Dual carbonate clumped isotopes ( Δ 47 - Δ 48 ) constrains kinetic effects and timescales in peridotite-associated springs at the Cedars, Northern California

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Ongoing serpentinization of mantle peridotite bodies by meteoric waters can be identified by highly alkaline water in proximate springs, stable isotope ratios of precipitated carbonate minerals, the formation of travertines, and carbonate veins in the hosting peridotite body (Bruni et al., 2002;Cipolli et al., 2004).
Early research on ultramafic formations undergoing serpentinization led to a conceptual model for this process (Barnes and O'Neil, 1969) (Fig. 1).Meteoric groundwater charged with atmospheric CO 2 reacts with the peridotite body near the surface and forms water that is rich in Mg 2+ and HCO 3 − , termed Type 1 waters (Barnes and O'Neil, 1969).As this water moves underground and encounters the peridotite body, the serpentinization process is catalyzed by CO 2 -charged H 2 O, leading to the precipitation of MgCO 3 and CaCO 3 into veins in the peridotite.A sharp elevation in pH accompanies the mineral precipitation due to the enrichment of the water solution with OH -anions, termed Type 2 water.This Type 2 water also exhibits significant enrichment in Ca 2+ and depletion in DIC.Type 2 water is brought up to the surface where it interacts with Type 1 water, instantly supersaturating the fluids with respect to carbonate and leading to the precipitation of calcite, aragonite, and travertine in surface springs.
A potential tool for probing carbon mineralization in these settings is carbonate clumped isotope geochemistry.The measurement of carbonate clumped isotopes in minerals precipitated from alkaline fluids can potentially constrain the mechanism(s) of kinetic isotope effects (KIEs) and rate of precipitation (Tripati et al., 2015;Watkins and Hunt, 2015;Guo, 2020;Bajnai et al., 2020).Carbonate clumped isotope analysis measures the abundance of CO 2 molecules with multiple heavy isotope substitutions, where the CO 2 is produced from the acid digestion of carbonate minerals.When carbonate minerals form at thermodynamic equilibrium, they have a temperature-dependent preference of heavy isotope aggregation based on relative zero-point energies (Ghosh et al., 2006;Schauble et al., 2006).The abundance of the most common multiply-substituted mass 47 ( 13 C 18 O 16 O) and mass 48 ( 12 C 18 O 18 O) isotopologues are given by Eqs. ( 8) and ( 9), Δ 47 = (R47 sample /R47 stochastic − 1) (8) where Ri is the ratio of the minor isotopologues (m/z 47 or m/z 48) relative to the most abundant isotopologue (m/z 44).Ri stochastic is calculated using the measured abundance of 13 C/ 12 C and 18 O/ 16 O (R 18 ) in the sample and the estimated abundance of 17 O/ 16 O (Eiler, 2007).The latter ratio is estimated from R 18 assuming a mass-dependent Fig. 1.Processes associated with CO 2 absorption and transformation at The Cedars.Surface waters from meteoric sources that are enriched with CO 2 from the atmosphere seep into the ground and interact with ultramafic peridotite, forming "Type 1" waters enriched in Mg 2+ and HCO 3 − .Through a series of serpentinization reactions (reactions (1)-( 3)), various carbonate minerals precipitate and are sequestered in pores and fractures resulting in veins in the peridotite body.Reaction by-products are ejected into pore waters, creating waters which are enriched in Ca 2+ and OH -ions, and depleted in CO 2 ("Type 2" waters), which are then shuttled to the surface.Type 1 and Type 2 waters interact at the surface in the presence of atmospheric CO 2 , resulting in rapid precipitation of CaCO 3 .Terminology from Barnes and O'Neil (1969).
To date, most studies mechanistically exploring KIEs in carbonate minerals using clumped isotopes have focused on isotopic disequilibria in paired Δ 47 and oxygen isotope (δ 18 O) signatures.Diffusion has been hypothesized to produce KIEs in Δ 47 -δ 18 O in atmospheric CO 2 and corals (Eiler and Schauble, 2004;Thiagarajan et al., 2011).KIEs in biotic and abiotic systems associated with (de)hydration and (de)hydroxylation reactions can drive deviations from Δ 47 equilibrium (Ghosh et al., 2006;Guo et al., 2009;Saenger et al., 2012;Falk et al., 2016;Spooner et al., 2016), as can CO 2 degassing, which has been used to explain Δ 47 disequilibrium in speleothems (Hendy, 1971;Affek et al., 2008;McDermott et al., 2011;Guo and Zhou, 2019).Tang et al. (2014) hypothesized that kinetic fractionation observed in inorganic calcite precipitation experiments at pH ≥ 10 occurred due to the DIC pool not having sufficient time to achieve isotopic equilibrium prior to mineral precipitation, and DIC speciation favoring CO 3 2-at higher pH.
Previously, Δ 47 values have been used to study CO 2 absorptiondominant disequilibria processes.Falk et al. (2016) reported data from carbonate minerals in hyperalkaline springs at the Oman ophiolite and attributed disequilibria to the increase in CO 2 absorption in water at elevated pH.This study showed that carbonate minerals from these highly alkaline systems exhibit significant increases in Δ 47 , accompanied by decreases in δ 18 O and δ 13 C.The observed pattern was found to be consistent with CO 2 absorption-driven disequilibrium processes related to the CO 2 hydroxylation reaction being expressed (Falk et al., 2016).
Here, we apply the novel dual carbonate clumped isotope approach, which combines the measurement of Δ 47 and Δ 48 , to carbonate minerals from alkaline springs at The Cedars, located in a coastal mountain range formed of peridotite in Northern California.The high alkalinity, elevated pH of 11.5, and low dissolved [CO 2 ] facilitate the uptake of CO 2 (Lívanský, 1982;Devriendt et al., 2017), which participates in hydration or hydroxylation reactions leading to the formation of HCO 3 -(reactions (10) and ( 11)).These two reactions are the most important in understanding 18 O/ 16 O isotopic equilibration as they provide the only route for the direct exchange of O atoms between H 2 O and DIC (Zeebe and Wolf-Gladrow, 2001).Reactions ( 12)-( 14) show the pathway from HCO 3 -to CO 3 2-and splitting of water molecules, and reactions (15)-( 16) result in carbonate mineral formation.Reactions ( 10)-( 16) contribute to isotopic equilibration of DIC in an aqueous solution.
The amount of time required for clumped and oxygen isotopic equilibrium to be achieved is governed by the temperature-dependent forward and reverse rate constants for the hydration and hydroxylation reactions, as well as DIC speciation (Zeebe and Wolf-Gladrow, 2001).DIC speciation is a function of temperature and pH (Uchikawa and Zeebe, 2012;Tripati et al., 2015).At pH > 10, similar to what is observed in waters in peridotite bodies such as The Cedars, the time to reach equilibration is significantly increased due to DIC speciation being dominated by CO 3 2-, resulting in low concentrations of CO 2 remaining for isotopic exchange reactions ( 10) and ( 11) (Beck et al., 2005;Tripati et al., 2015;Weise and Kluge, 2020).If the DIC pool does not have sufficient time to achieve isotopic equilibrium before precipitation begins, disequilibrium isotopic compositions may be recorded in the mineral during precipitation reactions ( 15) and ( 16).
In this study, our goal is to use multiple isotope systems including dual clumped isotopes (Δ 47 , Δ 48 ) and bulk stable isotopes (δ 18 O, δ 13 C) to mechanistically evaluate disequilibria, examine the origin of KIEs in DIC and carbonate minerals, and study the timescales associated with mineral precipitation.Our measurements are combined with modeling to study DIC and mineral isotopic evolution.Finally, we compare our results to published work from other peridotite bodies and evaluate our approach for its potential use in geological CO 2 sequestration applications.

