Earth and Planetary Science Letters The Ca and Mg isotope record of the Cryogenian Trezona carbon isotope excursion

The Trezona carbon isotope excursion is recorded on ﬁve different continents in platform carbonates deposited prior to the end-Cryogenian Marinoan glaciation (>635 Ma) and represents a change in carbon isotope values of 16–18‰. Based on the spatial and temporal reproducibility, the excursion previously has been interpreted as tracking the carbon isotopic composition of dissolved inorganic carbon in the global ocean before the descent into a snowball Earth. However, in modern restricted shallow marine and freshwater settings, carbon isotope values have a similarly large range, which is mostly independent from open ocean chemistry and instead reﬂects local processes. In this study, we combine calcium, magnesium, and strontium isotope geochemistry with a numerical model of carbonate diagenesis to disentangle the degree to which the Trezona excursion reﬂects changes in global seawater chemistry versus local shallow- water platform environments. Our analysis demonstrates that the most extreme carbon isotope values ( ∼ -10‰ versus +10‰) are preserved in former platform aragonite that was neomorphosed to calcite during sediment-buffered conditions and record the primary carbon isotope composition of platform-top surface waters. In contrast, the downturn and recovery of the Trezona excursion are recorded in carbonates that were altered during early ﬂuid-buffered diagenesis and commonly are dolomitized. We also ﬁnd that the nadir of the Trezona excursion is associated with a fractional increase in siliciclastic sediments, whereas the recovery from the excursion correlates with a relative increase in carbonate. This relationship suggests that the extreme negative isotopic shift in platform aragonite occurred in concert with periods of increased input of siliciclastic sediments, changes in water depth, and possibly nutrients to platform environments. Although the process for generating extremely negative carbon isotope values in Neoproterozoic platform carbonates remains enigmatic, we speculate that these excursions reﬂect kinetic isotope effects associated with CO 2 invasion in platform waters during periods of intense primary productivity.

Over geological time scales, the net input of carbon to the atmosphere must be balanced by the burial of organic matter and carbonate sediment, with bulk carbonate δ 13 C values controlled by the fraction of organic matter burial globally ( f org , e.g., Kaufman et al., 1997). However, δ 13 C values of platform-derived carbonate are sensitive to restriction of marine circulation, diurnal productivity (Patterson and Walter, 1994;Geyman and Maloof, 2019), and early diagenetic alteration driven by the advection of both seawater and meteoric water within the sediment pile (Allan and Matthews, 1982;Melim et al., 2002). During time periods where carbonate burial is concentrated in platform environments, the impact of widespread local changes of depositional environments on global mass balance needs to be reevaluated. As a major constituent in carbonate (CaCO 3 ), calcium isotope ratios (δ 44/40 Ca) provide an independent constraint on the average carbonate sink. The main sink for seawater Ca 2+ is the burial of carbonate sediments and a prediction for the global calcium cycle is that, on average, the isotope composition of carbonate through time should equal that of Bulk Silicate Earth (BSE = -1‰, Skulan et al., 1997;Blättler and Higgins, 2017). In other words, what comes in must go out, and if sampling the average carbonate sink, δ 44/40 Ca values should approach ∼-1‰ when averaged over thick carbonate successions. As a result, δ 44/40 Ca values provide a tool to reconcile the decoupling between platform environments and the global ocean, the requirements of global mass balance, and the lack of absolute time constraints from individual Neoproterozoic successions.
In this study, we investigate the variability of carbonate δ 44/40 Ca values across the Trezona excursion, a large negative δ 13 C excursion recorded on multiple continents prior to the Marinoan glaciation. This δ 13 C excursion reaches values of ∼ −10‰ and occurs stratigraphically above a prolonged interval with mostly high δ 13 C values (up to +10‰, Kaufman et al., 1997;Halverson et al., 2005). The timing of the excursion is broadly constrained to within the Cryogenian 'non-glacial' interlude (between 660 and 640 Ma, to what extent the Trezona δ 13 C excursion has been altered by diagenesis. We use the geochemical data to fingerprint samples that have preserved their primary δ 13 C values during sedimentbuffered diagenesis in contrast to δ 13 C values that have been reset during fluid-buffered diagenesis. We find that intervals characterized by fluid-buffered diagenesis have less extreme δ 13 C values, and δ 44/40 Ca closer to BSE, relative to intervals characterized by sediment-buffered diagenesis. These results demonstrate that the most extreme δ 13 C values, both positive and negative, are primary in origin and are associated with local controls on δ 13 C in shallowwater aragonite producing environments.

