A striking feature of the African continent is the ~1 km elevation of the eastern and southern African plateaus. This has been termed the African Superswell1, and is also manifest by the shallow bathymetry of the southeastern Atlantic Ocean basin2. Seismic imaging beneath the African continent has revealed a large anomalous zone of low seismic velocity3, similar to that identified beneath the Pacific4. Termed Large Low Shear Wave Velocity Provinces (LLSVP) or superplumes, these are imaged to extend upwards from the core-mantle boundary5. Mantle flow induced by these velocity anomalies has been proposed to dynamically support elevated crustal regions6. The high topography of the eastern African plateau and unusual bathymetry of the southeastern Atlantic basin has been attributed to recent thermal modification of the upper mantle associated with the East African Rift System7. Recent geophysical2 and geochemical8 studies have indicated that the deeply rooted African superplume is the primary cause of this mantle anomaly, and is a major contribution to the Cenozoic rifting and volcanism of eastern Africa.

However, it is currently unclear if the anomalous topography of southern Africa is supported by a thermal perturbation in the lithospheric mantle9, the sub-lithospheric upper mantle10, the lower mantle11, or a combination of all three2. Previous seismic studies of the upper mantle structure beneath southern Africa have recorded only a small decrease in seismic velocities within the sub-lithosphere mantle, indicating that a thermal anomaly is unlikely2. Alternative hypotheses for the uplift of the region include; heating of the lithosphere by the tail of a Mesozoic plume that was stationary beneath the area for more than 25 million years9, or that it is the result of buoyancy from the African superplume present in the lower mantle11.

The Lesotho-KwaZulu-Natal region exhibits the highest relief in southern Africa12 forming the southernmost part of the African Superswell. The region experiences active seismicity13 and the sedimentary record of the Durban Basin and other Cretaceous basins surrounding southern Africa provide evidence for deposits sourced from distinct pulses of uplift and erosion in the Turonian, Oligocene, mid-Miocene and Pliocene14. Offshore, the anomalous bathymetry15 and seamounts13 of the Mozambique Basin, have been linked to active mantle upwelling associated with the hypothesised Quathlamba mantle plume13. Onshore, this could also explain the seismicity16, anomalous topography12, small-scale volcanic activity17, thermal springs18, elevated geothermal gradient19 and active CO2 seeps13,20 of the region.

However, the nature of the upwelling mantle and whether it originates in the deep or shallow mantle is not understood, nor is the relationship to the underlying African superplume. The isotopic composition of the noble gases (He, Ne and Ar) are an established geochemical method of distinguishing between deep undegassed21,22 and shallow convective mantle sources23. The presence of a noble gas signature of the deep mantle source associated with the ongoing CO2 degassing would provide a measure of whether mantle upwelling is related to the deep-sourced African superplume24 as opposed to a shallow convection-driven process in the depleted upper mantle8.

Here, we show that whilst the 3He/4He are lower than a typical primordial mantle source of >8 RA (where RA is the 3He/4He of atmospheric air of 1.399 × 106), the Ne isotopic composition of the degassing mantle CO2 requires a deep mantle source, similar to that tapped by intraplate volcanism at Réunion25 or Kerguelen islands26, rather than the convecting depleted upper mantle. This confirms the existence of the previously hypothesised Quathlamba mantle plume13 and illustrates that even modest plume induced lithospheric mantle melting, which is yet to result in significant extrusive volcanism, has incorporated a noble gas signature of the deep mantle source. Our findings provide the first geochemical verification of ongoing deep mantle upwelling in Southern Africa and corroborates existing geophysical evidence that small-scale mantle plumes are emanating from the top of the African LLSVP in the region24.


Natural CO2 degassing in Lesotho-KwaZulu-Natal

CO2 gas seeps are common in areas of active or recent magmatism, and are frequently associated with fault-related fluid migration from depth27. Natural CO2 degassing is rare in South Africa; the natural cold CO2 seeps along the Ntlakwe-Bongwan fault in southern KwaZulu-Natal are the largest concentration of such phenomena. The fault was identified during geological mapping between 1911 and 191628 with the seeps first described in 192329 (Fig. 1a–c). The fault is expressed at the surface over ~80 km30 and is defined by a ~70 km wide arcuate zone of faulting that evolves southwards from an ENE-WSW to a north-south strike31. It is believed to be related to Gondwana rifting32 which commenced ~180 Ma and continues to the present (Fig. 1c).

