SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION DOI: /NGEO1482 Supplementary Information for: Volcanic arc fed by rapid puled fluid flow through ubducting lab Timm John, Nikolau Guone, Yuri Y. Podladchikov, Gray E. Bebout, Ralf Dohmen, Ralf Halama, Reiner Klemd, Toma Magna, Han-Michael Seitz Analytical Method Determination of Rb/Sr and 87 Sr/ 86 Sr ratio: Approximately 100 mg of whole-rock powder were weighed into 15 ml Teflon crew-cap vial and digeted in a mixture of 4 ml HF and 2 ml HNO 3. After 3 day of boiling on a hotplate at 120 C (with cloed cap), 1 ml HClO 4 wa added and the olution wa evaporated at ~190 C. The dried ample were re-diolved in 2 ml 10 N HCl, heated at 140 C on a hotplate for 12 h (cloed cap) and afterward evaporated at 125 C. The dried ample were then re-diolved in 6 ml 6 N HCl and heated (cloed cap) for 45 min to 100 C. The cooled olution wa inpected for the preence of precipitate. An 87 Rb- 84 Sr-mix-pike wa added to an aliquot of the olution. Rubidium and Sr were purified with tandard cation exchange chromatography uing 2.5 N HCl. The Sr cut wa purified twice. Rubidium concentration, Sr concentration and 87 Sr/ 86 Sr iotope ratio were determined by Thermal Ioniation Ma Spectrometry (TIMS) at the Intitut für Mineralogie (Univerität Münter). Rubidium wa loaded with H 2 O on Ta filament and analyed on a VG Sector 54 ma pectrometer, wherea Sr wa loaded with a TaF 5 activator on W-filament, and analyed on a Thermo-Fiher Triton T1 ma pectrometer. 87 Sr/ 86 Sr ratio of the rock were corrected for the offet between the meaured ( ) and the accepted ( ) 87 Sr/ 86 Sr ratio for NBS 987. Reproducibility (2σ) of 87 Sr/ 86 Sr wa better than The tandard deviation (2σ) of Rb/Sr ratio wa better than 1 %. NATURE GEOSCIENCE 1

2 Determination of Ca iotope compoition Approximately 100 mg of whole rock powder were weighed into 15 ml Teflon crew-cap vial and digeted with cloed cap in a mixture of 4 ml HF and 2 ml HNO 3 for three day on a hotplate at ~120 C. Afterward 1 ml HClO 4 wa added and the olution wa evaporated at ~190 C. The dried ample were re-diolved in 2 ml 10 N HCl, then heated at 140 C on a hotplate for 12 h with cloed cap. Afterward, thee ample were evaporated at 125 C. The dried ample were then re-diolved in 6 ml 6 N HCl and heated with cloed cap for 45 min at 100 C. The cooled olution wa checked for precipitate. Aliquot for δ 44/40 Ca analye were mixed with a 42 Ca- 43 Cadouble pike. Unpiked aliquot were checked for potential radiogenic 40 Ca. For the leaching experiment, 200 mg rock powder were treated with 3 ml 2.5 N HCl for 3h at ~40 C. The reidue wa eparated from the olution after centrifuging for 10 min at 4200 rpm. The reidue wa then treated in the ame way a the whole rock ample, following the HF-HNO 3 -HClO 4 digetion protocol decribed above. The piked and unpiked aliquot for Ca iotope analye were purified uing 100 µl MCI gel column with 1.8 N HCl chemitry 31. Calcium iotope ratio were determined by Thermal Ioniation Ma Spectrometry on a Thermo-Fiher Triton T1 at the Intitut für Mineralogie (Univerität Münter) following the method decribed in ref. 32 and 33. Calcium wa loaded with a TaF 5 activator on Re-filament. Calcium iotope ratio are expreed a δ 44/40 Ca relative to SRM 915a (δ 44/40 Ca [ ] = (( 44 Ca/ 40 Ca) ample /( 44 Ca/ 40 Ca) SRM 915a - 1) 1000) and the reproducibility of the ample wa about ~0.06 (2σ). No ignificant ma-independent 40 Ca enrichment were oberved over the profile we ampled, indicating no ignificant contribution of radiogenic 40 Ca from 40 K decay to the δ 44/40 Ca of the ample. Thee meaurement are in agreement with a maximum hift in δ 44/40 Ca of by 40 K decay, calculated from the highet 40 K/ 40 Ca ratio of the ample et ( ) and the age of the rock (~317 Ma). Hence, the oberved δ 44/40 Ca value can be fully attributed to madependent Ca iotope fractionation. 2

3 Determination of Li iotope compoition and concentration The analytical procedure for Li eparation and purification followed thoe outlined by ref. 34 and 35 and the work wa undertaken at the Intitut für Mineralogie (Univerität Münter). About 12.5 mg of ample powder were diolved in a mixture of concentrated HNO 3 and HF in crew-cap Teflon beaker at 130 C on a hot plate for ~48 hour. After complete decompoition, the ample were evaporated to dryne and equilibrated in 6 N HCl at ~60 C overnight. Two-tage cation-exchange rein chromatography wa employed for Li purification. Lithium concentration and iotope compoition were determined uing a Thermo-Fiher Neptune multi-collector ICPMS at the Univerität Frankfurt following the procedure outlined in ref. 35. Lithium concentration were determined along with the iotope compoition by comparing the ion beam intenitie with thoe for the 1- and 10-ppb L-SVEC Li reference olution. Preciion of thee concentration meaurement wa typically 10% (2σ). A tandardample bracketing routine wa applied to correct for the intrumental ma bia and ignal of unknown ample and bracketing reference olution were matched to vary le than 5% in order to avoid intrumental ma fractionation effect 34. The reult are expreed in per mil a δ 7 Li ( ) = [( 7 Li/ 6 Li) ample /( 7 Li/ 6 Li) L-SVEC 1] The external reproducibility of Li iotope meaurement wa better than ±0.5 (2σ), verified by meaurement of reference rock prepared together with the unknown ample. The reulting δ 7 Li value for baalt BHVO-2 (USGS; 4.48±0.31, 2σ, n=7), BCR-2 (USGS; 2.90±0.29, 2σ, n=3), JB-2 (GSJ; 4.81±0.50, 2σ, n=3), gabbro JGb-1 (GSJ; 4.19±0.28, 2σ, n=3), eclogite OK-1 (-8.49±0.18, 2σ, n=4) and erpentinite UB-N (CRPG; ±0.30, 2σ, n=3) were in excellent agreement with publihed data

