 40 Ar/ 39 Ar age and Sr-Nd-Hf-Pb isotope constraints from alkaline and carbonatite intrusives[END_REF] is fully supported by MAGLAB modeling. The compositions of erupted magmas correspond to those equilibrated at LAB depths (Fig. 9), from where they appear to be extracted. This may explain why low-SiO 2 melts such as kimberlites and aillikites are mainly found under geologically reasonable conditions on continental shields including cratons, which are characterized by the deepest known lithosphere-asthenosphere boundaries at 150-250 km depths (e.g., [START_REF] Aulbach | Origins of cratonic mantle discontinuities: A view from petrology, geochemistry and thermodynamic models[END_REF][START_REF] Tappe | Geodynamics of kimberlites on a cooling Earth: Clues to plate tectonic evolution and deep volatile cycles[END_REF] (Figs 7-9).

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Testing of MAGLAB on the petrologically-geophysically constrained Society hotspot

Mantle geophysical anomalies such as high electrical conductivities and sharp seismic shear-wave velocity reductions have been reported at various locations worldwide, beneath oceanic and continental settings [START_REF] Ellam | Geophysical evidence from the MELT area for compositional controls on oceanic plates[END_REF][START_REF] Baba | Mantle dynamics beneath the East Pacific Rise at 17°S: Insights from the Mantle Electromagnetic and Tomography (MELT) experiment[END_REF][START_REF] Baba | Electrical conductivity imaging of the Philippine Sea upper mantle using seafloor magnetotelluric data[END_REF]Baba et al., , 2017a;;[START_REF] Kawakatsu | Seismic Evidence for Sharp Lithosphere-Asthenosphere Boundaries of Oceanic Plates[END_REF][START_REF] Schmerr | The Gutenberg Discontinuity: Melt at the Lithosphere-Asthenosphere Boundary[END_REF][START_REF] Naif | Melt-rich channel observed at the lithosphere-asthenosphere boundary[END_REF][START_REF] Tada | Electromagnetic evidence for volatile-rich upwelling beneath the society hotspot, French Polynesia[END_REF]Tharimena et al., 2017a,b;Rychert et al., 2019). The presence and role of volatile-bearing melts is indisputable in these regions [START_REF] Gaillard | Carbonatite Melts and Electrical Conductivity in the Asthenosphere[END_REF][START_REF] Schmerr | The Gutenberg Discontinuity: Melt at the Lithosphere-Asthenosphere Boundary[END_REF][START_REF] Sifré | Electrical conductivity during incipient melting in the oceanic low-velocity zone[END_REF][START_REF] Tada | Electromagnetic evidence for volatile-rich upwelling beneath the society hotspot, French Polynesia[END_REF][START_REF] Katsura | Electrical conductivity of the oceanic asthenosphere and its interpretation based on laboratory measurements[END_REF]Tharimena et al., 2017a,b;Rychert et al., 2019;[START_REF] Gardés | Unravelling partial melt distribution in the oceanic low velocity zone[END_REF]. Among them, the Society hotspot in the Pacific Ocean is a good candidate to test MAGLAB since geochemical and geophysical boundary conditions in this ~70 Myr old oceanic lithosphere are rather well constrained [START_REF] Müller | Age, spreading rates, and spreading asymmetry of the world's ocean crust[END_REF].

