The natural, fresh and pure olivine with a gem-grade single crystal grain was collected from Damaping village, Wanquan County, Zhangjiakou City, Hebei Province, China. The chemical compositions of the olivine were tested using an electron probe microanalyzer (EPMA) at the State Key Laboratory of Ore Deposit Geochemistry, Chinese Academy of Science (CAS), Guiyang, China. The molar Fe/(Fe + Mg) ratio was 9.3%, which is very similar to that for San Carlos olivine (10%) (Supplementary Table S1). As described in supplementary material in detail, the samples of hydrous olivine aggregates, Ol–H₂O and Ol–NaCl/KCl/CaCl₂–H₂O systems were precisely prepared. For the saline fluid-bearing olivine aggregates, the salinity and fluid fraction ranges were 0–21 wt% and 5.1–20.7 vol%, respectively. The detailed salinity and fluid fraction values of the saline fluid-bearing olivine aggregates are listed in Table 1. High-temperature-resistant quartz glass sleeves (SiO₂ content: ∼100 wt%) with a 3-mm inner diameter, 6-mm outer diameter and 4-mm height were employed as the sample capsules. Although the reaction of quartz and olivine can take place at high temperatures and pressures and produce a very thin pyroxene-bearing layer, the contribution to the bulk conductivity could be negligible because the conductivity of pyroxene is much lower than that of interconnected fluid phases (Huang et al., 2021). Two Au stoppers were applied to seal the top and bottom of the sample capsule using a small amount of silver colloid.

Sample assembly for the in-situ measurement of electrical conductivity was displayed in Supplementary Figure S1. The high-temperature and high-pressure conditions were provided using a YJ–3000t cubic multi-anvil apparatus at the Key Laboratory of High-Temperature and High-Pressure Study of the Earth’s Interior, Institute of Geochemistry, CAS, Guiyang, China. The target pressure was achieved using a slow compression rate of 0.5 GPa/h to avoid damaging the quartz sleeve. Once reaching the target pressure, the temperature was rapidly increased to 1073 K. Our measurement results have shown that the resistance of saline fluid-bearing polycrystalline olivine dramatically increases with time to values greater than 1 MΩ at 1073 K when the quartz sleeve sample capsule is damaged. However, the quartz sleeves remained undamaged in the successful runs and the low resistance values of the saline fluid-bearing systems only slightly increased with time. This is because saline fluids might weakly diffuse to the exterior of the sample capsule when the aqueous fluids and olivine grains have approximately equilibrated. At a given pressure, the impedance spectra were firstly collected continuously at the highest temperature of 1073 K, and the spectra gradually reached stable after ∼30 min. It reflected that the saline fluids gradually diffused along olivine grain boundaries, and finally it reached a uniform distribution of fluid in the sample. Meanwhile, a very small amount of olivine is dissolved into the saline fluids with time. At a fixed temperature, pressure and volume fraction, the electrical conductivities of olivine–NaCl–H₂O systems slightly decreased due to the loss of saline fluids. In order to avoid the inevitable influence of the loss of saline fluids, at the highest measurement point of 1073 K, the olivine–NaCl–H₂O system was kept a relatively longer time in order to reach an equilibrium state by continuously checking the variation of impedance spectroscopy of sample. After that, a decreasing temperature cycle from 1073 to 773 K was chosen to quickly measure the electrical conductivity of sample at the temperature interval of 50 K. Due to the small solubility of olivine in the saline fluids, the change of the geometry of the olivine grain boundaries was feeble (Macris et al., 2003). We proposed that the distribution of saline fluids was dominated by the salinities and volume fractions of fluids, and the grain sizes and geometries of olivine grains. And thus, the textures of the olivine–NaCl–H₂O systems were almost stable, and the very slight change of texture due to the dissolution of olivine in the saline fluids cannot affect the conductivities of the olivine–NaCl–H₂O systems. The fluid fraction of the aqueous fluid-bearing system remained mostly stable during the impedance spectra measurements, with less than 10% error of the fluid fraction in the aqueous fluid-bearing system, and the salinity remained unchanged during the experiments. The impedance spectra of the aqueous fluid-bearing system were continuously collected twice at a given temperature, and the two measured resistances were similar. This supports that the impedance spectra of the aqueous fluid-bearing system were collected during a relatively stable state. It is worthily mentioned that the reaction of quartz and olivine can take place at high temperatures and pressures, and a very thin pyroxene-bearing layer might be produced. However, the contribution of the thin pyroxene-bearing layer to the bulk conductivity could be negligible because the conductivity of pyroxene is much lower than that of interconnected fluid phases (Huang et al., 2021). Stable impedance spectra of hydrous polycrystalline olivine were collected using a similar process to that for the aqueous fluid-bearing system. The detailed thermodynamic conditions of the runs are listed in Table 1. The errors of the experimental pressures and temperatures were ±0.2 GPa and ±10 K, respectively.