4 Fluid-mediated element tranport between vein and wall-rock In itu tudy of dehydration-related fluid flow in ubducting lab i not poible and, due to the dm- to m-ized dimenion of the flow tructure 13,14,39,40 (Fig. 1), thi fluid flow i alo not reolvable by geophyical method. Conequently, we mut rely on ample that have been exhumed long after the ubduction-zone fluid-rock interaction they record. Obtaining time contraint on relatively hort-lived procee that occurred long ago i problematic, a mot radiogenic chronometer provide abolute age contraint with preciion of one percent, with error repreenting time period longer than the duration of the fluid flow event, often lating le than a few thouand of year 3-5,41,42, well below the reolution for conventional geological clock." Geochronometry, baed on diffuion modelling of fat-diffuing element, i the only tool that allow determination of the rate of thee rapid but relatively low-temperature (< 700 C) geological procee 5,22,23,43,44. In fluid flow-related tructure, diffuion occur at two very different patial cale: 1) on the intra-grain cale between different growth zone of ingle crytal (e.g., in apatite or garnet 42 ) reulting from either continuou growth on exiting grain or partial recrytalliation during fluid-mediated diolution-precipitation procee 7,42, and 2) on the cm to outcrop (m) cale between pritine wall-rock and the fluid conduit, in ome cae reulting in the formation of reaction elvage 6,10,12,14,45,46. In thee metaomatic elvage, the eclogitiation reaction along the fluid rock interface i conidered to be rapid compared to the tranport of the component involved in the reaction 7,24. Conequently, for fluid-dominated ytem uch a thee, the element tranport within the reaction elvage i overall a bulk diffuion problem 5,23. A a firt approximation, we conider the tatic cae where the fluid i preent and react with the rock, and we do not addre the tranient veinforming proce, e.g., how the fluid entered and left the ytem. In a fluid-flow ytem aociated with fracture, the tranport controlled by fluid flow i trongly focued into the fracture. Thu, in the unfractured adjacent wall-rock, the tranport of element by fluid flow i inignificant relative to that due to diffuion 10,25,47. However, treating the fluid-rock interaction in a metaomatic reaction elvage a being purely diffuioncontrolled i till a implification. The vein-forming fluid created it pathway due to fluid overpreure 39,47 o that the high fluid preure might have induced an advective Darcy flow component into the wall rock while the reaction elvage formed 10. In the 4

5 following, we will evaluate how ignificantly thi cenario could affect the outcome of a purely diffuion-controlled model. A dominantly advective tranport would have hifted the compoition of the veinforming fluid into that equilibrated with the wall rock, o that if the advection term wa ufficiently trong, the chemical gradient would have had a hape imilar to that of a tep function (Fig. S1). The tronger the fluid preure gradient, the more dominant the advective component over the diffuional tranport would have been, and the more pronounced the tep-function-like pattern of the chemical gradient would have been. Diffuion would moothen the chemical gradient produced by advection and conequently the apparent duration calculated by diffuion modelling would infer too long a duration. Figure S1: Conceptual illutration of the effect of advection and diffuion on concentration profile in a ytem imilar to that of the vein-wall rock examined in thi tudy. Starting from a harp compoitional gradient, the compoition of the rock change with time wherea the vein compoition remain contant, pinned due to it huge capacity for diluting the incoming chemical component (virtually infinite reervoir). An additional advective tranport component into the wall rock caue a more S-like hape and deeper penetration of the reaction front (red curve). Additionally, for an advection-dominated cenario, the fluid velocity and poroity would be the ame for all element. Accordingly, the retardation -how much interaction with the olid caue a delay in the tranport of an element- i baically controlled by the element-pecific K d (Eq. S8, Supplementary Information). Rubidium, Ba and C are all fluid-mobile element with the highet affinity for white mica, thu the effect of changing mineral aemblage on K d i very low. The K d vary from ~7.6 for Rb over ~3.5 for Ba to ~1 for C (Ref. 48). Thi range in value would reult in tranport of C 5