The Society hotspot originates from an ascending plume [START_REF] Adam | South Pacific hotspot swells dynamically supported by mantle flows[END_REF] which supplies more heat and higher volatile contents compared with the ambient convecting mantle [START_REF] Tada | Electromagnetic evidence for volatile-rich upwelling beneath the society hotspot, French Polynesia[END_REF]. The mantle potential temperature has been estimated within 1450-1500°C [START_REF] Herzberg | Petrology of some oceanic island basalts: PRIMELT2.XLS software for primary magma calculation[END_REF]. The volatile content of the mantle source has been estimated at ~700 wt ppm CO 2 and 720 wt ppm H 2 O by studying the degassing in submarine lavas from the Society hotspot [START_REF] Aubaud | Degassing of CO 2 and H 2 O in submarine lavas from the Society hotspot[END_REF]. Average major element compositions of nearprimary OIBs erupted at various volcanic centers in the Society Islands have also been assessed, providing an estimation of the major element composition of melts produced from the plume beneath the Society hotspot (Dasgupta et al., 2010). Besides, the Society hotspot presents an anomalously strong electrical signature, called -Zone A‖ [START_REF] Nolasco | Magnetotelluric imaging of the Society Islands hotspot[END_REF][START_REF] Suetsugu | TIARES Project-Tomographic investigation by seafloor array experiment for the Society hotspot[END_REF][START_REF] Tada | Electromagnetic evidence for volatile-rich upwelling beneath the society hotspot, French Polynesia[END_REF]. It extends from the lowest part of the upper mantle to approximately 50 km below sea level. Electrical conductivities above 10 -1 S m -1 are recorded below ~90 km depth, with a maximum of 10 -0.3 S m -1 at about 130-150 km (Fig. 10, and see profile -Anomaly Zone A‖ in Fig. 11; [START_REF] Tada | Electromagnetic evidence for volatile-rich upwelling beneath the society hotspot, French Polynesia[END_REF]. This signature is clearly distinct from the electrical conductivity of neighbouring mantle, being about 1 to 2 log units lower (see profile -TIARES‖ in Fig. 11; [START_REF] Tada | Electromagnetic evidence for volatile-rich upwelling beneath the society hotspot, French Polynesia[END_REF].

We performed MAGLAB simulations using the pressures, temperatures and volatile contents reported for the Society hotspot as inputs, corresponding to the G13R1450 thermal model with T P = 1450°C from [START_REF] Grose | Comprehensive plate models for the thermal evolution of oceanic lithosphere[END_REF], together with ~700 wt ppm CO 2 and 720 wt ppm H 2 O. Around the LAB beneath this ~70 Myr old oceanic lithosphere, at approximately 120±10 km depth, MAGLAB yields ~1.2 to 1.5 wt% of primary silicate-rich melt, bearing about 3.5-3.8 wt% H 2 O and 4.7-5.6 wt% CO 2 . The SiO 2 content is within the range 39.2-40.4 wt%, i.e. 43.1-44.1 wt% on a volatile-free basis, compatible with the 43-48 wt% estimations of near-primary average SiO 2 contents of OIBs reported for the Society islands by Dasgupta et al. (2010) (Fig. 10). Good agreement is also observed for other major elements, such as Al 2 O 3 , FeO, MgO, CaO and alkalis (Fig. 10).

Simulated electrical conductivities are also in very good agreement (Fig. 10), being 10 - 0.59 -10 -0.48 S m -1 compared to the 10 -0.50 -10 -0.29 S m -1 measured between 110 and 130 km depth [START_REF] Tada | Electromagnetic evidence for volatile-rich upwelling beneath the society hotspot, French Polynesia[END_REF]. Hence, this case study demonstrates the robustness of MAGLAB in reproducing both petrological and geophysical data in a partially molten mantle column/volume. The presence of 1.2-1.5 wt% of volatile-bearing silicate melts beneath the Society hotspot as inferred by MAGLAB raises the question about mobility relative to host mantle rocks. According to [START_REF] Gaillard | The Link between the Physical and Chemical Properties of Carbon-Bearing Melts and Their Application for Geophysical Imaging of Earth's Mantle[END_REF], such melts should percolate at 10-14 cm yr - 1 , whereas mantle plume ascent is estimated at ~20-40 cm yr -1 on the basis of geodynamic J o u r n a l P r e -p r o o f simulations [START_REF] Arnould | Plate tectonics and mantle controls on plume dynamics[END_REF]. Melt ascent via convection thus appears to dominate over melt percolation in this oceanic mantle ‗hotspot' setting.

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Heterogeneous distribution of volatile-bearing melts in the oceanic upper mantle

Figure 11 reports electrical conductivity profiles derived from magnetotelluric surveys on various locations in the Pacific and Atlantic, from very young (<5 Ma) to relatively old (130 Ma) seafloors. These profiles illustrate the heterogeneous electrical signature of the oceanic upper mantle, spanning the range of 10 -3 -10 -0.3 S m -1 , and which must then be connected to the heterogeneities in temperature or volatile content in Earth's upper mantle. Figure 11 also reports the range of electrical conductivities for partially molten mantle peridotite calculated by MAGLAB from: (i) old and cold mantle (130 Ma geotherm of G13R1300 model with T P = 1300°C from Grose and Afonso ( 2013)) that is highly depleted in volatiles (20 wt ppm CO 2 and 50 wt ppm H 2 O; [START_REF] Dasgupta | The deep carbon cycle and melting in Earth's interior[END_REF]Shimizu et al., 2019) to (ii) young and hot mantle (0 Ma geotherm of G13R1450 model with T P = 1450°C from Grose and Afonso ( 2013)) that is highly enriched in volatiles (700 wt ppm CO 2 and 720 wt ppm H 2 O; [START_REF] Aubaud | Degassing of CO 2 and H 2 O in submarine lavas from the Society hotspot[END_REF].