The chemical compositions of the recovered olivine for the olivine–NaCl–H₂O system with 5 wt% salinity and 20.3 vol% volume fraction were measured by EPMA. The chemical compositions of olivine were similar before and after the electrical conductivity measurements, as shown in Supplementary Table S1. The internal structures of the recovered samples were also observed using a scanning electron microscope (SEM) at the Center for Lunar and Planetary Sciences, Institute of Geochemistry, CAS, Guiyang, China. The SEM images show that the boundaries of the large olivine grains were curved and smooth, and small ellipsoidal olivine grains were distributed in the triangular spaces between the large olivine grains. A corrosion border is clearly visible on the olivine grains and numerous small circular holes are observed in the grain interiors (Figure 1). These phenomena reflect the strong dissolution and corrosion of olivine by the saline fluids at high temperature and pressure. Furthermore, the median dihedral angle of the saline fluids in of the Ol–NaCl–H₂O system with 5 wt% NaCl and 5.1 vol% fluids was found to be 50° (Supplementary Figure S2). The detail relevant analysis process was described in the supplementary material.

Salinity directly affects the conductivity of saline fluids, and the fluid fraction significantly influences the interconnectivity of the fluids in the matrix. The salinity and fluid fraction are thus closely related to the conductivity of saline fluid-bearing olivine aggregates. The median dihedral angle for the saline fluids of the Ol–NaCl–H₂O system with a salinity of 5 wt% and fluid fraction of 5.1 vol% is 50°, which indicates that the saline fluids were interconnected on the polycrystalline olivine boundaries (Supplementary Figure S2). The dihedral angles of the Ol–(NaCl)–H₂O system are found to be higher than those of the Pl–NaCl–H₂O and Cpx–NaCl–H₂O systems and dehydration products of lawsonite (Supplementary Figure S3). This might imply that aqueous fluids in the uppermost mantle are more difficult to interconnect than those in the mid-to lower crust and interfaces of subduction slabs. It’s should be noted that pressure and temperature affect the dihedral angles for the aqueous fluids in the polycrystalline silicate minerals to some extent (Yoshino et al., 2007), but the dihedral angles for the aqueous fluids-bearing systems might be dominated by the mineral constituent and the salinity and fluid fraction of the saline fluids. As shown in Figure 5, the conductivities of the Ol–NaCl–H₂O system with a salinity of 1 wt% and fluid fraction of 14.5 vol% are ∼1–1.5 orders magnitudes higher than those of the Ol–H₂O system with the fluid fraction of 10.9 vol%. However, the conductivities of the Ol–NaCl–H₂O system with a salinity of 5 wt% and fluid fraction of 13.7 vol% are only ∼0.2–0.5 orders magnitudes higher than those of the Ol–H₂O system with a salinity of 1 wt% and fluid fraction of 14.5 vol%. This implies that a small quantity of salt can dramatically enhance the conductivity of the Ol–H₂O system owing to the sharp increase of charge carrier concentrations in the aqueous fluids. The molar concentration of Na⁺ and Cl⁻ increases with increasing salinity and accordingly enhances the conductivity of the Ol–NaCl–H₂O system. However, the decomposition ratio of the solute might decrease with increasing salinity at a certain temperature and pressure; thus the conductivity of saline fluid-bearing olivine aggregates does not proportionately increase with increasing salinity (0–21 wt%). Supplementary Figure S4 shows the logarithmic conductivity values versus salinity for the Ol–NaCl–H₂O system with similar fluid fractions (10.9–14.5 vol%). The conductivity of the Ol–NaCl–H₂O system dramatically increases with increasing salinity in the lower salinity range (< 17 wt%), but remains nearly unchanged in the higher salinity range (17–21 wt%). It should be noted that the conductivity of the Ol–NaCl–H₂O system with a salinity of 13 wt% and fluid fraction of 10.9 vol% is slightly lower than that of the Ol–NaCl–H₂O system with a salinity of 9 wt% and fluid fraction of 13.7 vol% at 2 GPa and 873–1073 K. We propose that the degree to which the fluid fraction influences the conductivity of saline fluid-bearing olivine aggregates is more