Three gravity piston cores (ROV1, ROV2, and ROV4; water depth approximately 1300 to 1400 m) were collected at the Haima seeps from the northwest South China Sea during the Haiyang-6 cruise in 2020 ( Figure 1 ). The presence of gas hydrates is inferred from widely distributed bottom simulating reflectors and gas chimneys (Hui et al., 2016). Gas hydrates, authigenic carbonates, and living chemosynthesis-based communities were recovered from the study area (Liang et al., 2017).

Immediately after recovery, the retrieved cores were brought to the onboard laboratory for pore water extraction. Pore water was collected at 5 to 20 cm intervals using Rhizon samplers with pore size of 0.28 μm. Subsamples for pore water DIC concentration were preserved with saturated HgCl₂ solution. For ions, dissolved elements, and Mg isotope analyses, subsamples were acidified with ultrapure concentrated HNO₃. All pore water subsamples were stored at 4°C. Carbonate nodules ranging in size from about 5 mm to 35 mm were distributed throughout the core ROV1, but were limited to the upper 230 cm in core ROV2. No nodules were observed in core ROV4.

Sulfate ( SO 4 2 − ) concentrations were measured on a Dionex ICS-5000 ion chromatograph with an analytical precision of < 2%. Calcium (Ca²⁺), magnesium (Mg²⁺), and strontium (Sr²⁺) concentrations were determined by ICP-OES. The analytical precision was better than 3%. Concentration and isotope composition of DIC was determined with a Gas-bench continuous flow Delta-V Plus mass spectrometer after acidifying the sample with pure H₃PO₄. About 0.5 ml pore water was treated with 6 drops of pure H₃PO₄ in a glass vial at 25°C. After reacting for 18 h, the produced CO₂ was separated through a gas chromatographic column and was transferred to the mass spectrometer for δ¹³C measurement. The isotopic ratio is expressed relative to the Vienna-Pee Dee Belemnite (V-PDB) standard and the analytical precision was better than ±0.1‰. NaHCO₃ lab-standard samples with concentration ranges from 1 to 30 mM were prepared for the determination of DIC concentration. Calculation of DIC concentration was based on the excellent linear correlation (R²>0.999, N=7) between the intensity of CO₂ gas produced and the DIC concentration of the NaHCO₃ lab-standard samples. The analytical precision of the DIC concentration was <2%. The analyses were conducted at Shanghai Ocean University.

The analytical procedure for Mg isotope analysis was based on Bao et al. (2019). Two columns were used to purify Mg from other matrix metals. Column #1 (loaded with 2 ml of Bio-Rad 200–400 mesh AG50W-X12 resin) was designated to separate Mg from Ca. Column #2 (loaded with 0.5 ml of Bio-Rad 200–400 mesh AG50W-X12 resin) was used to separate Mg from all other matrices (Na, Al, Fe, Ti). To acquire a pure Mg fraction, each sample was passed through column #1 twice, followed by two passages through column #2. The recovery of Mg after the whole procedure of column chemistry was better than 99%, and the total blank for the complete analysis was <10 ng Mg, which is insignificant compared to the mass of the sample. One in-house standard Alfa Mg, one USGS standard (BCR-2), and seawater from the South China Sea were processed with samples for the whole procedure of column chemistry to assess the accuracy of column chemistry. Magnesium isotope ratios were measured with a Thermo Scientific Neptune Plus high-resolution MC-ICPMS at Northwest University, China. Measurements were conducted with the standard-sample bracketing method to correct for the instrumental mass bias and drift. Analyses were performed in low mass resolution mode, simultaneously measuring ²⁶Mg, ²⁵Mg, and ²⁴Mg. The measured Mg isotope ratios are reported in the delta notation as per mil (‰) deviation relative to the DSM3 standard (Young and Galy, 2004): δ^xMg = [(^xMg/²⁴Mg) sample/(^xMg/²⁴Mg) DSM3] × 10³, where x refers to 25 or 26. All samples were analyzed three times within an analytical session. The internal precision determined on the basis of ≥3 repeated runs of the same sample solution during a single analytical session was better than ±0.10‰ (2SD). Analyses of the Alfa Mg, BCR-2, and seawater standards yielded δ²⁶Mg values of –3.92 ± 0.09‰ (2SD), –0.22 ± 0.07‰ (2SD), and –0.86 ± 0.04‰ (2SD), respectively. When the equivalent 2SD uncertainties are considered, the Mg isotopic compositions reported herein are consistent with previously published values (Foster et al., 2010; Huang et al., 2015; Teng, 2017).