Stratigraphical sections
In this study, we investigate the geochemical variability of three different Cryogenian carbonate successions (12 stratigraphic sections), from South Australia, Namibia, and Northwest Canada. At each locality, the sedimentology and δ 13 C chemostratigraphy has been extensively studied in previous publications (e.g., McKirdy et al., 2001;Rose et al., 2012;Klaebe and Kennedy, 2019;Hoffman, 2011;Macdonald et al., 2018), and we refer to the supplementary material for a detailed summary of the geological setting with Numerical model demonstrating the change in bulk carbonate chemistry over time with increasing degree of diagenesis, in this case modeled as dolomitization (from 0-100%), in both fluid-(box 1, blue dashed line) and sediment-buffered (box n, red solid line) conditions (following methods outlined by Ahm et al., 2018). A. The change in carbonate δ 13 C values over time from a primary value of 10‰ (blue star) towards a fluid value of -4‰ (red star), accounting for a fractionation factor of +1‰ between pore-fluid and the diagenetic carbonate minerals (Table S1). B. The change in carbonate δ 44/40 Ca values from a primary value of -1.7‰ towards a fluid value of -0.65‰, with a fractionation factor of 0‰ (Fantle and DePaolo, 2007). C. The change in carbonate δ 26 Mg values from a primary value of -2.4‰ towards a fluid value of -0.35‰, with a fractionation factor of -2‰ (Higgins and Schrag, 2010). As the rate of dolomitization decrease with time, the inflection in the sediment-buffered δ 26 Mg pathway represents the point where the supply of new Mg 2+ from advection overcomes the decrease of Mg 2+ due to dolomitization. D. Cross-plot of δ 13 C versus δ 44/40 Ca using the model outputs from A and B. E. Cross-plot of δ 26 Mg versus δ 44/40 Ca using the model outputs from B and C. Note that the model phase space in D and E is insensitive to changes in both reaction and advection rate, as changes in either of these parameters would have a similar impact on both the y and x-axis. The model is fit to the data using the phase space in D and E, where the goodness of fit is evaluated in part by the consistency of the model to predict a similar degree of alteration (%) for the same sample. A good model fit (pink square) is indicated by a similar degree of alteration across the phase spaces, whereas a bad fit (blue circle) is indicated by an offset in the predicted degree of alteration across the phase spaces and being outside the phase space in D.
location maps (Fig. S1-S3). For each locality, the stratigraphy and radiometric age constraints are summarized in Fig. 1.

Geochemical analyses
All measurements presented in this study are performed on carbonate powders that previously have been measured for δ 13 C and δ 18 O values (Strauss et al., unpublished;Hoffman, 2011;Rose et al., 2012;Macdonald et al., 2018). We refer to the supplementary material for a detailed outline of the Ca, Mg, and Sr isotope analyses and major and trace element analyses.
Calcium isotope measurements are reported for all samples as the relative abundance of 44 Ca relative to 40 Ca using standard delta notation, normalized to the isotopic composition of modern seawater. For Ca isotopes, the external reproducibility for SRM915b and SRM915a relative to modern seawater is −1.19 ± 0.14‰ (2σ , N = 120) and −1.86 ± 0.16‰ (2σ , N = 24), respectively.
A subset of samples was selected for strontium isotope analyses, performed at both Princeton University (samples from Namibia and Australia) and WHOI (samples from Northwest Canada). Strontium isotope measurements are reported as the ratio of 87 Sr over 86 Sr. At Princeton University, the long-term reproducibility of NBS987 is 0.710280 ± 0.000006 (N = 4). At WHOI, the long-term reproducibility of NBS987 is 0.710253 ± 0.000015 (N = 12). To reduce the influence of in-situ Rb decay ( 87 Rb to 87 Sr), measurements were filtered for Sr/Ca ratios >1.5 mmol/mol and reported as the average filtered value for each section, consistent with methods from previous publications (Halverson et al., 2005). In section F1228, where Sr/Ca ratios are low, 87 Sr/ 86 Sr ratios instead were filtered based on the least radiogenic values.

