Bernard Marty
email: bmarty@crpg.cnrs-nancy.fr

The origins and concentrations of water, carbon, nitrogen and noble gases on Earth

. If the depletion of Xe in the atmosphere was a long-term process that took place after the Earth-building events, then the amounts of atmospheric 129 Xe and 131-136 Xe, produced by the short-lived radioactivities of 129 I (T 1/2 = 16 Ma) and 244 Pu (T 1/2 = 82 Ma), respectively, need to be corrected for subsequent loss. Doing so, the I-Pu-Xe age of the Earth becomes ≤50 Ma after start of solar system formation, instead of ~120 Ma as computed with the presentday atmospheric Xe inventory.

ABSTRACT

The isotopic compositions of terrestrial hydrogen and nitrogen are clearly different from those of the nebular gas from which the solar system formed, and also differ from most of cometary values. Terrestrial N and H isotopic compositions are in the range of values characterizing primitive meteorites, which suggests that water, nitrogen, and other volatile elements on Earth originated from a cosmochemical reservoir that also sourced the parent bodies of primitive meteorites. Remnants of the proto-solar nebula (PSN) are still present in the mantle, presumably signing the sequestration of PSN gas at an early stage of planetary growth. The contribution of cometary volatiles appears limited to a few percents at most of the total volatile inventory of the Earth. The isotope signatures of H, N, Ne and Ar can be explained by mixing between two end-members of solar and chondritic compositions, respectively, and do not require isotopic fractionation during hydrodynamic escape of an early atmosphere.

The terrestrial inventory of 40 Ar (produced by the decay of 40 K throughout the Earth's history) suggests that a significant fraction of radiogenic argon may be still trapped in the silicate Earth. By normalizing other volatile element abundances to this isotope, it is proposed that the Earth is not as volatile-poor as previously thought. Our planet may indeed contain up to ~3000 ppm water (preferred range : 1000-3000 ppm), and up to ~500 ppm C, both largely sequestrated in the solid Earth. This volatile content is equivalent to a ~2 (±1) % contribution of carbonaceous chondrite (CI-CM) material to a dry proto-Earth, which is higher than the contribution of chondritic material advocated to account for the platinum group element budget of the mantle. Such a (relatively) high contribution of volatile-rich matter is consistent with the accretion of a few wet planetesimals during Earth accretion, as proposed by recent dynamical models.

The abundance pattern of major volatile elements and of noble gases is also chondritic, with two notable exceptions. Nitrogen is depleted by one order of magnitude relative to water, carbon and most noble gases, which is consistent with either N retention in a mantle phase during magma generation, or trapping of N in the core. Xenon is also depleted by one order of magnitude, and enriched in heavy isotopes relative to chondritic or solar Xe (the so-called "xenon paradox"). This depletion and isotope fractionation might have taken place due to preferential ionization of xenon by UV light from the early Sun, either before Earth's

Introduction

The origins and abundances of volatile elements (here, the highly volatile, also called atmophile, elements : water, carbon, nitrogen and noble gases) are still debated. Since the pioneering work of William W. Rubey in the 50's which showed that the oceans could not be derived from the alteration of rocks at the Earth's surface [START_REF] Rubey | Geologic history of sea water[END_REF], many studies have investigated the origin of terrestrial volatiles , often using noble gases as physical tracers [START_REF] Albarède | Volatile accretion history of the terrestrial planets and dynamic implications[END_REF][START_REF] Allègre | Constraints on evolution of Earth's mantle from rare gas systematics[END_REF][START_REF] Caffee | Primordial noble cases from Earth's mantle: Identification of a primitive volatile component[END_REF][START_REF] Dauphas | The dual origin of the terrestrial atmosphere[END_REF][START_REF] Fisher | Implications of terrestrial 40 Ar/ 36 Ar for atmospheric and mantle evolutionary models[END_REF][START_REF] Holland | Meteorite Kr in Earth's Mantle Suggests a Late Accretionary Source for the Atmosphere[END_REF][START_REF] Javoy | Carbon and nitrogen isotopes in the mantle[END_REF][START_REF] Marty | Neon and xenon isotopes in MORB : implications for the earth-atmosphere evolution[END_REF][START_REF] Ozima | Ar isotopes and Earth-atmosphere evolution models[END_REF][START_REF] Pepin | On the origin and early evolution of terrestrial planetary atmospheres and meteoritic volatiles[END_REF][START_REF] Phinney | Xenon in the CO 2 -well gas revisited[END_REF][START_REF] Porcelli | Deep Earth rare gases: initial inventories, capture from the solar nebula, and losses during Moon formation[END_REF][START_REF] Staudacher | Terrestrial xenology[END_REF][START_REF] Tolstikhin | The evolution of terrestrial volatiles: a view from helium, neon, argon and nitrogen isotope modelling[END_REF][START_REF] Turner | The outgassing history of the atmosphere[END_REF]. Relevant data to constrain models are from the geological record (present-day mantle and atmosphere, ancient sedimentary rocks) and from the analysis of the composition of cosmochemical reservoirs : primitive and differentiated meteorites sampling the asteroid belt and inner planetary bodies, planetary atmospheres analyzed by space probes, and samples returned by dedicated space missions. In the first part of this contribution, available cosmochemical data are used to assess the origin of terrestrial volatiles.

Contrary to the case of refractory elements, it is not possible to estimate the volatile element content of the mantle source from the analysis of mantle-derived lavas because, owing to their low solubility in silicate melts, these elements have been lost and fractionated during magma degassing. Only remnants are found in mantle-derived magmas emitted along mid ocean ridge and oceanic intraplate volcanoes. Thus indirect approaches are necessary, that are based on the calibration of a volatile element of interest to a tracer whose geochemical cycle is well documented, e.g., 3 He [START_REF] Marty | C/ 3 He in volatile fluxes from the solid Earth : Implications for carbon geodynamics[END_REF], or Nb [START_REF] Saal | Vapour undersaturation in primitive mid-ocean-ridge basalt and the volatile content of Earth's upper mantle[END_REF]. In this contribution, the volatile (H, C, N, noble gases) compositions of the mantle regions sampled by mantle-derived lavas are revisited. The best documented reservoir is the depleted mantle (DM) sampled by mid-ocean ridge volcanism. Documenting directly the bulk mantle (BM) volatile content is not possible because the size, the location and the composition of the deep reservoir(s), presumably sampled by mantle plumes, are not known.

A mass balance approach is attempted here based on the terrestrial budget of radiogenic 40 Ar.

From estimates of the K content of the Earth [START_REF] Arevalo | The K/U ratio of the silicate Earth: Insights into mantle composition, structure and thermal evolution[END_REF][START_REF] Jochum | K, U and Th in Mid-Ocean Ridge Basalt glasses and heat production, K/U and K/Rb in the mantle[END_REF], the amount of 40 Ar produced by the decay of 40 K (T 1/2 = 1.25 Ga) over the Earth's history can be computed. The amount of 40 Ar still trapped in the silicate Earth is then obtained by subtracting the known amount of 40 Ar present in the atmosphere [START_REF] Allègre | The argon constraints on mantle structure[END_REF][START_REF] Turner | The outgassing history of the atmosphere[END_REF]. The amount of other volatile species still trapped in the silicate Earth is then estimated based on their relations to 40 Ar in mantle-derived lavas and gases.

Cosmochemical end-members

The chondrite connection

The isotopic composition of hydrogen, expressed as the D/H ratio, shows large variations among cosmochemical reservoirs (Fig. 1). The solar system formed from a cloud of gas and dust, the protosolar nebula (PSN), the composition of which being best preserved in the Sun and in the atmospheres of the giant planets. The elemental composition of the Sun is known from wavelength measurements of the solar photosphere and by comparison with primitive meteorites for refractory elements. The D/H ratio of the protosolar nebula, largely inferred from Jupiter's atmosphere measurements, has been estimated to be 25±5 x 10 -6 [START_REF] Geiss | Abundances of deuterium and helium in the protosolar cloud[END_REF] In contrast, the D/H ratio of chondrites is a factor 5 to 12 higher, with a distribution peak coinciding with the terrestrial (oceanic) D/H ratio of 156 x 10 -6 (e.g., [START_REF] Robert | The D/H ratio in chondrites[END_REF]. Measurements of the D/H ratios of water in 5 comets [START_REF] Bockelée-Morvan | The composition of cometary volatiles[END_REF] show a ~two-fold enrichment in D compared to the chondritic signatures (Fig. 1). If such values characterize outer solar system objects, then the contribution of comets to terrestrial water must have been lower than ~10 % [START_REF] Dauphas | The late asteroidal and cometary bombardment of Earth as recorded in water deuterium to protium ratio[END_REF]. Recently however, a terrestrial-like D/H ratio has been measured on comet 103P/Hartley 2, a Jupiter-family object [START_REF] Hartogh | Ocean-like water in the Jupiter-family comet 103P/Hartley 2[END_REF], thus raising the possibility that terrestrial oceans could have originated from specific cometary material. The isotopic composition of nitrogen gives an independent constraint to this problem. The 15 N/ 14 N ratio of the PSN has been recently documented thanks to the analysis of solar wind sampled by the Genesis mission spacecraft [START_REF] Marty | A 15 N-poor isotopic composition for the solar system as shown by Genesis solar wind samples[END_REF][START_REF] Marty | Nitrogen isotopes in the recent solar wind from the analysis of Genesis targets: Evidence for large scale isotope heterogeneity in the early solar system[END_REF]. The protosolar 15 N/ 14 N ratio was 2.27±0.03 × 10 -3 or δ 15 N = -383±8 ‰ {δ 15 N = [( 15 N/ 14 N) sample /( 15 N/ 14 N) standard -1] x 1000, where the standard 15 N/ 14 N ratio is the composition of atmospheric N 2 (ATM) : ( 15 N/ 14 N) ATM = 3.678 x 10 -3 }. Not only the Earth but all inner solar system objects including Venus, the interior of Mars and meteorites are highly enriched in 15 N relative to the PSN (Fig. 1). All comets measured so far (23 in total, including 103P/Hartley 2) are even richer in 15 N than inner solar system objects as they present 15 N/ 14 N ratios of HCN and/or CN within 6.8±0.3 x 10 -3 (δ 15 N = +850 ‰) [START_REF] Arpigny | Anomalous Nitrogen Isotope Ratio in Comets[END_REF][START_REF] Bockelée-Morvan | The composition of cometary volatiles[END_REF], 2008;[START_REF] Jehin | Isotopic Ratios in Comets: Status and Perspectives[END_REF]. By combining D/H and 15 N/ 14 N data, the genetic relationship between asteroidal material is re-enforced, and the difficulty of deriving terrestrial water from comets is substantiated by the high 15 N/ 14 N ratios of comets even for the one showing an ocean-like D/H composition (Fig. 1). However, there is a possible analytical caveat that will need to be resolved by further cometary analyses. The cometary 15 N/ 14 N ratios have been measured in CN and HCN, the only molecules that could be analyzed by remote sensing. Other cometary N-bearing molecules like NH 3 and N 2 (if dinitrogen is effectively trapped in cometary ice, which is not granted) may not be isotopically equilibrated with CN nor HCN.

