Pierre Agrinier

Joris Gieskes

Gowtham Subbarao

Gerard Bardoux

Magali Bonifacie

Chloride exchanges between oceanic sediments and seawater: constraints from chlorine isotopes

Keywords: chloride, isotopes, pore fluids, oceanic sediments

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with the chlorine isotopic composition of seawater, δ 37 Cl = 0 ‰). (3) This lost 37 Cl-enriched chlorine has been released from the sediment into the overlying seawater, with fluxes of about 20 moles of chloride per square metre per kiloyear.

In order to evaluate the consequence of this unbalanced on a global scale, we extend this chlorine budget analysis to 22 other oceanic sites drilled by IODP in a variety of tectonic environments. It is estimated that worldwide oceanic sediment pore fluids contain 1 x 10 20 moles of chloride with mean δ 37 Cl at -2.3 ± 0.1 ‰ and mean chlorinity at 0.290 ± 0.055 mole Cl - per kg of sediment. Most of the calculated values of the lost 37 Cl-enriched chlorine flux are between 3.5 and 45.6 moles of chloride per square metre per kiloyear (mean value of 18.3 mole Cl.m -2 .kyr -1 ), corresponding to a typical chloride exchange time between sediments and seawater of between 5.5 and 71 Myr with a mean value of 14 Myr. Importantly, in oceanic sediments, a relationship between the  37 Cl of the chlorides in their pore fluids and the nature of the detrital minerals (smectite, illite, kaolinite, carbonate, quartz, ...) may exists. This relationship should be modulated by the detrital input from the continents to the oceanic sediments and should therefore be a consequence of the climatic conditions on the continents (mainly rain, temperature). The  37 Cl of the seawater should vary according to these detrital inputs. The expected range of variation would be between -0.3 to +0.3 ‰. This is consistent with the range of  37 Cl in seawater predicted by the study of evaporites deposited since 2 Ga [START_REF] Eggenkamp | The bromine and chlorine isotope composition of primary halite deposits and their significance for the secular isotope composition of seawater[END_REF].

I) Introduction

The budget of terrestrial chloride is important for constraining the stability of the Earth chlorine cycle and, in particular, the history of the ocean salinity -a factor influencing the evolution of life during the Earth's history. Despite this importance, the chloride budget in the Earth's surface domains (seawater, sediments, crust) is still poorly known. The present day amount of chloride in seawater is well known, but those in other surface reservoirs (oceanic sediments, continental basins and silicate crusts) and the exchanges of chloride between them are less well constrained. The chlorine stable isotopes ( 35 Cl & 37 Cl) of chloride have the potential to provide additional constraints on the Earth's surface chloride budget by characterizing oceanic crust (e.g., [START_REF] Bonifacie | Chlorine isotopic compositions of high temperature hydrothermal vent fluids over ridge axes[END_REF], 2008aand 2008b[START_REF] Barnes | Chlorine isotope variations across the Izu-Bonin-Mariana arc[END_REF]and 2009), halite deposits (e.g., Eggenkamp et al., 2015 and2019), or oceanic sediment pore fluids (e.g., [START_REF] Ransom | Stable Cl isotopes in subduction-zone pore waters: Implications for fluid-rock reactions and the cycling of chlorine[END_REF], Hesse et al., 2000, Spivack et al., 2002[START_REF] Deyhle | Evidence for fluid flow in the Japan Trench forearc using isotope geochemistry (Cl, Sr, B): Results from ODP Site 1150[END_REF], Godon et al., 2004a[START_REF] Bonifacie | Chlorine stable isotopic composition of basement fluids of the eastern flank of the Juan de Fuca Ridge (ODP Leg168)[END_REF], Wei et al., 2008, Agrinier et al., 2019and 2021).

These studies revealed a systematic 37 Cl depletion of chlorides compared to seawater chlorides. This depletion was unexpected since these interstitial fluids were originally seawater trapped at the seawater-sediment interface.

To explain these depletions in 37 Cl in pore fluids, suggestions have been made, ranging from external causes: the upward advection of 37 Cl-depleted fluid into the sediments from greater depths [START_REF] Ransom | Stable Cl isotopes in subduction-zone pore waters: Implications for fluid-rock reactions and the cycling of chlorine[END_REF][START_REF] Spivack | Elemental and isotopic chloride geochemistry and fluid flow in the Nankai trough[END_REF][START_REF] Hesse | Chlorine stable isotope ratios as tracer for pore-water advection rates in a submarine gas-hydrate field: implication for hydrate concentration[END_REF]Wei et al., 2008), to internal cause: the generation of 37 Cl-depletion by ion filtration of chlorides when pore fluids are transported through clays during the compaction of the sediments (Godon et al., 2004a;[START_REF] Bonifacie | Chlorine stable isotopic composition of basement fluids of the eastern flank of the Juan de Fuca Ridge (ODP Leg168)[END_REF][START_REF] Agrinier | Strong impact of ion filtration on the isotopic composition of chlorine in young clay-rich oceanic sediment pore fluids[END_REF][START_REF] Agrinier | Chlorine isotope data of chlorides challenge the pore fluid paradigm[END_REF], see an ilustration of the ion filtration process in Figure 1 of [START_REF] Agrinier | Chlorine isotope data of chlorides challenge the pore fluid paradigm[END_REF]. Based on the fact that these 37 Cl depletions have been ubiquitously observed in a large variety of investigated tectonic contexts (proto-oceanic basins, oceanic plateaus, continental margins, ridge flanks, prisms of subduction zones, fluvial fans) [START_REF] Agrinier | Chlorine isotope data of chlorides challenge the pore fluid paradigm[END_REF] concluded that these 37 Cl depletions were inherited from an internal process. [START_REF] Agrinier | Strong impact of ion filtration on the isotopic composition of chlorine in young clay-rich oceanic sediment pore fluids[END_REF][START_REF] Agrinier | Chlorine isotope data of chlorides challenge the pore fluid paradigm[END_REF] calculated the fractionation of chlorine isotopes of chlorides of pore fluids which could be caused by the ion filtration due to the repulsion of chloride by the negatively charged surface of clays [START_REF] Phillips | Isotopic fractionation during ion filtration: I. theory[END_REF]. We suggested that the mineralogical nature of the sediment would be the primary factor controlling the importance of the chlorine isotope fractionation in pore fluid chlorides. Smectite which has high charge surface density, would be associated with higher isotope fractionation than illitechlorite, which has lower charge density or kaolinite, which has an even lower charge density.

Carbonate and quartz with quasi-zero charge surface density would not produce chlorine isotope fractionation in chlorides.

In the light of this knowledge, we designed the present study with three main objectives: 1) to test the relationship between sediment mineralogy and 37 Cl depletion of chlorides in pore fluids from Sites U1456 and U1457, 2) to examine in detail, for these two sites, chloride reservoirs where missing 37 Cl-enriched chlorides from the pore fluids could be stored and to establish the chloride budget in sediments , and 3) to extend this chloride budget approach to a large number of oceanic sedimentary piles from different tectonic settings.

In relation to the first objective, constraints are provided by the study of young, thick continental terrigenous clastic sediments from the Indus fan drilled at the western margin of the Indian subcontinent during IODP expedition 355 at sites U1456 and U1457 (Pandey et al., 2016a,b & c). These sediments were deposited with high rates of sedimentation, mass transports (sands, turbidites, conglomerates and breccia) that produced complex histories of sedimentation including hiatuses. Their mineralogy is dominated by detrital minerals (quartz, chlorite, illite, feldspar, calcite) with minor clays of detrital origin [START_REF] Cai | Long-term history of sediment inputs to the eastern Arabian Sea and its implications for the evolution of the Indian summer monsoon since 3.7 Ma[END_REF][START_REF] Carter | Clay-fraction strontium and neodymium isotopes in the Indus Fan: implications for sediment transport and provenance[END_REF]. A priori, these sedimentary characteristics are not favorable to the production and the retention of large 37 Cl-depletion (ie., very negative  37 Cl) in pore fluid chlorides due to i) the low abundance of clays with high charge surface density (smectite) and ii) the high abundance of detrital mainly silt-sized grains and sand beds with high permeability sediments, where external fluids might have circulated after the deposition of the sediment.

For the second objective, it is necessary to establish chlorine budget equations (including isotopes) and review the chlorine isotope fractionations between chloride of the pore fluids and chlorine in the other sinks that can store chlorine. This is necessary to estimate the amount of missing 37 Cl required to balance the 37 Cl depletion of the pore fluid chlorides.

Finally, the third objective is to study the chlorine budgets of a set of 24 sedimentary piles (Ocean Drilling Sites) drilled from a wide range of tectonic contexts (proto-oceanic basins, oceanic plateaus, continental margins, ridge flanks, prisms of subduction zones, fluvial fans, ...)

where chlorine isotope data in pore fluids exist. This will lead to a calculation of the amount of 37 Cl missing in ocean sediments and deduce the consequences for chloride exchange between ocean sediments and seawater.