The Cedars samples
The Cedars is part of the Northern California Coastal Mountain Range and is located at N38 • 37′14.84″/W123• 08′02.13 (Fig. 2).The Cedars is inside of a 700 km long surrounding body of ultramafic rocks called the Coast Range Ophiolite (CRO).The broader Coastal Mountain Range consists of peridotites in contact with part of the Franciscan Subduction Complex (FSC).The FSC consists of primarily greywacketype sandstone, greenstone, radiolarian chert, and minor foraminiferal limestone (Blake et al., 2012).The peridotite body has an approximate surface area of 22.4 km 2 (3.5 km width, 6.4 km length) and extends 1-2 km below the surface (Coleman, 2000).The peridotite body consists primarily of olivine, orthopyroxene, and clinopyroxene in varying proportions as harzburgite (75% olivine and 25% orthopyroxene/clinopyroxene) and dunite (100% olivine) (Coleman, 2000).Interactions between the peridotite body and groundwaters derived from multiple sources has resulted in serpentinization of 5-20% of the ultramafic body, particularly around the perimeter that is in contact with the FSC, where the perimeter is predominantly composed of sheared serpentine (Coleman, 2000;Blake et al., 2012).
Groundwater discharge from the ultramafic body is highly alkaline, enriched in Ca 2+ and OH -, and is brought to the surface through various springs in the area (Coleman, 2004;Sleep et al., 2004) where it mixes with relatively neutral pH surface waters charged with atmospheric CO 2 at an elevation between ~275 and 335 m above sea level (Barnes and O'Neil, 1969;Morrill et al., 2013).
The samples used for this study are comprised of CaCO 3 and were collected from The Cedars by Christensen et al. (2021Christensen et al. ( ), spanning eight visits in 2013Christensen et al. ( , 2014Christensen et al. ( , 2016Christensen et al. ( , and 2018.Four major sites seen in Fig. 2 were sampled: NS1 "Wedding Cake" (samples: A, Q), The Barnes Spring Complex (BSC) (samples: AA, Alpha, C1, P, PA-C2, PB-C2, PE-C2, PE-C3, S, T1, T2, T3a, T3b, T4, T5, U, V, X), Grotto Pool Springs (GPS) (samples: J, K, L), and the "New Pool" (sample: B).The "Wedding Cake" is at the NS1 location above the Mineral Falls.The CaCO 3 samples were collected from several different localities adjacent to the springs seen in Fig. 2: (1) partially consolidated materials from rims of pools; (2) precipitates from the surface of pools, also known as floes; (3) dendritic forms and encrustations from sites of creek-spring mixing; (4) unconsolidated material, also known as snow, from the bottom of the pools; and (5) solid, old travertine deposits, taken as a hand sample representing different layers, collected from the BSC.Any consolidated, or partially consolidated surface materials were skimmed from the surface or captured on screens based on the location they were collected from.Specific sample information, including composition and location of recovery, is listed in Table 1.The terminology used to describe samples in this paper is after Christensen et al. (2021).
Water samples from the high pH springs were taken using a 0.22 µm Millipore filter unit, acidified to a pH of 2 using HNO 3 , and collected in high-density polyethylene (HDPE) bottles (Christensen et al., 2021).The pH of the water was measured on site using a Thermo-Scientific, Orion hand-held pH meter.Temperature measurements were taken of the water source at the time of carbonate sample recovery (Christensen et al., 2021).

Analysis and instrumentation
All clumped isotopic measurements were made in the Eagle-Tripati laboratory using two Nu Instruments Perspective isotope ratio mass spectrometers (IRMS) with methods described in detail in prior publications (Upadhyay et al., 2021;Lucarelli et al., 2023).Here we will refer to the first IRMS as Nu Perspective-1, and the second as Nu Perspective-2a and Nu Perspective-2b, as measurements on the latter instrument used two configurations.Both instruments and all configurations have been shown to produce statistically indistinguishable Δ 47 (Upadhyay et al., 2021;Lucarelli et al., 2023) and Δ 48 values (Lucarelli et al., 2023), with standard values that agree with published values from other laboratories for Δ 47 (Bernasconi et al., 2021) and Δ 48 (Bajnai et al., 2020;Fiebig et al., 2021;Swart et al., 2021).
Briefly, we describe analysis and instrumentation here.For this work, measurements were made between September 2018 and November 2021.The general configuration used for clumped isotope measurements on these two instruments is (1) phosphoric acid digestion of 0.5 mg CaCO 3 , (2) evolved CO 2 gas purification, and (3) isotopic measurements via the mass spectrometer.
The Nu Perspective IRMS is optimized for clumped isotope analysis with secondary electron suppression, which increases the signal-to-noise ratio.Energy filters and quadratic lenses fitted in front of the Faraday collectors for m/z 47, 48, and 49 drives the suppression.The detectors for m/z 44, 45, and 46 are registered through 3 × 10 8 , 3 × 10 10 , and 3 × 10 11 Ω resistors, respectively.The detectors for m/z 47, 48, and 49 are registered with 3 × 10 12 Ω resistors.A dual-inlet system allows for the input of the sample gas and a reference gas controlled by a bellows system that inputs both gasses through a changeover block, so the sample and reference gases can be compared in real-time.The reference gas and sample gas pressures are precisely matched with continuous pressure adjustments to achieve 24 V on mass 44 at the start of every acquisition block, and the pressure varies between 24 and 9 V during an acquisition block.Data were taken in 3 blocks of 20 cycles, for a total of 60 cycles of sample to standard comparison, with an 8 s changeover delay and 20 s of integration per cycle, for a total integration time of 1200 s.
Nu Perspective-1 and Nu Perspective-2a used an in-house built, automated system commonly referred to as the "Autoline," similar to the system from Passey et al. (2010).The autoline consists of (1) a Costech Zero Blank autosampler made of stainless steel that is capable of pulling high vacuum, (2) a common acid bath (CAB) containing 105 wt% phosphoric acid where 1 mg (Nu Perspective-1) or 0.5 mg (Nu Perspective-2a) of CaCO 3 is reacted at 90 • C, (3) cryogenic traps (dry ice and ethanol, and liquid nitrogen) for CO 2 purification through removal of water and other gases with low vapor pressures, and collection of CO 2 , (4) an in-line elemental-silver wool (Sigma-Aldrich) column to remove sulfur compounds from the gas mixture, (5) a gas chromatograph (GC) column (UHP Helium carrier gas, Porapak Type-Q TM 50/80 mesh column packing material) held at − 20 • C during the gas transit to separate CO 2 from the remaining components of the produced gas mixture, and (6) a final cryogenic purification stage before transfer of CO 2 into the bellows of the mass spectrometer.Nu Perspective-2b uses a Nu Carb Sample Digestion System instead of a CAB, where 0.5 mg of CaCO 3 is digested at 70 • C in individual glass vials with 105 wt% phosphoric acid.The sample gas is cryogenically purified in liquid nitrogen-cooled tubes called coldfingers before passing through a relatively short GC column packed with Porapak Type-QTM 50/80 and silver wool.This instrument operates under vacuum pressure and does not use a carrier gas.