significant than that of salinity when salinities are sufficiently high (>9 wt%). Salinity might also influence the solubility of olivine in saline fluids, which would explain the different activation enthalpies of the various saline fluid-bearing olivine aggregates (Table 1). Previous studies have shown that the solubility of quartz and albite in NaCl–H₂O fluids decreases with increasing salinity, whereas the solubility of diopside in NaCl–H₂O fluids positively relates to salinity (Newton and Manning, 2000; Shmulovich et al., 2001). According to the research of Macris et al. (2003), the solubility of olivine in the saline aqueous fluid is much higher than that of pure water, which increases the concentration of dissolved component and decreases the dihedral angle simultaneously. We propose that the dissolution of olivine in saline fluids might play an important role in the conductivity of the Ol–NaCl–H₂O system. The logarithmic conductivity of the Ol–NaCl–H₂O system with a salinity of 5 wt% linearly relates to the logarithmic fluid fractions (Supplementary Figure S5). The bulk conductivity and fluid fraction thus conform to Archie’s law (Archie, 1942): σ bulk = c Φ n σ f (4) where σ _bulk and σ _f are the conductivities of the Ol–NaCl–H₂O systems and saline fluids, respectively, Φ is the fluid fraction, and as well as c and n are constants, respectively. Upon increasing the temperature from 773 to 1073 K, n increases from 2.34 to 4.12. This reflects that the conductivity of the Ol–NaCl–H₂O system significantly increases with increasing fluid fraction, and the fluid fraction has a more significant influence on conductivity at higher temperatures. The electrical conductivity of aqueous fluids (σ _f ) distributed in the interspaces of the olivine aggregates remains unclear and is difficult to directly measure in the Ol–NaCl–H₂O system. The conductivity of interconnected aqueous fluids distributed in the solid matrix can be calculated based on the HS⁺ model and cube model (Hashin and Shtrikman, 1962; Waff, 1974). According to the HS⁺ model, the electrical conductivity of the aqueous fluids in the Ol–NaCl–H₂O system is calculated by: σ b = σ f + 1 − Φ 1 σ s − σ f − Φ 3 σ f (5) where σ _b, σ _s and σ _f are the conductivities of the Ol–NaCl–H₂O system, hydrous olivine aggregates and saline fluids, respectively. The mathematical formula for the cube model is expressed as: σ b = ( 1 − ( 1 − Φ ) 2 / 3 ) σ f (6)

We apply our experimental data to calculate the conductivity of aqueous fluids using Eq. 5, Eq. 6. As shown in Table 2, the conductivities of NaCl–H₂O fluids calculated from the HS⁺ and cube models are substantially lower than experimental data reported by Sinmyo and Keppler (2017) and Guo and Keppler (2019). A similar phenomenon was reported by Guo et al. (2015), Li et al. (2018) and Sun et al. (2020). This discrepancy might be mainly caused by the compositional differences between the pure NaCl–H₂O fluids and aqueous fluids in the Ol–NaCl–H₂O system. For aqueous fluids in the Ol–NaCl–H₂O system, Na⁺ and Cl⁻ have been proposed to be the dominant charge carriers and a small quantity of H⁺, OH⁻ and soluble ions from olivine slightly enhance the conductivity, whereas tiny particles of silicate minerals in the aqueous fluids might dramatically impede charge carrier migration. The degree of NaCl dissociation might decrease owing to the presence of olivine aggregates. Furthermore, the true distribution of aqueous fluids in the systems possibly differs from those for the ideal HS⁺ and cube models. Aqueous fluids are distributed in a variety of pathways, such as on mineral surfaces, spherical holes, triple junctions and local channels. Although the hydrodynamic pressure of the fluids is relatively homogeneous, the geometric shapes of the local aggregation fluids are constrained by the sizes and shapes of the olivine grains. In addition, the olivine has faceted interfaces due to its anisotropy, which could affect the fluid connectivity even with a low dihedral angle (Price et al., 2006), resulting in a more tortuous network of fluid. Notably, it is inevitable that a slow fluid movement from the temperature gradient of sample capsule is also of the possible effect on the measured conductivity results of the NaCl–H₂O and Ol–NaCl–H₂O systems.