Numerical diagenetic model
To analyze the geochemical data, we use a numerical model of early carbonate diagenesis. This model previously has been used to simulate diagenetic changes in both Bahamian and Neoproterozoic carbonate (e.g., Ahm et al., 2018Ahm et al., , 2019. The model computes the geochemical changes that occur during early diagenesis as metastable carbonate minerals (e.g., aragonite) are dissolved and more stable phases (e.g., dolomite) precipitate. The conceptual model framework is a simplification of the complex geometry of fluid flow and diagenesis in carbonate sediments, which is affected by local differences in porosity, permeability, and reaction rates. To account for these differences, we present the model results as 2-dimensional phase-spaces (Fig. 2). These model cross-plots represent the geochemical changes that occur at different stages of diagenetic alteration (from 0-100%) and fluid evolution along the flow path (fluid-to sediment-buffered). In other words, each cross-plot comprises the total geochemical variability that can be produced from reactions between a carbonate rock and a diagenetic fluid with a prescribed composition.  (Rose et al., 2012(Rose et al., , 2013. Sections C215, N424, and A1043 are from the Central Flinders Ranges, while section R2 is from the Northern Flinders Ranges (for location map see Fig. S1). We use the model results to evaluate to what degree the geochemical signals across the Trezona excursion are products of diagenesis. By fitting the model phase space to envelop the data, we can estimate the composition of diagenetic fluids and different primary sedimentary end-members ( Fig. 2D-E). We refer to the supplementary material for a detailed description of the model setup and evaluation of specific model fits using a bootstrap resampling technique.
The downturn of the Trezona excursion is not observed, due to a lack of carbonate in the Enorama Shale (Fig. 1). The nadir of the excursion is recorded in the lower part of the Trezona Formation, characterized by a high fraction of fine-grained siliciclastic material relative to carbonate, with δ 13 C values at ∼-10‰ (McKirdy et al., 2001;Rose et al., 2012). Generally, this interval also records low δ 44/40 Ca values down to ∼-2‰, low δ 18 O values (down to -15‰), and high Sr/Ca ratios averaging ∼1.7 mmol/mol. The most Sr-rich samples have 87 Sr/ 86 Sr ratios of ∼0.7073.
The recovery of the excursion spans ∼250 m, with a gradual return to higher δ 13 C values approaching ∼0‰ at the top of the succession. This interval also records broadly increasing δ 18 O values (towards -8‰), increasing δ 44/40 Ca values up to -1.2‰, and decreasing Sr/Ca ratios (Fig. 3). While the depositional environ-ment in the nadir of the excursion is characterized by siliciclastic sediments, the increase in δ 13 C values up section coincides with a broad increase in relative carbonate abundance (McKirdy et al., 2001;Rose et al., 2012). This coarsening upwards succession previously has been interpreted as representing a shallowing (McKirdy et al., 2001;Rose et al., 2012), although this interpretation has been challenged (Klaebe and Kennedy, 2019).

Namibia
Namibia is the only location that has a progressive record of the Trezona excursion downturn (Fig. 4). The Trezona excursion is found in the upper Ombaatjie Formation and records a steady decline in δ 13 C values down from ∼+7 to -7‰ over a stratigraphic interval of 40-80 m. This interval also records decreasing δ 44/40 Ca values (from -0.7 to -1.6‰), decreasing δ 18 O values (from -1 to -8‰), and increasing δ 26 Mg values (from -2.1 to -1.0‰). However, the changes in δ 44/40 Ca, δ 18 O, and δ 26 Mg values begin stratigraphically after the downturn of the δ 13 C excursion has reached 0‰ While the downturn of the excursion is hosted in the shallowwater dolostone of the Ombaatjie platform, the nadir of the excursion coincides with a change from carbonate to a unique finegrained siliciclastic unit (parasequence b8, Hoffman, 2011). The Ombaatjie platform has a well-defined southern limit, beyond which is a foreslope with redeposited carbonates (Hoffman, 2011). On the foreslope, the siliciclastic siltstone unit (the Narachaams Member) is thicker (>100 m) than on the platform, and the downturn of the Trezona excursion is not recorded. Above the siltstone, carbonate deposition returns in the form of a 100-m-thick coarsening upward succession (Franni-aus Member) that records the nadir and a somewhat more complete recovery from the Trezona excursion than is preserved on the platform (from -7 towards 0‰). In parallel, this interval also records increasing δ 18 O values (from -13 to -2‰), increasing δ 44/40 Ca values (from ∼-1.6 to -0.8‰), decreas- Fig. 4. Namibia: Section P4006, P7500, and P6503 are shallow-water carbonates from the Ombaatjie Formation that record the downturn of the Trezona excursion. Section P9500 is from the more distal Franni-aus Member and only records the recovery of the Trezona excursion. The nadir of the Trezona excursion coincides with deposition of a regional siltstone unit with varying thickness, termed the Narachaams Member on the foreslope. The platform sections are correlated (dashed lines) based on observed parasequences (previously termed b4-b8), while the foreslope section (P9500) is related to the platform using δ 13 C chemostratigraphy Hoffman for location map see Fig  ing Sr/Ca ratios, and δ 26 Mg values between -2 and -1.5‰ (Fig. 4). The Sr-rich limestone preserving 87 Sr/ 86 Sr ratios of ∼0.7074.