The isotopic composition of carbon shows much less pronounced variations among solar system reservoirs but are broadly consistent with those of H and N : solar carbon may be poor in the heavy, rare isotope 13 C compared to the Earth and meteorites. The δ 13 C value of the solar wind from lunar soil measurements has been estimated to be around -100 ‰ relative to the PDB international standard [START_REF] Hashizume | Protosolar carbon isotopic composition: Implications for the origin of meteoritic organics[END_REF], whereas most meteorites display δ 13 C values close to the terrestrial value within ~20 ‰ [START_REF] Kerridge | Carbon, hydrogen and nitrogen in carbonaceous chondrites: abundances and isotopic compositions in bulk samples[END_REF].

The stable isotopes of hydrogen and nitrogen seem to indicate that the Earth and the parent bodies of meteorites acquired their signatures from a common ancestor reservoir that was isotopically well mixed. In detail, the average D/H and 15 N/ 14 N compositions of chondrites (excluding enstatite chondrites which do not contain significant amounts of water) are undistinguishable from the terrestrial surface inventory (Fig. 2), suggesting that the latter resulted from contributions of diverse materials, whose remnants are now found in the different meteoritic classes. The terrestrial mantle end-member is depleted in the heavy isotopes of hydrogen and nitrogen and points to the possible occurrence of a solar-like component at depth (Fig. 2) that is discussed in the next section.

Solar-like gas in the mantle

The best evidence for the occurrence of a solar component in the mantle comes from neon isotopes [START_REF] Hiyagon | Noble-Gases in Submarine Glasses from Midoceanic Ridges and Loihi Seamount -Constraints on the Early History of the Earth[END_REF][START_REF] Honda | Possible solar noble-gas component in Hawaiian basalts[END_REF][START_REF] Marty | Neon and xenon isotopes in MORB : implications for the earth-atmosphere evolution[END_REF][START_REF] Sarda | Neon isotopes in submarine basalts[END_REF].

Variations in the Ne isotopic composition in mantle-derived rocks and minerals indicate mixing between an atmospheric Ne component ( 20 Ne/ 22 Ne = 9.80) and a mantle end-member with 20 Ne/ 22 Ne ≥ 12.5, likely to be solar in origin ( 20 Ne/ 22 Ne = 13.8 for the solar wind, [START_REF] Grimberg | Solar wind neon from Genesis: Implications for the lunar noble gas record[END_REF][START_REF] Meshik | Constraints on neon and argon isotopic fractionation in solar wind[END_REF]. The origin of this solar component is presently discussed between incorporation in Earth's accreting material of dust loaded with ancient solar wind [START_REF] Raquin | Atmospheric (38)Ar/(36)Ar in the mantle: Implications for the nature of the terrestrial parent bodies[END_REF][START_REF] Trieloff | The nature of pristine noble gases in mantle plumes[END_REF], or direct trapping of a PSN component during Earth's formation [START_REF] Yokochi | A determination of the neon isotopic composition of the deep mantle[END_REF]. In support of the first possibility, most mantle-derived samples admit an upper limit of 12.5 for the 20 Ne/ 22 Ne ratios, a value similar to an end-member composition labelled Ne-B [START_REF] Black | On the origin of trapped helium, neon and argon isotopic variations in meteorites-I. Gas-rich meteorites, lunar soil and breccia[END_REF] characterizing matter irradiated and processed by the solar corpuscular irradiation [e.g. lunar soils or (solar) irradiated meteorites]. Central to this possibility is the timing of planetary accretion. Trapping of solar ions onto accreting material requires the nebular gas to have been cleared off because otherwise the nebula would have been opaque to solar wind. If the nebular gas had already dissipated before the main stages of terrestrial accretion, this process could have been quantitatively efficient, especially because the corpuscular irradiation of the young Sun might have been enhanced by orders of magnitude. However, different lines of evidence suggest that the solar nebula lasted for several Ma after start of solar system formation [START_REF] Podosek | Theoretical, observational, and isotopic estimates of the lifetime of the solar nebula[END_REF], a time interval during which Mars-sized embryos were already grown up [START_REF] Dauphas | Hf-W-Th evidence for rapid growth of Mars and its status as a planetary embryo[END_REF]. If the proto-Earth reached such a significant size in a few Ma when the nebular gas was still present, a massive solar-like atmosphere could have been captured [START_REF] Sasaki | The primary solar-type atmosphere surrounding the accreting Earth : H 2 Oinduced high surface temperature[END_REF][START_REF] Yokochi | A determination of the neon isotopic composition of the deep mantle[END_REF]. Retention of a nebular, H 2 -rich atmosphere might have taken place when the proto-Earth was larger than ~1000 km in diameter [START_REF] Marty | Water in the early Earth[END_REF]. The growing proto-Earth was likely to be partially or totally melted due to release of gravitational energy and of heat from the decays of short-lived nuclides, and the probable contribution of greenhouse warming by the massive atmosphere [START_REF] Sasaki | The primary solar-type atmosphere surrounding the accreting Earth : H 2 Oinduced high surface temperature[END_REF]. Consequently, solar gases like neon would have been dissolved in the growing proto-Earth magmas. [START_REF] Marty | Water in the early Earth[END_REF] estimated that the atmospheric pressure of a solar-like atmosphere around the proto-Earth necessary to provide the amount of solar Ne in the mantle (computed from 21 Ne produced by nuclear reactions induced to the decay of U in the mantle) was quite modest about 8 x 10 3 hPa (~8 bar). This value represents a lower limit since solar Ne could have been lost from the proto-Earth. In support of the nebular model, [START_REF] Yokochi | A determination of the neon isotopic composition of the deep mantle[END_REF] have measured 20 Ne/ 22 Ne ratios higher than the Ne-B value of 12.5 and up to 13.0±0.2 in minerals from the Kola mantle plume, pointing to the occurrence of a remnant of nebular Ne in the mantle. Further progress on the origin of solar-like neon in the mantle will arise from future analyses of Ne isotopes in rocks and mineral related to mantle plumes.

The case of other noble gases is less straightforward. Mantle Ar, Kr, and Xe are dominated by a component having an atmospheric isotope composition, possibly gained by subduction of surface noble gases [START_REF] Holland | Seawater subduction controls the heavy noble gas composition of the mantle[END_REF]. However, the precise analysis of natural CO 2 gas of mantle origin suggests the occurrence of a minor nonatmospheric Xe component, either chondritic, or solar [START_REF] Caffee | Primordial noble cases from Earth's mantle: Identification of a primitive volatile component[END_REF][START_REF] Holland | Seawater subduction controls the heavy noble gas composition of the mantle[END_REF] and of a chondritic Kr component [START_REF] Holland | Meteorite Kr in Earth's Mantle Suggests a Late Accretionary Source for the Atmosphere[END_REF]. Interestingly, the Martian mantle, as sampled by the Chassigny meteorite, contains a solar Xe component [START_REF] Mathew | Martian atmospheric and indigenous components of xenon and nitrogen in the Shergotty, Nakhla, and Chassigny group meteorites[END_REF][START_REF] Ott | Noble gases in SNC meteorites : Shergotty, Nakhla, Chassigny[END_REF]. Thus there is evidence not only from neon but also from krypton and xenon that the terrestrial mantle still contains a non atmospheric, cosmochemical component.

