The evolution of Earth’s surficial Mg cycle over the past 2 billion years

doi:10.21203/rs.3.rs-2238947/v1

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The evolution of Earth’s surficial Mg cycle over the past 2 billion years

https://doi.org/10.21203/rs.3.rs-2238947/v1

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The surficial cycling of Mg is directly coupled with the global carbon cycle, a predominant control of Earth’s climate. However, how Earth’s surficial Mg cycle evolved with time had been elusive. Magnesium isotope signatures of seawater (δ²⁶Mg_sw) track the surficial Mg cycle, which could provide crucial information on the carbon cycle in Earth’s history. Here, we present a reconstruction of δ²⁶Mg_sw evolution over the last 2 billion years using marine halite fluid inclusions and sedimentary dolostones. The two independent archives yield consistent evolutionary trends of δ²⁶Mg_sw for the past 430 million years, and the dolostone records extend the δ²⁶Mg_sw curve to 2 billion years ago. Modeling results of the net CO₂ sequestration efficiency (E_Mg−CO2) by the surficial Mg cycle based on the δ²⁶Mg_sw record reveal a secular decline E_Mg−CO2 during the past 2 billion years, with the periods of low E_Mg−CO2 coinciding with ice ages in the Phanerozoic. Our work underlines a previously under-appreciated, but indispensable role of dolostones in regulating Earth’s climate on geologic time scales.

Earth and environmental sciences/Planetary science/Geochemistry

Earth and environmental sciences/Solid Earth sciences/Geochemistry

Earth and environmental sciences/Climate sciences/Ocean sciences/Marine chemistry

The key external forcings of Earth’s climate, including the solar luminosity, mantle outgassing intensity, and composition and exposure of crustal rocks, had changed remarkably and irreversibly over geological eons¹. Despite that, the Earth’s surficial temperature has remained within the habitable range for most of the Earth’s history, which is believed to be regulated by atmospheric CO₂ levels through negative feedback in the carbonate-silicate cycles. However, the exact mechanisms remain highly debated, that some invoked weathering of silicates on continents^2,3, whereas others emphasized reverse weathering on seafloors⁴. Addressing such problems requires the acquisition and interpretation of various secular records of different key elements for surficial processes both on land and in oceans⁵.

The surficial Mg cycle links continental weathering, high- and low-temperature alteration of the oceanic crust, as well as the formation of carbonates and clays on the seafloor, and through these processes, the Mg cycle closely interacts with geochemical cycles of carbon, calcium, and silicon ^6–8. Despite its importance in relevance to Earth’s habitability, quantitative study of ancient surficial Mg cycles is challenging, particularly for the Precambrian periods. Previous attempts to reconstruct Mg cycles based on the compiled volume of the sedimentary dolostones over geologic times⁶ were hampered by disproportional preservation of sediments and incomplete data for compilation, which worsened dramatically for older records⁹. By contrast, Mg concentration in seawater, recovered from halite inclusions¹⁰, had provided important insights into ancient Mg cycles, although the data are mainly restricted to the Phanerozoic time.

Because Mg is released by both carbonate and silicate weathering¹¹ and deposited as either carbonate minerals via dolomitization¹², or silicate minerals through marine clay formation⁷ and alteration of oceanic crust¹³, Mg isotopes are a very promising tracer for the silicate-carbonate cycle. Magnesium in the oceans is supplied from weathering of silicates and Mg-bearing carbonates (mainly dolomite), which have a large difference in Mg isotope ratios (expressed in delta notation: δ²⁶Mg = (R_sample/R_standard-1)×1000, R = ²⁶Mg/²⁴Mg, the standard is DSM3). The majority of igneous silicate rocks have similar δ²⁶Mg values that cluster around − 0.25 ± 0.07‰, whereas carbonates have much lower values of δ²⁶Mg, commonly between − 1‰ and − 5‰¹⁴. Thus, changes in the relative contribution of carbonate to silicate sources could lead to different Mg isotope compositions of Mg input into the oceans¹¹. On the other hand, Mg is removed from seawater via the formation of Mg-bearing silicates and Mg-bearing carbonates, which are also associated with distinct Mg isotope fractionation behaviors. Precipitation of dolomite and magnesian calcite under ambient temperature is associated with a fractionation factor (Δ²⁶Mg_min−aq = δ²⁶Mg_mineral - δ²⁶Mg_aqueous) of ca. -2‰ or lower, whereas uptake of aqueous Mg into silicates is associated with positive to zero Δ²⁶Mg_min−aq fractionations, depending on the temperature of the reaction¹⁴. Consequently, a change in the relative contribution of the carbonate Mg sink relative to the silicate sink would also change the isotopic ratio of seawater Mg¹⁵. Therefore, Mg isotopes in seawater respond to changes in the balance between silicates and carbonates of the surficial Mg cycles, on both the source side and the sink side. The geologic record of seawater δ²⁶Mg is thus a powerful tool for interrogating the long-term global carbonate-silicate cycles.