II) Lithostratigraphy of the U1456 and U1457 sedimentary piles

Sites U1456 and U1457 of IODP Leg 355, were drilled in close proximity (within ~ 100 km) in the Laxmi Basin of the eastern Arabian Sea. They document mainly the Indus River and Deccan trap detritus and recent (≤ 13 Ma) erosion of the high-relief topography of the western Himalaya, the Tibetan Plateau. In both sedimentary piles, detrital quartz, chlorite, illite, feldspar, and calcite are the main components. Clays (< 2µm, smectite, illite, chlorite, kaolinite) are minor constituents (Pandey et al., 2016b & c;[START_REF] Cai | Long-term history of sediment inputs to the eastern Arabian Sea and its implications for the evolution of the Indian summer monsoon since 3.7 Ma[END_REF][START_REF] Khim | Detrital Sr-Nd isotopes, sediment provenances and depositional processes in the Laxmi Basin of the Arabian Sea during the last 800 ka[END_REF][START_REF] Andò | Integrating heavy-mineral, geochemical and biomarker analyses of Plio-Pleistocene sandy and silty turbidites: a novel approach for provenance studies (Indus Fan, IODP Expedition 355)[END_REF][START_REF] Routledge | A revised chronostratigraphic framework for International Ocean Discovery Program Expedition 355 sites in Laxmi Basin, eastern Arabian Sea[END_REF]Chen et al., 2019[START_REF] Chen | Geochemical records of the provenance and silicate weathering/erosion from the eastern Arabian Sea and their responses to the Indian summer monsoon since the Mid-Pleistocene[END_REF][START_REF] Kumar | A late Pleistocene sedimentation in the Indus Fan, Arabian Sea, IODP Site U1457[END_REF][START_REF] Clift | Chemical weathering and erosion responses to changing monsoon climate in the Late Miocene of Southwest Asia[END_REF][START_REF] Carter | Clay-fraction strontium and neodymium isotopes in the Indus Fan: implications for sediment transport and provenance[END_REF]. A summary of the main characters is given below: II.1 Sediments at Sites U1456: Unit I (0 -121 mbsf) is composed of hemipelagic carbonate ooze and clay with intercalated silty-sandy turbidites. Unit II (121 -361 mbsf) consists of thickbedded sandy turbidites with intercalated silty and nannofossil-rich clay layers. Unit III (361 -731 mbsf) is composed of alternating silty-sandy turbidites, carbonate ooze, and clays. Unit IV (731 -1100 mbsf) consists of mass wasting deposits, including mainly clay with minor carbonate breccia in the middle-upper part and carbonate breccia in the lower part (Figure 1).

Figure 1:

Sites U1456 and U1457 drilled during IODP Leg 355. From left to right, summary of the lithostratigraphy and profiles of sedimentation rate, porosity, sodium and chloride concentrations, Sodium to chloride and bromide to chloride concentration ratios, Strontium isotope ratio, calcium and magnesium concentrations. All the data are from Pandey et al. (2016b and c) except the Strontium data which are from [START_REF] Carter | Data report: 87Sr/86Sr in pore fluids from IODP Expedition 355 Arabian Sea Monsoon[END_REF]. Horizontal dashed lines delimit the lithostratigraphic units (I, II, III & IV). Sedimentation rates are computed from the data of [START_REF] Routledge | A revised chronostratigraphic framework for International Ocean Discovery Program Expedition 355 sites in Laxmi Basin, eastern Arabian Sea[END_REF]. U1456 porosity data, , are fitted with compaction law  ≈ 75 * exp(z/400)) in Unit I (z ≤ 120 mbsf) and with compaction law  ≈ 48 * exp (-z/5500)

III) Chemical chracteristics of the pore fluids from Sites U1456 and U1457

During Leg 355, immediately after recovery, pore fluids were extracted from the sediment by squeezing core sections [START_REF] Manheim | A hydraulic squeezer for obtaining interstitial water from consolidated and unconsolidated sediments[END_REF], filtered through 0.45 µm and then stored in plastic vials. The squeezing on board the ship was conducted at very low pressure (< 200 MPa) which ensured that no or very little chemical and isotope fractionations occurred in the extracted pore fluids [START_REF] Coleman | Chlorine stable isotope characterisation of solute transport in mudrocks[END_REF][START_REF] Mazurek | Pore-water squeezing from indurated shales[END_REF][START_REF] Bonifacie | Chlorine stable isotopic composition of basement fluids of the eastern flank of the Juan de Fuca Ridge (ODP Leg168)[END_REF]. The The Br/Cl ratios are consistent with the organic carbon concentrations in these sites. They are high in unit 1 and markedly lower below, in units 2 and 3. Bromide enrichment of this kind is often found in sediments, It may be caused by the release of Br -from the solid part of organicrich sediments to the pore fluids during diagenesis [START_REF] Kendrick | Halogens in seawater, marine sediments and the altered oceanic lithosphere[END_REF]. A further contribution to this Br enrichment could be the filtration of the fluid through the clays. This would lead to an accumulation of Br-upstream of the clay membrane relative to Cl-if the clay membranes allow less Br-than Cl-to pass through. Indeed, the deep 87 Sr/ 86 Sr ratios are slightly lower than the contemporaneous value.

III.2 Cations

IV) Cl isotope methods

IV.1 Fluid sampling: We selected 25 pore fluids from Site U1456 and 20 pore fluids from Site U1457, which were sampled at regular depth intervals (every 50 meters) from 2 mbsf below the seawater-sediment interface to the bottom of the sedimentary piles (≈ 800 mbsf).

IV.2 Chlorine isotope measurements: All the pore fluids were analysed for their  37 Cl at the Institut de Physique du Globe de Paris (IPGP). We used the AgCl-CH3Cl method [START_REF] Kaufmann | Natural chlorine isotope variations[END_REF][START_REF] Eggenkamp |  37 Cl: The Geochemistry of Chlorine Isotopes[END_REF] with improvements made at IPGP (Godon et al., 2004b). Gaseous

CH3Cl was measured for  37 Cl using a dual-inlet gas source mass spectrometer (Delta plus XP or Delta V from ThermoFisher). The results are reported using the  37 Cl versus SMOC (Standard Mean Ocean Chloride). Over the course of the study, the external reproducibility of the Atlantique 2 seawater chloride reference was ± 0.025 ‰ (1, n = 48). This is comparable, if not better than, to the routine long-term precision reach at IPGP over the past two decades (e.g., Godon et al., 2004a[START_REF] Bonifacie | Chlorine isotopic compositions of high temperature hydrothermal vent fluids over ridge axes[END_REF], Bonifacie et al.2007[START_REF] Li | Chlorine isotopes of thermal springs in arc volcanoes for tracing shallow magmatic activity[END_REF][START_REF] Eggenkamp | Experimental determination of stable chlorine and bromine isotope fractionation during precipitation of salt from a saturated solution[END_REF]Giunta et al. 2017, Agrinier et al., 2019and 2021) .

V) Results

Isotope compositions of the pore fluids are given in the Table 1. Figure 2 shows the depth profiles of the pore fluid chloride chlorine isotopic compositions ( 37 Cl). In the  37 Cl depth profiles, decreasing trends are observed between the seawater boundary value at  37 Cl = 0 at the top of the sedimentary piles and the minima systematically located at the deepest depths and in lithologies with abundant clays ( 37 Cl = -2.50 ‰ at 741.45 mbsf in U1456 and -1.40 ‰ at 794.4 mbsf in U1457, Figure 2). At both sites, the shapes of the trends are similar and correlate with the lithostratigraphy. Transitions between lithostratigraphic units are marked by a break in the slope of the trends. The smoothness of the trends decreases with depth (the deepest parts of the trends are more noisy). Within units, the slope of the trend is constant. In Unit 1, U1456 and U1457 trends have similarly steep slopes (-0.7 ‰ per 100 m in U1456 and -0.5 ‰ per 100 m in U1457). Below, in Unit II, the slopes are clearly reduced to very small values (-0.2 ‰ per 100 m in U1456 and -0.02 ‰ per 100 m in U1457). At the bottom, in Unit III, the slope values are increased (-0.3 ‰ per 100 m in U1456 and -0.2 ‰ per 100 m in U1457). The difference between the two profiles is due to unit II. In U1456,  37 Cl continues to decrease, whereas it remains constant in U1457.

Figure 2:

Profiles of the chlorine stable isotope ratio of chlorides ( 37 Cl) of the pore fluids sampled in Sites U1456 and U1457 (data from Table 1). Lithostratigraphic logs (U1456 left and U1457 right) are from Pandey et al. (2016b and c). Horizontal dashed lines, (red for U1456 and green for U1457) delimit the lithostratigraphic units (I, II, III & IV). SMOC is the mean seawater chlorine isotope compostion.

Overall, the changes in the isotopes and chemical compositions of pore fluids of U1456 and U1457 fits in with changes identified since early works on sediment pore fluids (Lawrence et al., In general, at Sites U1456 and U1457, there is good agreement between the geochemical characteristics of the pore fluids and the lithology. Good agreement is also observed between the porosity and the chloride  37 Cl (Figure 3). Breaks in the profiles of porosity and of  37 Cl of chlorides occur at the same depths, systematically at the transitions between lithological units.