Northwest Canada
In the Mackenzie Mountains (sections J1132/33), the Trezona excursion is recorded in the upper Keele Formation. Stratigraphically below the excursion, the shallow-water carbonate of the lower Keele Formation is characterized by a plateau of high δ 13 C values (the 'Keele peak', ∼+10‰, Kaufman et al., 1997;Day et al., 2004). The limestone and dolostone found in this interval have δ 44/40 Ca values between -1.2 and -1.0‰, high δ 26 Mg values up to ∼-0.6‰, and Sr/Ca ratios averaging 0.7 mmol/mol (Fig. 5). The more Sr-rich samples have 87 Sr/ 86 Sr values of ∼0.7073.
The carbonates containing the 'Keele peak' are succeeded by siliciclastic dominated strata (the 'Keele clastic wedge', Aitken, 1991;Day et al., 2004). Overlying the Keele clastic wedge, the Trezona nadir is found within subtidal limestone and contains δ 13 C values down to -10‰, δ 44/40 Ca values down to -1.9‰, Sr/Ca values up to 4 mmol/mol, and 87 Sr/ 86 Sr ratios of ∼0.7074 (Fig. 5). Following the nadir of the excursion, the uppermost stata of the Keele Formation record increasing δ 13 C values before the deposition of glacial sediments. Across this interval, δ 44/40 Ca values increase towards -1‰ and Sr/Ca ratios decrease to <1 mmol/mol.
The Durkan Member consists of siltstone and shale with thinbedded limestone and multiple horizons of carbonate clast breccia (section F1228, Macdonald et al., 2018). This interval contains the nadir and recovery of the Trezona excursion, recording values that increase from -10‰ towards 0‰ across ∼250 m. The recovery of the excursion coincides with an increase in carbonate deposition relative to siliciclastics and an increase in δ 44/40 Ca values from -1.8 to -1.0‰. This interval also records high Sr/Ca ratios up to 2.5 mmol/mol, and relatively scattered δ 18 O values (from -6 to -12‰,

The Trezona excursion -global and local controls
Despite the fact that the Trezona downturn is followed by sometimes hundreds of meters of δ 13 C recovery towards 0‰, previous models have focused on interpreting the decline in δ 13 C as associated with global changes in sea water chemistry and the onset of Snowball Earth (e.g., Hoffman and Schrag, 2002). Here, however, we highlight three features of the relationship between carbon and calcium isotopes across the entire Trezona excursion that are inconsistent with this interpretation.
First, we consider to what degree the δ 44/40 Ca values that are observed across the Trezona excursion may reflect steady state changes in the global calcium cycle. The main sink for seawater Ca 2+ is the burial of carbonate. A prediction for the global calcium cycle is that, on average, the calcium isotope composition of carbonate sediments through time should equal that of BSE (∼ −1‰, on time-scales >10 6 years, Skulan et al., 1997;Blättler and Higgins, 2017). However, the majority of the Cryogenian samples have δ 44/40 Ca <-1‰ (Fig. 6), both before the Trezona excursion and in  the Trezona nadir, and mass balance requires that these sediments cannot represent the average carbonate sink over long time scales.
Second, we consider to what degree the synchronicity of the carbon and calcium isotope excursions are consistent with a transient change in global carbonate burial. On the surface of Earth, the residence time for calcium is an order of magnitude longer than for carbon (∼ 10 6 versus ∼ 10 5 years, e.g., Gussone et al., 2020). Therefore, any perturbation to carbonate burial should not result in a synchronous stratigraphic change in carbonate δ 13 C and δ 44/40 Ca values, if we assume that the relative residence time of the calcium and carbon cycles were scaled similarly to today, (Holmden et al., 2012b). If the Trezona excursion represents a transient perturbation, the δ 44/40 Ca excursion should take longer to recover than the δ 13 C excursion. However, the Trezona data records covariation with no lag between carbon and calcium isotopes (Fig. 3-5).
Third alteration of platform aragonite across a continuum of fluid-to sediment-buffered conditions (Fig. 6A). Modern platform settings show a similar correlation that reflects mixing between three different carbonate end-members : (1)  Calcium isotopes and Sr/Ca ratios are fingerprints of different diagenetic end-members because the Ca isotope fractionation factor and Sr partitioning are sensitive to both mineralogy and precipitation rate (Tang et al., 2008;Gussone et al., 2005). Primary aragonite is more depleted in 44 Ca and enriched in Sr (-1.5‰ and 10 mmol/mol) relative to primary calcite (-1‰ and ∼1 mmol/mol).
In the carbonates that record the Trezona excursion, no primary aragonite is preserved, and instead we interpret the correlation  Allan and Matthews, 1982), and instead indicates sediment-buffered diagenesis of former aragonite (Fig. 6A). The interpretation of precursor aragonite also is supported by petrographic observations of aragonitic ooid fabrics in the Trezona Formation in South Australia (Singh, 1987).
Across the excursion, two separate stratigraphic intervals record sediment-buffered neomorphism of former aragonite. First, preexcursion carbonate with high δ 13 C of up to +10‰ (Keele peak), and second, in the nadir of the excursion (Fig. 6C). It is likely that these extreme δ 13 C values of the Keele peak and Trezona nadir record the chemistry of the environment where the aragonite sediments originally precipitated. In contrast, the intermediate strata that record the downturn and recovery of the Trezona excursion likely were altered during early fluid-buffered diagenesis, and record the chemistry of the early diagenetic pore-waters (Fig. 6C).
In addition to evidence for early diagenesis, there is geochemi-  values were reset to lower and more variable values (down to -15‰, Fig. 6D) due to the increase in burial temperature (∼100°C, if assuming fluid values of 0‰ V-SMOW, Kim and O'Neil, 1997). In contrast, carbonate that was dolomitized and stabilized during early marine diagenesis was more resistant to late-stage alteration and δ 18 O values are less altered (values up to -1‰, Fig. 6D). Although it is possible to alter δ 13 C values during late-stage burial (Derry, 2010), the correlation between very depleted δ 44/40 Ca and δ 13 C values indicates that the deep burial pore-fluids were highly buffered by carbonate dissolution, and sediment-buffered with respect to both calcium and carbon.