MAGLAB simulations cover the range of mantle conductivities observed beneath the seafloors of various ages well. The high electrical conductivities of >10 -1 S m -1 reported at mantle depths of <130 km beneath the outer rise of Cocos plate seafloor (see profile -SERPENT‖ in Fig. 11; [START_REF] Naif | Melt-rich channel observed at the lithosphere-asthenosphere boundary[END_REF][START_REF] Naif | An upper bound on the electrical conductivity of hydrated oceanic mantle at the onset of dehydration melting[END_REF], the Reykjanes Ridge (see profile -RAMESSES AVR Centre‖ in Fig. 11; [START_REF] Heinson | Episodic Melt Transport at Mid-Ocean Ridges Inferred from Magnetotelluric Sounding[END_REF], or the Society hotspot (see profile -Anomaly Zone A‖ in Fig. 11; [START_REF] Tada | Electromagnetic evidence for volatile-rich upwelling beneath the society hotspot, French Polynesia[END_REF] require melt fractions of up to 0.5-1 wt% resulting from a high degree of volatile enrichment, even when elevated T P are accounted for (see Sections 4 and 5.2). Very high mantle electrical conductivities >10 -0.5 S m - 1 , e.g. beneath the ultraslow-spreading Mohns Ridge, would require even higher melt fractions of >>1 wt% [START_REF] Johansen | Deep electrical imaging of the ultraslow-spreading Mohns Ridge[END_REF]. On the other hand, the lowest electrical conductivities with values of ≤10 -2 S m -1 are compatible with the presence of very low melt fractions, i.e. <<0.1 wt%, in depleted mantle regions. Within the asthenosphere, at >125 km depth, mantle conductivities are typically between 10 -2 and 10 -1 S m -1 implying melt fractions of <1 wt% in all cases (Fig. 11).

Combined petrological and electrical simulations using MAGLAB confirm that the high variability of conductivity profiles in the oceanic upper mantle is related to strong heterogeneities in its volatile content [START_REF] Herzberg | Petrology of some oceanic island basalts: PRIMELT2.XLS software for primary magma calculation[END_REF][START_REF] Hirschmann | Partial melt in the oceanic low velocity zone[END_REF][START_REF] Hirschmann | Comparative deep Earth volatile cycles: The case for C recycling from exosphere/mantle fractionation of major (H 2 O, C, N) volatiles and from H 2 O/Ce, CO 2 /Ba, and CO 2 /Nb exosphere ratios[END_REF][START_REF] Ganne | Primary magmas and mantle temperatures through time[END_REF][START_REF] Voyer | Heterogeneity in mantle carbon content from CO 2 -undersaturated basalts[END_REF][START_REF] Clerc | Predicting Rates and Distribution of Carbonate Melting in Oceanic Upper Mantle: Implications for Seismic Structure and Global Carbon Cycling[END_REF]. Highly variable amounts of interconnected volatile-bearing melts, generally <<1 wt%, may be widespread in the uppermost convecting mantle, but their ‗geophysical' detection is challenging if very small fractions are produced [START_REF] Gaillard | The Link between the Physical and Chemical Properties of Carbon-Bearing Melts and Their Application for Geophysical Imaging of Earth's Mantle[END_REF][START_REF] Gardés | Unravelling partial melt distribution in the oceanic low velocity zone[END_REF]. This could explain the rarity of a geophysically detected discontinuity near cratonic LABs [START_REF] Eaton | The elusive lithosphere-asthenosphere boundary (LAB) beneath cratons[END_REF][START_REF] Mancinelli | How Sharp Is the Cratonic Lithosphere-Asthenosphere Transition[END_REF]. Alternatively, this reflects that the mantle at 200-250 km is too reducing to stabilize carbonated melt [START_REF] Aulbach | Cratonic Lithosphere Discontinuities: Dynamics of Small-Volume Melting, Metacratonization, and a Possible Role for Brines: Chapter 10 in Lithospheric Discontinuities[END_REF]. MAGLAB then allows providing bounds on the volatile content for such contexts. Moreover, heterogeneities in mantle volatile content question the role of melt migration in redistributing volatiles. For instance, the very high electrical conductivities reported in the relatively ambient upper mantle beneath Mohns Ridge might be caused by large melt fractions of >>1 wt%, originated from melt migration and accumulation processes [START_REF] Johansen | Deep electrical imaging of the ultraslow-spreading Mohns Ridge[END_REF], and shaping high bulk volatile contents (>>500 wt ppm CO 2 -H 2 O). Volatile and, thus, melt migration plus redistribution can be simulated if dynamic processes including mantle convection are combined with a rigorous petrological framework for mantle melting as provided here by MAGLAB (see also [START_REF] Keller | The Role of Volatiles in Reactive Melt Transport in the Asthenosphere[END_REF][START_REF] Keller | Volatiles beneath mid-ocean ridges: Deep melting, channelised transport, focusing, and metasomatism[END_REF][START_REF] Clerc | Predicting Rates and Distribution of Carbonate Melting in Oceanic Upper Mantle: Implications for Seismic Structure and Global Carbon Cycling[END_REF]. However, further development of these multi-disciplinary modeling techniques is required to continue the quest for better understanding mantle melting processes and their implications for crust-mantle evolution.