Standardization and data processing
Data was processed and corrected using Easotope 64-bit, release version 20201231 (John and Bowen, 2016) with IUPAC parameters (Brand et al., 2010;Daëron et al., 2016).The CO 2 reference gas used to establish real-time comparison to unknown sample compositions was sourced from Oztech and has an isotopic composition as follows: δ 18 O VSMOW = 24.9‰;δ 13 C VPDB = − 3.56‰.The Δ 47 values are reported in the Intercarb-Carbon Dioxide Equilibrium Scale (I-CDES) reference frame, meaning they were normalized to nominal carbonate standard values for ETH-1, ETH-2, and ETH-3 determined in Bernasconi et al. (2021), and additional in-house standards with values also determined in the I-CDES reference frame (Upadhyay et al., 2021;Lucarelli et al., 2023).The Δ 48 values are reported in the Carbon Dioxide Equilibrium Scale (CDES 90) reference frame and normalized to carbonate standards values digested at 90 • C reported in Lucarelli et al. (2023).The standards used in empirical transfer functions (ETFs) for data normalization, using methods detailed in Dennis et al. (2011), include Carmel Chalk, CM Tile (Carrara Marble Tile), ETH-1, ETH-2, ETH-3, ETH-4, and Veinstrom (Upadhyay et al., 2021;Lucarelli et al., 2023).International standards ETH-1 and ETH-2 (Bernasconi et al., 2018(Bernasconi et al., , 2021) ) were used for nonlinearity corrections associated with both Δ 47 versus δ 47 and Δ 48 versus δ 48 raw data.Both the ETFs and nonlinearity corrections are calculated using a moving average of ±10 standard replicates.The clumped isotope measurement errors are reported as ±1 standard error (SE) and ±1 standard deviation (SD), and the carbon and oxygen isotope measurement errors are given as ±1 SD.All data regressions were determined in PRISM Version 9.5.0 for macOS using the function "simple linear regression", where the slope and intercept error are reported as ±1 SE.
The reproducibility of standard Δ 47 and Δ 48 values on each instrument configuration are given in Table S1, and all sample and standard replicate data are reported in Tables S2 and S3, respectively.Figs.S1-S3 show the ETH-1 and ETH-2 values from each correction interval.Fig. S4 shows the standard residual values (measured valueexpected value), and Table S4 reports statistical tests (D'Agostino and Pearson test, performed in PRISM) which indicate standard residuals from each instrument configuration were normally distributed.All supplemental tables and information on clumped isotope data quality assurance can be found in the Data Availability statement.

Modeling of DIC-H 2 O-CO 2 system using IsoDIC
To study the time evolution of the HCO 3 -and CO 3 2-endmembers in a CO 2 absorption-driven pathway that simulated the conditions of springs at The Cedars, we used the IsoDIC modeling software developed by Guo and Zhou (2019) and Guo (2020).This modeling software simulates reactions ( 10)-( 14), predicting kinetic isotope fractionation in oxygen and clumped isotopes in a DIC-H 2 O-CO 2 system from (de)hydration and (de)hydroxylation reactions.The model tracks the isotopologue reactions involving all major isotopes of C and O, for a total of 155 reactions.The forward and reverse rate constants were estimated using Eq. ( 17), where k is the rate constant of the isotopically unsubstituted reactions, and a KIE is the kinetic fractionation factor (KFF) for the isotopically substituted reactions.The product of these variables yields k*, the modified rate constant for the isotopically substituted reactions.(De) hydration and (de)hydroxylation reactions, reactions ( 10) and ( 11), are the only reactions that contribute to isotopic fractionation where reactions ( 12)-( 14) are assumed to be at equilibrium due to their relatively fast reaction rates when compared to reactions ( 10) and ( 11) (Guo and Zhou, 2019;Guo, 2020).
Parameters measured in-situ for surface floe samples (Samples L, P, U, V, PE-C2, PB-C2, and X) from The Cedars were used to simulate conditions associated with The Cedars Springs (Morrill et al., 2013).The following parameters were input into the IsoDIC software to perform modeling in the CO 2 absorption regime: (1) solution temperature = 17.5 • C, (2) solution pH = 11.5, (3) air pCO 2 = 400 ppm, (4) δ 13 C VPDB of air = − 8.431‰, and (5) δ 18 O VPDB of water = − 36.3 ± 0.6‰, taken as the average of measurements from the NS1, GSP1, and BSC locations (Morrill et al., 2013).The system evolution time parameter was set to 1, 10, 50, 100, and 1000 h to simulate different timescales for the evolution of the HCO 3 -and CO 3 2-DIC species.We note that modern samples were collected from locations where surface creek (pH = 8.7) and spring waters (pH = 11.5) are mixing, resulting in a potential drop in pH to an intermediate value (pH = 8.7-11.5)that would reduce equilibration times from the longer values associated with highly alkaline solutions.
The equations used by this model are described in the Supplementary Material S.1.The conversion of carbonate minerals into gaseous CO 2 is associated with a temperature-dependent preferential removal of 16 O relative to 18 O and is corrected by an acid fractionation factor (AFF), denoted by y in Eqs. ( 18) and ( 19) (Guo et al., 2009).
An AFF is applied to measured Δ 47 and Δ 48 values for comparison to modeled Δ 63 and Δ 64 values.The reference frame and temperature to which the value is being converted also dictates the value of y.An AFF of y = 0.196‰ was used in the conversion between Δ 63 and Δ 47 values, and an AFF of y = 0.131‰ was used in the conversion between Δ 64 and Δ 48 values (Lucarelli et al., 2023).

Modeling of the CaCO 3 -DIC-H 2 O system using COAD
To model the KIEs in the clumped and stable isotope data of the carbonate minerals with respect to the conditions at The Cedars, we used the COAD (Carbon, Oxygen, α, Δ) model (Watkins and Devriendt, 2022), which builds upon the ExClump38 model (Chen et al., 2018;Uchikawa et al., 2021) by including the mineral precipitation reactions and growth rates (Watkins and Hunt, 2015).Mineral growth rates are important for two reasons.First, it has been hypothesized the KIEs attending these reactions can lead to differences between the clumped isotope composition of the solid phase relative to DIC (Tripati et al., 2015).Second, the mineral growth rates affect the reversibility of the hydration and hydroxylation reactions such that fast growth rates pull these reactions closer to the kinetic limit (Watkins and Devriendt, 2022).
For comparison between outputs from COAD and IsoDIC, we used the same KFFs and model input parameters for isotopic values, temperature, and pH in our calculations (see the previous section).The COAD model involves a total of 17 differential equations to model reactions (10)-( 16), which track the evolution of the δ 18 O, δ 13 C, Δ 47 , and Δ 48 values of DIC species in solution and the precipitating CaCO 3 (Watkins and Hunt, 2015;Watkins and Devriendt, 2022).The rate constants associated with precipitation reactions (15) and ( 16) are massdependent, and the flux of precipitated CaCO 3 is controlled by the [Ca 2+ ] and [CO 3 2-] ( Watkins and Hunt, 2015).In contrast to the IsoDIC model, this model only describes the most abundant isotopologues for the respective masses, while IsoDIC describes all isotopologues in the DIC-H 2 O system.The COAD model was also used to calculate the steadystate isotopic values as a function of mineral precipitation rate (R p ).A description of the equations and parameters used are reported in the Supplementary Material S.2.The code used is available for download in the Data Availability Statement.