Several studies reconstructed the Mg isotope composition of seawater during the Cenozoic using biogenic calcite or aragonite^8,16. Calcite and aragonite, however, are susceptible to alteration by diagenetic fluids, which prevents the use of these minerals to infer seawater Mg isotopes in deep geologic times (i.e., > 100Ma). In contrast, Mg isotopes in dolomite have proven to be robust against various post-depositional overprinting processes^17,18. Dolostones are abundant in ancient marine sedimentary sequences and the Mg isotope fractionation between dolomite and aqueous solution is well-constrained^15,19. These features facilitate reconstruction of the Mg isotope composition of ancient seawater. An alternative seawater Mg isotope archive is marine halite. Bedded halite from marine evaporites contains primary fluid inclusions, which preserve the Mg isotope composition of the contemporary seawater²⁰. The advantage of the halite record is that seawater δ²⁶Mg values can be directly measured from fluid inclusions without the application of Mg isotope fractionation factors, which are needed for the Mg-carbonates. That is because precipitation of halite from evaporating seawater occurs prior to precipitation of Mg-bearing evaporite minerals²⁰. Thus, the Mg in the brine and fluid inclusions has the same Mg isotopic composition as contemporaneous seawater.

In this study, we use Mg isotopes measured in halite fluid inclusions and dolostones to generate a record of Mg isotope composition of seawater (δ²⁶Mg_sw) for the past 2 billion years. Then based on the record, we explore the evolution of the geological carbon cycle from a Mg-isotope perspective.

Reconstructing Mg Isotope History Of Seawater In The Past 2 billion Years

We compiled a large set of Mg isotope data for marine sedimentary dolomite over the past 2 billion years, including 1342 analyses from 50 units reported in the literature and 425 new analyses from 25 units in this study (Supplementary Materials, Tables S1, S2, Fig. S1). For the Phanerozoic, 103 analyses of marine halite samples (analytical methods are in Supplementary Materials) from 37 units are also compiled, including 84 new analyses from 29 units (Supplementary Materials, Table S3). Halite samples were carefully selected based on geological and textural criteria to ensure that the fluid inclusions are primary and contain evaporated seawater (Supplementary Materials, Fig. S2). Additionally, only halites with ⁸⁷Sr/⁸⁶Sr ratios consistent with coeval seawater were included (Supplementary Materials, Fig. S3). Non-seawater ⁸⁷Sr/⁸⁶Sr ratios in halite indicate significant contributions of non-marine waters to the enclosed evaporite basin, which could alter the seawater Mg isotope composition of the brine.

Dolostones show large variations in δ²⁶Mg values over the last 2 billion years (Fig. 1, a and b). Even within a single sedimentary unit, the variability in δ²⁶Mg can be up to 2‰. Such large Mg isotope variability in dolostones poses a challenge for the use of sedimentary dolomite to constrain δ²⁶Mg_sw. Dolomitization processes can be diverse and it is not uncommon that dolomitization fluids evolve isotopically from pristine seawater^21,22. Isotopic evolution of Mg in dolomitization fluids can occur along a diffusion/advection profile on a scale of meters to hundreds of meters ^19,23, or across a carbonate platform on a scale of hundreds of kilometers (Supplementary Text, Fig. S4, S5), or even within an enclosed basin on the continental scale²⁴. Nonetheless, dolomitization invariably removes light Mg isotopes from the fluid, elevating the δ²⁶Mg value of the remaining fluid and the δ²⁶Mg values of dolomite precipitated from that fluid. Therefore, δ²⁶Mg values of dolostones tend to be higher than the seawater-equilibrated δ²⁶Mg value, and the lowest δ²⁶Mg values of syn-depositional dolostones have the greatest possibility of approaching the seawater-equilibrated δ²⁶Mg value¹².