6 farther into the wall rock than Ba, and Ba would be tranported further than Rb, leading to concentration profile imilar to thoe hown in Fig S2b. However, Fig S2a how that thee three element how imilar, overlapping concentration profile. The abence of an advection-dominated pattern reflected in the meaured data indicate either that the fluid-preure gradient exited over only a very mall ditance or duration and did not influence the fluid-mediated chemical tranport ignificantly or that the poroity wa imply too mall to afford ignificant advection. Thu, if advection occurred it had a negligible effect on the overall chemical tranport. Fig. S2: (a) Concentration profile for variou fluid-mobile element. The three white mica-hoted element Rb, Ba, and C have different concentration but identical pattern all deviating from the pattern for Li. If the ma tranport wa advection-dominated, the ditribution of thee element would extend to a greater extent into the wall rock (b), with Li being tranported 76-time and 10-time further into the wall rock than Rb and C, repectively. Note that the concentration profile in (b) are drawn for illutration only and are not properly caled. For the chronometry, we focued on Li becaue, due to it two table iotope ( 6 Li and 7 Li) that can eaily be meaured 23, and the diffuion model can be contrained not only uing concentration profile, but alo uing Li-iotope variation, greatly adding to their robutne. We compare our modelling to the meaured concentration and iotope compoition of the ampling profile perpendicular to the vein, a hown in Fig. 1 (Table S1). The vein aemblage i coare-grained and poor in Li-bearing ilicate 14 and the ample collected from nearet the vein i alo coare-grained with it Li inventory 6

7 dominated by Li-bearing omphacite. Thee two feature reflect nugget effect, and reult in a mimatch between what i ampled and what i needed to repreent the thermodynamic bulk compoition. Furthermore, the two ample were collected along our profile from o near to each other that their 1D-ampling location overlap. Thu, we combine the two ample and the vein-fluid Li compoition i inferred from the olid-fluid equilibrium Li concentration of their average. Thi approach i jutified by the fact that omphacite in both ample (JTS-G and JTS-D ) ha identical Li concentration within error 14. We aumed that the concentration and iotope compoition of the leat altered ample, i.e., the ample collected farthet from the vein, repreent the initial, pre-alteration value for the bluechit wall-rock (dotted black line in Fig. 3 a,b and Fig. S1). Mathematical Model We olve the bulk Li ma balance equation allowing for diffuion in the fluid phae a the only Li ma tranport proce, t ρ φ c + ρ φ c = ρ φ D x ( ) Eq. S1) ( 1 ) f f f f c f x coupled with a kinetic fluid-rock interaction equation for the fluid-olid element tranfer 49 : Eq. S2) c t = K c c d f τ, where c i the concentration in the fluid and c i the concentration in the olid, f K d c = i the ratio of olid/fluid concentration at equilibrium, c f τ i the characteritic time the reaction kinetic require to reach thi equilibrium, φ i the volume fraction of the fluid-filled interconnected pore, in the fluid, and ρf, ρ are denitie of fluid and olid, repectively. ( f c f 1 ) The expreion ρ φ ρ ( φ) D f i the diffuion coefficient + c repreent the total Li tored in the fluid and olid. The only poible way to change it amount (total Li of the ytem) through 7

8 time i by diffuion in the fluid phae with influx outflux (Eq. S1). Advection and diffuive flux through olid grain are neglected, becaue 1) the dominance of advection i incompatible with the oberved lack of evidence for patial eparation in concentration of component having different retardation factor (Fig. S2), and 2) an inefficiency of diffuion via olid grain i a prerequiite for preervation of the meaured patial variation. The effect of kinetic can be treated by auming that the rate for achieving equilibrium i proportional to the deviation from equilibrium (Eq. S2), in contrat with the aumption of intantaneou equilibrium between the olid and fluid. Initial condition conider equal wall-rock concentration along the entire profile and a fluid concentration in equilibrium with the olid. Boundary condition are a far-field fluid ( pinned compoition ) in equilibrium with the wall-rock at one end of the modelled profile, and a vein-forming fluid with a concentration kept at a new and lower value at the other end. Thi i the complete etup for the kinetic model ued for the calculation preented in Fig. S9 and ued to validate the forthcoming implified model. Simplified (local equilibrium) Mathematical Model Auming condition near local equilibrium τ 0 the unknown fluid concentration concentration c f can be eliminated by it equilibrium relationhip with the olid Eq. S3) c f = c K d In addition, auming contant fluid denity along the profile yield: c ρ c φ + φ c = φ D t K ρ x x K Eq. S4) ( 1 ) f d f d 8

9 Moreover, mall poroity approximation (φ <<1) implifie it to: Eq. S5) ρ c c = φ Df t ρf x x Kd Auming contant olid denity and fluid diffuivity along the profile yield our Model 2 and 3: Eq. S6) c φ K D φ R d_ WR = eff t x WR x Kd _ R c where the poroity and K d evolution through pace and time i repreented by plitting φ into φ R (reaction-induced poroity) and φ WR (background poroity of the wall-rock) and K d into K d_r (due to variation in the mineral aemblage) and K d_wr (bulk K of the wallrock). Eq. S7) D eff = D R f i the effective diffuivity and Eq. S8) R ρ ρ = f K d_ WR φ WR i the retardation factor. Auming contant poroity and K d along the profile yield Model 1: Eq. S9) c t c = Deff x 2 2 We utilized the above equation for both Li iotope. Becaue of the large relative ma difference between the two Li iotope, kinetic fractionation can reult from more rapid diffuion of 6 Li, with D (ref. 21,50). We ued a β (6Li/7Li) 7 = (6 /7) β 6Li /7Li D Li 6 Li value of 0.06, a determined for aqueou fluid 21, and performed a enitivity tet for thi election (Fig. S8). 9

10 The non-dimenional verion of the mathematical model The non-dimenional verion of our model reduce the number of parameter to be conidered. The non-dimenional form of Eq. S6 Eq. S10) c% φ K φ c% R d_ WR = t% x% WR x% Kd _ R can be obtained if the non-dimenional variable are choen a Eq. S11) c% c = c _ R _ WR x x% = L Deff t% = t 2 L where L i the length of the meaured profile. The non-dimenional model run were compared with normalied meaured Li concentration [Li] and iotope ratio (δ 7 Li). Minimum mifit (i.e. deviation of meaured data from modelled value) i ued to identify the non-dimenional time, Ω, at which the bet fit of the meaured profile i found. Finally, the correponding dimenional time i Eq. S12) t bet 2 L = Ω D eff Detail of modelling in non-dimenional time A brief outline of the modelling tructure i preented in the method chapter, and here we preent the pecific detail. 10