Estimation of CO 2 sequestered at the Cedars
Due to the similarity in rock composition and water pH in the Samail Oman and The Cedars peridotite and associated springs (Kelemen and Matter, 2008;Morrill et al., 2013;Christensen et al., 2021), we estimated the rate and amount of CO 2 that could naturally be sequestered at The Cedars based on an approach used in previous work from Kelemen and Matter (2008) for a peridotite body in Oman.Kelemen and Matter (2008) estimated that in the Omani ophiolite, the travertines and carbonate veins comprised a volume of roughly 5.5 × 10 7 m 3 , or a minimum of ≈10 11 kg of CO 2 .In addition, for the determination of rates of carbonation for the two different types of waters (Fig. 1), they make two key assumptions.First, in Type 1 waters, they assume the complete consumption of DIC to precipitate carbonate minerals as Type 2 waters are formed.Second, they assume that differences in dissolved Ca 2+ between the two types of waters leads to calcite precipitation as Type 2 waters reach the surface.Using this approach, they calculated that carbonate mineralization in the region consumes ~4 × 10 7 kg of atmospheric CO 2 per year, or ≈2 tons/km 3 /year of peridotite.
We estimated the total sequestration potential at The Cedars.For this calculation, we summed the amount of CO 2 that would be consumed if the total amount of Mg, Ca, and Fe in relict olivine was consumed by carbonation.We assumed that The Cedars peridotite is composed of 70% olivine which is 43.82 wt% Mg, 5.34 wt% Fe, and 0.52 wt% Ca (Coleman, 2000;Blake et al., 2012;Morrill et al., 2013), has a volume of 44.8 km 3 (Coleman, 2000), a density of partially serpentinized peridotite of 2800 kg/m 3 (Carnevale, 2013), total mass of 1.25 × 10 14 kg (calculated from the volume and density), and a carbonation rate of 1% (Kelemen and Matter, 2008).Below, we show how this calculation was performed for Mg.
We used the conservative estimate of calcite growth rate in The Cedars springs of 4.8 × 10 7 mol/m 2 /s (Christensen et al., 2021) to estimate the rate of CO 2 sequestered in the springs per year.
For comparison, we report a set of calculations for the CRO from Carnevale (2013) that also utilize the methods of Kelemen and Matter (2008).To estimate the amount of CO 2 sequestered in the CRO per year, we used the CO 2 sequestration potential reported in Carnevale (2013) and the natural carbonation rate for peridotite determined in Kelemen and Matter (2008).
Additionally, Kelemen and Matter (2008) assumed the natural rates of CO 2 uptake could be enhanced by ~10 6 times by drilling and hydraulic fracturing of the rock to increase the reactive surface area, initial heating of the rock to 185 • C using hot fluids, followed by the injection of CO 2 (pressure = 300 bars, temperature = 25 • C, flow rate = 0.040 m/ s).They estimate this would result in a sequestration rate of ~2 × 10 9 tons of CO 2 sequestered per km 3 .This rate was used to estimate the time elapsed before all peridotite would be converted into carbonate minerals from enhanced in situ carbonation at The Cedars, CRO, and Oman ophiolite.The parameters used in all calculations are reported in Table S5.

Table 2
Clumped and bulk isotopic values for all samples measured in this study.The calculations to determine Δδ 18 O, ΔΔ 47 , and ΔΔ 48 values were performed assuming equilibrium values for the average temperature at The Cedars of 17.5 • C (Kim et al., 2007;Dietzel et al., 2009;Morrill et al., 2013;Christensen et al., 2021;Lucarelli et al., 2023).sample can be seen in Fig. 2. A linear regression of the Δ 48 -Δ 47 values from The Cedars yields a slope of − 3.223 ± 0.519.

Clumped and stable isotopes
The δ 18 O and δ 13 C values for The Cedars samples range from − 19.3‰ to − 0.1‰ and − 27.3‰ to − 9.2‰, respectively (Table 2).The Δ 47 of modern and Holocene samples from The Cedars are plotted versus δ 18 O and δ 13 C and compared to samples from alkaline springs in the Oman ophiolite (Falk et al., 2016) (Fig. 4A, C).The measured values from The Cedars and Oman are also compared to calculated equilibrium values.The calculated equilibrium δ 18 O CaCO3 (VPDB) range was determined to be − 8.2‰ to − 6.6‰ for calcite and aragonite (Kim and O'Neil, 1997;Kim et al., 2007;Dietzel et al., 2009), given The Cedars δ 18 O water value of − 36.3 ± 0.6‰ (VPDB), taken as the average of measurements from the NS1, GSP1, and BSC locations (Morrill et al., 2013).The equilibrium Δ 47 value (Lucarelli et al., 2023) for the average water temperature of 17.5 ± 1 • C (Christensen et al., 2021;Morrill et al., 2013) was determined to be 0.616 ± 0.003‰.All samples show departures from equilibrium oxygen isotope values.

Modeled clumped isotope evolution
Measured Δ 47 and Δ 48 values for The Cedars samples were compared to IsoDIC (Guo, 2020)  , and equilibrated inorganic carbon (EIC) using the COAD model (Watkins and Devriendt, 2022) (Fig. 6B-D).Measured δ 18 O and Δ 47 values are largely consistent with model predicted values, however, the Δ 48 values for the ancient travertine samples and snow samples collected from the bottom of the pool (Table 1) were offset from the COAD model predicted values for CaCO 3 by up to 0.1‰ (Fig. 6D).
The average Δ 47 and Δ 48 values and growth rate for samples with relatively large KIEs that were collected at the BSC springs location (samples U, V, X; Fig. 2) were compared to COAD model predictions for the evolution of clumped isotope values for calcite with a varying precipitation rate (Fig. 6E, F).The model accurately predicted the measured Δ 47 value of 0.744 ± 0.010‰ within 1 SE, while the measured Δ 48 value of − 0.407 ± 0.037‰ was offset from the model predicted value of − 0.264‰ by − 0.143‰.