Fig. 1
figure 1

Location of study area and relevant geological features. a Map of the African continent illustrating depicting extent of panel 1b (inset box), the hypothesised track of the Quathlamba hotspot13 (red line), trace of the East African Rift System (EARS)64 (dashed orange lines) as picked out by earthquakes (black circles) between 2006 and 2016 (downloaded from the publicly available USGS database - and plotted onto open source map tiles from the leaflet-extras R-library using Open Street Map tiles available via a CC-BY-SA licence from with country boundaries defined by Open Street Map). b Expanded map depicting study area (Panel c); the Bongwan fault trace (orange dashed line); the location of a small (1 m3) basaltic eruption that took place in Lesotho in 198317 (red triangle); the locations of the Shu Shu and Lilani hot springs on the Tugela river (blue stars) which also exhibit minor CO2 degassing and hot water (up to 53 °C)65; the position of anomalous seafloor mounds in the northern Natal Valley54 (black stars) and the speculative track of the hotspot, based on African plate movement reconstructions, with corresponding proposed positions of the hotspot at the dates cited13. c Expanded map of Bongwan fault showing the location of the three sampling sites from this study marked as yellow stars (A – Baker Farm, B – Mjaja and C – Umtamvuna; location letters correspond to previous work27), the trace of the fault and the bedrock geology of the region. Historically reported28,33, but no longer accessible or existing seep locations are depicted as grey stars

The origin of the degassing CO2 is enigmatic, with initial work proposing a link to dissolution of carbonate rocks at depth by acidic groundwater33. Later δ13C and δ18O measurements of the CO2 indicated an origin from low temperature acidic groundwater reactions with carbonate rocks of similar composition to the Cambrian Matjies River Formation20 of the Western Cape Province. Carbonates of the nearby Marble Delta Formation were ruled out as a source, as their δ13C was found to be distinct from the δ13CCO2 measured in the exsolving CO220, but this work did not take into account the potential fractionation of δ13C that would result from formation of a free-phase CO2 during dissolution of carbonate rock. Mantle melting associated with the hypothesised Quathlamba mantle hotspot has also been proposed as both a potential CO2 source, and a cause of a local thermal anomaly13.

Natural CO2 can have multiple origins, including; shallow biogenic processes, carbonate hydrolysis, deep burial related mechanical breakdown or thermo-metamorphism of carbonates and degassing of magmatic bodies34,35. Whilst δ13CCO2 can often resolve these sources, CO2-rich natural gases frequently exhibit values that overlap with the range of carbon from magmatic source and carbonate breakdown34, making it challenging to resolve their origin36. Noble gas isotopes are powerful tracers of the origin of CO2, particularly in identifying mantle contributions37. Primordial isotopes, such as 3He, originate in the Earth’s mantle and gases from the depleted upper mantle define a narrow range of CO2/3He (of 1 to 10 × 109)38,39,40.

Combining δ13CCO2 with CO2 and helium measurements to resolve CO2 origin

Here we combine new noble gas analyses of Bongwan CO2 and δ13CCO2 from six separate gas seeps, sampled from three locations along the Bongwan fault and associated splays (Supplementary Tables 12). δ13CCO2 range from −2.0 to −3.3‰ (V-PDB standard) in line with previous determinations20. 3He/4He ratios corrected for air (3He/4Hec—see “Methods”) within the samples range from 3.6 to 4.5 RA. These are considerably above the atmospheric ratio (1 RA) indicating the presence of a significant amount of primordial 3He.

4He exhibits the widest range in concentration compared to the other noble gases, from 1.48 × 10−9 (Umtamvuna Mound 2) to 9.62 × 10−5 cm3(STP)cm−3 (Baker Farm). 20Ne concentrations range from 4.01 × 10−9 to 4.13 × 10−8 cm3(STP)cm−3, with 40Ar ranging from 6.34 × 10−6 to 7.83 × 10−5 cm3(STP)cm−3. As with 4He concentrations, the lowest 20Ne and 40Ar values are exhibited by the CO2 sampled from Umtamvuna Mound 2, and the highest values are from the Baker Farm sample. CO2 from the Baker Farm and Mjaja seeps (A and B on Fig. 1c) exhibit CO2/3He of 1.88 and 6.78 × 109, confirming a mantle origin (Fig. 2). The four seeps sampled at Umtamvuna exhibit considerably higher CO2/3He ratios. As 3He is inert and insoluble37, and there is no significant 3He in the crust37 (3He/4Hecrust = 0.05 RA)41, the variation in CO2/3He is predominantly linked to the addition of 3He-poor CO242.