11 Model 1: Bulk diffuion with contant Kd and poroity along the profile In Model 1, hown in Figure S3, we ued the average olid-fluid partition coefficient for Li, K d_li, and held the poroity contant throughout the entire profile, neglecting the generation of poroity during reaction 7,27,28. From Fig. S3, it become evident that thi imple model cannot fully reproduce the meaured data. It either reproduce the concentration (Fig. S3a) or the iotope (Fig. S3b), a their fit are produced at different time. Thi i illutrated in the ubfigure S3c and S3d, where the deviation of the model from the actual data i hown a a function of Ω and both fit require Ω variation of one order of magnitude. Figure S3: (a) fit of the meaured concentration along the ample profile obtained by Model 1, with the blue line howing the bet fit. (b) fit of the iotope data with the green line howing the bet fit. Subfigure (c) and (d) how the deviation of the modelled fit from the meaured data for variou duration of fluid-rock interaction. From thee figure, it i evident that either the duration i too hort to allow fitting the iotope or too long for any reaonable fit for the concentration. The mimatch between modeled and meaured data i likely due to variation in the ample-pecific mineral aemblage, i.e. the difference between the thermodynamic bulk-ample and what we ampled in the field (due to ample ize veru grain ize 11

12 relationhip). Hence, for each ample, we need to apply a pecific bulk olid-fluid K d to correct for thi. The bulk K d i the um of the mineral pecific K d weighted by their molar ma 30. Accordingly, the change of the bulk K d along the profile i a function of the reaction in progre, the eclogitiation of the bluechit wall-rock. The mot obviou meaure for thi reaction progre, ζ, i the Li exchange of the rock, a it required fluid-mediated diolution-precipitation mineral reaction 7,27,28 that caued the eclogitiation of the wall-rock bluechit within the reaction elvage. Hence, the wallrock bluechit repreent ζ = 0, no reaction, wherea the vein ample i characterized by ζ = 1, fully reacted. Model 2: Bulk diffuion with reaction-induced variation of Kd In Model 2, although the poroity i held contant, we ue the Li concentration of the vein and the extent, Δ Kd, at which the K d along the profile change a a function of the reaction-in-progre a free parameter to earch for the bet fit ( K d _ R = K d _0 (1 ΔK d ζ)). Figure S4 how that thi approach reult in the expected better fit of the Li concentration of the profile (green line in Fig. S4a), with a [Li] vein 5% higher than the calculated average of 6.2 µg/g. It i evident that the iotope data are fitted either for a hort duration (blue line, Fig. S4b) or a long duration (green line, Fig. S4b). Although a reaonably good fit of [Li] i reached for a rather large time range (Fig. S4c), thi etup doe not atifactorily fit the iotope data at any given time (Fig. S4d). 12

13 Figure S4: Demontration of the effect of conidering K d that vary in pace and time a a function of the reaction in progre. A expected, the fit of concentration i better (green line in a), but the iotope are till not atifactorly fitted (b). The blue line (hort duration) better fit with the data for ample farther from the vein, wherea the green line (longer duration) better fit with the data for ample nearer the vein. Although both data et how the bet fit at roughly the ame duration (c v. d), the fit for the iotope data i poor for all duration. Figure S5 how the very good agreement of the K d ditribution ued for our modelling and the ample pecific K d baed purely on the oberved mineral aemblage, their modal abundance and the mineral pecific olid-fluid partition coefficient of ref

14 Figure S5: Comparion of calculated K d and the final K d ditribution produced by the fitting procedure (ee text). The error hown on the calculated K d i 10% relative and conider both error in point counting the mineral aemblage 14 and experimental error in the determination of mineralfluid partitioning 30. Model 3: Bulk diffuion with reaction-induced K d and poroity variation The model 2 fit of [Li] of our profile i acceptable but the fit for the δ 7 Li value i not (Fig. S4). Therefore we in addition conidered increae in poroity during mineral reaction 7,27,28. In Model 3, beide the K d, alo the extent of poroity increae, Δ φ, i regarded to be a imple linear function of the reaction in progre, ζ, accordingly, we apply a reaction-induced poroity, φ R with φ R = φ 0 (1 + Δφ ζ). By imply increaing the ratio between the poroity created by the reaction, and the background poroity, φ 0, we are able to ignificantly improve the quality of fit of the δ 7 Li value (Fig. S6). Figure S7 illutrate, that for a given [Li] vein and a ratio of the K d_vein / K d_wall-rock of ~0.4, the bet fit of the data i for φ R /φ 0 between 7 and 20. In fact, although the [Li] fit i rather robut over thi range, only φ R /φ 0 ~10 reult in an excellent fit for the δ 7 Li value (Fig. 3). In addition, the deviation between the meaured data and the fit i lowet for both δ 7 Li and [Li] at an Ω of about ~0.025 ±0.005 (Fig. S6c,d). 14

15 Figure S6: The effect of reaction-induced poroity. Shown here are the reult for a φ R /φ 0 =10 with the green line illutrating too hort a duration, the blue line too long a duration, wherea the red line indicate the bet fit for both the concentration and the iotope (a, b). The concentration are le enitive to the overall duration (c) than the iotope data (d). The fitting of δ 7 Li require reactioninduced K d variation and poroity increae. The reactive poroity i about 10 time higher than the background poroity (Fig. 3). The fit i only poible for Ω value of about ~0.025 ±0.005 (d). 15