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Conclusion

MAGLAB is a new computing platform that models melt compositions, melt fractions and electrical conductivity at pressure-temperature conditions and volatile contents relevant to the upper mantle (i.e., 2-10 GPa, 900-1700°C, depleted to enriched peridotite compositions, up to many thousands of wt ppm of CO 2 and H 2 O). The platform can be accessed free of charge online at http://calcul-isto.cnrs-orleans.fr/apps/maglab/. MAGLAB can be used to model melting processes in oceanic and continental intraplate settings, including kimberlite melt formation beneath cratons. Our modeling results show that erupted intraplate magma compositions correspond to the melts equilibrated near LAB depths, and that a diversity of magma types can be produced from a homogeneous peridotitic mantle source. For ‗normal' upper mantle with 1350°C potential temperature and average volatile content of 140 wt ppm CO 2 and 240 wt ppm H 2 O, carbonatitic melt compositions with <15 wt% SiO 2 are produced beneath 200-250 km thick cratonic lithospheres and basanitic-basaltic melt compositions with >40 wt% SiO 2 beneath mature ocean basins with much thinner lithospheres (i.e., 60-100 km thick). Melts with SiO 2 contents between 15-35 wt% such as kimberlites form only at high pressures corresponding to depths of ≥120 km. Their formation is enhanced in peridotitic mantle sources with high H 2 O contents in addition to CO 2 . In a test case, our combined petrological and geophysical modeling reproduces known compositions of erupted melts and the measured mantle electrical conductivity for the Society hotspot. An important finding from MAGLAB simulations is that the commonly observed variability of mantle electrical conductivity can be linked to the presence and heterogeneous distribution of small volumes (generally <<1 wt%) of volatile-bearing melts within Earth's upper mantle.

J o u r n a l P r e -p r o o f Compositional range of natural intraplate melts, from low-SiO 2 carbonatitic melts to basaltic melts. Carbonatites (brown dots), nephelinites (green dots), basanites (purple dots) and OIBs (red dots) are selected from the GEOROC database (http://georoc.mpchmainz.gwdg.de/). Kimberlites (yellow dots) are from the compilation of [START_REF] Tappe | Sources and mobility of carbonate melts beneath cratons, with implications for deep carbon cycling, metasomatism and riftinitiation[END_REF] see their Supplementary File E and references therein). Lava compositions were selected from GEOROC database based on MgO content: carbonatites have MgO contents >12 wt% (and SiO 2 contents <15wt% to remove anomalous outliers), while nephelinites, basanites and OIBs have MgO contents >8 wt% and <16 wt%.

