Sulphur geodynamic cycle

Evaluation of volcanic and hydrothermal fluxes to the surface environments is important to elucidate the geochemical cycle of sulphur and the evolution of ocean chemistry. This paper presents S/3He ratios of vesicles in mid-ocean ridge (MOR) basalt glass together with the ratios of high-temperature hydrothermal fluids to calculate the sulphur flux of 100 Gmol/y at MOR. The S/3He ratios of high-temperature volcanic gases show sulphur flux of 720 Gmol/y at arc volcanoes (ARC) with a contribution from the mantle of 2.9%, which is calculated as 21 Gmol/y. The C/S flux ratio of 12 from the mantle at MOR and ARC is comparable to the C/S ratio in the surface inventory, which suggests that these elements in the surface environments originated from the upper mantle.


SAS, Gennevilliers, France) listed in Supplementary
are well within the variation of sulphur contents in MOR glass obtained using a conventional method 12 . The average value of S/ 3 He ratios in the glass matrix was (1.0 6 0.2) 3 10 10 (1s). Observed d 34 S values are consistent with those of MOR basalt and mantle values 12,13 , suggesting a typical mantle sulphur signature.

Discussion
The S/ 3 He ratio and 3 He flux at MOR are needed for sulphur flux calculations. The observed S/ 3 He ratios of vesicles in MOR basalt glass are 2.0 3 10 7 -9.9 3 10 7 . These values are lower than those in the glass matrix (See Table 1 and Supplementary Table 1). This observation suggests higher solubility of sulphur than of helium in basaltic melt, which is also supported by recent laboratory experiments 14 . We consider the average vesicle S/ 3 He ratio of 4.2 3 10 7 as the minimum for MOR for our flux calculations. The other independent means to estimate the S/ 3 He ratio of MOR is using the chemistry of high-temperature submarine vents. The average S/ 3 He ratio is (3.4 6 0.7) 3 10 8 (1s) among 10 high-temperature (.200uC) hydrothermal sites worldwide (Supplementary Table 2).
The d 34 S value of H 2 S in hot vent fluids is variable 13 , but the original value before the incursion of seawater is similar to the MOR basalt values 4,15 . A small part of H 2 S might be generated from the reduction of seawater SO 4 from the recharge zone 4 , although it is difficult to deconvolve the contribution quantitatively. Therefore the vent S/ 3 He ratio of 3.4 3 10 8 is expected to be the maximum estimate at MOR. We take an average of these two independent estimates (1.9 6 1.5) 3 10 8 as the upper mantle S/ 3 He ratio in the current study. The S/ 3 He ratio in MOR glass matrix is higher than this upper mantle value (Supplementary Table 1), which implies that helium has degassed from the melt before it was quenched to a glass and therefore these ratios should not be used for the sulphur flux estimate.
Based on the saturation anomaly of 3 He in deep seawater of the eastern Pacific, a value of 1070 6 270 mol/y was calculated for the 3 He flux from MOR 16 . A more recent estimate of the MOR 3 He flux is 530 6 100 mol/y derived from an ocean circulation model which also considers radiocarbons and chlorofluorocarbons 8 . This MOR 3 He flux, when combined with the average S/ 3 He ratio obtained in this study, provides the MOR sulphur flux of (1.0 6 0.8) 3 10 11 mol/y. This mantle flux is consistent with the estimate based on seawater-basalt  sulphur exchange during hydrothermal alteration 4 , but it is about an order of magnitude smaller than the value calculated from the production rate of the oceanic crust and sulphur contents therein 5 . This difference suggests that most sulphur remains in the magma and solidifies as sulphides in the MOR crust, and does not contribute to the MOR flux that discharges into the ocean. When we consider the mass balance of sulphur in global ocean water, the mantle flux of 1.0 3 10 11 mol S/y is a second-order flux 'compared to the riverine input of 8.9 3 10 11 mol S/y to the ocean and the output of 5.5 3 10 11 mol S/y as sedimentary pyrite and evaporitic sulphate 17 . However, the sulphur flux from the upper mantle into the ocean represents a deep Earth contribution and is therefore distinct from riverine sulphur input that is continent-derived. Sulphur and helium isotopic compositions are useful for investigating the origin of sulphur at arc volcanoes. The thermodynamic equilibrium between SO 2 and H 2 S together with their d 34 S values might provide constraints on the evolution of volcanic gases, such as an isochemical cooling path, under the assumption that the initial d 34 S SS value is 0% 13 , where d 34 S SS denotes the total sulphur isotopic ratio of SO 2 and H 2 S. In addition, the