Marine halites also exhibit variability in δ²⁶Mg values. This is because bulk dissolution of halite is used for Mg isotope analysis of the fluid inclusions. Measured δ²⁶Mg values are therefore complicated by possible soluble Mg-bearing evaporite mineral inclusions. This is manifested in the data-set from the Late Miocene of Egypt halite where measured δ²⁶Mg values vary from − 1.63‰ to -0.78‰. There is a negative correlation between Mg-K concentrations and δ²⁶Mg values for the dissolved bulk halite samples (Supplementary Materials, Fig.S6), suggestive of Mg- and K-bearing salt enriched in ²⁴Mg. Detailed SEM imaging confirmed the existence of polyhalite in the halite samples with low δ²⁶Mg values (Supplementary Materials, Fig.S7), a salt known to be enriched in light Mg isotopes²⁰. Thus, the δ²⁶Mg value measured from marine halite could be lower than contemporaneous seawater, and the highest δ²⁶Mg values from marine halite of a particular age can be used to define the lower boundary of the δ²⁶Mg_sw curve. Marine halites therefore provide an independent seawater Mg isotope record that is complementary to dolostone.

To establish a curve of δ²⁶Mg_sw through time, a contour is extended between the lowest δ²⁶Mg values of each dolomite data set in each time slice. A 2‰ offset (i.e., the Mg isotope fractionation factor between dolomite and seawater) is then applied to the contour (Fig. 1). The lowest data points from small sample sets (n < 10) are not used to define the contour because they may not be representative of that period. Data points that are abruptly higher than the neighbouring hinge points are also excluded as abrupt changes in δ²⁶Mg_sw are unlikely considering the long residence time of Mg in the oceans. Notably, the dolomite-based seawater δ²⁶Mg curve is consistent with the upper contour of halite δ²⁶Mg values within 0.2‰ for the Phanerozoic Eon (Fig. 1a). The curves suggest that δ²⁶Mg_sw was likely ≥ + 0.5‰ in the early Paleoproterozoic, which then decreased to 0 ± 0.2‰ during the Mesoproterozoic, and to -0.2 ± 0.2‰ during the Neoproterozoic (Fig. 1b). The reconstructed δ²⁶Mg_sw further decreased to ~ -0.7‰ in the late Paleozoic, but increased back to -0.3‰ in the late Permian, and then decreased to -0.8‰ in the Cenozoic^8,16. Notably, this pattern is also consistent with the statistical patterns for dolostone δ²⁶Mg in the six above-mentioned major geological time brackets, which also show continuous decreases in the median, average, and overall range of δ²⁶Mg values over time (Fig. 1c).

The secular changes in surficial Mg cycles constrained from δ²⁶Mg_sw

Based on the well-established record of δ²⁶Mg_sw, we next quantify how the surficial Mg cycles evolved over the past 2 billion years with a mass balance model. As described in the introductory paragraphs, the surficial Mg cycle is controlled by riverine input into the ocean by carbonate and silicate weathering¹¹ and Mg removal as either carbonate minerals via dolomitization¹², or silicate minerals through marine clay formation⁷ and alteration of oceanic crust¹³. In the classic view of the silicate-carbonate cycle, silicate weathering results in excess carbonate burial over carbonate weathering and consequently remove CO₂ from the Earth’s surface (Eq. 1)³.

MgSiO₃ + CO₂→MgCO₃ + SiO₂ (1)

On the other hand, if carbonate weathering exceeds carbonate burial, the excess cation and dissolved inorganic carbon (DIC) released by carbonate weathering would be consumed by authigenic silicate formation in marine sediment²⁵ or altered seafloor²⁶, turning DIC back into CO₂ (Eq. 2).

$$\text{Mg}{\text{CO}}_{\text{3}}\text{+Si}{\text{O}}_{\text{2}}\text{→MgSi}{\text{O}}_{\text{2}}\text{+C}{\text{O}}_{\text{2}}$$

Therefore, the imbalances between dolostone weathering and burial could have profound impact on the Earth’s climate system. We next build a model to particularly calculate variations in the imbalances between Mg carbonate weathering and burial.