CO 2 sequestration
We estimate the peridotite body at The Cedars could sequester a maximum of ~7.4 × 10 8 tons of CO 2 at a natural rate of ~63 tons/year.It would take ~3.7 × 10 8 years to reach the maximum amount of sequestration (Fig. 7).The Cedars springs could sequester an additional ~370 tons/year.If we utilize estimates of the volume and total sequestration potential of the CRO (Carnevale, 2013), we estimate that ~1.1 × 10 4 tons of CO 2 could be naturally sequestered per year at the CRO, with the maximum CO 2 sequestration potential achieved after ~4.9 × 10 10 years.If the enhanced in situ carbonation rate of ~2 × 10 9 tons CO 2 /km 3 /year described in Kelemen and Matter (2008) were used, all olivine in the CRO could be converted into carbonate minerals in <50 years.

Broad patterns in multi-isotope space: Comparison of sample sets
The similarity in Δ 47 /δ 18 O and Δ 47 /δ 13 C regression slopes for The Cedars data and data from surface springs and veins in the Samail ophiolite of Oman (Falk et al., 2016) (Fig. 4A, C) suggest the same processes are driving disequilibrium in both systems.However, regional, and possible local and temporal, variations in the δ 18 O of waters, and δ 13 C of DIC, also are reflected in these data.For example, the Oman dataset (Falk et al., 2016) may have larger fluctuations in δ 13 C and δ 18 O due to the amount and type of samples analyzed, and greater fluctuations in DIC δ 13 C and meteoric water δ 18 O due to the significantly larger area, 200 km × 50 km, of the Oman site (Christensen et al., 2021).In contrast, the Δ 47 -Δ 48 dual clumped isotope approach allows for mechanistic fingerprinting of the processes associated with disequilibria, and a rough estimation of timescales for equilibration.This represents a major advancement in the clumped isotope field as data from different localities, natural and synthetic, can be directly compared for potential sources of disequilibrium.An additional benefit of clumped isotopes is the method can be used without knowledge of additional parameters such as the isotopic composition of the parent fluid or DIC source.
The majority of Cedars samples exhibit an enrichment in Δ 47 accompanied by a depletion in Δ 48 , with a ΔΔ 48 /ΔΔ 47 slope of − 3.223 ± 0.519.Our observed slope is intermediate between the theoretically calculated slopes for KIEs from CO 2 hydration and hydroxylation reactions during CO 2 absorption (25 • C; pH 9) and in high pH travertine (28 • C; pH 11.5), which have slopes of − 1.72 and − 8.33, respectively (Guo, 2020) (Fig. 5).Thus, the disequilibria at The Cedars and Oman are occurring through a similar pathway that is largely associated with CO 2 hydroxylation.We note a similar trend was also reported by Bajnai et al. (2020) in their dual-clumped investigation of cold-water coral, warmwater coral, and brachiopods, and in a cold-water coral sample reported by Lucarelli et al. (2023).Both studies concluded hydration/ hydroxylation during CO 2 absorption drove kinetic biases in the dual clumped isotope values.

(Dis)equilibrium within the Cedars depends on sample location
Sample location within The Cedars was a major factor influencing whether bulk and clumped isotopic data exhibited departures from equilibria, likely linked to variations in DIC sources (i.e., Type 1 and Type 2 waters) and equilibration time.Modern samples L, P, U, V, PB-C2, and PE-C2 collected from surface pool floes located at the BSC and GPS locations (Fig. 2) exhibited the greatest KIEs (Figs. 3-6).At these   (Kim and O'Neil, 1997;Kim et al., 2007;Dietzel et al., 2009;Lucarelli et al., 2023).Panels A and C include data from carbonate veins precipitated from a peridotite body in Oman (gray cirlces) (Falk et al., 2016) (Falk et al., 2016).A linear regression fit to The Cedars values yields a slope of − 0.009 ± 0.001, and a linear regression fit to The Cedars and Oman values yields a slope of − 0.006 ± 0.001.(D) The Δ 48 versus δ 13 C values for The Cedars.A linear regression yields a slope of 0.038 ± 0.005.The Oman Δ 47 values were published in the CDES 25 reference frame and converted to the CDES 90 reference frame (which is comparable to the I-CDES reference frame used here) using an acid fractionation factor of 0.092‰ (Henkes et al., 2013).Equilibrium values were calculated using the average water temperature at The Cedars of 17.5 • C (Morrill et al., 2013;Christensen et al., 2021).Error bars indicate ± 1 SE for clumped isotope values and ± 1 SD for bulk isotope values.two localities, KIEs could be related to the rapid uptake of CO 2 at the surface, leading to similarly rapid carbonate mineral precipitation at the air and water interface.These results would be consistent with the interpretations of bulk stable isotopic data by Christensen et al. (2021), who investigated the dynamics associated with CaCO 3 precipitation and stable isotope fractionation in surface floes, and argued that at The Cedars, KIEs may be the largest when CaCO 3 precipitates at the surface of the springs.The BSC location had a high saturation state (Ω) value of ~13, while the GPS location had an Ω value of ~5.The [CO 2 ] of the surface layer at the BSC location was calculated to be 1.6 × 10 − 5 mol/ kg-solution, several orders of magnitude higher than the concentration of the bulk pool.The rate of Ca 2+ replenishment from the springs at the BSC was determined to be 1.5 × 10 − 6 mol/s, which is comparable to the DIC flux from the atmosphere.The CO 2 from the atmosphere is converted to HCO 3 -via hydroxylation (reaction (11)), with rapid and near-quantitative conversion to CO 3 2- (Tripati et al., 2015).With this higher influx of CO 2 and precipitation of CaCO 3 , the surface pH is reduced slightly from 11.5 in the bulk pool springs to 11.0 at the surface (Christensen et al., 2021).However, the pH is still high enough to favor CO 3 2-DIC speciation (Uchikawa and Zeebe, 2012;Tripati et al., 2015) preventing isotopic equilibrium through exchange reactions associated with the other DIC species.In addition, because the concentration of DIC is so high at the surface due to the large CO 2 gradient between the water and atmosphere, the supersaturation state of CaCO 3 is also considerably high, further promoting rapid precipitation of CaCO 3 outside of isotopic equilibrium (Christensen et al., 2021).The modern "snow" samples C1, K, PA-C2, PE-C3 and PB-C1 exhibited KIEs that were intermediate between equilibrium and pool  (Guo, 2020).The ΔΔ 47 , ΔΔ 48 , and Δδ 18 O values were calculated by taking the difference between the measured values and the calculated equilibrium values (Kim and O'Neil, 1997;Kim et al., 2007;Lucarelli et al., 2023) for the average water temperature of The Cedars of 17.5 • C (Morrill et al., 2013;Christensen et al., 2021) floe samples (Fig. 3).The term snow is used to describe the physical appearance of fine particulates of CaCO 3 aggregating at the bottom of the pools, however, their texture is similar to surface floe samples (Christensen et al., 2021).The thin-film model (Christensen et al., 2021) for surface dynamics suggests that as the surface floes thicken or are perturbed by falling debris, CaCO 3 aggregates detach and sink deeper into the springs.The floes would carry some surface waters with the particles (Christensen et al., 2021), and thus could mix in a pool of DIC that is not in isotopic equilibrium, driving KIEs in the clumped and bulk isotope signatures.Even though these detached layers, composed of a mixture of particle aggregates and solution, have moved away from the surface where the majority of rapid precipitation is occurring, isotopic equilibration of DIC within the detached layer is still hindered by the high pH of 11.5 (Beck et al., 2005), which favors hydroxylation and CO 3 2as the most abundant DIC species (Tripati et al., 2015).Given water temperatures, DIC in this fragmented layer can retain its kinetic signature for tens of days at a pH of 11.5 (Usdowski et al., 1991;Beck et al., 2005) which can contribute to the KIEs in dual clumped and bulk isotopes.DIC mixing can also drive deviations from equilibrium in Δ 47 values (Defliese and Lohmann, 2015).
Modern samples A, AA, B, and J fell within 1 SE of clumped isotope equilibrium (Fig. 3).They were collected where fresh creek water mixed with spring water at the New Pool and BSC localities, where the pH and the influx of Ca 2+ are reduced, leading to potentially more favorable conditions for isotopic equilibration in the DIC-H 2 O-CO 2 system.These samples reflect the composition of isotopically equilibrated DIC from the creek or surface water (pH 7.8-8.7)that occasionally mixes with the high-pH springs (Christensen et al., 2021).The Δ 47 -reconstructed temperature for the near equilibrium samples is 13.9 ± 3.8 • C and 14.2 ± 3.5 • C, using calibrations from Lucarelli et al. (2023) and Anderson et al. (2021), respectively.These reconstructed temperatures are within error (1 SD) of the average yearly temperature at The Cedars of 17.5 ± 1 • C (Morrill et al., 2013;Christensen et al., 2021).
Ancient travertine samples collected from rim formations at the NS1 locality (Alpha, T1, T2, T3a, T3b, T4, and T5) display a range of disequilibrium values .This range could be due to postdepositional events such as recrystallization in the presence of surface and groundwater mixing, which could have shifted disequilibrium isotopic values towards equilibrium in samples T1, T4, and T5.This would be analogous to what Falk et al. (2016) hypothesized occurred in Oman, where the absence of aragonite in travertine samples may have indicated post-depositional events had taken place, thereby influencing isotopic values.