J o u r n a l P r e -p r o o f S3. All melts coexist with a typical mantle assemblage (i.e., saturated in olivine-opx±cpx±garnet/spinel). (A) Pressure/depth-temperature space. The data range from 1 to 14 GPa and from 1020 to 1950°C. Melting curves for different bulk peridotite conditions are also reported as a function of temperature and pressure/depth conditions (dry solidus from [START_REF] Hirschmann | Mantle solidus: Experimental constraints and the effects of peridotite composition[END_REF]; CO 2 -and H 2 O-bearing solidus from [START_REF] Wallace | An experimental determination of primary carbonatite magma composition[END_REF] from ~1 to ~4 GPa, and [START_REF] Foley | The composition of near-solidus melts of peridotite in the presence of CO 2 and H 2 O between 40 and 60 kbar[END_REF] between 4 and 6 GPa, with extrapolation up to 10 GPa as shown by the dashed purple curve). (B) CaO -SiO 2 compositional space (see Fig. S3 for other major elements). The compositions of the silicate and carbonate melt end-members of our model are shown as red and purple circles, respectively. Combining these end-members yields compositions (light maroon shaded areas) covering a large proportion of the experimental database (yellow diamonds) as well as the chemical diversity of intraplate magmatism, from kimberlites to OIBs (green and light purple circles, respectively; see Fig. 1). , is ~15% on average.

J o u r n a l P r e -p r o o f 2007), [START_REF] Dasgupta | Carbon-dioxide-rich silicate melt in the Earth's upper mantle[END_REF] and [START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF] in their pressure range of applicability (3 GPa, 5 GPa, and from ~2 to 10 GPa, respectively) at a bulk rock CO 2 content of 140 wt ppm (i.e., average mantle source; Le [START_REF] Voyer | Heterogeneity in mantle carbon content from CO 2 -undersaturated basalts[END_REF]. Experimental melts reported here are H 2 O-free, contain at least SiO 2 , Al 2 O 3 , MgO, CaO, FeO and CO 2 , and match pressure within ±0.5 GPa.

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FiguresFig. 1

 1 Figures

  Fig. 1. Compositional range of natural intraplate melts, from low-SiO 2 carbonatitic melts to basaltic melts. Carbonatites (brown dots), nephelinites (green dots), basanites (purple dots) and OIBs (red dots) are selected from the GEOROC database (http://georoc.mpchmainz.gwdg.de/). Kimberlites (yellow dots) are from the compilation of Tappe et al. (2017; see their Supplementary File E and references therein). Lava compositions were selected from GEOROC database based on MgO content: carbonatites have MgO contents >12 wt% (and SiO 2 contents <15wt% to remove anomalous outliers), while nephelinites, basanites and OIBs have MgO contents >8 wt% and <16 wt%.

Fig. 2 .

 2 Fig. 2. Experimental database of melt compositions used for the calibration of MAGLAB. The description of the experimental database (i.e., pressure, temperature and composition space of melts) is presented in TableS3. All melts coexist with a typical mantle assemblage (i.e., saturated in olivine-opx±cpx±garnet/spinel). (A) Pressure/depth-temperature space. The data range from 1 to 14 GPa and from 1020 to 1950°C. Melting curves for different bulk peridotite conditions are also reported as a function of temperature and pressure/depth conditions (dry solidus from[START_REF] Hirschmann | Mantle solidus: Experimental constraints and the effects of peridotite composition[END_REF]; CO 2 -and H 2 O-bearing solidus from[START_REF] Wallace | An experimental determination of primary carbonatite magma composition[END_REF] from ~1 to ~4 GPa, and[START_REF] Foley | The composition of near-solidus melts of peridotite in the presence of CO 2 and H 2 O between 40 and 60 kbar[END_REF] between 4 and 6 GPa, with extrapolation up to 10 GPa as shown by the dashed purple curve). (B) CaO -SiO 2 compositional space (see Fig.S3for other major elements). The compositions of the silicate and carbonate melt end-members of our model are shown as red and purple circles, respectively. Combining these end-members yields compositions (light maroon shaded areas) covering a large proportion of the experimental database (yellow diamonds) as well as the chemical diversity of intraplate magmatism, from kimberlites to OIBs (green and light purple circles, respectively; see Fig.1).

Fig. 3 .