Dolomitization and fluid-buffered diagenesis
Intervals of early fluid-buffered diagenesis are observed during the downturn and recovery of the Trezona excursion, and in Namibia these intervals are associated with dolomitization. In addition to high δ 44/40 Ca values and low Sr/Ca ratios, the fluidbuffered dolostone is characterized by relatively low δ 26 Mg values.
Dolostone that formed during early diagenesis under fluid-buffered conditions tend to have lower and less variable δ 26 Mg values than dolostone forming in sediment-buffered conditions (Blättler et al., 2015). These trends are the product of a ∼-2‰ isotopic fractionation associated with the incorporation of Mg into dolomite (Higgins and Schrag, 2010). For example, fluid-buffered dolostone from the Bahamas platform and Neogene Monterey Formation are offset from modern seawater by -2‰ (values of -2.8‰, Blättler et al., 2015;Higgins et al., 2018). In contrast, sediment-buffered dolostone is enriched in 26 Mg due to Rayleigh-type distillation of the pore-fluid in more closed system settings (Blättler et al., 2015).
We use a numerical model of early diagenesis to estimate the composition and origin of the diagenetic fluids that dolomitized the Ombaatjie Formation, recording the downturn of the Trezona excursion (Fig. 7). Model results indicate that primary platform aragonite with high δ 13 C values (estimated at +10‰) were dolomitized by a fluid with δ 13 C values of -4‰ (uncertainty from -6.5 to -2.7‰). In addition, the model estimates fluid δ 44/40 Ca values of -0.65‰ and δ 26 Mg values of -0.35‰ (uncertainty of -0.68 to -0.55‰ and -0.4 to -0.1‰, respectively, Table 1).
Platform fluids can be modified from their original seawater compositions due to reactions in the subsurface and subsequent mixing with freshwater. For example, the low δ 44/40 Ca values of the downturn fluid (Fig. 7F) are consistent with modern observations from restricted platform settings influenced by submarine groundwater discharge and subsurface carbonate dissolution (∼-1.0 to -0.4‰, Holmden et al., 2012a;Shao et al., 2018). Similarly, subsurface reactions can modify fluid δ 26 Mg values and Mg 2+ /Ca 2+ ratios. Generally, submarine groundwater discharge and carbonate dissolution lead to lower Mg isotope values (Jacobson et al., 2010;Shirokova et al., 2013), while high δ 26 Mg values are associated with lagoonal and hypersaline environments that are dominated by evaporation and dolomitization (Shirokova et al., 2013). The model results indicate that the diagenetic fluid responsible for dolomitization in the Ombaatjie Formation had both low Mg 2+ /Ca 2+ ratios and relative low δ 26 Mg values (Table 1), consistent with platform waters influenced by submarine groundwater discharge enriched in 40 Ca and 24 Mg due to carbonate dissolution (Fig. 7).
The fluid-buffered interval recording the recovery of the Trezona excursion is observed on three separate continents (Table 1). Across this interval, model results indicate that primary platform aragonite with low δ 13 C values (estimated at -10‰) was dolomitized and/or neomorphosed by a fluid with δ 13 C values of +7‰, with an uncertainty range of +4 to +12.5‰. In addition, the model estimates fluid δ 44/40 Ca values of -0.5‰ and δ 26 Mg values of +0.1‰ (uncertainty of -0.65 to -0.40‰, and -0.05 to +0.25‰, respectively, Table 1).
The fact that a single diagenetic fluid may explain the trends observed during the recovery of the Trezona excursion on three continents could indicate a possible late Cryogenian seawater origin (Fig. 7). Fluid δ 44/40 Ca values of -0.5‰ would suggest more 44 Ca-depleted seawater relative to today, which is consistent with estimates of pre mid-Mesozoic seawater, prior to a deep-marine carbonate reservoir (e.g., Akhtar et al., 2020). However, the low fluid δ 44/40 Ca values also are within range of modern observations of restricted platform waters that are offset from modern seawater (Holmden et al., 2012a;Shao et al., 2018). Our results therefore cannot show conclusively that the 'recovery fluid' represents open-ocean seawater, but the relatively high δ 44/40 Ca values suggest a somewhat modified seawater origin. If the δ 26 Mg value and Mg 2+ /Ca 2+ ratio of the recovery fluid provide a close estimate of Cryogenian seawater (0.1‰ and 1.1 mol/mol, respectively, Fig. 7G), then seawater was significantly enriched in 26 Mg and had lower Mg 2+ /Ca 2+ ratios relative to the modern (modern values of -0.8‰ and 5.1 mol/mol, respectively, e.g., Higgins et al., 2018).