The mathematical framework of the model is based on elemental and isotopic mass balance equations, an approach that has proven effective for studies of elements with long-residence times in seawater⁵:

$${F_{{\text{carb}} - {\text{in}}}}+{F_{{\text{sili}} - {\text{in}}}}={F_{{\text{carb}} - {\text{out}}}}+{F_{{\text{sili}} - {\text{out}}}}~$$

$${\delta _{{\text{carb}} - {\text{in}}}}{F_{{\text{carb}} - {\text{in}}}}+{\delta _{{\text{sili}} - {\text{in}}}}{F_{{\text{sili}} - {\text{in}}}}={\delta _{{\text{carb}} - {\text{out}}}}{F_{{\text{carb}} - {\text{out}}}}+{\delta _{{\text{sili}} - {\text{out}}}}{F_{{\text{sili}} - {\text{out}}}}$$

where F and δ represent the fluxes and isotopic compositions of Mg for the silicates (subscript: _sili ) and carbonates (subscript: _carb) as influx (subscript: _−in ) and outflux (subscript: _−out ).

We first use a Monte Carlo method (details are provided in Methods and the code is available in Supplementary Materials) to numerically solve the elemental and isotopic mass balance equations for the modern Mg cycle (δ²⁶Mg_sw = -0.8‰). Infinite solutions of Mg influx and Mg outflux values for silicates and dolostones exist (red dots in Fig. 2). These solutions define a broad linear trend in a cross plot of F_carb−in/F_Total−in versus F_carb−out/F_Total−out for each given δ²⁶Mg_sw value, regardless of the freedom in flux values (Fig. 2). However, in reality F_carb−in/F_Total−in should have a much more restricted range. The contribution of silicate weathering to riverine input of Mg was estimated in several studies, which yielded a range of 0.41–0.52 (Methods). When we further take the contribution of submarine weathering of silicates into consideration, the actual F_carb−in/F_total−in ratio for modern seawater is estimated to be 0.42 ± 0.08 (2 sigma). The Monte Carlo calculation results for such a distribution of F_carb−in/F_Total−in are shown by colored red contours in Fig. 2, and the corresponding F_carb−out/F_total−out is constrained to be 0.38 ± 0.26 (2 sigma, red histogram in the right side of Fig. 2), which agrees with the modern F_carb−out/F_total−out (0.27–0.52) estimated recently¹³.

The same Monte Carlo method was also applied to Paleoproterozoic seawater that had a δ²⁶Mg_sw value of 0.6‰; the numerical solutions are shown as blue dots in Fig. 2. The modeling results, predominantly plotting above the 1:1 line, show that F_carb−out/F_total−out was remarkably greater than F_carb−in/F_total−in in seawater at 2 Ga. This means that in the Paleoproterozoic, a significant proportion of seawater Mg sourced from weathering of silicates, either from the continents or from submarine mafic rocks, was sequestered by dolomite precipitation rather than secondary silicate formation on the seafloor. It is important to note that, considering the classic silicate-carbonate cycle^21,22 (i.g., Eq. 1), the imbalance between F_carb−out/F_total−out and F_carb−in/F_total−in for the Mg cycle produces net CO₂-removal. Based on the modeling results shown in Fig. 2, it is estimated that for every 1 mole of Mg cycled on Earth’s surface at 2.0 Ga, 0.66 ± 0.19 (2 sigma) mole of atmospheric CO₂ was removed from the atmosphere (i.e., F_carb−out/F_total−out - F_carb−in/F_total−in). By contrast, modern oceans are in an approximate balance between F_carb−out/F_total−out and F_carb−in/F_total−in, with F_carb−out/F_total−out - F_carb−in/F_total−in ranging from − 0.16 to 0.09, as the data points in the contoured area are close to the 1:1 line on Fig. 2. This implies that the modern global Mg cycle is near neutral in atmospheric CO₂ sequestration, considering the uncertainty in the models. Therefore, the significant difference between δ²⁶Mg_sw at 2 Ga and the modern δ²⁶Mg_sw shows that the efficiency of atmospheric CO₂ sequestration by Earth’s surficial Mg cycles varied significantly over geological time.

To quantitatively understand how Earth’s surficial Mg cycles evolved through time, we extended the elemental and isotopic mass balance equations to the 2-billion-year record of δ²⁶Mg_sw from this study. For the Monte Carlo calculation, we assume that F_carb−in/F_total−in increased from 0.14 ± 0.04 at 2 Ga to 0.42 ± 0.04 at present or that F_carb−in/F_total−in could be any value between 0 and 1. We defined a parameter of CO₂-removal efficiency for the Mg cycle (E_Mg−CO2 = F_carb−out/F_total−out - F_carb−in/F_total−in), and calculated the E_Mg−CO2 over the past 2 billion years based on the δ²⁶Mg_sw curve using the above-mentioned Monte Carlo method. The results not only confirmed the decrease in CO₂-removal efficiency in the Mg cycle over the past 2 billion years but further revealed that the decrease was not steady and monotonic (Fig. 3). A notable feature of the E_Mg−CO2 trend is the large fluctuation between 330 and 250 Ma. The pattern of the average values of E_Mg−CO2 through time is markedly similar to the δ²⁶Mg_sw curve, which confirms the sensitivity of Mg isotopes in seawater as a tracer of surficial Mg cycles.