The electrical conductivity of hydrous olivine aggregates determined in this study (∼10^–3.5–10^−1.25) is similar to that reported by Dai and Karato, 2014b, and the iron contents of the two hydrous olivine aggregates are very similar (Figure 7). This supports that the water content in our olivine is similar to that in the olivine from Dai and Karato, 2014b (130 ppm). The presence of pure water dramatically enhances the conductivity of olivine aggregates at lower temperature, but the conductivity of the Ol–H₂O system is similar to those of hydrous olivine aggregates with increasing temperature. The effect of saline fluids on the conductivity of olivine aggregates is substantially more significant than that of pure water (Figure 7). As shown in Figure 7, we compared the electrical conductivities of iron-free forsterite–fluid system from Huang et al. (2021) and the conductivities of iron-bearing olivine–fluid system from the present study. It was shown that the conductivity of iron-free forsterite–fluid system was moderately higher than that of iron-bearing olivine–fluid system at the same salinity and similar fluid fractions. And thus, the existence of iron in the olivine might be obstructive to the interconnectivity of saline fluids. The influence of aqueous fluids on the various silicate mineral aggregates also differs to some extent. The conductivity of olivine aggregates with interconnected pure water (10.9 vol%) is approximately one order of magnitude lower than that of clinopyroxene aggregates with 25 vol% pure water. In comparison with the electrical conductivity of Cpx–NaCl–H₂O system with a salinity of 10 wt% and fluid fraction of 20 vol%, the conductivity of Ol–NaCl–H₂O system with a salinity of 9 wt% and fluid fraction of 20.7 vol% is slightly lower. Under similar salinity and fluid fraction conditions, the conductivity of the Ol–NaCl–H₂O system is slightly lower than that of the Pl–NaCl–H₂O system, but dramatically lower than that of the Ab–NaCl–H₂O system (Figure 7). For example, the conductivity of the Ol–NaCl–H₂O system with a salinity of 5 wt% and fluid fraction of 9.9 vol% is slightly lower than that of the Pl–NaCl–H₂O system with a salinity of 3.3 wt% and fluid fraction of 8.3 vol%, but approximately 1.5 orders of magnitude lower than that of the Ab–NaCl–H₂O system with a salinity of 3.4 wt% and fluid fraction of 8.9 vol% (Guo et al., 2015; Li et al., 2018). The interconnected saline fluids thus dominantly constrain the conductivity of saline fluid-bearing silicate mineral aggregates, but the silicate minerals still play a significant role in the electrical properties of the systems. This is because the conductivities of various silicate minerals, (e.g., olivine, clinopyroxene, plagioclase and albite) differ under a given temperature and pressure condition. The various dissolution mechanisms and solubilities of different silicate minerals in saline fluids might therefore significantly affect the species and migration speed of the charge carriers in the fluids. Furthermore, the distribution characteristics of saline fluids in the interspaces of the solid matrix might be closely related to the grain size and shape, viscosity, defect concentration, and solubility of the minerals in the saline fluids-bearing systems. The electrical conductivity of the Ol–NaCl–H₂O system slightly increases with increasing pressure. A similar effect of pressure on the conductivity of the NaCl–H₂O system was reported by Guo and Keppler (2019). Salinity significantly affects the conductivity of the NaCl–H₂O system at high temperatures and pressures (Sinmyo and Keppler, 2017; Guo and Keppler, 2019), and further influences the conductivity of saline fluid-bearing rocks. The electrical conductivity of the Ol–NaCl–H₂O system with a salinity of 9 wt% and fluid fraction of 20.7 vol% is similar to that of the NaCl–H₂O system with a molar concentration of 0.01 mol/L (salinity: ∼0.059 wt%), and approximately one order of magnitude lower than that of the NaCl–H₂O system with a molar concentration of 0.1 mol/L (salinity: ∼0.58 wt%). Furthermore, the conductivity of the NaCl–H₂O system with a molar concentration of 1 mol/L (salinity: ∼5.5 wt%) is substantially higher than that of the silicate mineral–NaCl–H₂O system with higher salinities (>5.7 wt%) (Figure 7). We propose that the dissolution of silicate minerals into the saline fluids might affect the conductivities of the aqueous fluids to some extent, and the hydrological regime in the silicate rocks dramatically affects the conductivities of fluid–rock systems. The measured conductivities of pure saline fluids are therefore significantly different from the calculated conductivities of saline fluids in silicate mineral–NaCl–H₂O systems based on the HS⁺ and cube models.