Overall conditions at the Cedars result in isotopic disequilibrium
Several factors control the expression of KIEs in carbonate minerals from The Cedars.These include the hydroxylation favored pathway, DIC speciation, increased rate of CO 2 uptake into the system, and mineral precipitation prior to isotopic equilibria.Because Type 1 and 2 waters are readily mixing at the surface, a hyperalkaline environment (pH > 11) is created due to excess OH -anions present in Type 2 fluids.At a pH > 10, the hydroxylation pathway represents > 95% of reactions transforming CO 2 to HCO 3  -(McConnaughey, 1989).This high pH also creates an environment that facilitates rapid uptake of CO 2 into the aqueous media (Lerman and Stumm, 1989) due to the concentration gradient created by the DIC speciation preference of CO 3 2-at pH > 10 ( Hill et al., 2014;Tripati et al., 2015).This condition, coupled with the rapid precipitation of CaCO 3 due to the high saturation state (Christensen et al., 2021), creates an even stronger gradient, further increasing the uptake of CO 2 from the atmosphere.The forward reaction rate associated with CO 2 hydroxylation is >1000 times the reverse reaction (Christensen et al., 2021), creating a pathway that is approximately unidirectional.We hypothesize this is preventing backwards conversion which is essential for O isotope exchange that would facilitate δ 18 O, Δ 47 , and Δ 48 equilibrium.The high pH results in a much greater equilibration time (>40 days) being required for the DIC pool to achieve clumped and oxygen isotopic equilibria prior to mineral precipitation (Beck et al., 2005;Tripati et al., 2015;Guo, 2020;Uchikawa et al., 2021).As the system moves into the deeper parts of the spring pool (below 100 µm), there are additional fluxes including advection and diffusion of Type 2 waters, CaCO 3 precipitation, and EIC contribution from the surface.