d 34 S SS values might provide information related to the origin of sulphur in ARC volcanic gases, even though they might be affected by a gas-melt separation and related fractionation processes 13,18 . Available data of 3 He and total sulphur contents, and d 34 S SS values for high-temperature volcanic gases (.200uC) in subduction zones were compiled from the literature (Table 2). Their 3 He/ 4 He ratios are consistent with the range of subduction-type He 1,19 . The d 34 S SS values are generally positive, except for one outlier from Galeras. This similarity suggests that the sulphur signature of an ARC magma source is due to incorporation of subducted sulphate partly derived from a seawater component 18,20,21 with high d 34 S values. The average value of S/ 3 He ratios among these high-temperature ARC gases is (6.5 6 1.1) 3 10 9 (1s), which is significantly higher than that of the upper mantle, suggesting enrichment of sulphur in the ARC mantle source by subduction processes.  22 . Results of a recent study 23 of the oceanic basement in northern Italy suggest that low-temperature serpentinization produces a negative d 34 S SS value with (28.9 6 8.0)%. Then the d 34 S value of sedimentary pyrite is defined as (214.9 6 6.0)%. No source of primordial helium exists in the pyrite, and the slab may have lost the original mantle helium as well 24 . It is therefore possible to adopt S/ 3 He larger than 1 3 10 13 for the sedimentary pyrite. Seawater sulphate has a d 34 S value of 121.0% 25 . Metasomatic fluids released from sediment, of which the sulphur is mostly in the form of sulphate, have a d 34 S value of 114% when their sulphur compositions resemble the bulk sediment composition 21 .
Using these values, the d 34 S value of subducted sulphate is here defined as (117.5 6 3.5)%. A defined S/ 3 He larger than 1 3 10 13 for sedimentary sulphate is consistent with the seawater SO 4 / 3 He of 1.0 3 10 14 .
The distribution of volcanic gas data in the S/ 3 He-d 34 S diagram (Fig. 2) suggests that ARC samples are explained by three-component mixing. When sulphur in a sample is a mixture of the upper mantle, subducted sedimentary pyrite, and subducted sulphate having respective masses M, P, and S, the following equations can be derived: Therein, the following relation holds: In   20 . Here we first provide a quantification of the relative amount of the seawater sulphate contribution to ARC gases, which allows us to evaluate the recycling capacity of ARC volcanoes within the global sulphur cycle. A conventional ARC 3 He flux was estimated from the MOR flux, given the assumption that the magma production rate of ARC is about 20% of that of MOR 9 . This percentage is consistent with the estimate of global magma emplacement and volcanic output averaged over the last 180 m.y. 26 . Recently, the MOR 3 He flux was calculated to be 530 mol/y 8 which would result in an ARC 3 He flux of 110 6 20 mol/y. This flux is consistent with the value obtained by summation of 3 He flux at arc volcanoes worldwide 1 . The average S/ 3 He ratio of (6.5 6 1.1) 3 10 9 (1s) is obtained from high-temperature volcanic gases. Therefore, the ARC sulphur flux is estimated to be (7.2 6 1.8) 3 10 11 mol/y based on the 3 He flux of 110 mol/y. This value is considerably larger than MOR sulphur flux calculated in this study. However the upper mantle contribution to ARC volcanic gases is only (2.9 6 0.5)% of total sulphur, on average. The sulphur flux from the wedge mantle at ARC then becomes (2.1 6 0.6) 3 10 10 mol/ y, which is less than the mantle sulphur flux discharging into the ocean at MOR. The major contribution of the ARC sulphur flux is derived from subducted sedimentary pyrite and subducted sulphate partly derived from the seawater component. A summary of the global sulphur flux is depicted in Fig. 3a. Present hot spot magmatism likely does not contribute substantially to the global flux of sulphur (See Supplementary Discussion). The total volcanic flux of sulphur is estimated as 8.2 3 10 11 mol/y and represents about one-third of the anthropogenic emissions due to coal burning and sulphide ore smelting 27 . This natural flux, if it has remained constant over 4.55 billion years of geological time, engenders an accumulation of 3.7 3 10 21 mol. This value is greater than the surface inventory of 5.3 3 10 20 mol 1 . If we take the MOR flux together only with the mantle wedge flux of 2.1 3 10 10 mol/y, then the accumulation becomes 5.6 3 10 20 mol in total, which is equivalent to the surface inventory. When steady-state recycling of sulphur is applied, the total subducting flux becomes 8.2 3 10 11 mol/y.