In terms of chloride geochemistry, the pore fluids exhibit the usual chloride geochemical features recorded in the vast majority of oceanic clay-rich sedimentary sites [START_REF] Agrinier | Strong impact of ion filtration on the isotopic composition of chlorine in young clay-rich oceanic sediment pore fluids[END_REF]2021). They are:

i) chloride profiles with δ 37 Cl steadily decreasing from the seawater value (δ 37 Cl = 0 ‰) while chloride concentrations remain quite close to that of seawater (≈ 558 mM). The slope of the δ 37 Cl profiles is steep just below the seawater-sediment interface and gradually decreases with depth.

ii) loss of smoothness of the δ 37 Cl profiles as a function of depth. The increase in δ 37 Cl noise in the deeper parts could be the result of late disturbing processes of relatively small magnitude that develop as the sediment ages.

These two points suggest that the process of lowering the δ 37 Cl is mainly in the sediments, below the interface between seawater and the sediment. Another possibility could be that the process develops quite deep and involves large chlorine isotope fractionations. The steep upper parts of the δ 37 Cl profiles would then result from mixing with seawater favoured by a relatively high permeability below the water-sediment interface. Furthermore, the process of lowering δ 37 Cl has little or no impact on the chloride concentration of pore fluids.

VI) Discussion

Because chlorides are highly soluble and because they are the second most abundant compound in oceanic sedimentary pore fluids, after water, the decrease in δ 37 Cl of pore fluid chlorides places important constraints on the history of these fluids. Whatever the process causing the decrease, the conservation of stable isotopes of chlorine requires that it is due to either the preferential removal of 37 Cl isotopes from the chlorides of the original pore fluid (seawater) or by the addition of 37 Cl-depleted chlorides. This latter possibility has been considered in previous works [START_REF] Ransom | Stable Cl isotopes in subduction-zone pore waters: Implications for fluid-rock reactions and the cycling of chlorine[END_REF][START_REF] Spivack | Elemental and isotopic chloride geochemistry and fluid flow in the Nankai trough[END_REF]Wei et al., 2008) does not operate for the many other sedimentary piles, not associated with subduction zones, that nevertheless systematically show the depletion in of their pore fluid chlorides [START_REF] Agrinier | Chlorine isotope data of chlorides challenge the pore fluid paradigm[END_REF]. The ubiquity of the 37 Cl depletion of chloride in sediments confirms that the process fractionating the chlorine isotope of chlorides is local and specific to the type of the sediments.

This results in the loss of 37 Cl-enriched chlorides from the pore fluids.

Further constraints can be provided by studying the budget of chlorides in sediments. First, we describe the methodology used to establish the chlorine budget in sediments. We illustrate this using data from Sites 1456 and 1457 of Leg 355. We then provide additional constraints from a review of the geochemical processes that fractionate chlorine isotopes and an open system 37 Cl-enriched chloride loss from the pore fluids. Finally, we calculate the amount of missing 37 Cl-enriched chlorides required to compensate for the 37 Cl-depletion of pore fluid chlorides, assuming that sediment pore fluids were originally seawater trapped on the seafloor.

This methodology is used to determine the chloride budget at 22 other IODP drilled sites in oceanic sediments of different tectonic settings (Table 2).

VI.1 Budget of chloride in the sediments

The pore fluids: In this section we calculate the amount of pore fluids present in the sediment and the amount of chlorides contained in the pore fluids. For a vertical sediment column of 1 square meter horizontal surface (S = 1 m 2 ), the volume of pore fluids, Vporefluid, is given by where z is the porosity law (from Figure 3) and dz is the depth element (m). Vporefluid are 457 and 454 m 3 for a vertical sediment column of ≈ 1 km in height in Sites U1456 and U1457 respectively (Table 2). Then, Qporefluid, the amount of pore fluid (expressed as water) can then be calculated as follows:

where CH2O is the concentration of water in the pore fluid (≈ 54.9 kmoles of H2O/m 3 using concentration of water in seawater at 0.965 kg H2O per Kg of seawater and density at 1023.6

Kg/m 3 ). Qporefluid values are 25081 and 24891 kmoles of water for the U1456 and U1457

sediment columns respectively (Table 2).

The amount of chloride in pore fluids, QCl porefluid, is given by :

(3)

where [Cl -]z is the chloride concentration in the pore fluid at depth z (in kmoles of chloride/m 3 ). Then QCl porefluid are 252 and 246 kmoles of chlorides for the U1456 and U1457

sediment columns respectively (Table 2). The mean δ 37 Cl values of the pore fluid chlorides are given by:

(4)

where  37 Clz is the isotopic composition of the chloride profile versus depth (in ‰ vs. SMOC).

The mean δ 37 Cl values of chlorides of the sediment columns U1456 and U1457 are -1.59 and -0.73 ‰, respectively (Table 2). The mean [Cl -] values, Cl per Kg of porefluid, are given by :

(5)

with seawater = 1023.6 kg.m -3

The solid fraction: The solid fraction of the U1456 and U1457 sediments consists of components that contain very small amounts of chlorine in their structure. As reported in Pandey et al. (2016a, b & c), they are mainly carbonates, clays (chlorite and illite ≥ smectite), detrital minerals (quartz, feldpars, micas, and rare hornblende, glaucophane, kyanite, tourmaline, clinopyroxene, apatite, and glauconite). Total organic carbon varies between 0 and 2.6 wt% (mean value ≈ 0.5 wt%). In these constituents, chlorine content is generally lower than 200 ppm Cl [START_REF] Ransom | Stable Cl isotopes in subduction-zone pore waters: Implications for fluid-rock reactions and the cycling of chlorine[END_REF]Wei et al., 2005and 2008, Bonifacie et al., 2008;[START_REF] Barnes | Chlorine isotope variations along the Central American volcanic front and back arc[END_REF][START_REF] Kendrick | Halogens in seawater, marine sediments and the altered oceanic lithosphere[END_REF] but can be up to the few percent level in rare high-temperature detrital minerals such as apatite, micas, and amphiboles. Serpentine minerals, absent in these sediments, may store up to 5000 ppm Cl.

In the sediment column, the amount of chloride in the solid part of the sediment is given by: with where CCl solid is the concentration of Cl in the solid (≤ 2 10 -4 kg of Cl/kg of solid = 200 ppm),

Vsolid is the volume of solid in the sediment (Vsolid = 543 and 546 m 3 for the 1 km high sediment column of Sites U1456 and U1457 respectively) and solid is the density of the solid part of the sediment (≈ 2800 ± 100 kg/m 3 of solid). Then we get Q Cl solid maxima values at 8.6 and 8.6 kmoles of Cl in Sites U1456 and U1457, respectively (Table 2). The isotopic composition of chlorine in the solid fraction of sediments has rarely been measured. Generally, it is depleted in 37 Cl compared to seawater. [START_REF] Barnes | Chlorine isotope variations across the Izu-Bonin-Mariana arc[END_REF] measured δ 37 Cl of "structurally bound chlorides" at δ 37 Cl = -1.1 ± 0.7 ‰ (15 sediment samples of Leg 125,129 & 189).

Chloride budget in the sediment:

In these sediments under consideration, chlorine is mainly present as chlorides in the pore fluids. Chlorine in the solid fraction is only at the level of a few percent (≤ 3 %), which is two orders of magnitude less than the amount of chloride in the pore fluids. As shown above the pore fluids in sediments lose 37 Cl-enriched chlorides and the amount of that loss can be assessed by looking at the chlorine isotope budget of chlorides in the pore fluids. This budget approach depends only on the chloride and isotope conservation equations which are uncontroversial. The nature of the geochemical process fractionating the chlorine isotopes, which may be controversial, does not come into play at this stage and will be discussed later.

Missing chlorides:

The loss of 37 Cl-enriched chlorides from the pore fluids can be evaluated in terms of the quantity of chlorides (QCl loss) and the chlorine isotope ratios (δ 37 Clloss) by examining the chloride budget including chlorine isotopes. By comparing the initial amount of of chlorides (Q∑Cl) with the amount of chlorides in the fluid (QCl porefluid), a conservation equation for chlorides can be written:

(8) and a conservation equation for the chlorine isotopes of the chlorides can be written:

(9)

where QCl loss and δ 37 Clloss is the pair of unknowns that cannot be evaluated independently because we have only one independent equation, the unknowns (QCl loss and δ 37 Clloss) are coupled. The unknown Q∑Cl is eliminated via equation 8. All the other parameters (δ 37 Cl∑Cl, δ 37 Clporefluid) have known values (assuming that the original pore fluids were seawater, δ 37 Cl∑Cl = δ 37 Clseawater). Then, P, the proportion of chloride lost is given by : (10)

which has an hyperbolic dependence on δ 37 Clloss (P = A/δ 37 Clloss, Figure 4). This shape reveals an antagonistic relationship between the amount of chloride lost, P, and the δ 37 Clloss: a large chloride loss (> 50 %) is associated with small δ 37 ClCl loss (< 1.5 ‰), that is small chlorine isotope fractionation between lost chlorides and porefluid chlorides whereas small loss (< 10 %) is associated with large δ 37 ClCl loss (> 8 ‰), i.e. large chlorine isotope fractionation between lost and porefluid chlorides.