Examination of kinetic isotope effects using modeling
IsoDIC (Guo, 2020) modeling of disequilibria in the DIC pool used input parameters taken from the surface floe conditions of The Cedars and accurately predicted the measured range of Δ 47 and Δ 48 values (Fig. 6A).The model was used to predict the evolution of disequilibria associated with HCO 3 -and CO 3 2-with respect to residence time in the system.The model indicated a rapid departure away from equilibria The estimated maximum CO 2 sequestration potential was calculated to be ~7.4 × 10 8 tons for The Cedars (green dotted line), ~9.7 × 10 10 tons for the CRO (Carnevale, 2013; blue dashed line), and ~7.7 × 10 13 tons for the Oman ophiolite (Kelemen and Matter, 2008; orange dash-dot line).The rate of mineral formation in The Cedars springs was measured by Christensen et al. (2021) and constrained here with our dual clumped isotope measurements and modeled carbonate mineralization rates.In addition, the CO 2 sequestered from enhanced in situ sequestration is shown for The Cedars (black triangles), CRO (dark gray circles), and the Oman ophiolite (light gray squares), following methods from Kelemen and Matter (2008) for enhanced geologic CO 2 sequestration in the Oman ophiolite of ~2 × 10 9 tons CO 2 /km 3 /year.For natural carbonation, we estimate that the sequestration potentials at The Cedars, CRO, and Oman ophiolite would be reached after ~3.7 × 10 8 years, ~4.9 × 10 10 years, and ~3.9 × 10 13 years, respectively.For enhanced in situ carbonation, the maximum sequestration potential at The Cedars, CRO, and Oman Ophiolite could be reached in ~0.37, ~49, and ~39,000 years, respectively.All calculated rates assume complete consumption of Mg, Ca, and Fe in the respective formations (Kelemen and Matter, 2008;Matter and Kelemen, 2009;Carnevale, 2013), and consider the ophiolite in Oman and the CRO to be ~30% relict olivine (Kelemen and Matter, 2008;Carnevale, 2013).The peridotite in The Cedars is ~70% relict olivine (Coleman, 2000;Blake et al., 2012;Morrill et al., 2013).
with maximum disequilibria achieved at ~1 h of DIC residence time.This initial departure rebounds back to equilibrium as the system has more time equilibrate, where equilibrium is eventually achieved after ~1000 h.Due to the low [CO 2 ] from DIC speciation favoring CO 3 2-at high pH (Beck et al., 2005;Tripati et al., 2015), the migration back to equilibria at these conditions is very slow.The IsoDIC (Guo, 2020) model can be used to predict the approximate timeframe associated with precipitation at the surface, which we hypothesize to be ≤1 h from when CO 2 is introduced into the surface spring system (Fig. 6A).A caveat is that this model only considers the KIEs associated with the DIC pool and does not factor those associated with mineral precipitation.Since the IsoDIC model did not consider KIEs associated with mineral precipitation, isotopic evolution was also predicted with the COAD model, which does predict KIEs from precipitation, using the same input parameters as for the IsoDIC model.This model predicted a similar trend for Δ 47 and Δ 48 (Fig. 6B) when compared to the IsoDIC model, in terms of migration from equilibrium to disequilibrium.However, while the two models yield initial values for CO 3 2-and HCO 3 -that are very similar, these values deviate up to 0.1 ‰ from the KIEs associated with mineral precipitation.Additionally, the measured Δ 47 values and COAD predictions are in good agreement (Fig. 6C), while some measured Δ 48 values for travertine samples and snow samples collected from the bottom of the pool (Table 1) deviate from model predicted Δ 48 values by up to 0.1‰ (Fig. 6D).The ancient travertine samples (T1, T2, T3a, T3b, T4, T5) contained multiple layers, and therefore mixing may impact clumped isotopes (Eiler and Schauble, 2004;Defliese and Lohmann, 2015), and there is no current knowledge of possible differences in travertine versus typical calcite Δ 48 values.Mixing may also bias clumped isotope values in the snow samples, which may experience temporal variations in DIC isotopic composition.Further, some of the snow samples have mixed minerology (aragonite, calcite, brucite), such as samples PB-C1, PE-C2, and PE-C2 (Table 1).The brucite [Mg(OH) 2 ] composition ranges from 4% to 7%, which has unknown effects on acid digestion and potentially the clumped isotope values.COAD modeling enables us to determine and predict the rates of mineral precipitation associated with the respective system, which is constrained by measured dual clumped isotope values.The COAD model was also used to predict the dependence of Δ 47 and Δ 48 values from The Cedars samples on the precipitation rate (Fig. 6E-F).The model accurately predicted the average Δ 47 value at the BSC springs, given the measured precipitation rate (Christensen et al., 2021).Comparison of dual clumped data to model results supports a natural precipitation rate of ~4.8 × 10 − 7 mol/m 2 /s (Fig. 6E).However, the model underpredicted the average Δ 48 value (Fig. 6F).This may be due to greater measurement uncertainty for Δ 48 , which is an order of magnitude greater than for Δ 47 (1 SE for Δ 47 ≈ 0.001 ‰; 1 SE for Δ 48 ≈ 0.01 ‰), and no previous experimental constraints on how Δ 48 values vary from increased precipitation rates.
We find the two models provide a slightly different set of tools.The IsoDIC model focuses on the time evolution of the isotopic composition of DIC species from an initially perturbed or disequilibrium state.In this framework, the steady state of the system is equivalent to the equilibrium state.By contrast, the COAD box model involves fluxes of CO 2 and CaCO 3 such that the isotopic composition of DIC species is continually perturbed.In this framework, the steady state of the system is not equivalent to the equilibrium state unless the CO 2 flux is extremely small compared to the size of the DIC pool.Using the COAD model, accurately measured Δ 47 and Δ 48 values can be compared to model predicted values as a function of the CO 2 influx and CaCO 3 outflux (i.e., mineral precipitation rate).
Field measurements and modeling may be useful for application to other peridotite bodies to help determine the natural mineral precipitation rates and DIC residence time.Our work here shows this approach is useful for predicting the natural rates of CO 2 uptake.If the rate of CO 2 uptake was enhanced using a feed of high-pressure CO 2 and hydraulic fracturing, dual clumped isotope measurements could be interpreted within a modeling framework to evaluate the enhanced rates of DIC equilibration and mineral formation.
Previous work by Kelemen and Matter (2008) proposed a method for enhanced in situ carbonation of peridotite for the Samail Ophiolite in Oman.This method increases the natural carbonation reaction (reaction (10)) rate by up to 10 6 times by drilling and hydraulic fracturing of the rock to increase the reactive surface area, initial heating of the rock to 185 • C using hot fluids, followed by the injection of CO 2 (pressure = 300 bars, temperature = 25 • C, flow rate = 0.040 m/s) (Kelemen and Matter, 2008).After the initial heating, the exothermic carbonation reaction maintains the system temperature at 185 • C (Kelemen and Matter, 2008).As the reactive surface becomes depleted, the rock may require additional fracturing, although some cracking may occur from the temperature changes and increases in solid volume from mineral hydration and carbonation (Kelemen and Matter, 2008).If we assume the fully catalyzed reaction rate of ~2 × 10 9 tons CO 2 /km 3 /year, it would take <50 years and <40,000 years, respectively, for all Mg, Ca, and Fe in the CRO and Oman peridotite to be converted into carbonate minerals (Fig. 7).This would consume billions of tons of CO 2 per year.
Yet there are major potential environmental justice issues that are problematic.A hurdle to employing mineral carbonation technology in peridotite formations is that ~1 million drill holes (Kelemen et al., 2011) may be required to offset 34.9 × 10 9 tons (Liu et al., 2022) of anthropogenic CO 2 emissions per year.Further, these operations could result in deforestation (Drohan and Brittingham, 2012), loss of wildlife habitats (Kiviat, 2013), and contaminated wells (Holzman, 2011), as has been observed with fracking.The latter could potentially strain water resources, and have negative impacts on human and environmental health.While it is notable that the in-situ CO 2 sequestration potential in peridotite bodies is high when compared to other potential technologies, the potential short and long-term consequences need to be considered.High-temperature mineral carbonation reactors, which would use mineral feedstock from mines and direct CO 2 injection, could rapidly convert serpentine and olivine to magnesite and quartz, resulting in ~8.8 × 10 5 to ~8.8 × 10 6 tons of CO 2 sequestered per year (Power et al., 2013).The injection of CO 2 into ponds containing serpentinite mine tailings could sequester up to ~1 × 10 6 tons of CO 2 per year (Power et al., 2013).This may be enhanced if the ponds utilize photoautotrophic microbes, such as algae and cyanobacteria, which use CO 2 as an energy source (Power et al., 2011).Yet associated land use and biosphere changes could negatively impact emissions reduction, and the adverse effects on water and environmental health may counter potential benefits.It is likely that multiple strategies will need to be used in parallel to reach global carbon dioxide reduction goals, which are 10 Gt/yr by 2050 and 20 Gt/yr by 2100 (UNEP, 2019), and the breadth of consequences of each approach should be carefully assessed before moving forward with implementation.