Mantle nitrogen is depleted in 15 N relative to the surface (Fig. 2), with δ 15 N values estimated between -5‰ and -30‰ relative to ATM [START_REF] Cartigny | Eclogitic diamond formation at Jwaneng: No room for a recycled component[END_REF][START_REF] Javoy | Carbon and nitrogen isotopes in the mantle[END_REF][START_REF] Marty | Volatiles (He, C, N, Ar) in mid-ocean ridge basalts: Assesment of shallow-level fractionation and characterization of source composition[END_REF][START_REF] Murty | Nitrogen and heavy noble gases in ALH 84001 : Signatures of ancient Martian atmosphere[END_REF]. Among chondritic classes, enstatite chondrites are the only ones to show systematic depletions of 15 N relative to Earth, with δ 15 N values of -30±10‰. This similarity lead [START_REF] Javoy | Carbon and nitrogen isotopes in the mantle[END_REF] to propose that mantle nitrogen has kept a memory of its genetic relationship with enstatite chondrites (otherwise attested by similarities in key isotope ratios). [START_REF] Marty | The nitrogen record of crust-mantle interaction and mantle convection from Archean to present[END_REF] proposed alternatively that the negative δ 15 N values of the mantle may represent past subduction of ancient surface N depleted in 15 N. Because solar Ne is present in the mantle, the mantle δ 15 N end-member value could also result from mixing about 8% solar N (δ 15 N = -383‰) with surface N (0‰ for air, ~+5‰ for sediments). Estimates of the 22 Ne and 14 N contents of the present-day terrestrial mantle are 2 × 10 -14 mol/g and ~1 ppm, respectively, [START_REF] Marty | The nitrogen record of crust-mantle interaction and mantle convection from Archean to present[END_REF][START_REF] Yokochi | A determination of the neon isotopic composition of the deep mantle[END_REF], yielding a 14 N/ 22 Ne molar ratio of ~3×10 6 , much higher than the solar ratio of ~12. Assuming that ~8% of mantle nitrogen was trapped from the PSN, the rest originating from a chondritic source from isotope mass balance), then solar N should have been enriched by a factor of ~10 4 relative to solar neon during trapping in the proto-Earth by dissolution of a PSN-like atmosphere into a magma ocean, or ~10 5 if the amount of nitrogen in the silicate Earth was higher initially as argued in section 4. Such an enrichment relative to inert neon could be the result of chemical trapping of N under reducing conditions. Indeed, the solubility of N in molten silicates increases significantly with decreasing oxygen fugacity [START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF][START_REF] Miyazaki | Solubilities of nitrogen and noble gases in silicate melts under various oxygen fugacities: Implications for the origin and degassing history of nitrogen and noble gases in the earth[END_REF]. The oxygen fugacity during terrestrial differentiation has been estimated to be between 4 and 2 log units below the iron-wüstite buffer [START_REF] Rubie | Heterogeneous accretion, composition and core-mantle differentiation of the Earth[END_REF][START_REF] Wood | Core formation and the oxidation state of the Earth: Additional constraints from Nb, V and Cr partitioning[END_REF]. For IW-4, the solubility of N is increased by 3 orders of magnitude relative to that of noble gases (using the parameterized equation of [START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF], which is still lower than the requested enrichment factor of 10 4 -10 5 . Thus the negative δ 15 N values of the mantle may not trace the occurrence of solar-like N at depth but may instead represent a chondritic ancestor [START_REF] Javoy | Carbon and nitrogen isotopes in the mantle[END_REF] or past subduction of a fractionated N component [START_REF] Marty | The nitrogen record of crust-mantle interaction and mantle convection from Archean to present[END_REF].

Hydrogen in mantle-derived rocks and minerals presents a range of negative δD values (Fig. 2), down to -125‰ in magmatic minerals from the Hawaiian mantle plume [START_REF] Deloule | Hydrogen isotope heterogeneities in the mantle from ion probe analysis of amphiboles from ultramafic rocks[END_REF]. It is not clear if this signature represents isotopic mass fractionation, for instance during subduction, or traces the occurrence of ~15% solar H (depleted in D) at depth, based on H isotope mass balance. Calculations involving Ne isotopes suggest independently that about 10 % water could have resulted from the dissolution of a primordial, solar-like atmosphere [START_REF] Marty | Water in the early Earth[END_REF], consistent with the D/H message. Further analyses of D/H ratios in mantle plume-related minerals may help resolving this other important issue.

Hydrodynamic escape of an early atmosphere ?

The difference in the isotopic composition of neon between the mantle and the atmosphere is commonly attributed to fractionation during hydrodynamic escape of an early atmosphere (e.g., Pepin, 2006, and refs. therein). However, isotope fractionation during escape of volatile species would also impact the stable isotope signatures of major volatiles like water, carbon, and nitrogen, which is not observed (Figs. 1 &2). In fact, variations in the elemental and isotopic compositions of all terrestrial volatiles (but xenon, see section 4) can be accounted by mixing between two cosmochemical end-members and do not necessitate isotope discrimination during atmospheric escape. In a 20 Ne/ 22 Ne vs. 36 Ar/ 22 Ne diagram (Fig. 3), the atmospheric and the mantle values can be accounted for by mixing between a solar component and a chondritic component (Component A defined by [START_REF] Black | Trapped neon-argon isotopic correlations in gas meteorites and carbonaceous chondrites[END_REF]Mazor et al., 1970, for carbonaceous chondrites). These end-member values do not fit an evolution following kinetic fractionation proportional to m -1/2 , as represented by the red curve in Fig. 3).

These variations are consistent with the contribution of gas-rich bodies of carbonaceous chondrite compositions to a growing Earth that had already trapped a solar component presumably from the PSN. During impact degassing, chondritic noble gases would had been released into the growing terrestrial atmosphere and not readily trapped into the proto-mantle due to their chemical inertness. Furthermore, atmospheric argon has a 38 Ar/ 36 Ar ratio (0.188) in the range of chondritic values [START_REF] Mazor | Noble gases in carbonaceous chondrites[END_REF][START_REF] Ott | Noble gases in meteorites -Trapped components[END_REF], different from the solar ratio of 0.182, [START_REF] Heber | Noble gas composition of the solar wind as collected by the Genesis mission[END_REF][START_REF] Meshik | Constraints on neon and argon isotopic fractionation in solar wind[END_REF]. Thus there is no need to invoke isotopic fractionation for establishing the isotopic composition of light noble gases. The case of xenon, which is isotopically different from any potential cosmochemical end-member (solar or chondritic) compositions will be discussed in Section 4.

Cometary shower during the Late Heavy Bombardment ?

A cometary contribution to the terrestrial inventory of volatile elements appears limited from D/H [START_REF] Dauphas | The late asteroidal and cometary bombardment of Earth as recorded in water deuterium to protium ratio[END_REF]; however, as noted above, this argument may weaken if further cometary D/H measurements confirm Earth-like compositions) and 15 N/ 14 N systematics [START_REF] Jehin | Isotopic Ratios in Comets: Status and Perspectives[END_REF][START_REF] Marty | Water in the early Earth[END_REF] The lunar surface bears scares of a late spike of bombardment around 3.8 Ga ago and this Late Heavy Bombardment (LHB) episode should have also affected the Earth by supplying an amount of ET material equivalent to a layer of 200 m on average on the Earth's surface. [START_REF] Gomes | Origin of the cataclysmic Late Heavy Bombardment period of the terrestrial planets[END_REF] proposed that the LHB consisted of ~50 % cometary material, due to the destabilisation of the Kuiper belt by catastrophic resonances of the giant planets. From mass balance consideration, [START_REF] Marty | Noble gas signature of the late heavy bombrdment in the Earth's atmosphere[END_REF] have argued that the amount of noble gases in the atmosphere constrain the cometary contribution to less than 1 %, as comets are expected to be rich in noble gases (Bar-Nun and [START_REF] Bar-Nun | Trapping of gases in water ice and consequences to comets and the atmospheres of the inner planets[END_REF]. Measurement of cometary neon has been reported for a Stardust grain and indeed indicates that the original material was rich in Ne [START_REF] Marty | Helium and neon abundances and compositions in cometary matter[END_REF]. From mass balance also, it can be shown that such a contribution would have limited effect on the isotopic compositions of H and N [START_REF] Marty | Noble gas signature of the late heavy bombrdment in the Earth's atmosphere[END_REF]. The overabundance of comets during the Earth/Moon bombardment in the LHB model of [START_REF] Gomes | Origin of the cataclysmic Late Heavy Bombardment period of the terrestrial planets[END_REF] is a wellknown problem (A. Morbidelli, personal communication). It may suggest that most comets disintegrated during their journey into the inner solar system, before having a chance to collide with our planet and its satellite. Alternatively, a possible caveat is that the noble gas content of cometary matter has not yet been measured and is only estimated from experiments aimed at measuring the trapping efficiency of noble gases in growing amorphous ice [START_REF] Owen | Possible cometary origin of heavy noble gases in the atmospheres of Venus, Earth and Mars[END_REF]. A test of the [START_REF] Gomes | Origin of the cataclysmic Late Heavy Bombardment period of the terrestrial planets[END_REF]'s model and of a cometary origin for terrestrial oceans (Hartlog et al., 2011) will be to analyze cometary material, either in situ or in a pristine sample returned by a dedicated space mission, a high priority in the mind of the author.

Reservoir inventories

In this section, three different terrestrial reservoirs are considered : the atmosphere sensu lato (air, oceans, sediments, crust), the "depleted mantle" (DM) sourcing basalts at mid-ocean ridges, and the bulk mantle (BM) that represents the silicate Earth (excluding the atmosphere).

The amounts of volatile elements in the different terrestrial reservoirs are normalized to the carbonaceous chondrite composition for comparison purpose . Such normalisation is justified from stable isotopes, but is more speculative for elemental abundances. Carbon and nitrogen in meteorites are mostly hosted by a common phase which is insoluble organic matter (IOM), whereas a significant fraction of water (equivalent OH -) is from aqueous alteration of the chondrite parent bodies. Different origins and alteration imply fractionation between elements. Fortunately, H and C correlate in un-metamorphosed carbonaceous chondrites, and the H/C ratio of the terrestrial mantle is within the range of values observed in chondrites [START_REF] Hirschmann | The H/C ratios of Earth's near-surface and deep reservoirs, and consequences for deep Earth volatile cycles[END_REF]. The case of the noble gases poses another problem. The noble gas isotopic compositions of chondrites are significantly different from those of the proto-solar nebula, being elementally enriched in heavy noble gases and isotopically enriched in heavy isotopes. Chondritic noble gases are trapped in very small weight fractions (< 1 % in mass) of the bulk meteorites [START_REF] Lewis | Host phase of strange xenon in Allende[END_REF], the so-called Phase Q (the residue of acid -HF, HCl-attack of bulk chondrites) which is associated with IOM [START_REF] Ott | Noble-Gas-Rich Separates from the Allende Meteorite[END_REF][START_REF] Marrocchi | Interlayer trapping of noble gases in insoluble organic matter of primitive meteorites[END_REF]. The abundance of noble gases varies from one meteorite to another, but roughly correlates with the C content, especially for carbonaceous chondrites [START_REF] Otting | Total carbon content and primordial rare gases in chondrites[END_REF]. Despite variations in their absolute abundances, the noble gas abundance and isotope patterns are comparable among different meteorites, suggesting a common fractionation process from the protosolar nebula. Thus, adopting a chondritic reference pattern appears justified when discussing the origin(s) and fractionation of volatile elements during terrestrial accretion and subsequent evolution. In the following a mean carbonaceous chondrite (CC) composition is computed for normalization using data from Orgueil (CI; [START_REF] Mazor | Noble gases in carbonaceous chondrites[END_REF] and from Murchison (CM; [START_REF] Bogard | Noble gases and radionuclides in Lost City and other recently fallen meteorites[END_REF]) (Table 1), since these meteorites are among the most primitive ones and have suffered little thermal metamorphism.