This relationship between chlorine isotope fractionation and the amount of chloride lost significantly reduces the range of possible processes that can be invoked to explain the decrease in chloride δ 37 Cl. Figure 4 : Relationship between P, the proportion of chloride lost from the porefluid and δ 37 Clloss, the mean δ 37 Cl value of the lost chlorides. The model is based on the evolution of the δ 37 Cl of chlorides in pore fluids from the initial δ 37 Cl at seawater δ 37 Cl (= 0 ‰) to a mean value of δ 37 Clporefluid values of -1.51 ‰ (U1456) and -0.88 ‰ (U1457). Small P's are associated with large δ 37 Clloss and conversely large P's with small δ 37 Clloss. A 50 % loss of chloride (P = 0.5, upper horizontal dashed line) requires a loss of 37 Cl-enriched chlorides with mean values of δ 37 Clloss values of 1.5 ‰ and 0.9 ‰ for Sites U1456 and U1457, respectively. A 10 % loss (P = 0.1, lower horizontal dashed line) requires a loss of 37 Cl-enriched chlorides with mean values of δ 37 Clloss values of +13.6 ‰ and +7.9 ‰ respectively.

Chlorine isotope fractionation between pore fluid chlorides and lost chlorides

Additional constraints may be provided by a review of chlorine isotope fractionations between chlorides and phases that could incorporate lost chlorides. The thermodynamic properties of isotopes dictate that chlorine isotope fractionation factors, are close to 1.000 to a few permil, at temperatures above 0°C regardless the process (Urey, 1947;[START_REF] Richet | A review of hydrogen, carbon, nitrogen, oxygen, and chlorine stable isotope fractionation among gaseous molecules[END_REF][START_REF] Schauble | Theoretical estimates of equilibrium chlorine-isotope fractionations[END_REF][START_REF] Balan | First-principles modeling of chlorine isotope fractionation between chloride bearing molecules and minerals[END_REF][START_REF] Liu | Chlorine isotope mantle heterogeneity: Constraints from theoretical first-principles calculations[END_REF]. Indeed, such ranges of chlorine isotope fractionation are observed in natural and experimental systems (Desaulnier et al;[START_REF] Desaulniers | 37 Cl-35 Cl variations in a diffusion-controlled groundwater system[END_REF][START_REF] Lavastre | Chlorine transfer out of a very low permeability clay sequence (Paris basin, France): 35Cl and 37Cl evidence[END_REF][START_REF] Eggenkamp | The effect of aqueous diffusion on the fractionation of chlorine and bromine stable isotopes[END_REF][START_REF] Sharp | An experimental determination of chlorine isotope fractionation in acid systems and applications to volcanic fumaroles[END_REF][START_REF] Richard | An evaporated seawater origin for the ore-forming brines in unconformity-related uranium deposits (Athabasca Basin, Canada): Cl/Br and  37 Cl analysis of fluid inclusions[END_REF]Giunta et al., 2017a,b). For the ion filtration process of chlorides in clay-rich oceanic sediments undergoing compaction, α values in the range of 1.00025 to 1.008 are proposed [START_REF] Agrinier | Chlorine isotope data of chlorides challenge the pore fluid paradigm[END_REF]. Larger chlorine isotope fractionations are produced when chlorine is oxidised to an oxydation number of +2 to +7. Values of up to 1.07 have been obtained for the fractionation between chloride and perchlorate (Urey, 1947;[START_REF] Schauble | Theoretical estimates of equilibrium chlorine-isotope fractionations[END_REF]Ader et al., 2008) but these require extremely oxidizing conditions in contrast to those of oceanic sediments, which are reducing.

By writing an open system chlorine loss model, a Rayleigh distillation law, the chlorine isotope fractionation can be related to the proportion of chlorine lost (P). It gives the δ 37 Cl of the pore fluids as the loss of 37 Cl-enriched chlorides increases :

with

This modelling shows that for small  37Cl/35Cl loss-porefluid ≤ 1.008, a large portion of the chlorides must be lost from the sediment pore fluids (Figure 5). At least 35%, P= 0.35, for  37Cl/35Cl loss- porefluid = 1.008 is required to produce 37 Cl depletions up to δ 37 Cl = -2.51 ‰. The smaller the  37Cl/35Cl loss-porefluid, the larger the loss. Obviously, the model predicts that the loss is enriched in 37 Cl. The smaller the  37Cl/35Cl loss-porefluid, the lower the 37 Cl enrichment of the loss. If the  37Cl/35Cl loss-porefluid is very large, greater than 1.02, chloride loss is low (P ≤ 0.2), but this requires oxidizing conditions, to produce ClOn, that are not compatible with the reducing conditions found in ocean sediments.

are obtained for a range of loss-porefluid ranging from 1.000 to 1.07. This range covers the known fractionation factor values for chlorine isotopes for a lot many processes including (diffusion, ion filtration, gravitational settling, for small values (≤ 1.01) and larger values, up to 1.07 when chloride get oxidised to a redox state of +7). The ranges of δ 37 Clpore fluids in U1456 and U1457 sediments are shown as vertical red and green bars respectively on the right. The red and the green horizontal lines are the mean δ 37 Clpore fluids values of chlorides for Sites U1456 and U1457, respectively. The U1456 and U1457 δ 37 Clpore fluids data can be explained by small loss-porefluid ≤ 1.002 and large proportions of chloride lost from the porefluid (P).

If  37Cl/35Cl loss-porefluid is very large, greater than 1.02, the chloride loss is small (P ≤ 0.2), but the thermodynamic conditions it requires (oxydation to produce ClOn) are not compatible with those found in oceanic sediments (reducing).

Using the Cl filtration isotope mass balance model (Closed sedimentary pile : CSP), described in appendix B of [START_REF] Agrinier | Strong impact of ion filtration on the isotopic composition of chlorine in young clay-rich oceanic sediment pore fluids[END_REF], the Sites U1456 and U1457 pore fluids can be fitted with small  37 Cl/ 35 Cllost-porefluid ranging between 1.00025 and 1.0025 (Figure 6). Note that at the top of the sediment column, this model has a boundary condition to set chlorinity and  37 Cl to seawater values. This condition is imposed to represent the rapid exchange of chlorides across the sediment-seawater interface [START_REF] Agrinier | Strong impact of ion filtration on the isotopic composition of chlorine in young clay-rich oceanic sediment pore fluids[END_REF]. It erases the accumulation of 37 Clenriched chlorides, which are expelled from the bottom of the column where 37 Cl-depleted chlorides remain. The small  37 Cl/ 35 Cllost-porefluid values were expected because i) the 37 Cldepletion of chlorides are small, less than -2.5 ‰ from the seawater'  37 Cl value and ii) the nature of sediments with low clay content. Furthermore, the model shows that for such small  values,

to produce the most 37 Cl-depleted pore fluids (δ 37 Cl ≤ -0.5), the proportion of initial chloride loss, P, equal to Fchloride of [START_REF] Agrinier | Strong impact of ion filtration on the isotopic composition of chlorine in young clay-rich oceanic sediment pore fluids[END_REF]2021), must be greater than 0.4.

Then large proportions of the initial chloride, ≥ 40 %, would have been lost from the pore fluids and hence from the sediments. This is consistent with the open system modelling reasoning developed above, which shows that large fractions of the original chlorides must have been lost (Equation 11, Figure 6). the boundary condition where the column is open at the top to allow complete chloride exchange between sediment and seawater (CSP model of [START_REF] Agrinier | Strong impact of ion filtration on the isotopic composition of chlorine in young clay-rich oceanic sediment pore fluids[END_REF]. Error bars on Fchloride values are due to the uncertainty on the   values of the compaction laws. In the -Fchloride plot (right), all the model curves with this range of  are plotted on the same vertical black line at 558 mM.