16 Figure S7: Illutration of the deviation of the modeled iotope data from the meaured δ 7 Li value for the mot favourable duration at a given K d_vein / K d_wall-rock of 0.4. The y-axi how the ratio between the average vein compoition (6.2 µg/g Li) and the compoition ued by the model, wherea the x-axi how the φ R /φ 0. The tar indicate the value ued for our final model. Potential effect of the β value on the Model 3 To tet the potential effect of beta on the outcome of our model, we performed a enitivity tet, uing three different β value 0, 0.06 and 0.12, which are repreentative of no kinetic Li iotope fractionation during diffuion and diffuion in aqueou fluid with different propertie 21,23. Figure S8 how that the bet fit of our modelling i not enitive to uncertaintie on the value for β. Any minor fine tuning of the input parameter would reult in the ame duration for fluid-rock interaction a illutrated in Figure S7. Wherea Model 1 i very enitive to change in β, Model 3 i not. Conequently, we cannot ue the data to provide further contraint on the value for β. 16

17 Figure S8: Senitivity tet illutrating the effect of the β value on the model fit for Li iotope. The model i identical to Model 3 (all parameter identical), except for the changing value for β. Input data for converion to dimenional time A input data, we et the ρ f to 1.21 g/cm 3, calculated for 500 C at 2 GPa from the IAPWS-95 equation of tate for pure water 51 and ρ to 3.24 g/cm 3, the average denity of the rock meaured along the profile 14. The poroitie of metamorphic rock are not well contrained but modeled approximation and meaured value do exit, and thee range from ~10-6 to ~10-3 (e.g., ref. 25, 27, 52). The lower value of 10-6 i derived from a numerical olution for flow-inenitive part of high-grade marble 52, it reflect the lowet poroity at which an interconnected poroity may be maintained, and it may alo be pecific to carbonate or related to the low permeability of ~10-22 m 2 applied in the modelling by thee author. Recently, Ingebriten and Manning (ref. 28) evaluated the permeability of the continental crut and found that, although permeability decreae with depth, it remain rather contant at the brittle-ductile tranition and into the ductile realm, at value of about m 2, for non-reacting or deforming rock. Re-evaluating the poroity calculation of ref. 52, uing the more recently publihed contraint on 17

18 permeability, would reult in a poroity of >10-5. Laboratory poroity meaurement on rock by ref. 25 howed that karn and limetone have poroity a low a 10-5, wherea all other high-grade metamorphic rock and unaltered porphyritic granitoid motly have poroity of Thee ilicate rock are imilar in texture and bulk chemitry with the rock invetigated here. Importantly, the vein wall-rock i a bluechit-facie mafic rock that already ha been partially converted to eclogite prior to the vein-forming fluid-rock interaction. Dehydration and denification of thee rock occurred during thi eclogitization 14. During dehydration, mineral-bound water wa continuouly releaed into a dynamically forming poroity, which reulted from the denification of the rock and the incompreibility of the fluid 6. Accordingly, the ynmetamorphic poroity, φ, i et to the laboratory-determined value of , which repreent the tortuoity conidering fluid-filled interconnected poroity in the direction of the flux vector 25. In the geological context of a dehydrating wall rock, thi poroity reflect the lower bound for the background poroity, a the (igneou) rock for which the poroity wa meaured were not affected by poroity-generating dehydration procee or the dehydration proce topped long before the (metamorphic) rock were ampled for poroity meaurement 25 and the poroity wa ubequently decreaed due to econdary procee. The diffuion coefficient for Li in aqueou fluid (D f ) i calculated from the data et of ref. 29. They provide D f value for a large range of T and P (up to 500 C and 0.5 GPa), allowing an extrapolation to the given P-T condition (500 C at 2 GPa), which reult in D f of m 2-1. Duration of fluid-rock interaction All input data combined with outcome of our modelling reult in: Eq. S13) Ω ρ K ( ) L ( 1.78) 2 d_ WR d_ WR total,year = ρ f φwr Df 310 ρ f φwr Df ρ Kd_ WR Kd_ WR φwr Df φwr Df = K 2 18

19 The calculated duration of ~200 year i mot enitive to variation in the bulk K d, D f and background poroity. 1) Uncertaintie produced by the extrapolation of D f can caue a relative variation of 50%, either reducing the calculated time to ~125 year or increaing it to ~370 year. 2) The bulk K d can alo be off by a maximum of 50% relative, reulting in duration of ~90 year or ~280 year, repectively. 3) The larget uncertainty i related to the choice of the value for background poroity. We ued the lowet laboratory-determined value for the diffuion-relevant poroity in comparable rock and mot likely it wa higher, up to an order of magnitude 25, confirmed by the time-averaged fluid-filled interconnected poroity of metamorphoed baaltic rock 27, reducing the calculated duration to ~20 year. However, if the poroity wa lower, e.g. by an order of magnitude, the calculated duration extend to ~1850 year. In the unlikely cae that all three parameter are off their true value by 30% relative, in a way that each change increae (or decreae) the calculated time pan, the reulting etimate for the duration i ~ year. One major outcome of thi model i that increae in reaction-induced tranient poroity i required for fitting with the meaured δ 7 Li value of the ample acro the travere. By applying a background poroity of , a 10-time increaed reactioninduced poroity agree well with value of the time-averaged poroity uggeted for baaltic ill at regional greenchit-facie metamorphic condition 27. The effect of kinetic and rate The diffuion modelling decribed in the previou ection aumed local thermodynamic equilibrium at the mineral-fluid interface, caled up to a bulk-rock equilibrium along the meaured profile, which i the baic concept for a bulk diffuion approach 22,49. More luggih kinetic of mineral reaction could low the proce of fluid-rock equilibration, leading to a longer duration for the invetigated fluid-rock interaction 22,50. We numerically olved the fluid-rock interaction equation Eq. S1 and Eq. S2 for both fluid and olid concentration allowing for kinetic for the fluid-olid element tranfer