The Trezona excursion as a local phenomenon linked to siliciclastic input
In this section, we explore the link between the geochemical signals, our diagenetic interpretation, and the observed changes in siliciclastic relative to carbonate input across the Trezona excursion. In general, on continent fringing platforms, mixed deposition of carbonate and siliciclastic sediments is influenced by regional climate and local factors such as sediment and nutrient influx from river drainage systems that meander, avulse, and reorganize. Changing inputs of siliciclastic material can drive changes in platform water-depth, affecting platform fluid circulation, due to differences in permeability, porosity, and in the changing size of the The significance level represents the 95th percentile of model fits to randomly generated data (see methods for details). For comparison, modern seawater (e.g.,  and re-calculated model results for post-Marinoan seawater also are plotted (basal Ediacaran cap carbonates, Ahm et al., 2019). freshwater lens. For example, an increase in siliciclastic input often suffocates carbonate production, leading to a decrease in sediment accumulation rate relative to subsidence rate, and increases platform water-depth (Schlager, 1989). An increase in local sea-level can drive upwelling of deep-seated groundwater from the platform interior as thermally-driven circulation increases and pore-fluids are pushed upwards (Kohout et al., 1977). In contrast, reducing the supply of siliciclastic material often allows carbonate accumulation to keep up with subsidence rate, decreasing platform water-depth and expanding the freshwater lens in platform interiors. As the less dense freshwater flows seawards, it drives an increase in the deeper compensating flow of seawater into platforms (Henderson et al., 1999). Reorganization of rivers can change, not only the platform water depth and subsurface fluid flow, but also the chemical composition of the coastal surface waters (inputs of siliciclastics, nutrients, alkalinity, and remineralized organic carbon) and therefore the δ 13 C of carbonate precipitated from them (Patterson and Walter, 1994).

Cryogenian 13 C enriched platform aragonite
On all three continents, the interval preceding the Trezona excursion is characterized by a high fraction of carbonate relative to siliciclastic material, with high carbonate δ 13 C values (∼+10‰, Fig. 8, panel 1). Calcium isotopes and Sr/Ca ratios indicate that these stata originally were primary aragonite. High δ 13 C values in Cryogenian platform surface waters may reflect generally high Cryogenian seawater δ 13 C values, but we speculate that at least part of this enrichment is related to a combination of elevated pri-mary productivity and diurnal cycling in microbial mat dominated platform environments (Geyman and Maloof, 2019). The combination of low δ 44/40 Ca (<-1‰) and high δ 13 C values imply that these 13 C-enriched intervals cannot represent the average carbonate sink and need to be balanced by the burial of 44 Ca enriched (and possibly more 13 C depleted) carbonate in other localities.