Depth profiles of dissolved sulfate, DIC concentrations, and δ¹³C_DIC values are shown in Figure 2 . Sulfate concentrations remain unchanged from 0 to 28 cm depth and linearly decrease to 140 cm for core ROV1, while sulfate concentrations decline from the topmost sediments to 200 cm below the seafloor for core ROV2. At site ROV4, sulfate reveals bottom-water concentration down to 240 cm below the seafloor and then linearly decreases to a depth of 460 cm. The approximate depths of the SMTZ at sites ROV1, ROV2, and ROV4 are 140 cm, 200 cm, and 460 cm below the seafloor, respectively. Concentrations of DIC steadily increase from 4 mM at 20 cm depth to 18 mM at the SMTZ at site ROV1, while rising from 3.3 mM in the topmost sediments to 18 mM at the SMTZ at site ROV2. For core ROV4, concentrations of DIC increase from 3.8 mM at 210 cm to 21 mM at the SMTZ. The δ¹³C_DIC values decrease with depth toward the SMTZ. The lowest δ¹³C_DIC values for the ROV1, ROV2, and ROV4 study sites are –48.3‰, –54.1‰, and –50.6‰, respectively.

Depth profiles of Ca²⁺, Mg²⁺, and Sr²⁺ concentrations are presented in Figure 3 . Calcium concentration drops rapidly from the surface layer to the SMTZ at sites ROV1 and ROV2, while Ca concentration remains constant down to 240 cm below the seafloor before declining toward the SMTZ at the ROV4 site. Magnesium concentrations decline from 52.2 mM to 49.9 mM and from 53.9 mM to 48.2 mM with depth in the measured profiles at the ROV1 and ROV2 sites, respectively. For core ROV4, Mg²⁺ exhibits bottom water concentration down to a depth of 240 cm below the seafloor and before concentration decreases by 7 mM toward the base of the profile. For Sr²⁺ concentrations, only pore water at the ROV1 site shows a significant decline of approximately 70 μM within the upper 150 cm. Strontium concentrations at sites ROV2 and ROV4 decrease only little with depth (< 20 μM).

Depth profiles of δ²⁶Mg values are represented in Figure 3 . The δ²⁶Mg and δ²⁵Mg values are converted to δ²⁶Mg′ and δ²⁵Mg′ values (Young and Galy, 2004), which are then presented in a δ²⁵Mg′ vs. δ²⁶Mg′ plot ( Figure 4 ). All samples and standards analyzed in this study fall on a single mass-dependent fractionation line with a slope of 0.5169. The Mg isotopic composition of pore water from the three sites is close to seawater composition. The Mg isotopic composition of pore water from core ROV1 remains almost constant, ranging from −0.87‰ to −0.82‰. The δ²⁶Mg values of pore water extracted from the ROV2 and ROV4 cores increase with depth from −0.88‰ to −0.71‰, and −0.87‰ to −0.73‰, respectively.

The δ¹³C values of DIC generated from SD-AOM and OSR are close to δ¹³C values of parent methane and organic matter, respectively (cf. Whiticar, 1999). The δ¹³C values of methane in the study area range from −72.3‰ to −71.5‰ (Wei et al., 2020). The δ¹³C value of South China Sea organic matter is approximately −20‰ (Chen et al., 2012). Therefore, the low δ¹³C_DIC values of pore water from the study sites ( Figure 2 ) indicates that SD-AOM is the dominant biogeochemical process. This is confirmed by the observed rapid depletion of sulfate and the shallow depth of the SMTZ. Intense SD-AOM resulted in a DIC concentration, which is known to facilitate carbonate precipitation at methane seeps (Berner, 1980; Aloisi et al., 2000; Naehr et al., 2007). The decrease of Ca²⁺, Mg²⁺, and Sr²⁺ concentrations with depth agrees with carbonate authigenesis in the local sedimentary environment ( Figure 3 ), with the decline of Sr concentration best explained by aragonite formation (Snyder et al., 2007).