Conclusions
We analyzed carbonate mineral samples collected from springs at The Cedars, a peridotite body in Northern California, for dual clumped and bulk stable isotopes.We combined measured Δ 47 , Δ 48 , δ 18 O, and δ 13 C and model calculations to study kinetic isotope effects associated with CO 2 absorption, high pH, and precipitation rate.Our work suggests kinetic biases in dual clumped and bulk isotope values arise due to carbonate mineral precipitation from highly alkaline waters through a CO 2 absorption-driven pathway.Our analysis indicates that the largest KIEs are from samples recovered from surface floes.In surface floes, there is sufficient contact between the spring waters and the atmosphere where CO 2 absorption and rapid precipitation conditions are favored.Modern samples with isotopic values within error of equilibrium occur in locations where there is significant mixing of surface and spring waters.Other samples with kinetically biased isotopic values include "snow" samples recovered from the bottom of springs and ancient travertine samples.We report slopes (Δ 48 /Δ 47 , Δ 47 /δ 18 O, Δ 48 /δ 18 O, Δ 47 /δ 13 C, Δ 48 /δ 13 C) for CO 2 (de)hydration and (de)hydroxylation disequilibria processes from The Cedars samples.The slopes are consistent with Δ 47 /δ 18 O and Δ 47 /δ 13 C slopes from a peridotite body in Oman, as well as modeling predictions for KIEs from CO 2 (de)hydration and (de) hydroxylation.
This work sets up the potential use of the Δ 47 -Δ 48 dual clumped isotope method, combined with modeling, to examine sites of interest for geological CO 2 sequestration, including in the Coast Ranges and other peridotite bodies.This relatively non-invasive method can be used to determine the natural rate of CO 2 uptake, mineral precipitation rate, and for determining evolution time and (dis)equilibria in DIC.We recommend expansion of dual clumped isotope research into carbonate minerals precipitating from peridotite veins to compare surface and subsurface processes, and better understand the feasibility of sites for CO 2 sequestration, alongside assessment of the potential adverse environmental and human health impacts of implementation in different locations.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 3 .
Fig.3.The Δ 47 and Δ 48 values for modern (green symbols) and Holocene (orange symbols) carbonate mineral samples from The Cedars.Results are compared to equilibrium values (gray line)(Lucarelli et al., 2023), with the average water temperature at The Cedars of 17.5 ± 1 • C(Morrill et al., 2013;Christensen et al., 2021) indicated (X symbol).The samples that exhibit the largest KIEs were primarily recovered from surface floes (pool floe, downward triangles).The samples that are within error (±1 SE) of equilibrium are from areas where surface and spring waters mix (squares), 1 wedding cake sample (triangle), and 1 sample from the GPS location from an unspecified formation (circle).A linear regression through all samples indicates a slope of − 3.223 ± 0.519.Error bars indicate ± 1 SE.
model predictions for the time-dependent isotopic evolution of HCO 3 -and CO 3 2-(Fig.6A).The measured values are consistent with the range of Δ 47 and Δ 48 values predicted by the model for Z.A. Parvez et al.

Fig. 4 .
Fig.4.Clumped isotope (Δ 47 , Δ 48 ) versus bulk isotope (δ 18 O, δ 13 C) results of modern (green symbols) and Holocene (orange symbols) surface spring carbonate samples from The Cedars.Results are compared to calculated equilibrium values (striped rectangle)(Kim and O'Neil, 1997;Kim et al., 2007;Dietzel et al., 2009;Lucarelli et al., 2023).Panels A and C include data from carbonate veins precipitated from a peridotite body in Oman (gray cirlces)(Falk et al., 2016).(A) Δ 47 versus δ 18 O values for The Cedars and Oman.A linear regression fit to The Cedars values yields a slope of − 0.009 ± 0.001, and a linear regression for the Cedars and Oman values yields a slope of − 0.007 ± 0.001.(B) Δ 48 versus δ 18 O values for The Cedars.A linear regression fit to The Cedars values yields a slope of 0.041 ± 0.003.(C) Δ 47 versus δ 13 C values for The Cedars and Oman(Falk et al., 2016).A linear regression fit to The Cedars values yields a slope of − 0.009 ± 0.001, and a linear regression fit to The Cedars and Oman values yields a slope of − 0.006 ± 0.001.(D) The Δ 48 versus δ 13 C values for The Cedars.A linear regression yields a slope of 0.038 ± 0.005.The Oman Δ 47 values were published in the CDES 25 reference frame and converted to the CDES 90 reference frame (which is comparable to the I-CDES reference frame used here) using an acid fractionation factor of 0.092‰(Henkes et al., 2013).Equilibrium values were calculated using the average water temperature at The Cedars of 17.5 • C(Morrill et al., 2013;Christensen et al., 2021).Error bars indicate ± 1 SE for clumped isotope values and ± 1 SD for bulk isotope values.
Fig.4.Clumped isotope (Δ 47 , Δ 48 ) versus bulk isotope (δ 18 O, δ 13 C) results of modern (green symbols) and Holocene (orange symbols) surface spring carbonate samples from The Cedars.Results are compared to calculated equilibrium values (striped rectangle)(Kim and O'Neil, 1997;Kim et al., 2007;Dietzel et al., 2009;Lucarelli et al., 2023).Panels A and C include data from carbonate veins precipitated from a peridotite body in Oman (gray cirlces)(Falk et al., 2016).(A) Δ 47 versus δ 18 O values for The Cedars and Oman.A linear regression fit to The Cedars values yields a slope of − 0.009 ± 0.001, and a linear regression for the Cedars and Oman values yields a slope of − 0.007 ± 0.001.(B) Δ 48 versus δ 18 O values for The Cedars.A linear regression fit to The Cedars values yields a slope of 0.041 ± 0.003.(C) Δ 47 versus δ 13 C values for The Cedars and Oman(Falk et al., 2016).A linear regression fit to The Cedars values yields a slope of − 0.009 ± 0.001, and a linear regression fit to The Cedars and Oman values yields a slope of − 0.006 ± 0.001.(D) The Δ 48 versus δ 13 C values for The Cedars.A linear regression yields a slope of 0.038 ± 0.005.The Oman Δ 47 values were published in the CDES 25 reference frame and converted to the CDES 90 reference frame (which is comparable to the I-CDES reference frame used here) using an acid fractionation factor of 0.092‰(Henkes et al., 2013).Equilibrium values were calculated using the average water temperature at The Cedars of 17.5 • C(Morrill et al., 2013;Christensen et al., 2021).Error bars indicate ± 1 SE for clumped isotope values and ± 1 SD for bulk isotope values.

Fig. 7 .
Fig.7.Calculations of natural rates of CO 2 sequestration in The Cedars peridotite (green triangles), spring water at the site (green diamonds), the Coastal Range Ophiolite (CRO; blue circles), and the Oman ophiolite (orange squares).The estimated maximum CO 2 sequestration potential was calculated to be ~7.4 × 10 8 tons for The Cedars (green dotted line), ~9.7 × 10 10 tons for the CRO(Carnevale, 2013; blue dashed line), and ~7.7 × 10 13 tons for the Oman ophiolite(Kelemen and Matter, 2008; orange dash-dot line).The rate of mineral formation in The Cedars springs was measured byChristensen et al. (2021) and constrained here with our dual clumped isotope measurements and modeled carbonate mineralization rates.In addition, the CO 2 sequestered from enhanced in situ sequestration is shown for The Cedars (black triangles), CRO (dark gray circles), and the Oman ophiolite (light gray squares), following methods fromKelemen and Matter (2008) for enhanced geologic CO 2 sequestration in the Oman ophiolite of ~2 × 10 9 tons CO 2 /km 3 /year.For natural carbonation, we estimate that the sequestration potentials at The Cedars, CRO, and Oman ophiolite would be reached after ~3.7 × 10 8 years, ~4.9 × 10 10 years, and ~3.9 × 10 13 years, respectively.For enhanced in situ carbonation, the maximum sequestration potential at The Cedars, CRO, and Oman Ophiolite could be reached in ~0.37, ~49, and ~39,000 years, respectively.All calculated rates assume complete consumption of Mg, Ca, and Fe in the respective formations(Kelemen and Matter, 2008;Matter and Kelemen, 2009;Carnevale, 2013), and consider the ophiolite in Oman and the CRO to be ~30% relict olivine(Kelemen and Matter, 2008;Carnevale, 2013).The peridotite in The Cedars is ~70% relict olivine(Coleman, 2000;Blake et al., 2012;Morrill et al., 2013).