The overall decrease in E_Mg−CO2 may be caused by an increase in F_carb−in/F_total−in and a decrease in F_carb−out/F_total−out. The secular evolution of ancient continental crust towards a less mafic average composition would produce a decrease in the supply of silicate-sourced Mg into oceans²⁷, whereas tectonic processes would accumulate marine dolostones onto continents due to the lower density of dolostones (2.90 g/cm³) relative to mafic silicates (> 3.20 g/cm³). These two processes, presumably irreversible, should have contributed to the background increase of F_carb−in/F_total−in over time. Using a simple crustal growth and tectonic model (Supplementary Text), we estimated that changes in F_carb−in/F_total−in contributed 31% of the overall E_Mg−CO2 decrease, whereas changes in F_carb−out/F_total−out contributed the rest (69%) of the 2-billion-year E_Mg−CO2 decrease. This suggests that a secular decrease in dolomitization intensity in the oceans is the dominate contributor to the decrease in F_carb−out/F_total−out in geologic history.

The Response Of The Surficial Mg Cycles To Earth’s Climates And Volcanic Outgassing

Based on the calculations above, we propose that the surficial Mg cycle driven by weathering-burial cycle of dolostone (WBCD) operates as a geological thermostat. Geological thermostats prevent catastrophic level of CO₂²⁸ and maintain the habitability of our planet. In other words, they efficiently reduce CO₂ removal from the Earth’s surface when the climate gets colder or the volcanic supply of CO₂ decreases, and vice versa. To test if the WBCD meets the criteria, we explore the response of the E_Mg−CO2 to Earth’s climate and volcanic outgassing. To date, the Phanerozoic history of Earth’s climate has been well-reconstructed²⁹ and a first-order evolution of volcanic degassing rate can be constrained from the thermal history of Earth’s mantle³⁰. During the past 500 Myr, higher temperature resulted in higher CO₂ removal efficiency by the Mg cycle (Fig. 4a), counteracting climate warming by reducing the greenhouse effects. Also, as volcanic degassing declined by two-fold from 2000Ma to 500Ma³⁰, E_Mg−CO2 decreased by a factor of three, which helped prevent depletion of atmospheric CO₂ (Fig. 4b). These correlations demonstrate that the weathering-burial cycle of dolostone is a potent geological thermostat.

It is important to understand the why the WBCD respond to climate change. The relatively rich and detailed Phanerozoic global environmental records provide an opportunity to explore the mechanism of the thermostat. The E_Mg−CO2 curve shows broad correlations (or anti-correlations) with records of continental glaciation, sea level, and average surface temperature over the Phanerozoic (Fig. 5). When the Earth was in ice-house climate states (i.e., low-latitude glaciation, low sea level, low average temperature), lower sea levels led to exposure of carbonate platforms which increased carbonate weathering. Dolomite precipitation is suppressed at lower temperatures³¹, so less Mg was removed by dolomitization in seawater during ice-house climates. These two processes produced the decrease in E_Mg−CO2 (i.e., lower F_carb−out/F_total−out, but higher F_carb−in/F_total−in), that prevented further decline in atmospheric CO₂ (Fig. 5), and created an effective negative feedback to low atmospheric CO₂ levels and low surficial temperatures and vice versa.

Another geo-thermostat called “reverse weathering” is frequently proposed recently^4,32,33. The thermostat mainly functioned during the Precambrian, because rise of marine siliceous organisms reduced low Si concentration in ocean³⁴, and consequently shut down the “reverse weathering” thermostat⁴ during the Phanerozoic. On the other hand, whether continental silicate weathering act as a driver of climate change or stabilized the climate remained intensely debated^3,35−37. The WBCD thermostat proposed by our study operated during both Phanerozoic and Precambrian, provides a complementary mechanism that maintained the habitability of our planet during the past 2 billion years.