Earth's surface inventory

Following [START_REF] Rubey | Geologic history of sea water[END_REF], the Earth's surface inventory includes the atmosphere, the oceans, and sedimentary rocks (and the continental and oceanic crusts, which are minor reservoirs compared to the other ones). Noble gases of the surface inventory are concentrated in the atmosphere [START_REF] Ozima | Noble gas geochemistry[END_REF]. The water and carbon budget at the Earth's surface is from [START_REF] Hirschmann | The H/C ratios of Earth's near-surface and deep reservoirs, and consequences for deep Earth volatile cycles[END_REF] and refs. therein, and that of nitrogen is from [START_REF] Marty | The nitrogen record of crust-mantle interaction and mantle convection from Archean to present[END_REF].

When normalized to CC (Fig. 4), the atmospheric abundance pattern is by no mean chondritic. The H 2 O/C ratio of the terrestrial surface is too high, as noted previously [START_REF] Hirschmann | The H/C ratios of Earth's near-surface and deep reservoirs, and consequences for deep Earth volatile cycles[END_REF], and Ne, Ar and Kr are enriched by 1-2 orders of magnitude compared to major volatiles. This pattern cannot be ascribed to any known cosmochemical ancestor and has to be the result of planetary processing. The overabundance of noble gases could be a signature of a cometary contribution, possibly during the late heavy bombardment (Marty & Meibom, 2006) and/or the result of the depletion of major volatiles at the Earth's surface due to their trapping in the solid Earth, or a combination of both processes.

To investigate such possibilities, it is necessary to evaluate the amount of volatile elements stored in the solid Earth.

Depleted mantle (DM)

The mantle source of mid-ocean ridge basalts (MORBs) is generally labelled depleted mantle (DM) in geochemical budgets. The term "depleted" refers to the most incompatible trace elements, like the light rare earth elements (REE), which are depleted in the mantle region source of MORBs as a consequence of past extraction of melts. MORBs depleted in light REE are labelled N-MORB ("N" for normal). Some MORBs are not depleted, and even enriched in light REE and other highly incompatible elements, and are termed E-MORBs ("E" for enriched; [START_REF] Leroex | Source regions of Mid-Ocean Ridge Basalts : Evidences for enrichment processes[END_REF]. Although the distinction between these different mantle sources may be somewhat arbitrary [START_REF] Albarède | The survival of mantle geochemical heterogeneities[END_REF], the carbon/ 3 He ratio varies by a factor of ~4 between N-and E-MORB [START_REF] Cartigny | Volatile (C, N, Ar) variability in MORB and the respective roles of mantle source heterogeneity and degassing : the case of the Southwest Indian Ridge[END_REF][START_REF] Marty | Volatiles (He, C, N, Ar) in mid-ocean ridge basalts: Assesment of shallow-level fractionation and characterization of source composition[END_REF][START_REF] Nishio | Volatile element isotopic systematics of the Rodrigues Triple Junction Indian Ocean MORB : implications for mantle heterogeneity[END_REF][START_REF] Nishio | Carbon and helium isotope systematics of North Fiji Basin basalt glasses : carbon geochemical cycle in the subduction zone[END_REF], justifying to keep this nomenclature for volatile elements. The fraction of the different MORB types along mid ocean ridges is relatively well known, thus an average volatile composition of N-, and E-MORBs, weighted by their frequency of occurrence, results in an average MORB source equivalent to DM [START_REF] Marty | Volatiles (He, C, N, Ar) in mid-ocean ridge basalts: Assesment of shallow-level fractionation and characterization of source composition[END_REF].

The solubility of water is relatively high compared to other volatile elements, therefore water loss during degassing is minor compared to that of other volatiles. As a result, the abundance of H 2 O in the DM source is estimated from measurements of H 2 O contents in MORB glasses (which erupted at sufficient ocean depth to prevent significant water degassing). Global estimates converge to 150±50 ppm H 2 O for the DM [START_REF] Dixon | Recycled dehydrated lithosphere observed in plume-influenced mid-ocean-ridge basalt[END_REF][START_REF] Michael | The concentration, behavior and storage of H2O in the suboceanic upper mantle -Implications for mantle metasomatism[END_REF][START_REF] Saal | Vapour undersaturation in primitive mid-ocean-ridge basalt and the volatile content of Earth's upper mantle[END_REF][START_REF] Salters | Composition of the depleted mantle[END_REF].

The carbon content of the MORB mantle can be estimated from the flux of volatile elements to the oceans. The flux of 3 He is 1000±250 mol/yr [START_REF] Craig | Excess 3 He in deep waters on the East Pacific Rise[END_REF], which, for a magma generation rate at ridges of 20±4 km 3 /yr and a partial melting degree of 12±3 % gives a 3 He content of the MORB mantle of 2.0±0.8 x 10 -15 mol/g. The C/ 3 He ratio of the MORB mantle is 2.2±0.6 x 10 9 [START_REF] Marty | Volatiles (He, C, N, Ar) in mid-ocean ridge basalts: Assesment of shallow-level fractionation and characterization of source composition[END_REF][START_REF] Resing | CO 2 and He-3 in hydrothermal plumes: implications for mid-ocean ridge CO 2 flux[END_REF], therefore (assuming a 3 He flux of 1000 mol/yr) the content of the MORB mantle is 50±25 ppm C. The fact that the C/ 3 He ratio of the N-MORB (1.4±0.4 x 10 9 ) is significantly different from that of E-MORB (5.9±1.3 x 10 9 ; Marty & Zimmermann, 1998) suggests that the C mantle content is heterogeneous, varying between 30±10 ppm and 140±30 ppm for the N-MORB and the E-MORB end-members, respectively.

Alternatively, C can be estimated from melt inclusions trapped in olivine in order to constrain the average mantle CO 2 /Nb ratio, assuming that the C/Nb ratio is little fractionated and that the mantle Nb concentration is relatively well known. [START_REF] Saal | Vapour undersaturation in primitive mid-ocean-ridge basalt and the volatile content of Earth's upper mantle[END_REF] estimated this ratio to be ~250 and proposed a DM carbon content of 19±5 ppm. [START_REF] Salters | Composition of the depleted mantle[END_REF] used the same CO 2 /Nb constraints to obtain a slightly different mantle Nb concentration, resulting in a mantle C concentration of 16±9 ppm. [START_REF] Cartigny | Towards a consistent mantle carbon flux estimate: Insights from volatile systematics (H 2 O/Ce, delta D, CO 2 /Nb) in the North Atlantic mantle (14 degrees N and 34 degrees N)[END_REF] The nitrogen content of the DM mantle can be estimated in two ways. First, N 2 in MORB vesicles correlates well with radiogenic 40 Ar*, yielding a near-constant N/ 40 Ar for this reservoir [START_REF] Dauphas | Heavy nitrogen in carbonatites of the Kola Peninsula: A possible signature of the deep mantle[END_REF][START_REF] Marty | Nitrogen content of the mantle inferred from N 2 -Ar correlation in oceanic basalts[END_REF][START_REF] Marty | The nitrogen record of crust-mantle interaction and mantle convection from Archean to present[END_REF]. From estimates of the 3 He content of the mantle source of MORBs (see above), of the mean MORB 3 He/ 4 He (8±1 Ra), and using a 4 He/ 40 Ar* of 2.2 +0.8 -0.6 (see below) for this reservoir, [START_REF] Marty | The nitrogen record of crust-mantle interaction and mantle convection from Archean to present[END_REF] estimated a N content of the MORB mantle source of 0.27±0.16 ppm.

Independently, the DM nitrogen content can be also estimated from the C/N (molar) ratio of the MORB source. The resulting N content depends on the mantle source region considered.

For the whole MORB mantle source (N-and E-MORBs), taking a C content of 50±25 ppm (see above), and a whole mantle C/N ratio of 535±224 [START_REF] Marty | Volatiles (He, C, N, Ar) in mid-ocean ridge basalts: Assesment of shallow-level fractionation and characterization of source composition[END_REF], one obtains a N content of 0.11±0.07 ppm. Taking the N-MORB mantle source as representative of the DM, the N content becomes 0.09±0.05 ppm (C = 20±8 ppm, see above; C/N = 270±100; [START_REF] Marty | Volatiles (He, C, N, Ar) in mid-ocean ridge basalts: Assesment of shallow-level fractionation and characterization of source composition[END_REF]. All these estimates compare well within errors and therefore it appears that there is not significant C/N fractionation during recycling. It is notable also that the N content obtained from C is lower by a factor of two than the one obtained from the noble gas calibration approach. This difference could be due to an overestimate of the 3 He flux in the oceans (see above for discussion of C/ 3 He uncertainties).