Changes of Ca²⁺, Mg²⁺, and Sr²⁺ concentrations in pore water can be used to identify the mineralogy of the carbonate minerals deemed to precipitate under current conditions (e.g. Nöthen and Kasten, 2011). Formation of high-Mg calcite, which has lower Sr/Ca ratios than seawater, results in an increase of the Sr/Ca ratios in pore water. Conversely, aragonite has higher Sr/Ca ratios but lower Mg/Ca ratios than seawater; its removal from pore water will lead to the decrease of Sr/Ca ratios and the increase of Mg/Ca ratios in pore water. Accordingly, the current pore water conditions favor aragonite formation at the ROV1 site, but high-Mg calcite formation at the ROV2 and ROV4 sites ( Figure 5 ).

The Mg concentrations of pore water are typically related to Mg concentration of seawater, carbonate authigenesis, and formation/dissolution of clay minerals (Higgins and Schrag, 2010). Considering that the samples were collected from continental slopes, terrigenous clasts rather than authigenic clay minerals were the main source of silicate minerals in sediment at seeps. The formation of clay minerals was characterized by negative ΔMg/ΔCa (~ −0.95) in pore water profiles and mainly occurs in deeper layers of sediments (Higgins and Schrag, 2010). Likewise, silicate weathering, which may exist at seeps, generally occurs at greater depth (e.g. Torres et al., 2020). Authigenic carbonate precipitation caused by intense SD-AOM tends to occur in the shallow sediments where the decline in Mg is accompanied by a decline in Ca. Since Mg isotope fractionation during formation of clay minerals and carbonate precipitation head in opposite directions (Galy et al., 2002; Higgins and Schrag, 2010), the increase of pore water δ²⁶Mg values with depth helps to eliminate the influence of clay minerals. Therefore, we suggest that the concentration of Mg and change in isotopic composition at a depth of several meters mainly account for the effect of carbonate precipitation rather than the formation of clay minerals. Although carbonate precipitation consumes Ca²⁺ and Mg²⁺ in pore water and preferentially incorporates light Mg isotopes, the δ²⁶Mg value of pore water at the study sites of the South China Sea is still close to that of seawater ( Figure 3 ). The invariance of δ²⁶Mg values observed for core ROV1 can be attributed to the minimal decrease in pore water Mg²⁺ concentration (~2 mM). Because aragonite is the dominant carbonate mineral precipitating in sediment at the ROV1 site and aragonite accommodates very little Mg in its crystal lattice (Snyder et al., 2007), the concentration of Mg²⁺ in pore water does not significantly decline with depth. The shallow depth of the SMTZ at this site also facilitates sufficient replenishment of Mg²⁺ ions by downward diffusion of seawater. Although the precipitation of high-Mg calcite consumes much more Mg²⁺ in pore water, the δ²⁶Mg values of pore water only decreased slightly with depth at the ROV2 and ROV4 sites compared to seawater ( Figure 3 ). Bubble irrigation at the ROV4 seep site apparently promoted the supply of Mg from seawater to an extent similar to the amount of Mg taken up by high-Mg calcite, although the SMTZ at this site is deeper than at the other two sites. We ascribe the small observed variation of pore water δ²⁶Mg values at the ROV seeps to a low rate of carbonate precipitation and sufficient downward replenishment of Mg from seawater. The concentration of Mg²⁺ in seawater is about five times that of Ca²⁺, and the precipitation of carbonate minerals at seeps consumes more Ca²⁺ than Mg²⁺ (Himmler et al., 2013; Zwicker et al., 2018). Therefore, carbonate precipitation typically does not cause large variation of δ²⁶Mg compared to δ⁴⁴Ca values of pore water at seeps (Blättler et al., 2021). At seeps with carbonate authigenesis, the Rayleigh effect in pore water is consequently much weaker for Mg isotopes than for Ca isotopes, and authigenic carbonate derived from SD-AOM can be assumed to form from pore water with a Mg isotopic composition similar to that of seawater. Therefore, the Mg isotopic composition of seep carbonates is probably more affected by fractionation during precipitation than by a variation of pore water Mg isotopic composition caused by a Rayleigh effect. Understanding the behavior of Mg isotopes during carbonate precipitation at seeps may provide the means to use seep carbonate as a proxy of seawater Mg isotope composition and geochemistry in Earth’s history.