 3 Fig. 3. Comparison of the molar fraction of SiO 2 in melt calculated with MAGLAB to that from the experimental database. The relative deviation of MAGLAB calculations, taken as | |

Fig. 4 :

 4 Fig. 4: Comparison of melt SiO 2 content calculated by MAGLAB with experimental data at (A) 3 GPa, (B) 5 GPa, (C) 7 GPa, and (D) 10 GPa. Also compared are the models of Dasgupta et al. (2007),[START_REF] Dasgupta | Carbon-dioxide-rich silicate melt in the Earth's upper mantle[END_REF] and[START_REF] Massuyeau | A model for the activity of silica along the carbonatite-kimberlite-mellilitite-basanite melt compositional joint[END_REF] in their pressure range of applicability (3 GPa, 5 GPa, and from ~2 to 10 GPa, respectively) at a bulk rock CO 2 content of 140 wt ppm (i.e., average mantle source; Le[START_REF] Voyer | Heterogeneity in mantle carbon content from CO 2 -undersaturated basalts[END_REF]. Experimental melts reported here are H 2 O-free, contain at least SiO 2 , Al 2 O 3 , MgO, CaO, FeO and CO 2 , and match pressure within ±0.5 GPa.

  proportions of olivine, orthopyroxene, clinopyroxene, garnet and spinel, respectively, calculated from Hirschmann et al. (2009), and , , , and are the partition coefficients of H 2 O of olivine, orthopyroxene, clinopyroxene, garnet and spinel, respectively, in equilibrium with melt, calculated from Hirschmann et al. (2009) and Novella et al. (

	where	,	,	,	and	are the modal
	) or from H 2 O partitioning J o u r n a l P r e -p r o o f
					. (6)
	and		are the mass fractions of CO 2 and H 2 O in bulk peridotite rock in wt%,
	respectively.	and		are the mass fractions of CO 2 and H 2 O in melt in wt%,
	respectively, converted from the molar fractions	and	calculated above.
			is the pressure-dependent partition coefficient of H 2 O between peridotite and
	melt, calculated as follows:
							,
	(7)

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Acknowledgements

We thank Mark Jellinek for manuscript handling, as well as Michel Grégoire and two anonymous reviewers for their valuable comments. We also sincerely thank Tim Holland and Eleanor Green for helpful discussions whose our modeling work has benefited, and Claude Herzberg for providing comments on a previous version of the manuscript. This work was part of the ElectroLith project and benefited from funding by the European Research Council (ERC project #279790) and the French agency for research (ANR project #2010 BLAN62101). GR also gratefully acknowledges funding by the French agency for research under grant Labex VOLTAIRE ANR-10-LABX-100-01. The DEEP Research Group at the University of Johannesburg is supported by the DSI-NRF CIMERA Center of Excellence, South Africa. MM was partially funded through a scholarship from the Department of Science and Technology Research Chairs Initiative as administered by the NRF South Africa (SARChI Chair grant #64779 awarded to K.S. Viljoen), which we gratefully acknowledge. Additional financial support was provided to ST via the NRF-IPRR funding framework. MM also gratefully acknowledges funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 842339. SA gratefully acknowledges funding by the German Research Foundation under grant AU356/11. Readers can access data and additional information not reported in the main paper via the supporting online resources.

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Supplementary

Information; MAGLAB hyperlink: http://calcul-isto.cnrsorleans.fr/apps/maglab/). [START_REF] Wallace | An experimental determination of primary carbonatite magma composition[END_REF]. The dashed white curve is an estimation of the LAB depth. S7), and considering a single average mantle source with 140 wt ppm CO 2 -240 wt ppm H 2 O (Le [START_REF] Voyer | Heterogeneity in mantle carbon content from CO 2 -undersaturated basalts[END_REF]. Similarly to the TAS diagram (e.g. Fig. 1), the melt SiO 2 content is here used as a proxy for the compositional range of intraplate magmas as found at the Earth's surface: 15-35 wt% for kimberlites, a progressive transition between 35 to 45 wt% from melilitite to nephelinite to basanite, and >45 wt% for regular basalts. Note OIB compositions as reported in Fig. 1 span basanitic to basaltic compositions.

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Journal Pre-proof Fig. 10: Reproducing the petrological and electrical data at the LAB beneath Society hotspot (Pacific Ocean) using MAGLAB. Calculations are performed at LAB depth (120±10 km) according to the P-T conditions and mantle volatile content reported for the hotspot. The reported mantle potential temperature T P is 1450°C [START_REF] Herzberg | Petrology of some oceanic island basalts: PRIMELT2.XLS software for primary magma calculation[END_REF]; mantle thermal structure simulated with G13R1450 model from Grose and Afonso 2013), and the mantle volatile content is ~700 wt ppm CO 2 and 720 wt ppm H 2 O [START_REF] Aubaud | Degassing of CO 2 and H 2 O in submarine lavas from the Society hotspot[END_REF]. The average major element compositions of near-primary OIBs reported for the Society Islands are from Dasgupta et al. (2010), on a volatile-free basis (also applied to the melt compositions from MAGLAB simulations). The high mantle electrical conductivities reported beneath Society hotspot are estimated within 110-130 km depth from the averaged 1-D electrical conductivities [START_REF] Tada | Electromagnetic evidence for volatile-rich upwelling beneath the society hotspot, French Polynesia[END_REF]; see also Fig. 11: ‖Anomaly Zone A, Society Islands‖).