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Analytical Methods

This study performed Mg isotope analysis on halite and dolostone samples. In addition, XRD analyses of bulk dolostone powder helped further screen dolomite-dominated samples for Mg isotope analysis. SEM-EDS analysis of halite samples is used to identify trace amounts of Mg-bearing evaporite minerals. Sr isotope analysis of halite provides an effective way to identify non-marine signals. All analyses were done at facilities at the State Key Laboratory of Mineral Deposit Research, Nanjing University, China.

Sample preparation

Halite samples were first cleaned by wiping with lint-free paper towels (Kimwipes®); about 1-2g sample was scraped off by a tungsten carbide scraper and subsequently ultrasonically cleaned in anhydrous ethanol (> 99.7%) for 5 min. After the sample was cleaned and dried, it was dissolved in 12ml deionized water (18.2 MΩ cm) as a stock solution^20,42. The dolostone samples were ground into 200 mesh in a pre-cleaned agate mortar. About ten milligrams of powder were weighed and dissolved in 5 mL 1.5 M HAC in a Teflon beaker. Then the dolostone sample solution was placed on a hotplate (96℃) for about 12 hours for digestion.

Mineral analyses

The mineralogy of the dolostone samples was determined by Rigaku RAPID II and Bruker D8 Advance X-ray diffractometer, respectively. The Rigaku RAPID II instrument operates at 50 kV and 90 mA on a rotating Mo anode X-ray source, while the Bruker D8 Advance instrument runs at 40 kV and 40 mA with a Cu anode X-ray source. The XRD data processing and mineral identification were performed using Jade 6.5 software. The relative abundance of dolomite (104), calcite (104), and quartz (101) are estimated via the area of characteristic diffraction peak⁴³. The morphology of the halite samples was performed on a Hitachi SU1510 Variable Pressure Scanning Electron Microscope (VP-SEM), and the chemical compositions were characterized using Energy-Dispersive X-ray Spectroscopy (EDS) equipped with SEMs.

Element analyses

A small fraction of the stock solution from the halite and dolostone samples was extracted and diluted to 4 ml in 2% double-distilled HNO₃. The concentrations of elements (such as Mg, Ca, and Sr) were measured using the inductively coupled plasma optical emission spectrometer (ICP-OES, Skyray ICP- 3000). The calibration curves for a series of gravimetrically prepared commercially-available multi-element standards with linear correlation coefficients (R²) are better than 0.999. A 1ppm multi-element standard was bracketed every ten samples to monitor and correct the instrument drift. The long-term external accuracy (2RSD, or two times of relative standard deviation) of elemental analysis is better than 10%^20,42.

Isotope analyses

Mg isotope analyses

Based on the stock solution concentration measured by ICP-OES, an aliquot of the sample containing approximately 20µg Mg was used for Mg isotope analysis. In order to remove sodium, the halite sample needs pre-enrichment of Mg by Mg(OH)₂ precipitation before undergoing the ion-exchange procedure²⁰. Halite and dolostone samples were further purified by cationic resin (AG50W-X12 and X8) together; see ¹⁸ for the process. After column chemistry treatments, Mg recovery was better than 95%, and the total matrix elements were less than 1% of Mg.

Mg isotopes were measured on a Thermo Scientific NEPTUNE Plus MC-ICP-MS and Nu 1700 Sapphire MC-ICP–MS. Both instruments operated on a standard low resolution, wet plasma mode, and the sample solution was introduced at an uptake rate of 100 uL/min. The method of standard-sample-standard bracketing was used to correct the instrumental drift and mass bias, and each Mg isotope ratio measurement consisted of fifty cycles of 4 s integrations. Two pure Mg stock solutions (HPS909104: produced by High purity Standards Company; A-Mg: prepared by dissolution guaranteed reagent Mg(NO₃)₂ solid) were served as in-house bracketing Mg standards. Although there is a difference in the on-machine concentration of pure Mg between the two instruments (Nu 1700: 0.5ppm; Neptune: 1ppm), the sample concentration was required to match the standard (the difference less than 10%) in the respective analysis process. Moreover, the δ²⁶Mg value of the in-house bracketing Mg standards (δ²⁶Mg_HPS909104= -0.67 ± 0.13‰, n = 47,⁴⁴); δ²⁶Mg_A–Mg= -3.25 ± 0.06‰, n = 107) relative to international standard DSM3 has been well-calibrated. The Analytical accuracy was monitored by international Mg isotope standards DSM3 and Cambridge1. The IAPSO seawater and USGS rock (DTS-2) standards were processed along with samples to verify the accuracy of chemical procedures. The measured δ²⁶Mg values of the standards (Table S4) match the published values^14,44, and the long-term external analytical precision was better than ± 0.1‰.