Losses of fluids and chlorides from the sediment :

Vlost porefluid can be estimated from a fluid balance. It is obtained by substracting the amount of porefluid of the current compacted sediment column, Vporefluid, from the amounts of porefluid in the decompacted sediment column, Vporefluid decompacted. The decompacted sediment column thickness, Hdecompacted, can be estimated assuming that the volume of solid, Vsolid, is unchanged during compaction of the sediment, according to : [START_REF] Perrier | Thickness Changes in Sedimentary Layers During Compaction History; Methods for Quantitative Evaluation[END_REF][START_REF] Perrier | Thickness Changes in Sedimentary Layers During Compaction History; Methods for Quantitative Evaluation[END_REF][START_REF] Lucazeau | The blanketing effect of sediments in basins formed by extension: a numerical model. Application to the Gulf of Lion and Viking graben[END_REF]. This relationship assumes that the compaction law,  , has remained the same since sediments started to accumulate. It allows to get an estimate of the amount of the volume of the fluid in the decompacted sediment column, Vporefluid decompacted, according to : (14) where S = 1m 2 . Then the volume of lost porefluid, Vlost porefluid , that has been expelled from the sediment since the sediment started to accumulate is given by the porefluid budget :

In the same way the amount of lost chloride from the sediment, QCl lost can be estimated from the chloride balance : (16) where the amount of chloride in the porefluid for the decompacted sediment column is given by : (

QCl loss values are of about 187 ± 45 and 231 ± 50 kmoles of chlorides. Then δ 37 ClCl loss are 2.3 ± 0.15 ‰ and 0.8 ± 0.15 ‰ respectively because the lost chlorides must be 37 Cl-enriched in order to compensate for the 37 Cl-depletion of the chlorides of the pore fluids (mean δ 37 Cl of -1.59 and -0.73 ‰, respectively, Table 2). These chloride losses are very large, about 40 % of the "original" chlorides. They are the same magnitude as the QCl porefluid, the amount chlorides still present in the pore fluids (≈ 250 kmoles for the U1456 and U1457). The mean chlorinity of the lost pore fluids can be calculated with (18) where  is the density of pore fluid (≈ 1026 Kg.m -3 ). They are, respectively, 0.512 and 0.562 Mole of chloride per kg for U1456 and U1457, and very close to that of seawater (≈ 0.558 Mole of chloride per kg). This consistency of chlorinities is expected in light of the chlorinities of the pore fluids, which have remained very close to that of seawater (Figure 1). Then the process that fractionates the chlorine isotopes of chlorides in the porefluids of the sediments would not have a large impact on the chlorinity.

A sink can be proposed. As mentioned above, the current knowledge of the geochemistry of chlorides indicates that there is no reservoir in the sediment capable of sequestering that much of lost chlorides. The lack of storage capacity for chlorides in the sediment then leads to the conclusion that they have been expelled into the overlying seawater. This expulsion of chlorides from the sediment is necessary to produce the decrease of the δ 37 Cl of pore fluid chlorides with depth. Chlorine isotope fractionation at the sediment-water interface, which would force 37 Cl-enriched chlorides into the seawater as the sediment settles, does not have the capacity to produce the observed progressive decrease in δ 37 Cl with depth. Then the chlorine isotope fractionation then takes place in the sediment.

An estimate of this mean flux of 37 Cl-enriched chlorides out of the sediment pile is given by (in Mole of chloride. m -2 . Kyr -1 ) (19) The flux of chloride expelled out of the sediment 17.0 and 23.1 (± 5) moles of chloride per square metre per 1000 years for Sites U1456 and U1457 (using QCl lost values, about 187 and 231 kmoles of chlorides, Table 2). Since this lost chloride flux cannot be pure chloride, there must be a vector transporting 37 Cl-enriched chloride out of the sediment. The only chloride carrier available in the sediment is the pore fluid water. Therefore, the expulsion of pore fluid from the sediment to the seawater is a necessary consequence to produce the decrease in δ 37 Cl of chlorides in the sediment.

The lost fluid flux would be 1783 and 2201 moles of water per 1000 years per square metre for Sites U1456 and U1457 respectively, using : where CH2O is the concentration of water in the pore fluid (54.9 kmoles of H2O/m 3 ). This is in contrast to models of compaction of sediments which suggest that, at the seawater-sediment interface, the fluid enters the sediment, although not as fast as the solid [START_REF] Berner | Early Diagenesis: A Theoretical Approach[END_REF]Hutchinson, 1985;[START_REF] Boudreau | Diagenetic Models and Their Implementation, Modelling Transport and Reactions in Aquatic Sediments[END_REF] but such conditions cannot explain the decrease in δ 37 Cl of chlorides below the seawater-sediment interface. Another implication of this outflow of chlorides into the seawater is that imposed by the condition of electroneutrality of the ion flux.

The outflow of negative charges from chlorides must be accompanied by an outflow of positive charges carried by cations (Na + , Ca 2+ , Mg 2+ , ...) or by an inflow of negative charges which may be electrons and anions. As the Na + /Cl -ratio of the pore fluids remains very close to that seawater (Figure 1), chloride losses are most likely coupled to sodium ion losses.

V.2 Chloride exchanges between sediments and seawater

In Table 2, we calculated the budgets of pore fluids and pore fluid chlorides for the 24 sites representing sediments from a variety of oceanic environments (references in Table 3).

Chlorides are systematically 37 Cl-depleted ( 37 Cl < 0 ‰) compared to seawater. They form a chlorine reservoir with weighted average δ 37 Cl at -2.3 ± 0.2 ‰ and chlorinity at 0.290 ± 0.055 mole Cl -/kg of sediment or 0.552 ± 0.070 mole Cl -/kg of pore fluid, assuming that the investigated sites (n = 24) represent a good sampling of the population of the oceanic crustal sediments in terms of diversity and statistical weight. In that case the pore fluid reservoir would be ≈ 1.8 10 8 ± 0.5 km 3 of pore fluid in the oceanic sediments (≈ 3.4 10 8 km 3 of sediment, [START_REF] Straume | GlobSed: Updated total sediment thickness in the world's oceans[END_REF]. This amount of pore fluids is calculated using an average compaction law of (z) ≈ 0.80 * exp(-z/1000) obtained from the data compiled by [START_REF] Perrier | Thickness Changes in Sedimentary Layers During Compaction History; Methods for Quantitative Evaluation[END_REF].

Of course, this evaluation of the volume of fluid is affected by a great uncertainty, about ± 25%, but this approach allows to obtain a good order of magnitude of this volume to compare it with that of the sea water. Using the pore fluids chlorinity at 0.552 mole Cl.kg -1 , we deduce that pore fluids would contain 1 10 20 moles of chloride (= ∑Qporefluid), that is about one tenth (13 % exactly) of the chlorides contained in seawater (7.6 10 20 moles of chloride).

We also provide estimates of the fluxes of expelled chloride from sediment to seawater. They range from 3.5 to 45.6 moles of chloride per square metre per kiloyear (mole Cl.m -2 .ky -1 ) (Figure 7). Most of the flux data are in the range between 3 and 25 mole Cl.m -2 .kyr -1 . The mean value is 18.3 mole Cl.m -2 .kyr -1 . These fluxes are very important in terms of controlling the composition of seawater. Using the amount of chloride in the pore fluids of the oceanic sediments and the flux of chloride expelled through the surface of the seafloor (0.14 to 1.8 10 16 moles of chloride.kyr -1 = 3.5 to 45.6 mole Cl.m -2 .kyr -1 * 4 10 14 m 2 ), we estimate the equilibration time of chloride between the seawater and the pore fluids of the oceanic sediments: it ranges from 5.5 to 71 Myr. The mean value is ≈ 14 Myr. Although small, it is of the same order of magnitude as the mean age of oceanic crust (64.2 Myr; Seton, 2020) and the residence time of chloride in seawater calculated from the chloride river flux (65 Myr; [START_REF] Lecuyer | Seawater residence times of some elements of geochemical interest and the salinity of the oceans[END_REF] On this timescale, the process fractionating chlorine isotopes in sediments, possibly ion filtration by clays, controls the chloride isotopic contrast between pore fluids and seawater. In this case, an increase of the content of smectites, which are associated with large chlorine isotope fractionation of chlorides, in the sediment would produce more 37 Cl-depleted pore fluids and consequently induces an increase in the δ 37 Cl of seawater chlorides.

Other clays, such as kaolinite, chlorite and illite, which are associated with smaller chlorine isotope fractionation of chlorides, would produce less 37 Cl-depleted pore fluids and a smaller increase in the δ 37 Cl of seawater chlorides. By writing a balance equation ( 20 Assuming that i) the amounts of Cl in the pore fluid (QClporefluid) and in the seawater reservoir (QClseawater) remain constant and ii) the δ 37 Cl∑ remains constant, equation 23 shows a linear dependence between δ 37 Clseawater and δ 37 Clporefluid (Figure 8). The second term of equation 23 gives the sensitivity of the δ 37 Clseawater response to the isotopic fractionation of chlorine between the pore fluids and the seawater. The sensitivity is weak because it depends on the ratio QClporefluid/QClseawater (= 0.13) which is small (current values are QCl pore fluid = 1 10 20 moles of Cl, QCl seawater = 7.6 10 20 moles of Cl, δ 37 Clseawater = 0.0 ‰, δ 37 Clpore fluids = -2.3 ‰). A first extreme case is when there is no chlorine isotope fractionation of chloride, δ 37 Clseawater and δ 37 Clpore fluids would be equal to -0.27 ‰. This would be the case if the sediments consisted mainly of carbonates, silica, i.e. minerals that do not fractionate chlorine isotopes from chlorides in the pore fluids. The other extreme is when the fractionation of chlorine isotopes of chloride is maximal. This would be the case if the sediments consisted mainly of smectites, i.e. minerals that fractionate a lot of chlorine isotopes of chlorides. From the available data (Table 2), this condition seems to occur at Sites 1174, C0011 and C0012 where the lowest  37 Clporefluids are measured (-4.7, -5.1 and -4.3 ‰ respectively). δ 37 Clseawater would increase to ≈ + 0.25 ‰. The range of variation of δ 37 Clseawater predicted by this chloride partitioning model is between +0.3 and -0.3 ‰. It is consistent with the range of variations of δ 37 Clseawater reconstructed from halite deposits for the last 800 million years by [START_REF] Eggenkamp | The bromine and chlorine isotope composition of primary halite deposits and their significance for the secular isotope composition of seawater[END_REF].