Electrical conductivities of the Ol–NaCl–H₂O systems were the latest measuring results at the various thermodynamic conditions of 2.0–3.0 GPa and 773–1073 K. Effects of temperature and pressure on the conductivities of the Ol–NaCl–H₂O systems were very slight, but salinity and fluid fraction are important influence factors on the conductivities. Electrical conductivities of the Ol–NaCl–H₂O systems were compared with the conductivities of the Ol–KCl–H₂O and Ol–CaCl₂–H₂O systems with a certain salinity and fluid fraction. It was shown that the conductivities of the Ol–NaCl–H₂O systems were close to those of the Ol–KCl–H₂O systems, but moderately higher than the Ol–CaCl₂–H₂O systems at the similar salinities and fluid fractions. Although the formation mechanism and evolution low for the saline fluids in the mantle wedges have not been researched in detail, the previous studies have proposed that NaCl is the dominant salt in the saline fluids based on the material compositions of the inclusion fluids in the mantle xenoliths (Kawamoto et al., 2013; Morikawa et al., 2016; Huang et al., 2019). And thus, the presence of NaCl fluids might be the origin of the high-conductivity anomalies in the mantle wedges. It’s important to constrain the volume fractions of the saline fluids in the high-conductivity layers of the mantle wedges.

Subduction zones are the most active geological environments on Earth, where various geological processes lead to complex material compositions and structural characteristics. Magnetotelluric profiles indicate that high-conductivity geological bodies are widely distributed in the mantle wedges of subduction zones. Various hypotheses regarding the origin for the high-conductivity anomalies have been proposed based on field geological investigations and high-temperature and high-pressure experiments (Dai and Karato, 2014a; Manthilake et al., 2015; Guo et al., 2017; Hu et al., 2018; Li et al., 2018). In subduction zones, the dehydration products of hydrous minerals, which contain residual minerals and aqueous fluids, are located along the interface between the subduction slab and mantle wedge. Owing to the wide distribution of aqueous fluids in mantle wedges (Peslier et al., 2017), hydrogen-related defects are likely to exist in nominally anhydrous minerals (Karato, 1990), causing a significant increase of the electrical conductivity in relevant regions (Dai and Karato, 2014b). According to the magnetotelluric profiles, the unusually high electrical conductivities of the high-conductivity layers in the mantle wedges were ∼10⁻²–1 S/m (Yamaguchi et al., 2009; Burd et al., 2013; McGary et al., 2014; Hata et al., 2017). The largest conductivity of hydrous San Carlos olivine with 0.1 wt% H₂O (close to the solubility of water in olivine) is approximately 10^–1 S/m under the uppermost mantle conditions (Dai and Karato, 2014b), and thus the unusually high electrical conductivities of ∼10⁻²–10⁻¹ S/m in the high-conductivity layers of the mantle wedges can be interpreted by the conductivities of hydrous peridotite. However, the unusually high conductivities of 10⁻¹–1 S/m in the mantle wedges were higher than the largest conductivity of hydrous peridotite (10^–1 S/m), indicating that the conductivities of hydrous peridotite cannot interpret the unusually high electrical conductivities of 10⁻¹–1 S/m in the mantle wedges. Therefore, it’s possible that the interconnected saline fluids cause the high-conductivity anomalies with the conductivities of ∼10⁻¹–1 S/m in the mantle wedges.