Laboratory experiments have been conducted to investigate the fractionation of Mg isotopes between calcite and solution (Δ²⁶Mg_cal-sol) during carbonate precipitation (e.g. Immenhauser et al., 2010; Li et al., 2012; Mavromatis et al., 2013; Chen et al., 2020). Immenhauser et al. (2010) and Mavromatis et al. (2013) reported a correlation between Δ²⁶Mg_cal-sol and precipitation rate of higher Δ²⁶Mg_cal-sol values at higher precipitation rates. This trend is opposite to the rate-dependent Ca isotope fractionation during calcite precipitation (Tang et al., 2008). It was attributed to the incorporation of partially dehydrated Mg²⁺ ions into the calcite crystal lattice at faster precipitation rates, given that the hydration energy of Mg²⁺ is close to 4 orders of magnitude higher than that of Ca²⁺ (Mavromatis et al., 2013). In contrast, no such correlation was observed in precipitation experiments conducted by Li et al. (2012) and Chen et al. (2020), although the precipitation rates in their experiments varied widely. An equilibrium Δ²⁶Mg_cal-sol value of −2.47 ± 0.09‰ at 25°C was reported by Chen et al. (2020). Our study now documents higher carbonate precipitation rates than those at ODP Site 1082 and higher Δ²⁶Mg_cal-sol values, corresponding to a smaller degree of Mg isotope fractionation at the studied seeps. This is consistent with the conclusion drawn from laboratory experiments and travertine calcite precipitation that the extent of Mg isotope fractionation decreases with increasing carbonate growth rate (Immenhauser et al., 2010; Mavromatis et al., 2013; Pogge von Strandmann et al., 2019). However, the carbonate precipitation rates calculated herein, based on pore water geochemistry at seeps, are generally lower than those in laboratory experiments ( Figure 6 ). According to Mavromatis et al. (2013), such low carbonate formation rates should lead to equilibrium fractionation of Mg isotopes. The equilibrium Δ²⁶Mg_cal-sol would be ~ −2.47‰ at 25°C (Chen et al., 2020). However, our modeled results show a smaller fractionation compared to that in calcite equilibrium experiments, indicating kinetically controlled fractionation. This discrepancy may be caused by several factors. Firstly, conversion of the fluxes of Ca and Mg in natural environments to precipitation rates of carbonate per unit reactive surface area requires several assumptions (Blättler et al., 2021). It is currently unrealistic to accurately constrain all the physical and chemical conditions in the natural environment where carbonate formation occurs. Mineralogy, choices of the roughness factor, and the error in the estimation of grain size distribution at seeps may result in large uncertainties in the estimation of carbonate precipitation rates in natural environments (Beckingham et al., 2016). The second factor is the uncertainty in the calculation of the extent of Mg isotope fractionation. Carbonate precipitation was the only process considered in our model outlined above to fit the concentration and isotopic composition of pore water profiles. The real situation is probably more complex due to the precipitation-dissolution equilibrium of carbonate minerals (cf. Karaca et al., 2010) and other processes that influence both concentration and isotopic composition of Mg (e.g. dissolution and desorption of exchangeable Mg from clay minerals; Mavromatis et al., 2014). In our model, the finite consumption of Mg²⁺, leading to a limited variation of the Mg isotopic composition in pore waters, resulted in a relatively large error of the estimated isotope fractionation. The third factor is the difference between the experimental conditions in the laboratory and the conditions in the natural environment. Calcite seeds are usually used in experiments, and experimental conditions are generally controlled by a chemostat, free drift, and constant addition of ions (e.g. Li et al., 2012; Mavromatis et al., 2013; Chen et al., 2020). Other possible factors not considered in experiments such as dissolved sulfide in pore water and microbial activity (e.g. methanogens and sulfate-reducing bacteria) may also influence the behavior of Mg isotopes in nature (Lu et al., 2017; Jin et al., 2021). Hence, it is difficult to reproduce carbonate precipitation in the environment during laboratory experiments. More research is needed to better constrain the physical and chemical conditions in natural environments and the array of factors that may influence the behavior of Mg isotopes during carbonate precipitation.