20 Variation of τ S allow an evaluation of the influence of the kinetic on the fluid-rock interaction. Figure S9 how a comparion between the olution for bulk diffuion and kinetic, with the red curve repreenting the bulk diffuion olution a ued in Model 3. The coloured curve are derived from the numerical olution of the fluid-rock equation conidering the kinetic (ytem of two equation Eq. S6, S7). Although the iotope data are already fitted for rather low kinetic (Fig. S9b), the condition under which the kinetic model fit the meaured Li concentration are reached when τ S 1 20τ total (blue line, Fig. S9a). The yellow curve, for example, illutrate the attempt to model the Li concentration profile by auming = τ, which repreent a cenario with low 1 τ S 3 kinetic. Slightly fater kinetic are aumed for the green curve ( total = τ ) and it i 1 τ S 6 total evident that conidering lower kinetic than thoe atifying τ (blue and 1 τ S 20 total purple curve) produce a modeled [Li] profile that doe not match the meaured [Li]. One outcome of thi modeling i that we can obtain, in a rather imple way, a contraint on the characteritic reaction time baed on meaured field data. The τ S < 1 20 τ total -relationhip implie that the reaction rate were rapid enough that auming local thermodynamic equilibrium, caled up to bulk fluid-rock equilibrium, and applying the bulk diffuion approach, are appropriate for conideration of the Li chronometry acro thi travere. In fact, for a duration of ~200 year for the overall fluid-rock interaction, the reaction rate would have been high enough that the olid wa in equilibrium with the fluid in 10 year, much fater than expected 53,54. 20

21 Figure S9: Comparion between the outcome of bulk diffuion modeling (red curve) with that conidering kinetic (coloured curve). The coloured curve are derived from the numerical olution of the fluid-rock equation incorporating kinetic and conidering different relationhip between τ S and τ total. Rb/Sr-mixing with age ignificance The mixing between the wall-rock reervoir and the vein-forming fluid reult in an apparent whole-rock iochron caued by Sr enrichment and Rb depletion in the eclogitic elvage and the garnet-omphacite-quartz-carbonate vein. The concentration of Rb and Sr in the vein-forming fluid differed ignificantly from thoe in the wall-rock, o that the reacted rock volume became trongly enriched in Sr wherea Rb concentration in the rock decreaed during fluid-rock interaction (Tab. S1). The initial Sr iotope compoition of the infiltrating fluid, which i preerved in the Rb-poor vein, i identical 21

22 within uncertainty to the initial value of the hot-rock bluechit, calculated uing Lu-Hf garnet age 16. A a conequence, a gradient of decreaing Rb/Sr ratio from the wallrock toward the vein wa etablihed, wherea the 87 Sr/ 86 Sr ratio remained virtually contant, becaue the fluid had, within uncertainty, the ame 87 Sr/ 86 Sr a the bluechit wall-rock at the time of infiltration. Thi i expectable a the initial 87 Sr/ 86 Sr i typical for eawater-altered lithophere 55 and both, fluid ource and wall-rock bluechit repreent eawater altered oceanic lithophere 14. Due to the relative lo of Rb in the rock in the reaction halo, the 87 Sr/ 86 Sr value of the vein and the reaction halo now have le radiogenic value compared to thoe of the hot rock. The reduced production of 87 Sr in the vein and the reaction halo led to the etablihment of the apparent wholerock iochron with an age of 317 ± 5 Ma (Fig. 1; Fig. S10). Figure S10: Origin of the apparent whole-rock Rb/Sr-iochron: Varying degree of Rb depletion and Sr enrichment during the fluid-rock interaction, at about 317 Ma, led to differential increae in 87 Rb/ 87 Sr in rock acro the ampling travere. Calcium iotope In the profile ampled in thi tudy, Ca concentration increae from the wall-rock bluechit toward the garnet-omphacite-quartz-carbonate vein 14 (Fig. 2). Calcium iotope ratio appear to repreent binary mixing between the hot-rock and the quartzcarbonate-vein with uperimpoed deviation related to the carbonate content of the repective ample, howing hift toward lower δ 44/40 Ca value in ample with high carbonate content (Fig. S11a). 22

23 Figure S11: Determination of δ 44/40 Ca in the ilicate fraction of the ample. a: Correlated increae in δ 44/40 Ca and CaO wt. % and a modulated ignal correponding to the carbonate content of the ample. b: Leaching experiment for two ample revealing a uniform fractionation of 0.62 ± 0.02 between the ilicate and carbonate fraction. c: Recontruction of δ 44/40 Ca of the ilicate fraction uing δ 44/40 Ca WR, the fractionation factor between the ilicate and carbonate fraction, and the carbonate content of the rock (ee Eq. S14 to S16). Note that, in thi diagram, the vein i located on the right ide. Thee deviation are related to a uniform Ca iotope fractionation of ~0.62 between the carbonate and the ilicate phae, revealed by leaching experiment (Fig. S11b). The δ 44/40 Ca of the ilicate fraction (δ 44/40 Ca ilicate ) wa calculated uing Equation S14 to S16: 23