Fig. 2
figure 2

CO2/3He against δ13C for the Bongwan CO2 samples. Individual samples are plotted as red circles along with labels outlining their associated air-corrected 3He/4Hec in RA (where RA is the atmospheric 3He/4He of 1.399 × 10−6) and their location corresponding to Fig. 1 (A – Baker Farm, B – Mjaja and C – Umtamvuna). Mixing lines (black lines and grey shading) are shown for CO2 derived from the mantle, limestone and organic sediments38. End-member compositions cover the range of values38,62 (mantle CO2/3He = 1–10 × 109; mantle δ13C = −9 to −4‰; Crustal CO2/3He = 1 × 1012–1014; Limestone δ13C = 0 ± 2‰; Organic sediment δ13C = −30 ± 10‰). The range of δ13C values for South African carbonate sources from the Marble Delta20, Matjies River Formation20, and the Transvaal Supergroup66 are provided. The extent of δ13CCO2 that would be produced by acid groundwater dissolution of Marble Delta Formation carbonate is also shown (grey box and black lines depicting the minimum δ13CCO2 that would result from dissolution of the formation carbonate between 10 °C (left) and 100 °C (right)) (see Methods). The trend between CO2/3He and δ13CCO2 are consistent with the mixing of mantle-derived CO2 with CO2 derived from the overlying Marble Delta Formation carbonates at up to 70 °C (see “Methods”). δ13CCO2 was not measured from the sample collected at the Umtamvuna River Spring and hence this sample cannot be depicted on the plot

Combining CO2/3He with δ13CCO2 allows organic sediment and limestone-derived CO2 to be distinguished from magmatic sources38 (Fig. 2). The trend between CO2/3He and δ13CCO2 are consistent with the mixing of mantle-derived CO2 with CO2 derived from the overlying Marble Delta Formation carbonates at up to 70 °C (see “Methods”). Based on the regional geothermal gradient of 30 °C/km19 and an average surface temperature of 14 °C43, we estimate that mixing occurred at depths of less than ~1900 m.

Linking CO2/3He, CO2/4He and 3He/4He in a ternary plot allows CO2 sources to be resolved44,45, permitting direct comparison of the relative proportions of CO2, 3He, and 4He, regardless of absolute concentrations (Fig. 3). Binary mixtures and loss or gain of a single component plot as straight lines on ternary plots. Figure 3 demonstrates that the Baker Farm gas requires the ingrowth/addition of 33 to 50 % radiogenic 4He, derived from the lithosphere, to mantle magmas, relative to the depleted upper asthenosphere mantle (DM) (8 ± 1 RA)46 or sub-continental lithospheric mantle (SCLM) (6.1 ± 0.9 RA)47, respectively. The remaining samples require the addition of 3He-poor CO2. The modest 4He required in this gas confirms a shallow crustal origin for this non-magmatic CO2 (also see Supplementary Fig. 1). The low 4He/20Ne in these samples contrasts with the higher values measured in the Mjaja and Baker Farm gases and implies that the CO2 has interacted with atmosphere-saturated groundwaters.

Fig. 3
figure 3

Ternary plot of CO2/3He, CO2/4He and 3He/4He of Bongwan CO2 samples. Relevant end-members, after45, with relative concentrations calculated for CO2, 3He, and 4He, based on these ratios. Scaling factors are introduced to the CO2 and 3He values, as labelled, to allow the full spread of data to be represented. The scaled relative concentrations are then normalised to a three-component system where CO2 + 3He + 4He = 100%, permitting direct comparison of the relative proportions of CO2, 3He, and 4He, regardless of absolute concentrations. Binary mixtures and loss or gain of any single component will plot as straight lines. The plot shows that the Bongwan CO2 samples have been influenced by two separate processes: (1) Mixing between depleted upper mantle (DM) (8 ± 1 RA)46 or sub-continental lithospheric mantle (SCLM) (6.1 ± 0.9 RA)47 and a radiogenic 4He component, and (2) Addition of a high-CO2, low-3He and 4He component and/or loss of both 3He and 4He relative to CO2. The Baker Farm sample lies on the first mixing line, and the addition of CO2 free of 3He and low in 4He and the effect of shallow preferential degassing of He relative to CO2 in the near-surface48 can account for the second trend. ECLT – East Cape Large Travertine, ECST – East Cape Small Travertine, UM-RS – Umtamvuna River Spring and UM – Umtamvuna

Recent work undertaken on CO2 seeps in Australia, similar to those at Bongwan, has highlighted that equilibration of mantle-sourced CO2 with atmosphere-saturated groundwaters, followed by solubility controlled fractionation during exsolution of the CO2 from the groundwater at CO2 seeps, can result in depleted He concentrations and elevated CO2/3He from values which are originally within the magmatic source range48. Given the wide range of 4He concentrations observed between the different seeps, it is likely that both mixing with crustal derived CO2 and solubility fractionation, resulting in a relative loss in He, have acted to produce the observed CO2/3He ratios at Bongwan (Fig. 3).