Sr isotope analyses

An aliquot of the halite stock solution containing approximately 500 ng Sr was extracted for Sr isotope analyses. The Sr-spec resin was used to purify the sample⁴⁵. The sample loaded in 3N HNO₃ and Sr was collected with 0.05N HNO₃. The USGS rock (AGV-2) and IAPSO seawater standards were treated as unknown samples to monitor the analysis procedure. The Strontium isotope analysis was performed using a Finnigan Triton thermal ionization mass spectrometer (TIMS). At the beginning of every analytical sequence, the international standard NIST 987 (⁸⁷Sr/⁸⁶Sr = 0.710228 ± 0.000033, 2σ = 100) was measured to verify the instrument status. With exponential law, the Sr isotope data were normalized to ⁸⁶Sr/⁸⁸Sr = 0.1194. All the measured ⁸⁷Sr/⁸⁶Sr ratios of standards (Table S4) are consistent with published values^18,42,46.

An isotopic mass balance model based on a Monte Carlo approach

The model framework

This appendix introduces the modeling of the Mg cycle. The primary sources of Mg in the ocean include silicate weathering and carbonate weathering. The major outputs are dolomitization, low-temperature and high-temperature alteration of basalt, and authigenic clay formation⁸. For simplification, we use a single symbol sil-out to represent all the processes that uptake Mg from seawater into silicate minerals, including low-temperature and high-temperature alteration of basalt and authigenic clay formation. Similarly, carb-out, carb-in, and sil-in represent dolomitization, carbonate weathering, and silicate weathering, respectively. By assuming that the Mg cycle is at a steady-state (such treatment had been universally applied in relevant studies such as Li^5,47, Mg^8,13,48, K^49,50, Mo^51–53, U^54–57, we have:

F_carb–in + F_sili–in = F_carb–out + F_sili–out (1)

δ_carb–inF_carb–in + δ_sili–inF_sili–in = δ_carb–outF_carb–out + δ_sili–outF_sili–out (2)

where F represents the Mg fluxes and δ stands for isotopic compositions of the Mg flux for the major components that participate in the Mg cycle.

Then, for ease of programming, we divided the two sides of the equation by the total flux that goes into the ocean (i.e., F_carb–in + F_sili–in), and let fcarb-in represent the fraction of the Mg flux derived from carbonate weathering in the total Mg input flux, and f_carb–out stand for a fraction of Mg in the seawater that deposited as carbonates. The two equations can be simplified as:

δ_carb–in f_carb–in + δ_sili–in (1- f_carb–in) = δ_carb–out f_carb–out + δ_sili–out(1- f_carb–out) (3)

Here δ_carb–out, δ_sili–out are functions of the Mg isotopic composition of seawater (δ_sw):

δ_carb–out = δ_sw + ∆_carb–out (4)

δ_sili–out = δ_sw + ∆_sil–out (5)

With the equations 3, 4, and 5, we build a model that calculates how the Mg cycle evolves with the record of the Mg isotopic composition of seawater.

Model Parameters

In this section, we describe how we quantify the model parameters. Considering that Mg, sourced from carbonate weathering (F_carb–in), is dominated by dolomite⁵⁸, and in the long-run, dolomite weathering is congruent, δ_carb–in is set to be the weighted average of δ²⁶Mg of the previously deposited dolostones, which are compiled in Fig. 1 of the main text. The fraction of dolostones that remain on the continent (R) is estimated from a time-dependent decay function following ⁹:

R = e^{– 0.001T} (6)

Here T (in Myr) is the time elapsed since the deposition of dolostone at t Ma. The δ²⁶Mg of the dolostone is calculated from the Mg isotopic composition of seawater by assuming a fractionation factor of -1.5 ± 0.2‰ (1 standard deviation). Then δ_carb–in is determined as the R-weighted average of δ²⁶Mg of the weathered dolostones, and the calculation results are shown in Fig. S8a. Considering that silicate weathering is associated with clay formation that generally enriches heavy Mg isotopes, δ_sili–in is assumed to be close to, but slightly lighter than, the δ²⁶Mg of the bulk silicate earth¹⁴, with a value of -0.4 ± 0.1‰ (1 standard deviation). For the calculation of δ_carb–out with Eq. 4, ∆_carb–out is estimated to be ~ -1.5‰ with one standard deviation of 0.2‰¹⁵. The fractionation factor during the alteration of seafloor basalt and the formation of authigenic marine clays varies significantly, ranging from 0 ~ 1.6‰^13,19. To cover this range and account for the uncertainty, we assume that ∆_sil–out is 0.8‰ with 1sd of 0.4‰.