24 Eq. S14) δ 44 Ca WR = (1-a) δ 44 Ca ilicate + a δ 44 Ca carb ; a = proportion of Ca bound in the carbonate fraction Eq. S15) δ 44 Ca carb = δ 44 Ca ilicate Eq. S16) δ 44 Ca ilicate =δ 44 Ca WR + a 0.62 The ilicate fraction of the ample collected from thi travere define a binary mixing trend in the δ 44/40 Ca v. Ca concentration diagram (Fig. 2) between the bluechit (typical MORB value 0.7 to 0.9 (ref.20)) and the vein-forming fluid (1.3 to 1.5 ). Calcium iotope fractionation between the ilicate fraction of a rock and a reacting fluid ha not yet been documented, therefore, the increae of the Ca iotope compoition of the ilicate fraction toward the vein appear to reflect the increaing contribution from the fluid. Thi aumption appear to be jutified becaue the correction of the δ 44/40 Ca WR for the carbonate content reveal a trong mixing relationhip independent of the varying proportion of Ca-bearing ilicate mineral in the repective rock. The heavy Ca iotope ignature of the fluid that wa involved could be related either to a primarily iotopically heavy fluid ource or to the depletion of 40 Ca in the fluid by interaction with rock along the flow path. Geological reervoir with relatively high δ 44/40 Ca that could have contributed to the infiltrating fluid are retricted to eawater (Carboniferou eawater: ~1.4 to 1.8 ; ref. 56) or partly altered lab mantle (Fig. S12). Figure S12: a: Calcium iotope compoition veru lo on ignition (LOI) of erpentinied lab mantle rock (Tab. S2). δ 44/40 Ca decreae with increaing degree of erpentiniation (alteration). b: iotopic evolution of fluid Ca with an initial AOC ignature during flow and progreive fluid-rock interaction during Ca-carbonate formation, leading to enrichment of 44 Ca in the fluid. 24

25 Seawater can be excluded a a ignificant component in the metamorphic fluid becaue of it very high 87 Sr/ 86 Sr, (ee main text), leaving altered lab mantle or evolved AOC a the iotopically heavy fluid ource that mot viably produce the oberved Ca and Sr iotopic compoition. However, it i unclear whether dehydration of the low-ca lab-mantle erpentinite could have produced fluid with Ca concentration ufficiently high to produce the metaomatim in the bluechit. In contrat, ufficient amount of Ca could have been provided by dewatering of AOC, for which δ 44/40 Ca value are ignificantly lower than that of the metaomatiing fluid but could have evolved to higher value during Ca-carbonate precipitation a the fluid were tranported over large ditance and channelized into the vein tructure. Thi carbonate precipitation would have preferentially removed light Ca iotope, hifting the δ 44/40 Ca of the fluid to heavier value (Figure S12b) (Ref. 57, 58). Conidering a Ca iotope fractionation of 0.62, roughly % of the diolved Ca would have needed to be precipitated into carbonate to explain the hift in δ 44/40 Ca of 0.7 from the AOC value to that of the reacting fluid. Thu, the fluid, and likewie the ource rock, would have needed to have high-ca concentration 14 in order to reult in the Ca metaomatim oberved in the bluechit (i.e., if 40-70% of the Ca initially in the fluid wa incorporated into carbonate along fluid flow path). 25

26 Table S1: Element concentration and iotope ratio of bluechit, eclogitic reaction halo and quartz-carbonate vein. Whole Rock Carbonate Silicate Sample Rock Ditance Rb* Sr* 87 Rb/ 86 Sr 87 Sr/ 86 Sr Li * δ 7 Li 2SD n Ca* δ 44/40 Ca 2SE n δ 44/40 Ca 2SE n δ 44/40 Ca 2SE n Δ 44/40 Ca (m) µg/g µg/g µg/g % JTS-A b JTS-B b JTS-C b/ec JTS-D b/ec JTS-E b/ec JTS-F b/ec JTS-G ec JTS-D' qz/ca *: Data from (ref.14); b: bluechit, ec: eclogite, qz/ca: quartz-carbonate vein; : Uncertainty (2 S.D.): Table S2: Ca iotope ratio and LOI of altered MORB and variably erpentinized mantle rock Sample Rock LOI δ 44/40 Ca ( SRM915a ) 2 SE ( ) n Reference % SEC 26-9 HP Serpentinite SEC 40-1 HP Serpentinite SEC 34-1 HP Serpentinite SEC 35-2 HP Serpentinite JP-1 Peridotite PCC-1 Peridotite (20) DTS-1 dunite (20) 801 C 43R Altered MORB C 7R3 0-5 Altered MORB C 10R Altered MORB C 1R Altered MORB C 12R Altered MORB C 5R Altered MORB High-preure erpentinite are from the Rapa Complex, Ecuador, belong to the paleo lab and have experienced peak P-T condition of C and GPa (ref.59). Altered MORB ample are from DSDP/ODP ite 801 in the NW Pacific. JP-1, PCC-1 and DTS-1 are international reference material. 26