Constraining the mantle source using Ne and Ar isotopes

The 3He/4He of the SCLM of the Karoo Large Igneous Province and the nearby volcanic ocean islands (Comores, Tristan da Cuna and Gough) are characterised by low 3He/4He (4.9–7.1 RA)49. Hence, the mantle source in the region may have 3He/4He that is lower than MORB, but is most likely to be above the highest measured 3He/4Hec of 4.27 RA. The CO2 degassed at the Bongwan seeps has migrated from the mantle through the crust and will have incorporated radiogenic He from the Precambrian metamorphic basement and sedimentary cover. Radiogenic 4He is required to account for CO2-He isotope systematics of the Baker Farm seep gas (Fig. 3) and can account for the 4He/21Ne* ratio of 1.23 × 107 in the sample, below the crustal ratio of 1.71 × 107 41. Neon isotopes provide less ambiguous insights into the mantle source, enabling differentiation of depleted, convecting upper mantle (DM), the source of mid-ocean ridge basalts (MORB) and the primordial 20Ne-enriched mantle that is sampled by intraplate magmatism, the source of ocean island basalts (OIB)50.

The Ne isotope composition of Baker Farm and Mjaja seeps show a clear mantle component, which is distinct from both atmospheric Ne and the mass fractionation line (Fig. 4). 40Ar/36Ar of the Mjaja and Baker Farm gases (550 ± 2 and 961 ± 4 respectively) are higher than the air value, consistent with a partial mantle origin of the non-atmospheric 40Ar. This is supported by the 4He/40Ar* (1.55 and 1.77 respectively) which are close to the mantle value of 237. The remaining samples have atmospheric dominated Ne and Ar isotope compositions consistent with derivation of Ne and Ar from air-equilibrated groundwater. This corresponds to the crustal CO2 addition from groundwater and/or He loss due to degassing of CO2 from groundwater48, required to account for the elevated CO2/3He in these samples, compared to the more mantle-rich values of Mjaja and Baker Farm.

Fig. 4
figure 4

20Ne/22Ne plotted against 21Ne/22Ne for the Bongwan CO2 samples. Lower precision analysis performed on the MAP 215-50 mass spectrometer are plotted as red diamonds, higher precision analysis undertaken on the ARGUS VI mass spectrometer are depicted as red circles, with air plotted as a black square. 1σ errors associated with each measurement are provided along with mixing lines between air67, continental crust41, MORB46 and solar end members62 shown as solid black lines. The Kerguelen, Reunion, Loihi-Kilauea, and Iceland hotspots are depicted as thin dashed lines46 with the mass fractionation line (MFL) shown as a thick dashed line. The Baker Farm (BF) and Mjaja (M) gases plot above the established air-MORB mixing line40,68, plotting between the Kerguelen and the Reunion mantle source25, implying an undegassed mantle origin for the Bongwan CO2. The uncertainty differences reflect different analytical procedures and the ARGUS samples have been corrected for the contributions to 21Ne from NeH+, which is controlled by the amount of H2 present in the mass spectrometer during analysis61 (see “Methods”)

Importantly, the results of the high precision Ne analysis of Mjaja and Baker Farm seep gases do not plot on the MORB-air mixing line in Ne isotope space (Fig. 4). Instead they provide a clear indication that the mantle source of the CO2 is more primordial than that of the convecting upper mantle (Fig. 4). The duplicate high precision determinations of the Baker Farm and Mjaja CO2 samples overlaps with the trend defined by the Kerguelen26 and Réunion hotspots25, implying the ultimate source of the upwelling mantle is deep. The low 3He/4He of the Bongwan gases relative to Kerguelen (12.3 ± 0.3 RA) and Réunion (11.5–13.1 RA) would require the incorporation of crustal radiogenic 4He.