The quantification of f_carb–in is more complicated. In the modern world, estimates of the fraction of Mg flux derived from silicate weathering vary significantly, ranging from 0.48 to 0.59^8,58–60. Accordingly, f_carb–in ranges from 0.41 to 0.52. Another factor that affects the quantification of f_carb–in is marine silicate weathering, which has drawn increasing attention recently ^61–63. Based on a methane generation estimate of 7 ~ 300 × 10¹²mol/yr^64,65, ref⁶³ estimated that the CO₂ consumption rate by marine silicate weathering is 5 ~ 20 × 10¹²mol/yr. Using an updated methane generation flux of ∼1.2 ×10¹²mol/yr⁶⁶, the estimation of marine silicate weathering is revised as 1 ~ 4 × 10¹²mol/yr⁶². The latter is close to the estimation of 1× 10¹²mol/yr by Sun and Turchyn (2014) based on the global authigenic Ca carbonate flux. Therefore, in this study, we use 1 ~ 4 × 10¹²mol/yr as the best estimate of the global marine silicate weathering rate, which is 8.5 ~ 34.1% of the subaerial silicate weathering rate⁶⁷. Assuming silicate weathering follows the same stoichiometries in both terrestrial and marine environments, f_carb–in would range from 0.34 to 0.50 if we consider the marine silicate weathering flux. In other words, a f_carb–in value of 0.42 ± 0.04 (1sd) is used in the modern world.

During the Earth’s history earlier than 3Ga, f_carb–in is assumed to be 0 because carbonates cannot be exposed to weathering without tectonic uplift ^64,65. For anytime between 0 and 3 Ga, we assume that f_carb–in increased from 0 to the modern value and with a standard deviation of 0.1. In other words, let t represent the age (in Ma), we have:

f_carb–in=0.42–0.42*t/3000 (7)

The curve of f_carb–in is presented in Fig. S8b. For δ_sw at a specific time spot, we estimate the δ_sw value with linear interpolation and similarly, we assume that the δ_sw record has a one sd uncertainty of 0.1‰ (Fig. S8c).

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Acknowledgement

This study was supported by the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (XDB26020101), the National Key R&D Program of China Project 2017YFC0602801, the National Natural Science Foundation of China (Grants No: 41622301, 41873004). WLi was additionally supported by the Research Funds for the Frontiers Science Center for Critical Earth Material Cycling, Nanjing University. We are very grateful to Changzhi Wu, Xiaolei Wang, Xuelei Chu, Linzhi Gao, Yongsheng Zhang, Genming Luo, Juske Horita, Dr. Yusuke Kubo, Lars Reuning, Juan Li, Zhong Han, Lichao Wang, Hao Tang, Junyong Li, and Yingfan Song, Xiaomin Wang, Yu Huang for providing samples or help with sampling.

Author contributions

W.L. designed the research. W.L., Z.X., S.L., and T.L. wrote the manuscript. W.L. and S.L. made the Mg isotope mass balance model. Z.X., Z.H., O.B., M.F.W., X.W., H.X., J.C., Z.J., T.K.L., and W.L. collected the samples in the field. Z.X., S.A., H.X., and J.C. carried out the research and sample analyses. All authors joined in the revision and discussion of the manuscript.

Competing interests

The authors declare that they have no competing interests.

Additional information

Excel source file of the Mg isotope data for all dolostones and halite samples can be downloaded in these addresses: https://kdocs.cn/l/cme0YIXeWPxd (Datafile for dolostones), https://kdocs.cn/l/crjVqhktZaxI (Datafile for halites).

Code for this Monte Carlo elemental and isotopic mass balance model is written in Matlab, and is available for download at: https://github.com/shileigeo/Mg-cycle.

There is NO Competing Interest.

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SUPPLEMENTARY AND ADDITIONAL MATERIAL

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The evolution of Earth’s surficial Mg cycle over the past 2 billion years

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Reconstructing Mg Isotope History Of Seawater In The Past 2 billion Years

The Response Of The Surficial Mg Cycles To Earth’s Climates And Volcanic Outgassing

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