Alternatively, the C content of the DM mantle may have been underestimated, as suggested by [START_REF] Cartigny | Volatile (C, N, Ar) variability in MORB and the respective roles of mantle source heterogeneity and degassing : the case of the Southwest Indian Ridge[END_REF]. Whatever the reason behind these differences, for the present exercise, a factor of 2 uncertainty is not crucial and is well within the uncertainties.

The noble gas abundance pattern is the mean composition of the popping rock [START_REF] Moreira | Rare gas systematics in Popping Rock : Isotopic and elemental compositions in the upper mantle[END_REF] and of the Bravo Dome gas [START_REF] Ballentine | Neon isotopes constrain convection and volatile origin in the Earth's mantle[END_REF]. The absolute amounts were anchored using the C/ 3 He ratio and the DM carbon content.

The DM abundance pattern is lower than the range of compositions that would have been carried by a late veener consistent with the abundance of platinum group elements in the mantle (Fig. 4). However, the DM represents only a fraction of the mantle inventory, which is estimated in the next subsection.

Bulk mantle (BM)

The bulk mantle (BM) is defined as the silicate Earth, excluding the surface inventory. For non specialists of mantle geochemistry, it may look strange that this reservoir is not equivalent to the one (DM) discussed previously which sources the largest flux of mantlederived magmas. This is because all budgets of incompatible elements indicate that the DM does not contain enough of these elements to fit the terrestrial composition and that there must be other reservoir(s) that host a large fraction of these. These reservoirs are not readily sampled by magmas reaching the surface, and their surface expressions may be volcanic provinces related to mantle plumes. Even in those cases, it is not clear which deep reservoirs are sampled. Furthermore, their sizes is model-dependent. Thus derivation of the BM abundance of the volatile elements should not depend on the reservoir sizes and is estimated here from a global mass balance, which involves the 40 Ar budget of the Earth. As outlined in the Introduction, this budget indicates that only a fraction of 40 Ar produced by the decay of 40 K is now in the atmosphere, the rest presumably being in the silicate Earth. The most recent estimate of the terrestrial K content for the bulk silicate Earth (BSE) is 280±60 ppm (1 σ, [START_REF] Arevalo | The K/U ratio of the silicate Earth: Insights into mantle composition, structure and thermal evolution[END_REF], so that 40 K has produced 3.9±0.9 x 10 18 moles of 40 Ar over 4.5 Ga. 1.6 x 10 18 moles of 40 Ar are in the atmosphere [START_REF] Ozima | Noble gas geochemistry[END_REF], and [START_REF] Arevalo | The K/U ratio of the silicate Earth: Insights into mantle composition, structure and thermal evolution[END_REF] estimated the maximum 40 Ar amount in the continents to be 3.5 x 10 17 mol. Thus the mantle and continental crust may still contain 2.3±0.8 x 10 18 mol 40 Ar. This mass balance implies that ~50 % of radiogenic 40 Ar is trapped at depth [START_REF] Allègre | The argon constraints on mantle structure[END_REF][START_REF] Turner | The outgassing history of the atmosphere[END_REF].

The K content of the Earth is, however, subject to discussion. For instance, [START_REF] Jochum | K, U and Th in Mid-Ocean Ridge Basalt glasses and heat production, K/U and K/Rb in the mantle[END_REF] proposed a silicate Earth K/U ratio of ~12,000 that results in a K content of 250 ppm (still consistent with the Arevalo et al's value given the uncertainty of 60 ppm for the latter).

In a more extreme view, Albarède (1998) remarked that the K content could be off by a factor of two, suggesting the possibility that almost all 40 Ar produced by 40 K is now in the atmosphere. However, recent geoneutrino measurements [START_REF] Gando | Partial radiogenic heat model for Earth revealed by geoneutrino measurements[END_REF] are consistent with a high U(+Th) content of the Earth, and therefore a similarly high K content, although uncertainties are still too high to permit a quantitative assessment of these concentrations.

The N/ 40 Ar ratio of mantle volatiles shows limited variation in either MORBs or plumederived magmas, and [START_REF] Marty | The nitrogen record of crust-mantle interaction and mantle convection from Archean to present[END_REF] estimated that the silicate Earth N/ 40 Ar ratio is 160±40. Hence, the nitrogen content of the silicate Earth (excluding the atmosphere) is 3.6±1.8 x 10 20 moles (0.84±0.43 ppm for a silicate Earth mass of 4x10 27 g). Note that this mass balance does not make any assumption about the size of mantle reservoirs since the N/ 40 Ar ratios are comparable among the surface, the DM and the BM inventories.

The volatile content of the bulk mantle can be derived from calibration to either 40 Ar or N.

The flux of mid-ocean ridge basalts dominates magma production from the mantle. The C/N ratio of all MORB types has been estimated at 535±224 [START_REF] Marty | Volatiles (He, C, N, Ar) in mid-ocean ridge basalts: Assesment of shallow-level fractionation and characterization of source composition[END_REF]. This ratio represents primarily the DM reservoir and the value corresponding to mantle plume should also be considered if C and N are fractionated during mantle extraction. C/N data for lavas associated with mantle plume provinces are scarce, but available data (submarine lava with high 3 He/ 4 He ratios from the Red Sea, Hawaii and the North Fidji Basin, lavas from the Pacific hot spot area like the society islands) are within the MORB range [START_REF] Marty | Volatiles (He, C, N, Ar) in mid-ocean ridge basalts: Assesment of shallow-level fractionation and characterization of source composition[END_REF]. The corresponding C content is 1.9±1.3 x 10 23 moles (580±380 ppm for the silicate Earth).

The carbon content of the mantle can also be computed from C/ 4 He ratios of plumerelated gases for which there are much more data (Réunion, Hawaii, Iceland ;[START_REF] Craig | Helium isotope ratios in Yellowstone and Lassen Park volcanic gases[END_REF][START_REF] Hilton | Large variations in vent fluid CO 2 /He-3 ratios signal rapid changes in magma chemistry at Loihi seamount, Hawaii[END_REF][START_REF] Marty | Gas Geochemistry of Geothermal Fluids, the Hengill Area, Southwest Rift-Zone of Iceland[END_REF][START_REF] Sedwick | Carbon-dioxide and helium in hydrothermal fluids from Loihi Seamount, Hawaii, USA -Temporal variability and implications for the release of mantle volatiles[END_REF] and of rock/mineral fluid inclusions from plume provinces [START_REF] Trull | C-He systematics in hotspot xenoliths : Implications for mantle carbon contents and carbon recycling[END_REF]. The log mean ratio of hotspot-associated fluids and fluid inclusions is 1.05±0.32 x 10 5 (n = 52). For these samples, 40 Ar data are not generally available (not measured or air-contaminated for volcanic and geothermal gases), so instead I use the 4 He/ 40 Ar production/accumulation ratio in order to calculate the source region C concentration. This approach is valid because C/He ratios do not vary significantly during magmatic or mantle processes [START_REF] Fischer | Upper-mantle volatile chemistry at Oldoinyo Lengai volcano and the origin of carbonatites[END_REF][START_REF] Resing | CO 2 and He-3 in hydrothermal plumes: implications for mid-ocean ridge CO 2 flux[END_REF]. In Fig. 5 the mantle source 4 He/ 40 Ar production/accumulation ratio is modelled using published values of the mantle K/U ratio [START_REF] Arevalo | The K/U ratio of the silicate Earth: Insights into mantle composition, structure and thermal evolution[END_REF][START_REF] Vlastelic | Th/U and other geochemical evidence for the Reunion plume sampling a less differentiated mantle domain[END_REF]. The residence time of incompatible elements in the MORB mantle has been estimated to be between 0.6 and 1.0 Ga [START_REF] Galer | Residence time of thorium, uranium and lead in the mantle with implications for mantle convection[END_REF], thus for such time durations, the 4 He/ 40 Ar ratios are within

8 . 0 6 . 0 2 . 2 + - .
The bulk mantle accumulation time admits an upper limit of 4.5 Ga, therefore, despite the lower K/U ratio of OIBs, it is likely the OIB source reservoir has a 4 He/ 40 Ar of 1.9 ±0.5, very similar to that of MORBs.

With the bulk mantle 40 Ar concentrations calculated above, the corresponding BSE carbon content is 3.8±2.7 x 10 23 moles (1164±544 ppm), comparable to the above estimate but with a larger uncertainty. From these two approaches, I use a weighted average C amount of 2.5±1.0

x 10 23 moles (765±300 ppm) for carbon sequestrated in the interior of the silicate Earth, equivalent to 530±210 ppm C (Table 1) for the bulk Earth when normalized to the total mass of our planet (5.98 x 10 27 g). The water amount still in the silicate Earth is computed with the estimate of the mean mantle H/C mass ratio by [START_REF] Hirschmann | The H/C ratios of Earth's near-surface and deep reservoirs, and consequences for deep Earth volatile cycles[END_REF], which yields a water content of 2700±1350 ppm for the bulk Earth (Table 1).

As shown by [START_REF] Trieloff | Isotope systematics of noble gases in the Earth's mantle: possible sources of primordial isotopes and implications for mantle structure[END_REF], the noble gas abundance patterns of plume-related magmas are not significantly different from those of MORB's and I use the same abundance pattern as for the MORB source. The absolute abundances are anchored in two ways. First, as stated above, the mantle 40 Ar content is reasonably known. For the bulk mantle, a 40 Ar/ 36 Ar ratio of 6,000±2000 appears representative [START_REF] Trieloff | Isotope systematics of noble gases in the Earth's mantle: possible sources of primordial isotopes and implications for mantle structure[END_REF], which yields a 36 Ar abundance of 8 x 10 -14 mol/g. The 40 Ar/ 36 Ar ratios are notably derived from correlations between 40 Ar/ 36 Ar and 20 Ne/ 22 Ne ratios and extrapolated to the solar value for the latter [START_REF] Marty | Plume-derived rare gases in 380 Ma carbonatites from the Kola region (Russia) and the argon isotopic composition in the deep mantle[END_REF], so they are unlikely to be perturbed by shallow atmospheric contamination of the magmas. Second, the C/ 3 He ratio of both plumes and MORBs are not significantly different [START_REF] Trull | C-He systematics in hotspot xenoliths : Implications for mantle carbon contents and carbon recycling[END_REF] and average 3±1 x 10 9 , giving a comparable 36 Ar content of 13 x 10 -14 mol/g. The abundances of volatile elements in terrestrial reservoirs are listed in Table 1 together with their uncertainties.