As new 3 He flux data at MOR have been reported 8 , we revise the carbon geodynamics along with sulphur. The CO 2 / 3 He ratio at MOR was calculated to be (2.2 6 0.7) 3 10 9 using CO 2 / 3 He data for MOR basalt glass and hydrothermal fluids 28 . This ratio, combined with the new MOR 3 He flux, engenders the global MOR CO 2 flux of (1.2 6 0.4) 3 10 12 mol/y, which is consistent with the most recent estimate based on vesicularities of MORB worldwide 29 .
For ARC volcanism, we selected 24 volcanic gas and steam well data with temperatures higher than 200uC (Supplementary Table 3). Their carbon source is well explained by the mixing of three components: The upper mantle (M), organic sediment (S) and limestone with a slab component (L) (Fig. 4; Ref. 30). These end-member components are described in Supplementary Table 3. Using those values, we calculate the respective percentages of the three components in the ARC samples (Supplementary Table 3). The contribution of the upper mantle carbon is 3.2%-36% (average 11%), whereas a major part is attributable to subducted carbonate and organic carbon. Because the average CO 2 / 3 He ratio of these data is (2.0 6 0.3) 3 10 10 , the carbon flux from ARC is (2.2 6 0.5) 3 10 12 mol/y using the ARC 3 He flux of 110 6 20 mol/y, which is also consistent with the recent estimate using volcanic gas observations worldwide 31 .
A summary of global carbon flux is depicted in Fig. 3b. The total volcanic flux of carbon is 3.4 3 10 12 mol/y, which is two orders of magnitude smaller than anthropogenic emission by fossil fuel combustion and cement production 32 . The MOR flux combined with the wedge mantle flux is 1.4 3 10 12 mol/y. This value, if accumulated for 4.55 billion years, results in 6.6 3 10 21 mol of carbon, which closely approximates the surface inventory of 7.0 3 10 21 mol 1 . If steady-state recycling of carbon is applied, then the total subduction flux becomes 3.4 3 10 12 mol/y. This estimate is consistent with the influx of carbon 1 .
In conclusion, the best estimates of MOR sulphur and carbon flux are 1.0 3 10 11 mol/y and 1.2 3 10 12 mol/y, respectively at present,   which are less than their volcanic fluxes at ARC. Sulphur and carbon fluxes from only the mantle wedge to the surface environment at ARC are calculated as 2.1 3 10 10 mol/y and 2.4 3 10 11 mol/y, respectively. These data provide a C/S flux ratio of 12 which is similar to the C/S ratio in the surface inventory of 13 (Ref. 1). Our results suggest that the main source of sulphur and carbon is the upper mantle. To balance the mass between the crust and the mantle, the sulphur subducted into the mantle and not immediately recycled to the surface is expected to be equivalent to 1.2 3 10 11 mol/y, which is about 17% of the recycling sulphur of 7.0 3 10 11 mol/y. We calculated sulphur and carbon fluxes from the mantle based on the plausible S/ 3 He and C/ 3 He ratios and the recently reported 3 He flux at MOR, which constrained geochemical cycles of sulphur and carbon, and evolutionary histories of the atmosphere and hydrosphere.

Methods
Glass vesicle. It is difficult to measure the abundance of sulphur species such as H 2 S and SO 2 in vesicles of MOR basalt glass together with 3 He because the gases are highly reactive. They easily adhere to the inner surface of a vacuum crushing vessel. We have developed a gas-extraction method, 'Frozen Crushing Method', by which sulphur gases are fixed immediately in semi-frozen alkaline solution during mechanical fracturing of glass 7 . The abundance of helium and 3 He/ 4 He ratios were measured using a noble gas mass spectrometer (VG5400; Waters Corp.) at the Atmosphere and Ocean Research Institute (AORI). Subsequently, the vacuum was broken and the Sbearing solution was filtered. All sulphur compounds were converted into sulphate ion by oxidation with hydrogen peroxide. The concentration was measured using an ion chromatography system (ICS-2100; Thermo Fisher Scientific Inc.) at AORI. Blank contributions of sulphur and helium were considerably smaller than the actual amounts in samples. Experimental details are presented in an earlier report 7 . Sulphate ion in the alkaline solution was converted into BaSO 4 precipitations by adding BaCl 2 solution and d 34 S values obtained with an elemental analyzer (vario PYRO cube; Elementar Analysensysteme, GmbH) coupled to an isotope-ratio mass spectrometer (Delta XP; Thermo Fisher Scientific Inc.) via an interface (ConFlo IV; Thermo Fisher Scientific Inc.) at the University of Ottawa.
Glass matrix. Sulphur contents in glass matrix were measured (NanoSIMS; Cameca SAS, Gennevilliers, France) at AORI, whereas d 34 S values were obtained using an elemental analyzer isotope-ratio mass spectrometer system 33 (Isoprime-EA; Isoprime Ltd.) at the University of Tsukuba.