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Journal Pre-proof Fig. 11: Comparison between electrical profiles observed beneath various ocean floors and MAGLAB simulations. MAGLAB conductivities for partially molten peridotite rocks (light red area) range from (i) old, cold and highly depleted mantle (130 Ma, with T P = 1300°C and 20 wt ppm CO 2 -50 wt ppm H 2 O) to (ii) young, hot and highly enriched mantle (0 Ma, with T P = 1450°C and 700 wt ppm CO 2 -720 wt ppm H 2 O). The mantle thermal structures are G13R1300 and G13R1450 models from Grose and Afonso ( 2013), with T P = 1300°C and 1450°C, respectively. Electrical conductivity profiles of the oceanic upper mantle in dark grey are from various magnetotelluric studies. 1 and 1', conductivity profile in the northeastern Pacific Ocean between Hawaii and California [START_REF] Lizarralde | Northeastern Pacific mantle conductivity profile from long-period magnetotelluric sounding using Hawaii-to-California submarine cable data[END_REF]. 2, Tomographic Investigation by seafloor ARray Experiment for the Society hotspot (TIARES) profile representing the ‗background' mantle beneath the Society hotspot in the Pacific Ocean [START_REF] Tada | Electromagnetic evidence for volatile-rich upwelling beneath the society hotspot, French Polynesia[END_REF]. 3 and 3', Mantle Electromagnetic and Tomography (MELT) profile in the region of the East Pacific Rise [START_REF] Ellam | Geophysical evidence from the MELT area for compositional controls on oceanic plates[END_REF][START_REF] Baba | Mantle dynamics beneath the East Pacific Rise at 17°S: Insights from the Mantle Electromagnetic and Tomography (MELT) experiment[END_REF]. 4, conductivity profile in the central Pacific Ocean (-NoMelt‖ experiment in [START_REF] Sarafian | The electrical structure of the central Pacific upper mantle constrained by the NoMelt experiment[END_REF]. 5, conductivity profile in the northwestern Pacific Ocean (-Area A‖ in [START_REF] Baba | Electrical conductivity imaging of the Philippine Sea upper mantle using seafloor magnetotelluric data[END_REF][START_REF] Baba | Electrical conductivity of old oceanic mantle in the northwestern Pacific I: 1-D profiles suggesting differences in thermal structure not predictable from a plate cooling model[END_REF]. 6, conductivity profile beneath the Philippine Sea [START_REF] Baba | Electrical conductivity imaging of the Philippine Sea upper mantle using seafloor magnetotelluric data[END_REF]. 7, conductivity profile beneath the Tristan da Cunha hotspot in the southern Atlantic Ocean (Baba et al., 2017a). 8, conductivity profile in the northern East Pacific Rise [START_REF] Key | Electrical image of passive mantle upwelling beneath the northern East Pacific Rise[END_REF]. 9, Reykjanes Axial Melt Experiment: Structural Synthesis from Electromagnetics and Seismics (RAMESSES) profile in the northern section of the Mid-Atlantic Ridge, i.e. the Reykjanes Ridge (-AVR Centre‖ in [START_REF] Heinson | Episodic Melt Transport at Mid-Ocean Ridges Inferred from Magnetotelluric Sounding[END_REF]. 10, Serpentinite, Extension, and Regional Porosity Experiment across the Nicaragua Trench (SERPENT) profile beneath the outer rise of 22-24 Ma Cocos plate seafloor in the Pacific Ocean [START_REF] Naif | Melt-rich channel observed at the lithosphere-asthenosphere boundary[END_REF][START_REF] Naif | An upper bound on the electrical conductivity of hydrated oceanic mantle at the onset of dehydration melting[END_REF]. 11, conductivity J o u r n a l P r e -p r o o f