Comparison between Atmosphere and Bulk Mantle abundance

The major volatile/noble gas patterns of the atmosphere and the bulk mantle reservoirs (Fig. 6) are somewhat symmetrical : the major, chemically reactive volatile elements are mostly stored in the mantle, whereas the inert noble gases are largely in the atmosphere. This fractionation could be due to either preferential degassing of the chemically inert noble gases, with carbon, water and nitrogen being sequestrated in the mantle during early degassing. This possibility requires more reducing conditions of the ancient mantle than the present day one to retain these elements [START_REF] Kadik | Influence of Oxygen Fugacity on the Solubility of Nitrogen, Carbon, and Hydrogen in FeO-Na(2)O-SiO(2)-Al(2)O(3) Melts in Equilibrium with Metallic Iron at 1.5 GPa and 1400 degrees[END_REF]. Alternatively, the fractionation may instead indicate preferential recycling of major volatiles into the mantle, with much more limited recycling of the noble gases. Notably, the BM inventories for water and carbon are high: up to 90 % of water may be in the mantle, and up to 97 % carbon may be stored at depth. If these mass balance budgets are correct, then the amounts of H 2 O and C at the surface might have been buffered by the mantle inventories, and could have decreased with time if recycling was responsible for the fractionation between major volatiles and noble gases. Such massive recycling should have occurred early in the geological history in order to get mild environmental conditions at the Earth's surface and allow the existence of liquid water as early as the Hadean eon [START_REF] Sleep | Initiation of clement surface conditions on the earliest Earth[END_REF].

The volatile content of the Earth

The bulk Earth volatile content is obtained by adding the ATM and BM inventories (Fig. 7). Overall, a chondritic abundance for volatile elements emerges, consistent with the evidence of a genetic link with chondrites from H and N isotopes. The bulk Earth abundance of noble gases is dominated by the atmospheric inventory, and Ne and Ar isotopic ratios are effectively within the chondritic values. The isotopic composition of atmospheric krypton is slightly different from the chondritic composition, which could be the result of atmospheric escape to a lesser extent than Xe (see below). The case of solar-like Ne in the mantle requires fine tuning : solar-like neon is indeed present in the mantle, but its entire terrestrial budget is dominated by a component more akin to chondrites (Fig. 3).

The volatile abundances estimated here are high with respect to those of other works [START_REF] Bolfan-Casanova | Water in the Earth's mantle[END_REF][START_REF] Dixon | Recycled dehydrated lithosphere observed in plume-influenced mid-ocean-ridge basalt[END_REF][START_REF] Hirschmann | The H/C ratios of Earth's near-surface and deep reservoirs, and consequences for deep Earth volatile cycles[END_REF]. Uncertainties on the BM mantle abundances include those on the K abundance and therefore the results are fairly robust as far as orders of magnitude are concerned. The bulk Earth water content between of 2700±1350 ppm, corresponding to 10±5 ocean masses, is one order of magnitude higher than estimates of the upper mantle water content based on the H 2 O/Ce ratios ( 50-200 ppm, ≤ 1 ocean mass in the mantle, [START_REF] Michael | The concentration, behavior and storage of H2O in the suboceanic upper mantle -Implications for mantle metasomatism[END_REF][START_REF] Saal | Vapour undersaturation in primitive mid-ocean-ridge basalt and the volatile content of Earth's upper mantle[END_REF]. It is, however, consistent with a bulk Earth abundance of 1300 ppm (range : 550-1900 ppm) obtained using the measured H 2 O/K 2 O ratios in MORBs and OIBs [START_REF] Jambon | Water in oceanic basalts -evidence for dehydration of recycled crust[END_REF]. The lower limit of the present estimate is also marginally consistent with the range of values for the mantle source of plumes (300-1000 ppm; [START_REF] Dixon | Recycled dehydrated lithosphere observed in plume-influenced mid-ocean-ridge basalt[END_REF]. The present budget assumes that radiogenic 40 Ar in the atmosphere did not escape to space (if this would have been the case, the computed mantle content would be lower since it is computed by removing the atmospheric budget from the total amount of 40 Ar produced from 40 K). This possibility is unlikely however, since it is not supported by identical 38 Ar/ 36 Ar ratios in the atmosphere and in chondrites. Another source of uncertainty is the potassium budget of the Earth. Indeed the 280 ppm K content of the Earth given by Arevalo et al. ( 2009) may be at the upper range of possible values (F.

Albarède, personal communication). Taking instead the 250 ppm K estimate derived from the canonical U/K ratio of [START_REF] Jochum | K, U and Th in Mid-Ocean Ridge Basalt glasses and heat production, K/U and K/Rb in the mantle[END_REF] would reduce the bulk Earth water content to 1700 ppm, closer to independent estimates of the bulk Earth water content. In view of these uncertainties, a range of 1000-3000 ppm for the water content of the bulk Earth is compatible with the range given by [START_REF] Jambon | Water in oceanic basalts -evidence for dehydration of recycled crust[END_REF] and [START_REF] Dixon | Recycled dehydrated lithosphere observed in plume-influenced mid-ocean-ridge basalt[END_REF], and is preferred here.

The volatile abundances presented here correspond to the contribution of ~2 (±1) % of CC material (Table 1). This fractional contribution seems to be also seen in the abundance of terrestrial halogens: terrestrial abundances of Cl, Br and I are also consistent with a contribution of 2±1 % of carbonaceous chondrite material (Fig. 8). The abundance of F would requires, however, a much higher contribution of 17 %, for a reason unknown to the author.

The oxygen [START_REF] Javoy | Carbon and nitrogen isotopes in the mantle[END_REF], chromium [START_REF] Trinquier | Widespread Cr-54 heterogeneity in the inner solar system[END_REF], titanium [START_REF] Leya | Titanium isotopes and the radial heterogeneity of the solar system[END_REF] and molybdenum [START_REF] Dauphas | Inference on terrestrial genesis from molybdenum isotope systematics[END_REF] isotope signatures of the Earth point to a enstatite chondrite (EC) composition rather than to a CC ancestor. However, EC are very reduced and do not contain significant amounts of water. Hence the classical model of heterogeneous accretion of Earth starting with a dry, reducing material and evolving towards more oxidizing contributions by addition of different material [START_REF] Javoy | Carbon and nitrogen isotopes in the mantle[END_REF][START_REF] Wänke | Chemical-Composition and Accretion History of Terrestrial Planets[END_REF] appears substantiated by the present inventory. The contribution of volatilerich bodies from the snow line region is in fact a logical consequence of planetary growth in the inner planet region : the locally dry bodies that were present in the Earth's forming region became depleted due to their accretion, which allowed more distant wet planetesimals to contribute to the proto-Earth as accretion proceeded [START_REF] Morbidelli | Source regions and timescales for the delivery of water to the Earth[END_REF][START_REF] Raymond | Building the terrestrial planets: Constrained accretion in the inner Solar System[END_REF][START_REF] Walsh | A low mass for Mars from Jupiter's early gas-driven migration[END_REF].

The case of Nitrogen

There are two notable exceptions to the chondritic abundance pattern : nitrogen and xenon are both depleted by ~one order of magnitude relative to other volatile elements. For N, this depletion can be due to trapping in the interior of the Earth. Under mantle oxygen fugacity conditions, nitrogen is presumably incompatible and presents a low solubility in basaltic melt similar to that of noble gases [START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF][START_REF] Miyazaki | Solubilities of nitrogen and noble gases in silicate melts under various oxygen fugacities: Implications for the origin and degassing history of nitrogen and noble gases in the earth[END_REF][START_REF] Roskosz | Dual speciation of nitrogen in silicate melts at high pressure and temperature: An experimental study[END_REF]. However this might have not be the case in the early, more reducing mantle conditions [START_REF] Kadik | Influence of Oxygen Fugacity on the Solubility of Nitrogen, Carbon, and Hydrogen in FeO-Na(2)O-SiO(2)-Al(2)O(3) Melts in Equilibrium with Metallic Iron at 1.5 GPa and 1400 degrees[END_REF], and/or in the presence of water [START_REF] Roskosz | Dual speciation of nitrogen in silicate melts at high pressure and temperature: An experimental study[END_REF]. Furthermore, preliminary metal-silicate partition experiments suggest that nitrogen is siderophile, with a partition coefficient of 1 to 10 in favour of iron at high pressure [START_REF] Bouhifd | Nitrogen solubility in a molten assemblage of an (Fe,Ni) alloy and a CI chondritic silicate up to 18 GPa[END_REF][START_REF] Kadik | Influence of Oxygen Fugacity on the Solubility of Nitrogen, Carbon, and Hydrogen in FeO-Na(2)O-SiO(2)-Al(2)O(3) Melts in Equilibrium with Metallic Iron at 1.5 GPa and 1400 degrees[END_REF]. Hence the "missing" N could have been sequestrated in the core and this possibility is consistent with the accretion of wet planetesimals during terrestrial differentiation, since their inventory is higher than the PGE one. This implies that carbon and hydrogen were not quantitatively partitioned in the core.

The case of Xenon

Xenon is depleted by one order of magnitude relative to other volatile elements when normalized to the chondritic composition (Fig. 7). Furthermore, atmospheric xenon is enriched in the heavy isotopes by 3-4 % amu -1 relative to chondritic and solar compositions.