Then, the clays (content and nature) of the oceanic sediments would play a role in controlling the chlorine isotope composition of chloride of seawater and pore fluids. Since most of the clay minerals present in oceanic sediments, probably more than 90%, are detrital, physically eroded from continental soils [START_REF] Hillier | Erosion, sedimentation and sedimentary origin of clays[END_REF][START_REF] Petschick | Clay Minerals in surface sediments of the South Atlantic: Sources, transport and relation to oceanography[END_REF][START_REF] Thiry | Palaeoclimatic interpretation of clay minerals in marine deposits: an outlook from the continental origin[END_REF][START_REF] Fagel | Clay Minerals, Deep Circulation and Climate[END_REF], the nature of clays in oceanic sediments is controlled by the transport of continental clays to the oceans and the alteration style of continental bedrocks. Both are controlled by climatic parameters (precipitation and temperature). This may illustrate a link between the δ 37 Cl of seawater and the Earth's climate. If kaolinite is mainly transported to the oceans, the δ 37 Cl of seawater would increase slightly. If smectite is mainly transported to the oceans, the δ 37 Cl of seawater would increase more (Figure 8).

Figure 8:

Relationship between the chlorine isotope composition of seawater (δ 37 Clseawater) and the mean chlorine isotope composition of pore fluids of the oceanic sediments (δ 37 Clporefluid). Today's compositions is represented with the blue dot, with seawater δ 37 Clseawater = 0 ‰ and mean pore fluid δ 37 Clpore fluids= -2.3 ‰ (resulting from the chlorine isotope fractionation of chlorides in the sediment induced by ion filtration). In the case where no chlorine isotope fractionation of chlorides due to low abundances of clay minerals and dominance of carbonates and silica in the sediments, the chlorine isotope composition of seawater and that of pore fluids are the same (δ 37 Clseawater = δ 37 Clpore fluids, = -0.27 ‰, red dot). An increase of the abundance of smectite in the sediment would increase the chlorine isotope fractionation of chlorides by ion filtration resulting in a large 37 Cl depletion of the pore fluids and an increase in the δ 37 Clseawater. The yellow vertical bar indicates the range of possible δ 37 Cl variations of the seawater over the last 800 Myr as determined by [START_REF] Eggenkamp | The bromine and chlorine isotope composition of primary halite deposits and their significance for the secular isotope composition of seawater[END_REF] from halite deposits.

VI) Conclusions

Chlorine isotope ratios of chlorides in pore fluids from globally distributed clay-rich oceanic sedimentary sites (n=24) show a progressive depletion of 37 Cl in chlorides with depth. Mean value for δ 37 Cl is -2.3 ± 0.2 ‰ and chlorinity is 0.290 ± 0.055 mole Cl -/kg of sediment.

Assuming that the pore fluids were originally seawater trapped at the seawater-sediment interface, the balance of chlorine isotopes in the pore fluids forces the disappearance of 37 Cl-enriched chlorides and since chlorides are the dominant ions in these fluids, this loss of 37 Clenriched chlorides reveals a very important process operating in the sediment. This process seems independent of the tectonic environment in which the sediments were deposited and amplified by the presence of clays in the sediments.

The chlorine budget in these sediments shows that the dominant reservoir of chlorine is the pore fluid chlorides. The other chlorine reservoirs (carbonates, clays, organochlorides) are very modest. Consequently, they do not have the capacity to store the 37 Cl-enriched chlorides that the fluids have lost. A review of all the processes that are known to cause a decrease in the  37 Cl of chlorides either by fractionation of chlorine isotopes in chlorides (diffusion, gravity, filtration) or by mixing (advection of 37 Cl-depleted chlorides) leaves ion filtration of pore fluid chlorides by clay membranes during the compaction of the sediments as the only known process to date that could explain the widespread 37 Cl-depletion in sedimentary pore fluids.

The chloride fluxes expelled out of the pore fluids into the seawater calculated here required to explain the observed 37 Cl depletions range from 3.5 to 46 moles of chlorides per square metre per kiloyear. Most of the values are between 1 and 25 mole Cl.m -2 .kyr -1 suggesting that pore fluids and seawater exchange chlorides on the 5.5 to 71 Myr time scale (mean value at ≈ 14 Myr). At this time scale, the δ 37 Cl of seawater would be controlled by the nature of the continental detrital clays that are deposited on the seafloor. Minerals with high surface charge density, such as smectites, which are associated with strongly 37 Cl-depleted pore-fluids in the sediments, greatly increase the δ 37 Cl of seawater, whereas minerals with low surface charge density, such as kaolinites, illites-chlorites, which are associated with weakly 37 Cl-depleted pore-fluids in the sediments, slightly increase the δ 37 Cl of seawater. The range of δ 37 Clseawater variations must be within -0.3 to +0.3 ‰.

VII) Acknowledgement

We are indebted to the shipboard and drilling personnel, and the Scientific Parties of drillship R/V JOIDES Resolution for their dedication and assistance with all aspects of coring, sampling, 105, 131, 134, 162, 164, 168, 172, 181, 186, 190, 195, 322 and 333) were also used in this work. We wish to thank Mark Kendrick, the two anonymous referees for useful criticisms and Benjamin Tutolo

  shipboard pore fluid extractions and analyses of Chloride, Sodium, Calcium, Magnesium, Potassium, Alkalinity, pH, Sulfate and Bromide concentrations were carried out on board following the protocols of[START_REF] Gieskes | Technical Note 15: Chemical Methods for Interstitial Water Analysis Aboard JOIDES Resolution[END_REF],[START_REF] Murray | Technical Note 29: Analysis of Major and Trace Elements in Rocks, Sediments, and Interstitial Waters by Inductively Coupled Plasma-Atomic Emission Spectrometry[END_REF],Pandey et al. (2016d) and the IODP user manuals for shipboard instrumentation. Chemical data are taken fromPandey et al. (2016b, & c). 87 Sr/ 86 Sr ratios are taken from[START_REF] Carter | Data report: 87Sr/86Sr in pore fluids from IODP Expedition 355 Arabian Sea Monsoon[END_REF]. All these data from published literature are shown in Figure1.III.1 Concentration in chloride, [Na + ], [Na + ]/[Cl -] and [Br -]/[Cl -] molar concentration ratios:Chlorinity and Na + profiles are similar at both wells. They are generally within 2 %, close to seawater concentrations, ~ 558 mM and ~ 480 mM respectively. They do not vary much with depth. Towards the bottom of the two sedimentary piles, in Unit III, the profiles are more noisy.Similarly, the [Na+]/[Cl-] ratios are consistent in both sites and remain very close to that of seawater. The [Br -]/[Cl -] ratios increase rapidly below the water-sediment interface in Unit I, then more slowly in Unit II, becoming constant at depth in Unit III. Most of the increase in the [Br-]/[Cl-] ratio is due to the variation in bromide, the variation in chloride being very small.

Figure 3 :

 3 Figure 3: U1456 and U1457 porosity and δ 37 Cl depth profiles (Left and center). Porosity data are from Pandey et al. (2016b & c). The inset for Site U1456 shows the upper part of the porosity and δ 37 Cl depth profiles. U1456 porosity data, , are fitted with compaction law  ≈ 75 * exp(-z/400)) in Unit I (z ≤ 120 mbsf) and with compaction law  ≈ 48 * exp(-z/5500) in Units II, III & IV (z > 120 mbsf). U1457 porosity data, , are well fitted with compaction law  ≈ 75 * exp(-z/250)) in Unit I (z < 100 mbsf) and with compaction law  ≈ 50 * exp(-z/3000) in Units II & III (z > 100 mbsf.

Figure 6 :

 6 Figure 6: The  37 ClCl porefluid -Fchloride and -Fchloride relationships for pore fluids from Sites U1456 and U1457. The data can be fitted with the Cl filtration isotope mass balance model curves (closed sedimentary pile : CSP of Agrinier et al., 2019) with small value of chlorine isotope fractionation between the lost chloride and the pore fluid chloride ( 37 Cl/ 35 Cllost-porefluid) ranging between 1.0025 and 1.00025 shown as black labelled curves (left and centre). This 1D model uses

Figure 7 :

 7 Figure 7: Histogram of expelled chloride flux from the sediments to seawater versus the sedimentation rate for 24 sites drilled by IODP. Mean flux value is 14 mole Cl.m -2 .kyr -1 .