Hydrous minerals (e.g., chlorite, epidote, serpentine, phengite) in subducting plates are transported into the Earth’s deep interior, and subsequent dehydration reactions are triggered under the dehydration thermodynamic conditions of high temperatures and pressures (Zheng, 2019). A large proportion of free water released from hydrous minerals migrates upwards to a certain depth within the mantle wedges. A certain amount of solutes dissolve into the free water during the compositional differentiation of free water and residual minerals. The presence of NaCl-bearing aqueous fluids has been determined to be a significant cause of the high-conductivity anomalies in the middle to lower crust of subduction zones (Guo et al., 2015; Sinmyo and Keppler, 2017; Li et al., 2018; Guo and Keppler, 2019; Sun et al., 2020). The question of whether or not saline fluids are present and interconnected in the mantle wedges of subduction zones has been long debated. Huang et al. (2019) recently demonstrated that interconnected NaCl-bearing aqueous fluids are present in mantle wedges based on high-temperature and high-pressure experiments. This was an important discovery, which implies that NaCl-bearing aqueous fluids might cause the high-conductivity anomalies in the mantle wedges. Fluid fraction and salinity are significant factors that influence the conductivities of HCLs that might be caused by saline fluids. To quantitatively constrain the origin of the high-conductivity anomalies related to NaCl-bearing aqueous fluids in mantle wedges, we compare the conductivities of the HCLs in mantle wedges and NaCl-bearing aqueous fluids with various salinities and fluid fractions. Magnetotelluric profiles indicate that the highest conductivities of the HCLs in most mantle wedges are close to 1 S/m (Yamaguchi et al., 2009; Burd et al., 2013; McGary et al., 2014; Hata et al., 2017). The conductivities of ellipsoidal HCLs gradually decrease from core to edge. In regions with aqueous fluids, the lattice water in nominally anhydrous minerals should be saturated. The presence of hydrous olivine can be employed to interpret the origin of HCLs with conductivities on the order of 10⁻²–10⁻¹ S/m (Dai and Karato, 2014b), but regions with conductivities of 10⁻¹–1 S/m are possibly related to saline fluids. The conductivities of the Ol–NaCl–H₂O system with various fluid fractions (0.1–100 vol%) and salinities (1–21 wt%) were calculated based on the HS⁺ and cube models, as shown in Figure 8. The effects of temperature and pressure on the conductivities of the interconnected saline fluid-bearing olivine aggregates are very limited; thus the calculated conductivities are obtained based on the experimental data at 2.0 GPa and 1073 K. In the conductivity range of 10⁻¹–1 S/m, the conductivities of the Ol–NaCl–H₂O system estimated from the HS⁺ and cube models at a certain salinity and fluid fraction differ slightly. This discrepancy might be caused by differences of the fluid distribution in the ideal cube and HS⁺ models and real Ol–NaCl–H₂O system. For the Ol–NaCl–H₂O system with a certain salinity and electrical conductivity, the real fluid fractions are close to the average fluid fractions obtained from the HS⁺ and cube models. The fluid fractions in the HCLs can be approximated by combining the electrical conductivities of HCLs in mantle wedges and those of the Ol–NaCl–H₂O system at a certain salinity. For the lower bound of conductivity (10^–1 S/m) in the HCLs, the fluid fractions of the Ol–NaCl–H₂O system with a salinity of 1, 5, 9, 17 and 21 wt% are 9.0, 1.8, 1.5, 0.7 and 0.5 vol%, respectively. For the upper bound of conductivity (1 S/m) in the HCLs, the fluid fractions of the Ol–NaCl–H₂O system with a salinity of 5, 9, 17 and 21 wt% are 21.9, 17.9, 6.9 and 5.9 vol%, respectively. For the Ol–NaCl–H₂O system with a salinity of 1 wt%, the fluid fraction employed to interpret the upper bound for the high conductivities (1 S/m) is close to 100 vol%. The presence of the Ol–NaCl–H₂O system with a salinity of ∼1 wt% can therefore not be the origin of the HCLs in mantle wedges. The original salinities of the aqueous fluids from the dehydration of subduction slabs are proposed to be 0.5–2.0 wt% NaCl (Li and Hermann, 2015). However, the salinity of the saline fluids measured in a peridotite xenolith from a mantle wedge was reported to be 5.1 ± 1.0 wt% NaCl (Kawamoto et al., 2013). In addition, the NaCl contents in slab-derived aqueous fluids that upwell up to forearc regions are close to 6.6 wt% (Morikawa et al., 2016). The higher salinities might be caused by the chromatographic fractionation during the hydration reaction of the mantle wedge after the fluid is released from the subduction slab (Huang et al., 2019). According to all of these above-mentioned evidences, it makes clear that the salinities of most stable aqueous fluids in the mantle wedges are close to 5.0 wt%. The Ol–NaCl–H₂O systems with the salinity of ∼5.0 wt% and fluid fractions larger than 1.8 vol% might thus be the origin of the HCLs in mantle wedges.