In contrast, the isotopic composition of atmospheric krypton is little fractionated (< 1 % amu - 1 ) relative to that of cosmochemical end-members. This discrepancy, known as the xenon paradox, has led to sophisticated models of atmospheric evolution coupled with mantle geodynamics [START_REF] Pepin | On the origin and early evolution of terrestrial planetary atmospheres and meteoritic volatiles[END_REF][START_REF] Tolstikhin | The evolution of terrestrial volatiles: a view from helium, neon, argon and nitrogen isotope modelling[END_REF] and cometary contributions [START_REF] Dauphas | The dual origin of the terrestrial atmosphere[END_REF][START_REF] Owen | Possible cometary origin of heavy noble gases in the atmospheres of Venus, Earth and Mars[END_REF] that could explain terrestrial noble gas patterns under ad hoc conditions, but which fail to account for the fact that atmospheric Martian volatiles present a comparable paradox. Because the other volatile elements, not only noble gases but also major volatiles, are in chondritic proportions and have isotopic compositions close to Chondritic (or solar for Ne), xenon might have been initially chondritic too, and could have been affected by a process that enriched the heavy isotopes and depleted its abundance relative to other volatiles. It has been proposed that xenon could be sequestrated in minerals at high pressure [START_REF] Sanloup | Retention of xenon in quartz and Earth's missing xenon[END_REF], but this possibility cannot account for the specific Xe isotope composition of the atmosphere. Processes able to fractionate the isotopes of Xe at the percent level require ionization of xenon [START_REF] Bernatowicz | Xe isotopic fractionation in a cathodeless glow discharge[END_REF][START_REF] Frick | Noble gas trapping and fractionation during synthesis of carbonaceous matter[END_REF][START_REF] Hohenberg | Active capture and anomalous adsorption: New mechanisms for the incorporation of heavy noble gases[END_REF][START_REF] Marrocchi | Adsorption of xenon ions onto defects in organic surfaces: Implications for the origin and the nature of organics in primitive meteorites[END_REF][START_REF] Ponganis | Isotopic fractionation in low-energy ion implantation[END_REF]. Such processing should have affected mostly xenon and not the other noble gases (although there is room for fractionating to a much lesser extent Kr). It may be related to the specific electronic structure of Xe, which makes Xe the most reactive element among noble gases. Xenon has the lowest ionization potential among noble gases, CO 2 , CH 4 , N 2 , and H 2 O. In experiments aimed at fractionating Xe isotopes upon ionization, ionized Xe implanted in solids is enriched the heavy isotopes, whereas neutral Xe is much less efficiently trapped and is not isotopically fractionated. It is possible that Xe was fractionated and depleted due to interactions with UV light from the young Sun in the gas/dust medium in the inner solar system before planetesimal formation, since the irradiation flux was orders of magnitude higher than Today's [START_REF] Ribas | Evolution fo the solar activity over time and effects on planetary atmospheres. II. kappa(1) Ceti, an analog of the Sun when life arose on Earth[END_REF]. Ionized Xe might have escaped via the magnetic field of the early Sun and only a small fraction of Xe ions implanted into dust and enriched in heavy isotopes would have been preserved. This possibility is, however, not consistent with the fact that none of the meteorites documented so far show atmospheric-like Xe.

Recently, xenon having an isotopic composition intermediate between the atmospheric and the chondritic ones has been documented in Archean ( ≤ 3Ga-old) sedimentary rocks (Fig. 9), suggesting that the atmosphere at that time had a less evolved Xe isotopic composition [START_REF] Pujol | Chondritic-like xenon trapped in Archean rocks: A possible signature of the ancient atmosphere[END_REF]. Thus Xe depletion and isotope fractionation could have taken place by progressive escape of Xe ions from the atmosphere, possibly through interaction with UV light from the young Sun. Assuming a Rayleigh type isotope evolution for atmospheric Xe :

where f is the depletion factor (= 1/20; [START_REF] Pepin | Atmospheres on the terrestrial planets: Clues to origin and evolution[END_REF], the instantaneous fractionation factor α requires enrichment of 1.3 % in heavy isotopes for Xe remaining in the atmosphere. This In both cases however remains the problem of keeping Xe ionized long enough to permit its escape from the atmosphere.

The Xe isotopes produced by the extinct radioactivities of 129 I and 244 Pu permit to compute closure ages for the atmosphere and, by inference, for the Earth. 129 I was present at the birth of the Solar system and decayed with a half-life of 16 Ma into 129 Xe. Mono-isotopic excesses of 129 Xe are found both in the mantle and in the atmosphere. Because most terrestrial Xe is within the atmosphere (Fig. 6), it is straightforward to compute a 129 I-129 Xe retention age of about 100 Ma (see for instance [START_REF] Pepin | Origin of noble gases in the terrestrial planets[END_REF] for data and computation) from the terrestrial budget of I [START_REF] Deruelle | Iodine Abundances in Oceanic Basalts -Implications for Earth Dynamics[END_REF] and the amount of radiogenic 129 Xe in the atmosphere. A comparable age of ~120 Ma is obtained by combining the 129 I-129 Xe and 244 Pu-136 Xe (T 1/2 = 82 Ma) systems [START_REF] Ozima | Formation age of Earth from I-129/I-127 and Pu-244/U-238 systematics and the missing Xe[END_REF][START_REF] Pepin | Origin of noble gases in the terrestrial planets[END_REF][START_REF] Yokochi | Geochemical constraints on mantle dynamics in the Hadean[END_REF]. These ages are consistent with the Pb-Pb model age of the Earth [START_REF] Albarède | Volatile accretion history of the terrestrial planets and dynamic implications[END_REF] and with the identical W isotope composition of the Moon and Earth [START_REF] Touboul | Late formation and prolonged differentiation of the Moon inferred from W isotopes in lunar metals[END_REF]. If xenon was lost long after Earth's formation, then the ~20 fold Xe depletion in the atmosphere might have occurred when production of Xe isotopes by extinct radioactivities was achieved. For instance, Xe trapped in Archean rocks 3.5 Ga ago presents an isotopic composition intermediate between Chondritic and modern Atmospheric, indicating in the model of [START_REF] Pujol | Chondritic-like xenon trapped in Archean rocks: A possible signature of the ancient atmosphere[END_REF] that only half of initial Xe was already lost at that epoch. Thus the atmospheric contents of Xe isotopes produced by the decays of extinct radioactivities need to be corrected for subsequent loss and multiplied by a factor of ~20 to get the real age. Doing so, one finds a I-Pu-Xe closure age of 40-50 Ma for the Earth instead of ~120 Ma. This younger age is fully consistent with the Hf-W age of the Earth relative to primitive meteorites [START_REF] Yin | A short timescale for terrestrial planets from Hf-W chronometry[END_REF], and does not contradict the identity of tungsten isotopic ratios between Earth and Moon if these two bodies have similar Hf/W ratios [START_REF] Touboul | Late formation and prolonged differentiation of the Moon inferred from W isotopes in lunar metals[END_REF].

Conclusions

The origin of terrestrial volatile elements has been re-evaluated in the light of the stable and noble gas isotopes. These tracers point to a chondritic, rather than solar or cometary, source. A small (≤10 %) fraction of mantle volatiles might have been derived from the protosolar nebula during an early stage of the proto-Earth growth. Light noble gas compositions are consistent with mixing between chondritic and solar end-members, rather than due to fractionation of an originally solar component in the atmosphere during hydrodynamic escape. Likewise, the stable isotopes of H and N do not support atmospheric escape because their compositions are very similar to those of primitive meteorites.

A bulk Earth inventory has been achieved by calibration to noble gas isotopes produced by extant radioactivities. Most of water and carbon are within the Earth whereas noble gases are mostly in the atmosphere. This fractionation testifies for active exchanges of volatile elements between the mantle and the surface. The high water and carbon contents of the bulk Earth (equivalent to the contribution of 2±1% of carbonaceous chondrite) suggest the accretion of volatile elements from wet planetesimals during the main Earth forming events, rather than contribution of a late veener after Earth's differentiation required from the platinum group element budget.

Bulk Earth water, carbon, neon, argon and krypton are in chondritic relative proportions, but nitrogen and xenon are depleted by one order of magnitude relative to the other volatiles.

Nitrogen could be partitioned in the core or in a retentive mantle phase. The depletion of xenon could be the result of Xe preferential escape during the geological history of the Earth, as suggested by the occurrence of chondritic-like Xe in Archean sediments, presumably representing the composition of the ancient atmosphere [START_REF] Pujol | Chondritic-like xenon trapped in Archean rocks: A possible signature of the ancient atmosphere[END_REF]. If this model is correct, then the 129 I-129 Xe age of the Earth needs to be corrected for Xe loss that occurred after Earth's formation, which gives an age of ~40-50 Ma after start of solar system formation rather than ~120 Ma as previously inferred. The solar abundances are anchored to a 22 Ne content equal to the average of carbonaceous chondrites (from [START_REF] Mazor | Noble gases in carbonaceous chondrites[END_REF], the abundances of the other elements are computed with data from [START_REF] Anders | Abundances of the elements : Meteoritic and Solar[END_REF]. The chondritic composition (CI-CM) is an average of Orgueil and Murchison data. Sources of data; carbon and nitrogen : [START_REF] Kerridge | Carbon, hydrogen and nitrogen in carbonaceous chondrites: abundances and isotopic compositions in bulk samples[END_REF], H 2 O [START_REF] Robert | The D/H ratio in chondrites[END_REF]; noble gases : [START_REF] Mazor | Noble gases in carbonaceous chondrites[END_REF], [START_REF] Bogard | Noble gases and radionuclides in Lost City and other recently fallen meteorites[END_REF]. The atmospheric inventory comprises the atmosphere sensu stricto, the oceans and sedimentary rocks. the highest end-member 20 Ne/ 22 Ne ratio of MORBs [START_REF] Trieloff | The nature of pristine noble gases in mantle plumes[END_REF]. For comparison, the evolution of a solar composition upon kinetic fractionation (Rayleigh distillation, where the fractionation factor is the square root of masses) is represented by the curve at the left hand side. Neither the atmosphere nor the DM compositions fit this evolution trend. et al., 2009;[START_REF] Srinivasan | Barites -anomalous xenon from spalation and neutron-induced reactions[END_REF]. The quartz sample data are from fluid inclusions trapped in hydrothermal quartz in 3.5-Ga old komatiite lava vacuoles. The Ar-Ar age of the fluid inclusions is 3.0 Ga. The younger, 170 Ma-old barite sample is from the Belorechenskoe deposit, Northern Caucasus, Russia [START_REF] Meshik | Weak decay of Ba-130 and Ba-132: Geochemical measurements[END_REF]. The data fit an exponential decay curve, suggesting that the Xe isotopic fractionation was progressive with time.