27 Reference: 31 Teichert B.M.A., Guone N. & Torre M.E. Control on Calcium Iotope Fractionation in Sedimentary Porewater. Earth and Planetary Science Letter 279, (2009). 32 Guone N., Zonneveld K. & Kuhnert H. Minor element and Ca iotope compoition of calcareou dinoflagellate cyt of cultured Thoracophaera heimii. Earth and Planetary Science Letter 289, (2010). 33 Guone N., Nehrke G. & Teichert B.M.A. Calcium iotope fractionation in ikaite and vaterite. Chemical Geology 285, (2011). 34 Magna T., Wiechert U.H. & Halliday A.N. Low-blank iotope ratiomeaurement of mall ample of lithium uingmultiple-collector ICPMS. International Journal of Ma Spectrometry 239, (2004). 35 Magna T., Wiechert U.& Halliday A.N. New contraint on the lithium iotope compoition of the Moon and terretrial planet. Earth and Planetary Science Letter 243, (2006). 36 Seitz H.-M., Brey G.P., Lahaye Y., Durali, S. & Weyer S. Lithium iotopic ignature of peridotite xenolith and iotopic fractionation at high temperature between olivine and pyroxene. Chemical Geology 212, (2004). 37 Košler J., Magna T., Mlčoch B., Mixa P., Nývlt D. & Holub F.V. Combined Sr, Nd, Pb and Li iotope geochemitry of alkaline lava from northern Jame Ro Iland (Antarctic Peninula) and implication for back-arc magma formation. Chemical Geology 258, (2009). 38 Benton L.D, Ryan J.G. & Savov I.P. Lithium abundance and iotope ytematic of forearc erpentinite, Conical Seamount, Mariana forearc: Inight into the mechanic of labmantle exchange during ubduction. Geochemitry, Geophyic, Geoytem 5, article number Q08J12 (2004). 39 John T. & Schenk V. Interrelation between intermediate-depth earthquake and fluid flow within ubducting oceanic plate: contraint from eclogite-facie peudotachylyte. Geology 34, (2006). 40 John T., Klemd R., Gao J. & Garbe-Schönberg C. D. Trace-element mobilization in lab due to non teady-tate fluid rock interaction: contraint from an eclogite-facie tranport vein in bluechit (Tianhan, China). Litho 103, 1 24 (2008). 41 Bon, P.D. The formation of large quartz vein by rapid acent of fluid in mobile hydrofracture. Tectonophyic 336, 1-17 (2001) 42 Ague J.J. & Baxter E.F. Brief Heat Pule During Mountain Building Recorded by Sr Diffuion in Apatite. Earth and Planetary Science Letter 261, (2007). 43 Chakraborty, S. Diffuion in olid ilicate: A tool to track timecale of procee come of age. Annual Review of Earth and Planetary Science 36, (2008). 44 Keller L.M., Abart R., Wirth R., Schmid D.W. & Kunze K. Enhanced ma tranfer through hort-circuit diffuion: Growth of garnet reaction rim at eclogite facie condition. American Mineralogit 91, (2006). 45 Ague J. J. Fluid flow in the deep crut, in Rudnick, R. L. (ed.); Holland H. D. and Turekian K. K., Editor-in-Chief, Treatie on Geochemity 3, The Crut: Amterdam, Elevier, (2003). 27

28 46 Penniton-Dorland S.C. & Ferry J.M. Element mobility and cale of ma tranport in the formation of quartz vein during regional metamorphim of the Wait River Formation, eat-central Vermont: American Mineralogit 93, 7-21 (2008). 47 Connolly J.A.D. & Podladchikov Y.Y. Decompaction weakening and channeling intability in ductile porou media: Implication for athenopheric melt egregation. Journal of Geophyical Reearch 112, B10205 (2007). 48 Zack T., River T., & Foley S. C-Rb-Ba ytematic in phengite and amphibole: an aement of fluid mobility at 2.0 GPa in eclogite from Trecolmen, Central Alp. Contribution to Mineralogy and Petrology 140, (2001). 49 DePaolo D.J. & Getty S.R. Model of iotopic exchange in reactive fluid-rock ytem: Implication for geochronology in metamorphic rock. Geochimica et Comochimica Acta 60, (1996). 50 Richter F.M., Davi A.M., DePaolo D.J., Waton E.B. Iotope fractionation by chemical diffuion between molten baalt and rhyolite. Geochimica et Comochimica Acta 67, (2003). 51 Haar L., Gallagher J.S. & Kell G.S. NBS/NRC Steam Table. Taylor & Franci, London, p. 320 (1984). 52 Bickle M.J. & Baker J. Advective-diffuive tranport of iotopic front: an example from Naxo, Greece. Earth and Planetary Science Letter 97, (1990). 53 Baxter E.F. & DePaolo D.J. Field meaurement of low metamorphic reaction rate at temperature of 500 to 600 C. Science 288, (2000) 54 Baxter E.F. Natural contraint on metamorphic reaction rate, in Vance D., Müller W. & Villa I.M. (ed) Linking the iotopic record with petrology and texture, Geological Society, London, Special Publication 220, (2003). 55 Staudigel H. et al. Large cale iotopic Sr, Nd and O iotopic anatomy of altered oceanic crut: DSDP/ODP ite 417/418. Earth and Planetary Science Letter 130, (1995). 56 Farkaš J. et al. Calcium iotope record of Phanerozoic ocean: Implication for chemical evolution of eawater and it cauative mechanim. Geochimica et Comochimica Acta 71, (2007). 57 Guone N. et al. Calcium iotope fractionation in calcite and aragonite. Geochimica et Comochimica Acta 69, (2005). 58 Teichert B.M.A., Guone, N., Eienhauer, A., Bohrmann, G. Clathrite - Archive of near-eafloor pore fluid evolution (δ 44/40 Ca, δ 13 C, δ 18 O) in eep environment. Geology 33, (2005). 59 John T. et al. Subducted eamount in an eclogite-facie ophiolite equence: the Andean Rapa Complex, SW Ecuador. Contribution to Mineralogy and Petrology 159, (2010). 28

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