  ), one can obtain a model (equation 21) that describes the control of the seawater  37 Cl as a function of chloride partitioning between the seawater and the sediment pore fluids:

  describing and shipboard laboratory measurements during the Ocean Discovery Program (IODP) Expeditions 355. All the pore fluid samples and most of the data used in this study were acquired during this leg. Additional pore fluids were obtained from the Bremen Core Repository (Holger Kuhlmann) and the Kochi Core Center (Lallan Gupta, Kazuhiro Yoshida, Yusuke Kubo). Data acquired by the Ocean Drilling Program (ODP), the Integrated Ocean Drilling Program (IODP) and the International Ocean Discovery Program (IODP) and many scientific parties (Legs

  that helped us improve the paper. The Comité IODP-France and the TelluS (Syster) Program of CNRS/INSU supported this project.

  [START_REF] Gieskes | Interstitial water studies, Leg 35. Initial Rep[END_REF]. They are increases in Ca 2+ , decreases in Mg 2+ . The magnitudes of these changes are modest. Mg 2+ is only reduced by only 30 mM,  37 Cl by -1.5 ‰, Ca 2+ is increased by 5 mM compared to pore fluids of other kilometre thick sedimentary pile, where these parameters are much more changed. The largest gradients of changes are systematically located in Unit I, i.e., in the upper 100 metres just below the sediment-seawater interface. Similarly, the Br/Cl ratios of interstitial fluids also show this pattern of variation gradient damping as depth increases.

	1975;
		Dominant lithology
	Carbonate chalk/limestone	Silt/Siltstone	Gravel	Carbonate breccia
	Clay/Claystone	Sand/Sandstone	Calcarenite

  for the sediments of subduction zone accretionary prisms: fluids of deep origin, depleted in 37 Cl, produced in the subduction zone, entered the sedimentary pile from greater depths. However, this is very difficult to consider in the present study because advection must have occurred under unfavourable hydrogeological conditions with porosity and permeability decreasing with depth. Considering the shape of the  37 Cl and [Cl -] profiles, the potentially advected fluid would have chlorides with  37 Cl lower than the lowest measured  37 Cl value (-2.50 & -1.40 ‰ in Sites U1456 & U1457, respectively) and higher chlorinity than the highest measured value (573 and 568 mM, respectively). Futhermore, this advection of fluid up through the sedimentary pile

Table 3 :

 3 References for the 24 oceanic sites drilled by IODP 945

	Site	Leg

 Srivastava, S.P., Arthur, M., Clement, B., et al., (1987b) Proc. ODP, Init. Repts., 105: College Station, TX (Ocean Drilling Program), Shipboard Scientific Party. Site 646. 419-674. Srivastava, S.P., Arthur, M., Clement, B., et al., (1987c) Proc. ODP,Init. Repts.,105: College Station,TX (Ocean Drilling Program), Shipboard Scientific Party,. Site 647. 675-905. Urey H.C. (1947) The thermodynamic properties of isotopic subtances. The Journal of the Chemical Society, 562-581.

Wei, W., Kastner, M., Deyhle, A., and Spivack, A.J., (2005). Geochemical cycling of fluorine, chlorine, bromine, and boron and implications for fluidrock reactions in Mariana forearc, South Chamorro Seamount, ODP Leg 195. In Shinohara, M., Salisbury, M.H., and Richter, C. (Eds.), Proc. ODP, Sci. Results, 195, 1-23. Wei W., Kastner M. and Spivack A. J. (2008). Chlorine stable isotopes and halogen concentrations in convergent margins with implications for the Cl isotopes cycle in the ocean. Earth Planet. Sci. Lett. 266, 90-104.


A new control strategy for shape memory alloys actuators ⋆ Pierre-Antoine Gédouin 1 , Cédric Join 2,3 , Emmanuel Delaleau 1 , Jean-Matthieu Bourgeot 1 , Shabnam Arbab Chirani 1,4 , and Sylvain Calloch 4 Abstract. Shape memory alloys (SMA) are more and more integrated in engineering applications. These materials with their shape memory effect permit to simplify mechanism and to reduce the size of actuators. SMA parts can easily be activated by Joule effect but their modelling and consequently their control remains difficult, it is principally due to their hysteretic thermomechanical behaviour. Another difficulty is that the characteristics of the material are timevarying, especially during cyclic loadings. So, most of successful control strategy applied to SMA actuator are particularly heavy and used the Preisach model or neural networks to model the hysteretic behaviour of these material but this kind of models are difficult to identify and to use in real time. That is why this study deals with an application of the new framework of model-free control and restricted model control applied to a SMA spring based actuator. This control strategy is based on new results on fast derivative s estimation of noisy signals, its main advantages are: its simplicity, its robustness and the fact that it is easy to compute. Experimental results and comparisons with PID control are exposed that demonstrate the efficiency of this new control strategy despite thermal perturbations.

Introduction

Shape memory alloys (SMA) offer the possibility to recover a known shape after a thermomechanical cycle. This property, known as the "shape memory effect", is due to the transition between the two crystallographic phases in their composition. This variation of shape, controlled by temperature variation, may be used in the development of actuators (see e.g., [START_REF] Peirs | Proceedings of The International conference on new actuator[END_REF] and [START_REF] Kohl | [END_REF]). SMA can easily be heated by Joule effect, but their control is not completely solved and it is principally due to their hysteretic behaviour (see [START_REF] Patoor | Mechanics of phase transformation and shape memory alloys[END_REF]). Another difficulty is that the characteristics of the material are time-varying, especially during cyclic loadings. Phases kinetic transformations and 3-dimensional models are proposed in [START_REF] Leclerc | [END_REF], [5], [6] and [7]. These complex models can render very subtle properties of SMA, but often need to compute a finite element code, what is not suitable for real time control. On the opposite side, Robotics research have been done on SMA actuator by using simpler model and classical control method. A lot of control strategies have been applied to SMA actuators, classical PID loop are used in [START_REF] Calin | Proceedings of the 1997 IEEE/RSJ Intelligent Robots and Systems[END_REF], [START_REF] Shameli | [END_REF] and [10]. A feedforward path is added in [11]; the feedforward command is obtain by using a Preisach model for the hysteretic effect. In [START_REF] Dutta | International Symposium on Intelligent Control[END_REF] feedforward scheme is also used but the hysteretic behaviour is described by a Duhem differential hysteresis model. In [START_REF] Song | [END_REF]14] a feedforward loop is combined with sliding mode control to obtain robustness, the feedforward path is respectively given by neural network and by a physical model. An H ∞ loop based on physics modelling is design in [START_REF] Jayender | Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005[END_REF]. Passivity property of the system is used in [START_REF] Madill | [END_REF] to prove stability of a proposed proportional law. Nonlinear control techniques based on the Lie algebra are also used in [START_REF] Benzaoui | Smart Structures and Materials[END_REF]. Even if their model are quite good enough, using a dynamic model for computing the control law, need firstly to identify the model parameter. As we have already mention the model parameter of SMA vary during cycling, then a classical model based control is ineffective or particularly complex. We report our experience, where industrial partners still explain that in order to realise the process control, the part of process modelling represents 90 % of project global time. Indeed, to define the physical model structure, to identify unknowns parameters, to collect experimental data, to valid the model are never simple. However, how is it possible to control a complex process without any model?

In this paper, a solution to this difficult problem is proposed. The proposition is based on some new results in the framework of "Model-free control" (see [START_REF] Fliess | In 15th IFAC Symposium on System Identification (SYSID 2009)[END_REF][START_REF] Fliess | Proc. 14th IFAC Symposium on System Identification (SYSID'06)[END_REF][START_REF] Fliess | Proc. Conférence internationale francophone d'automatique (CIFA'06)[END_REF][START_REF] Join | Proc. 2 e Journées Identification et Modélisation Expérimentale (JIME'06)[END_REF]). The approach uses a derivative estimation (see [START_REF] Mboup | [END_REF][START_REF] Mboup | In 15th Mediterrean Conference on Control and Automation (MED'07)[END_REF][START_REF] Fliess | [END_REF]) which provides good results even if signals are corrupted by noise. Thus a non-physical model valid a very short part of time is estimated and permits classical control design.

The present work constitutes an extension of a previous paper [START_REF] Gédouin | 17th IFAC World Congress[END_REF], in which only simulations have already highlighted the advantages of the proposed method in the area of SMA actuators.

The paper is organised as follows: The next Section is a short review and introduction to the new "Model-free control"and explains the design of a control law within this new framework; Sec. 3 develops the model-free control of a shape memory alloys actuator and gives experimental results. Sec. 4 concludes the paper and raises some perspectives.

Model free control

Model free control is a very recent approach to nonlinear control that has been introduced in [START_REF] Fliess | Confrence internationale francophone d'automatique (CIFA 2006)[END_REF], (See [START_REF] Fliess | In 15th IFAC Symposium on System Identification (SYSID 2009)[END_REF] for a thorough presentation). A first industrial and convincing application is reported in [START_REF] Join | Proc. 2 e Journées Identification et Modélisation Expérimentale (JIME'06)[END_REF].