  proposed a different CO 2 /Nb ratio (530) for the MORB mantle, which yields a higher C content of 44 ppm. It is possible that mantle heterogeneities could explain this discrepancy, but these estimates are within errors of the DM carbon concentration obtained by normalisation to 3 He. Hirschmann and Dasgupta (2009) proposed lower C contents of the DM of 14±3 ppm , probably because these estimates are more relevant to the N-MORB component of the DM . Here we select a value of 20±8 ppm C for the DM, obtained from a weighted average of all estimates.

  fractionation is clearly within the range of values observed for Xe trapped in solids during Xe ionization experiments. For instance, Marrocchi et al. (2011) observed an enrichment of 1.4 % per amu for Xe trapped in growing carbon films under high frequency ionization of a rarefied Xe atmosphere. In the Hadean/Archean atmosphere, ionized Xe could have been partly trapped and enriched in the heavy isotopes in atmospheric dust while other Xe isotopes would have escaped. Alternatively, ionized Xe + could have been pushed up by escaping H + ions, with the heavier Xe isotopes remaining preferentially (K. Zahnle, personal communication).

  H 2 O :[START_REF] Lecuyer | The hydrogen isotope composition of seawater and the global water cycle[END_REF], carbon :[START_REF] Hirschmann | The H/C ratios of Earth's near-surface and deep reservoirs, and consequences for deep Earth volatile cycles[END_REF], nitrogen :[START_REF] Marty | The nitrogen record of crust-mantle interaction and mantle convection from Archean to present[END_REF], noble gases :[START_REF] Ozima | Noble gas geochemistry[END_REF]. The atmospheric abundances are normalized to the mass of the Earth (5.98 x 10 27 g) for comparison purpose. "DM" is the mantle region sampled by mid-ocean ridges (see text for data sources and explanations on the computations). "Bulk mantle" are concentrations in the silicate Earth, not comprising the surface inventory. Both DM and BM abundances are normalized to the mass of the silicate Earth (4 x 10 27 g). Their computations based on the 40 Ar amount of the silicate Earth and, for C, also on the C/He ratios of mantle gases, are described in the text. "Bulk Earth" are the global concentrations obtained by adding the atmospheric and bulk mantle quantities and normalized to the total mass of the Earth. Uncertainties are 1 σ.

Fig 1 :

 1 Fig 1 : Co-variations of D/H and 15 N/ 14 N ratios among solar system reservoirs and objects.Meteorite, solar and Jupiter data are from refs in[START_REF] Marty | A 15 N-poor isotopic composition for the solar system as shown by Genesis solar wind samples[END_REF], cometary data are from[START_REF] Hartogh | Ocean-like water in the Jupiter-family comet 103P/Hartley 2[END_REF][START_REF] Jehin | Isotopic Ratios in Comets: Status and Perspectives[END_REF],[START_REF] Manfroid | The CN isotopic ratios in comets[END_REF][START_REF] Meech | EPOXI : Comet 103P/Hartley 2 observations from a worldwide campaign[END_REF], Mars data are from[START_REF] Deloule | D/H ratio ion probe measurements on magmatic minerals from martian meteorites : Implications for degassing of the Martian mantle[END_REF],[START_REF] Leshin | Hydrogen isotope geochemistry of SNC meteorites[END_REF],[START_REF] Murty | Nitrogen and heavy noble gases in ALH 84001 : Signatures of ancient Martian atmosphere[END_REF],[START_REF] Owen | The composition of the atmosphere at the surface of Mars[END_REF]. CI; CM, CO, CV, CR and CB-CK refer to the different carbonaceous chondrite groups. As their name imply, carbonaceous are rich in carbon and other volatile elements compared to ordinary chondrites. CI and CM are presumably the most primitive carbonaceous chondrite groups. The composition of the Martian atmosphere is attributed to isotopic fractionation of N and H during escape. However, the fact that the Martian atmosphere composition is within the field of cometary values could indicate a cometary contribution that could be more prominent on Mars than on Earth due to the small size of the Martian atmosphere. The newly determined D/H value of comet 103P/Hartley 2 is terrestrial-like reviving the possibility of a cometary origin for oceans, but its 15 N/ 14 N ratio measured in CN, is above the terrestrial value.

Fig 3 :

 3 Fig 3 : Mixing diagram between Solar and the Planetary-A component of[START_REF] Black | Trapped neon-argon isotopic correlations in gas meteorites and carbonaceous chondrites[END_REF] and[START_REF] Mazor | Noble gases in carbonaceous chondrites[END_REF], defined by the lower boundary of the envelope delimiting carbonaceous chondrite data. "DM" is defined by the mean of the 36 Ar/ 22 Ne ratios of the Popping rock[START_REF] Moreira | Rare gas systematics in Popping Rock : Isotopic and elemental compositions in the upper mantle[END_REF] and the CO 2 well gases from[START_REF] Ballentine | Neon isotopes constrain convection and volatile origin in the Earth's mantle[END_REF] on one hand, and

Fig. 4 :

 4 Fig. 4 : Comparison of the abundance patterns of the atmosphere (surface inventory : air + oceans + sedimentary rocks) and of the depleted mantle (DM) . Abundances are normalized to the mass of the Earth for the atmosphere, and to the mass of the mantle for DM, and both to the carbonaceous chondrite composition. The shaded area represents the chondritic composition to account for the abundance of platinum group elements (PGEs) in the mantle[START_REF] Righter | Metal-silicate partitioning of siderophile elements and core formation in the early Earth[END_REF].

Fig. 6 :

 6 Fig. 6 : Comparison of the abundance patterns of the atmosphere (ATM) and of the bulk mantle (BM). Same format as Fig. 4.

Fig. 7 :

 7 Fig. 7 : Volatile composition of the bulk Earth, obtained by adding the number of atoms in the surface and the bulk mantle inventories, normalized to the mass of the Earth. Same format as Fig. 4.

Fig. 8 :

 8 Fig. 8 : Terrestrial composition of volatile elements extended to halogens. Data are from Deruelle et al. (1992) for iodine, and from compilation in McDonough and Sun (1995) for chondrites and bulk silicate Earth.

Fig. 9 :

 9 Fig. 9 : Proposed evolution fof the Xe isotopic fractionation, expressed as a δ deviation, relative to modern atmospheric Xe, in per mil per mass unit, as a function of time (adapted from Pujol et al., 2011). The 3.5 Ga-old barite samples are from North Pole, Australia (Pujol

Table 1 : Reservoir compositions

 1

Acknowledgments

This work was supported by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013 grant agreement no. 267255 to B.M.). I am grateful to Pete Burnard for having contributed the 4 He/ 40 Ar subsection and for helpful comments on the ms. Although the ideas presented here are on my own responsibility, this work benefitted from discussions with Francis Albarède, Nicolas Dauphas, Colin Goldblatt, Allessandro Morbidelli, Robert Pepin, Magali Pujol, Kevin Zahnle, among others, from constructive reviews by A. Morbidelli and F. Albarède, and from careful editing by Yannick Ricard. This is CRPG contribution n° 2135.

Fig. 2 : Detail of Fig. 1. Two terrestrial values are given for the surface inventory ( large mauve dot, D/H and 15 N/ 14 N ratios for the oceans and the atmosphere, respectively) and for a putative mantle end-member (large square dot) defined with the lowest D/H ratio found in Hawaiian lava minerals [START_REF] Deloule | Hydrogen isotope heterogeneities in the mantle from ion probe analysis of amphiboles from ultramafic rocks[END_REF] and the lowest terrestrial 15 N/ 14 N ratio which was found in diamonds [START_REF] Cartigny | Nitrogen isotopes in peridotitic diamonds from Fuxian, China : the mantle signature[END_REF]. The mean value of carbonaceous chondrites (excluding extreme values from CR-CB and the Bells CM chondrite) and ordinary chondrites, shown by the brown diamond, is very close to the terrestrial surface value. Enstatite chondrites are not represented because they do not contain sizeable amounts of water. The presumed mantle end-member composition is suggestive to the occurrence of a solar-like component at depth for N and H, as in the case of neon. K/U and U/Th of 11900 (±2200) and 3.9 respectively; dark grey: MORB K/U and Th/U ratios of 19000 (±2600) and 3, respectively. The K/U ratios are from [START_REF] Arevalo | The K/U ratio of the silicate Earth: Insights into mantle composition, structure and thermal evolution[END_REF] and the Th/U are from [START_REF] Vlastelic | Th/U and other geochemical evidence for the Reunion plume sampling a less differentiated mantle domain[END_REF]. Uncertainties of 30% have been attributed to the Th/U ratios although the uncertainties in Th/U do not significantly affect the range in 4 He/ 40 Ar. The 4 He/ 40 Ar values fro accumulation times of 4.5 Ga in the bulk mantle, and 1Ga in the depleted mantle, respectively, are shown by arrows.