The Trezona excursion
The downturn of the Trezona excursion only is recorded in dolostone in Namibia, while in other localities pre-Trezona carbonate gives way to siliciclastic strata (Fig. 8, panel 2). In Namibia, we hypothesize that progressive platform drowning is responsible for a temporary increase in platform fluid-flow that resulted in dolomitization of the underlying carbonate (parasequence b7, Fig. 4). This phase of dolomitization declines in intensity in concert with the decline in δ 13 C values towards the nadir. The model results suggest that the pore-fluids generated from re-circulating platform waters had δ 13 C values ∼-4‰ (Table 1), likely due to subsurface mixing between platform surface waters (more 13 Cdepleted, see below) and upwelling seawater (open-ocean, less 13 C-depleted).
Although the downturn of the Trezona excursion is observed only in Namibia, low δ 13 C values (between -7 and -10‰) are observed in former aragonite in the nadir of the Trezona excursion worldwide. These observations suggest that δ 13 C values of DIC in platform water, where aragonite likely precipitated, shifted from high to low in concert with increasing siliciclastic relative to carbonate input. The nadir of the Trezona excursion is recorded in settings where aragonite is interbedded with fine-grained siliciclastic sediments, decreasing permeability and possibly protecting the aragonite from early diagenesis (Fig. 8, panel 3).
The driving mechanism for generating extremely depleted δ 13 C values in Cryogenian surface waters remains enigmatic, but our analysis indicates a link to siliciclastic input and a strong diurnal engine in platform surface waters (with background δ 13 C values of >+7‰). We speculate that an increase in the input of siliciclastic sediments from river drainage may be associated with an influx of nutrients, which could lead to a localized burst in productivity of microbial mats. Increased microbial productivity provides a possible link to the extremely depleted δ 13 C values observed in the Trezona nadir. In modern hypersaline ponds dominated by microbial mats, periods of intense productivity have been associated with low δ 13 C values of DIC (<-10‰, Lazar and Erez, 1992). These low values are a product of kinetic isotopic fractionation during CO 2 hydration (estimated kinetic fractionation factors ∼-11‰, Zeebe and Wolf-Gladrow, 2001). In other words, while surface water DIC concentrations are significantly depleted due to high productivity rates, CO 2 is replenished by the relatively slow invasion from the atmosphere, which is associated with a large negative carbon isotope fractionation (Lazar and Erez, 1992).
There are some important differences between the modern hypersaline ponds (Lazar and Erez, 1992) and the Cryogenian platform environments. First, while the modern ponds are hypersaline, there is no evidence for evaporites in the Cryogenian successions. Second, in the modern ponds, carbonate precipitation is limited during the most extreme periods of disequilibrium, because the invasion of CO 2 decreases carbonate saturation (Lazar and Erez, 1992). However, CO 2 invasion has been connected to rapid carbonate precipitation in alkaline environments with a high supply of Ca 2+ (Clark et al., 1992). In these environments, subsurface fluids with very low DIC/Ca 2+ ratios come into contact with the atmosphere, resulting in rapid invasion of CO 2 and precipitation of carbonates with δ 13 C values down to -25‰ (Clark et al., 1992). We imagine that Cryogenian platform waters were poised somewhere in-between these modern end-members, consistent with model results of low DIC/Ca 2+ ratios in the 'downturn fluid' (Table 1). Additionally, while hypersalinity promotes disequilibrium due to very slow rates of air-sea gas exchange, disequilibrium also has been observed in freshwater lakes during intense algal blooms where rates of productivity exceed rates of CO 2 invasion (Herczeg and Fairbanks, 1987). We therefore speculate that Cryogenian platform environments dominated by microbial mats and associated with high background diurnal productivity (as evidence by background δ 13 C values of up to +10‰), may be poised close to a disequilibrium threshold where the kinetic effects of CO 2 invasion could be readily expressed. In this world, the Trezona excursion captures a period where an increase in siliciclastic influx drove platform surface water across this threshold, resulting in δ 13 C values of ∼-10‰.