Derivatives of noisy signals

Firstly, we recall basic of derivative estimation. Interested reader might refer to [START_REF] Mboup | [END_REF] for a complete presentation. We consider a signal y that is available through a measurement y m corrupted by some additive noise ̟, i.e. y m = y + ̟. The objective is to estimate time derivatives of signal y(t), up to a finite order, from its measurement y m .

The Taylor expansion of y around 0 reads:

y(τ ) = ∞ n=0 y (n) (0) τ n n!
Approximate y(t) in the interval [0, T ], T > 0, by the polynomial y N (τ ) = N n=0 y (n) (0) τ n n! of degree N . The operational1 analogue (see [START_REF] Mikusiński | Operational calculus[END_REF]) Y N (s) of y N (τ ) is given by:

Y N (s) = y(0) s + ẏ(0) s 2 + • • • + y (N ) (0) s N +1
It is possible to isolate each coefficient y (i) (0) appearing in the previous expression by applying a convenient operator to Y N (s) (see [START_REF] Mboup | [END_REF] for details2 ). Indeed:

∀i = 0, . . . , N, y (i) (0) s 2N +1 = (-1) i N !(N -i)! • 1 s N +1 • d i ds i • 1 s • d N -i ds N -i s N +1 Y N (s) (1)
Having in mind that the operator 1 s α corresponds to the function t → t α-1 (α-1)! , that the operator d ds corresponds to the multiplication in the time domain by -t and using the Cauchy formulae to transform a multiple integral in a simple one:

T 0 τα-1 0 • • • τ1 0 f (µ)dµ dτ 1 . . . dτ α-1 = T 0 (T -µ) α-1 (α -1)! f (µ)dµ (2)
One obtain in the time domain the expression of y (i) (0) as:

y (i) (0) = T 0 P (µ; T )y N (µ)dµ (3)
where P (µ; T ) is polynomial in µ and T . Notice that (3) gives the calculation of y (i) (0) from an integral on the time interval [0, T ] for a given small T > 0. As d i y(t-µ)

dµ i | µ=0 = (-1) i y (i) (t)
it is possible to express y (i) (t) as an integral which evolves values of y N on the time interval [t -T, t]:

y (i) (t) = (-1) i T 0 P (µ; T )y N (t -µ)dµ (4)
A simple estimator of the derivative y (i) (t) is then obtained from the noisy signal y m by:

y (i) (t) e = (-1) i T 0 P (µ; T )y m (t -µ)dµ (5)
which is deduced from (3) by replacing y N by y m in (4). Note that the integral operation plays the role of low-pass filter and reduced the noise that corrupts y m The choice of T results in a trade-off: the larger is T , the smaller is the effect of the noise ( the larger is T the better is integrals low pass filtering) and the larger is the error due to truncation. In practise, ( 5) is evaluated at each sample time t = k.T s , k = 0, 1, . . . as a discrete sum using basic trapezoidal method or Simpson method to calculate integrals:

y (i) (kT s ) e = ns i=0 w(i)P (iT s ; n s T s )y m ((k -i)T s ) (6)
with n s the number of samples used in the time window and n s T s = T .

Model-free control design

Assume we have a plant whose we do not know any model. For the sake of simplicity of the presentation we assume that this plant is single-input and single-output. The control input is denoted by u and the output is denoted as y. As seen in the previous section, we are able to estimate on-line some derivatives of y and u. Model-free control consist in trying to estimate via the input and the output measurements what can be compensated by control in order to achieve a good output trajectory tracking. This implies the construction of a purely numerical model of the plant that can be written as:

y (ν) = F + αu (7)
where α ∈ R is a non-physical constant3 design parameter; F ∈ R represents all what is unknown on the system and can be compensated from the knowledge of the input-output behaviour of the system; the order ν ∈ N of the numerical model ( 7) is also a design parameter that can be arbitrarily chosen.

Eqn. (7) should not be confused with a "black-box" identified model. In the present approach, ( 7) is update at each sampling time from the knowledge of the input-output behaviour of the unmodeled plant. At sampling time k (i.e. t = kT s , where T s denotes the sampling period), the estimation of F reads:

[F (k)] e = [y (ν) (k)] e -αu(k -1) (8)
where [y (ν) (k)] e is the estimation of the ν-st derivative of the output that can be laid at time k and u(k -1) is the control input that has be applied to the plant during the previous sampling period.

Based on the numerical knowledge of F the control for sampling period k is calculated on (7) as a simple cancellation of the non-linear terms F plus a closed loop tracking of a reference trajectory t → y * (t):

u(k) = - [F (k)] e α NL Cancellation + [y * (ν) (k)] e + ∆(ǫ(k)) α Closed loop tracking (9)
where ǫ(k) = y(k)y * (k) is the tracking error and ∆(ǫ(k)) is a closed-loop feedback controller base on the tracking error. Note that the term

-[F (k)]e α + [y * (ν) (k)]e
α is also the "nominal control" in the "flatness-based" control of (7) (see e.g., [START_REF] Fliess | [END_REF][29][30]). When the closed loop controller is of "PID" type, Model free control can be named as "intelligent PID" (i-PID) (see [START_REF] Fliess | In 15th IFAC Symposium on System Identification (SYSID 2009)[END_REF]).

This control scheme is summarised in Fig. 1 3 Prototype of SMA Actuator A simple prototype of SMA spring actuator has been built, a picture of the actuator is given in Fig. 2. The upper extremity of a Ni-Ti spring is electrically isolated and fixed to rigid structure and the lower extremity is attached to a 450 g mass. The mechanism of this kind of actuator is decomposed into three steps. Firstly, when the temperature is constant and lower than the austenite start temperature A s , the SMA spring is purely martensitic and the tensile force provided by the mass deforms the SMA spring to an initial deflection. Secondly the spring is heated, when its temperature goes past A s , the martensite begins to change into austenite, so the spring tries to achieve its high temperature shape consequently the mass goes up. Finally during cooling austenite changes into martensite so the force provided by the mass permit the mass to go down. For this actuator, the spring is heated by joule effect and cooled by free convection. The electric current crossing the spring is measured using a shunt resistance and a voltage amplifier, we also measure electric voltage with a voltage amplifier and the position of the mass using a laser sensor. We use an input output board connected to a computer with RTAI/Linux coupled with an electric power generator to acquire and generate real time control signals.

Position control development

For this application the very simple first-order local numerical model ẏ = F + αu (10) is considered. The control input u corresponds the electric power crossing the SMA spring and the output y is the measured vertical position of the mass. According to section 2.2, the control is given by:

u = 1 α (-[F ] e + ẏ⋆ + K p (y -y ⋆ ))
where K p is a positive constant. Note that as ( 10) is here first order, a simple proportional controller is enough to ensure convergence of the error to zero. This controller is called an i-P controller.

Experimental results

The previous control law was applied to our SMA actuator. The performances in closed loop are compared with the performances obtained with a PI controller4 for two scenarios.

Scenario 1 (Fig. 3 ):

We present classical closed loop step response with thermal disturbance. In this scenario the mass has to reach a reference position of 70 mm. when the actuator is control with i-P controller, we can observe that the mass reaches the reference position in approximately 8 seconds without overshoot whereas a 17 mm overshoot and 34 s time response are observed when the actuator is control by a PI controller. This overshoot should be reduced (reducing the integral gain) nevertheless rejecting perturbations would be bad. At time t = 56 s a thermal perturbations is applied using a fan. We can observe that the perturbation is rejected faster by the i-P controller than the PI one.

Scenario 2 (Figs. 4 and5 ):

We present classical tracking. We can observe that tracking is very good when the actuator is controlled by an i-P (see Fig 3) whereas it is unsatisfactory for the PI (see Fig 4). A A first solution would be to increase the gains of the PI controller but for this experiments the choice of gains level results in a trade-off because the larger are the gains the better are performances in transient however high level gains degrade performances in steady-state.

Conclusion

This paper presents a convincing application of the new model-free control in the area of SMA actuators control, a field in which control-model is especially difficult to obtain. Experimental results on a SMA spring based actuators show that the robustness towards thermal perturbations and tracking performances of this controller are better than the PI ones, whereas the design of the two controller needs the same numbers of tuning parameters. Finally, we are very confident to be able to efficiently control SMA micro actuators as micro servomotors in a very short time.

Fig. 1 .

 1 Fig. 1. Model free control

Fig. 2 .

 2 Fig. 2. Prototype of a SMA spring based actuator.

Fig. 3 .Fig. 4 .

 34 Fig. 3.Step response of the actuator with thermal disturbance (PI and i-P)

Fig. 5 .

 5 Fig. 5. Classical tracking when the actuator is controlled with a PI controller.

Reader not familiar with operational calculus can just think in terms of Laplace transform to understand the development of the derivatives estimators.

Note that those operators are not unique, we have chosen here to use the ones with the least order of integration for the sake of simplicity of the presentation.

Note that this parameter could also be chosen time varying for some applications.

The Classical control involves an integral terms in order to avoid static error.

⋆ This work was supported in part by the Agence nationale de la recherche (France) -Project "MAFESMA", in part by Brest métropôle océane, in part by Conseil génénéral du Finistère. P.-A. Gédouin is partially supported by Brest métropôle océane.