The Trezona recovery
Following the nadir of the Trezona excursion, platform carbonate δ 13 C eventually recovers before the onset of the Marinoan glaciation. On all three continents, this interval is characterized by an increase in carbonate deposition relative to siliciclastics, and coincides with increasing fluid-buffered diagenesis (Fig. 8, panel  4). As carbonate input increased and accommodation space diminished, platform water-depth decreased, the fresh-water lens expanded, and seawater re-circulation in platforms intensified (Fig. 8,  panel 4). An increase in fluid-flow across this coarsening upwards succession is consistent with observations of fluid-flow patterns from the Bahamas where periods of relative sea-level fall are characterized by increased aragonite neomorphism and dolomitization (Vahrenkamp et al., 1991;Melim et al., 2002).
The late-Cryogenian 'recovery fluid' responsible for widespread diagenetic resetting of platform carbonate had a δ 13 C value of ∼+7‰, and most likely reflects the composition of platform surface waters that have returned to pre-Trezona conditions (from being 13 C-depleted to 13 C-enriched, Fig. 8, panel 4).

Local platform signals and global mass balance
The prevalence of local geochemical signals in Cryogenian carbonate successions has implications for the global mass balance of both carbon and calcium, and the degree to which the platform carbonates represent the average carbonate sink. An important observation is that the majority of carbonates measured in this study have δ 44/40 Ca values that are lower than BSE (-1‰, Skulan et al., 1997), and mass balance requires that these low δ 44/40 Ca values are balanced by the precipitation of 44 Ca enriched carbonates elsewhere (Blättler and Higgins, 2017). As the geological record is incomplete, it is not possible to show conclusively where this sink should be. One possibility is authigenic carbonate and cements, which tend to have high δ 44/40 Ca values (Blättler et al., 2015). Another possibility is the precipitation of carbonate veins during hydrothermal alteration of basalt (Bjerrum and Canfield, 2004). A third possibility is to reexamine the extent to which the Trezona excursion is observed in Cryogenian strata globally. For example, the excursion is not observed in the Cryogenian carbonatedominated successions of Mongolia and Panamint Range, Death Valley (Bold et al., 2020;Nelson et al., 2021), which previously has been interpreted as a result of sub-glacial erosion (Bold et al., 2016). Alternatively, it is possible that these platforms simply did not reach a disequilibrium threshold where δ 13 C values switch to -10‰, and due to relatively less siliciclastic input, also remained more susceptible to early diagenesis and fluid-buffered alteration. Mass balance could be achieved if fluid-buffered intervals characterized by high δ 44/40 Ca values (and less extreme δ 13 C values closer to ∼0‰) were correlated with sediment-buffered intervals characterized by low δ 44/40 Ca (and more extreme δ 13 C values, ∼+10 and -10‰). These intervals would not have been correlated previously due to the practice of using carbon isotope stratigraphy in Cryogenian successions.
Another feature of our hypothesis is that it suggests that the correlation between siliciclastic input and negative δ 13 C excursions in platform aragonite could be a common Neoproterozoic phenomenon during periods of high background diurnal carbon cycling (baseline δ 13 C>+5‰). Indeed, other excursions such as the Shuram-Wonoka, the Taishir, and the Islay anomaly are associated with a change from 13 C-enriched to 13 C-depleted carbonate, coinciding with a fractional increase in siliciclastic material (e.g., Husson et al., 2015;Bold et al., 2016;Park et al., 2019). It may be possible to change global siliciclastic fluxes though either global climate change or rapid glacio-eustatic sea-level rise, although currently there is no evidence for land-based ice-sheets in the Cryogenian 'non-glacial interlude'. Alternatively, in modern mixed platform environments, the influx of siliciclastic material largely is controlled by stochastic fluvial-deltaic and tectonic processes that operate on timescales from thousands to millions of years. If similar local processes are operating in Cryogenian mixed carbonate-siliciclastic platforms and contributing to the switch to negative δ 13 C values, it would be consistent with the lack of the Trezona excursion in some Cryogenian successions (e.g., Mongolia and Panamint Range) and the lack of the Taishir anomaly in others (e.g., Australia, Namibia, Northwest Canada). Moreover, in the localities where the excursion is found, it is not yet clear if it correlates across continents on time-scales that are relevant for the global carbon and calcium cycle (<10 5 − 10 6 years). Strontium isotope ratios and glacial diamictite-cap carbonate lithostratigraphical correlations broadly constrain the Trezona excursions within ∼10 Myr (Fig. 1), but these correlation tools do not provide the resolution to confirm that these excursions are coeval. Instead, it is possible that the switch from 13 C-enriched to 13 C-depleted carbonate on local platforms occurred separately across a broader period (e.g., between 1-5 Myrs), where global climate and tectonics contributed to a locally variable, increased flux of siliciclastic material to platform environments.

Conclusions
This study demonstrates that stratigraphic changes in Cryogenian platform carbonate δ 13 C values are characterized by intervals of fluid-versus sediment-buffered diagenesis linked to changes in the relative input of carbonate and siliciclastic sediments.

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.