However, the 3He/4He of the sub-lithospheric mantle source of the nearby Karoo Large Igneous Province is cited as 7.03 ± 0.23 RA51 and the most proximal volcanic ocean islands (Comores, Tristan da Cuna and Gough) are characterised by low 3He/4He (4.9 to 7.1 RA)51. Hence, the mantle source in the region may have a 3He/4He that is not elevated above the MORB range (8 ± 1 RA), though is most likely to be above the highest measured 3He/4Hec of 4.5 RA. It is also possible that the He and Ne systematics of the mantle under southern South Africa are decoupled, as has been observed in the Icelandic and the Colorado Plateau mantle sources23,52,53. This decoupling was attributed to either more compatible behaviour of He during low-degree partial melting or more extensive diffusive loss of He relative to the heavier noble gases. Incorporation of crustal-radiogenic 21Ne to the Bongwan gases is also probable, but without constraint of the original Bongwan mantle 3He/4He this is impossible to determine.


The Bongwan CO2 seeps are located at the end of the hypothesised Quathlamba hotspot track. Hotspot migration has been proposed to explain chain of volcanic seamounts that track across the Mozambique Basin13, orientated in a direction that closely resembles reconstructions of the African plate movement (Fig. 1). Recently, anomalous 30 km elongate seamounts, have been identified within the Northern Natal Valley offshore of Durban54. The geospatial positioning of these could extend the East African Rift System southwards, but they are also within range and age of the proposed Quathlamba hotspot track (Fig. 1b). Furthermore, recent work has found that the seafloor adjacent to the Mozambican continental margin, and that of the central Mozambique Channel is 300 m and 1300 m shallower, respectively, than the conjugate basins in Antarctica, or than oceanic thermal subsidence models predict15. This has been attributed to the presence of thickened oceanic crust, linked to the passage of a mantle plume beneath the basin during the Paleogene15.

Plate movement reconstructions indicate that this hotspot moved under the continent approximately 10 million years ago (Fig. 1), coinciding with several periods of regional uplift55. The Ne isotope systematics of the CO2-rich gas seeps provide the first geochemical evidence that small volumes of melting is occurring beneath the continental lithosphere in the region. This confirms the existence of the previously hypothesised Quathlamba mantle plume13 and illustrates that even modest plume induced lithospheric mantle melting, which is yet to result in significant extrusive volcanism, has incorporated a noble gas signature of the deep mantle source. These findings provide the first geochemical verification of ongoing mantle upwelling in Southern Africa, confirming geophysical evidence that small-scale mantle plumes are emanating from the top of the African superplume24. Buoyant underplating of Southern Africa by the African superplume provides an explanation for the anomalous elevation, high heat flow, and how the Quathlamba mantle plume has incorporated deep-sourced mantle volatiles.



The CO2 seeps were identified in the field as bubble streams in pools of water, rivers and wellbores (Fig. 1, Supplementary Table 1). Gas samples were collected in September 2015 by placing a plastic funnel over the site of the CO2 seep and flowing the gas through a 70 cm length of refrigeration grade copper tubing fitted with an exhaust hose to prevent turbulent back-mixing of air into the sample. The tubing was purged with the seeping gas for between 10 and 15 min before being clamped by a purpose built tube clamp at both ends to seal the copper tube with a cold-weld that is impervious to helium36. Tedlar sample bags were filled at each seep for stable isotope analyses. The Baker Farm borehole was sampled by sealing the well and using a soil gas probe to collect gas from as deep as possible within the well. A Geotechnical Instruments GA2000 portable gas analyser was then used to extract gas from the Baker Farm well, with the pump being connected downstream of the sampling apparatus. Further details on individual field sites and other surveys undertaken in the area are outlined in Supplementary Table 1 and in previous work27,56.

Laboratory analysis

Bulk gas, stable isotope and noble gas analysis was undertaken at the Scottish Universities Environmental Research Centre (SUERC), using previously described techniques57. Bulk gas content as a percentage was determined using a Pfeiffer Vacuum QMS 200 quadrupole mass spectrometer with all seeps sampled exhibiting concentrations of >99% CO2. δ13CCO2 were measured using a VG SIRA II dual inlet isotope ratio mass spectrometer following established procedures58. Precision and reproducibility are typically better than ±0.2‰ for δ13C (Supplementary Table 2).

Noble gas analyses from all samples were performed on volumes of ~10 cm3 gas stored in copper tubes. Each sample was expanded to a titanium sublimation pump (900 °C) and a series of SAES GP50 ZrAl getters (250 °C) operating under ultra-high vacuum, following established procedures57,58,59,60. The isotopic composition of He, Ne and Ar of all six samples was measured using a MAP 215-50 mass spectrometer using established techniques57,58,59,60 (Supplementary Tables 2 and 3). Analytical errors are governed by the reproducibility of air calibrations, and for Ne, standard reproducibility was assessed using the best Gaussian fit to the probability density distribution of 21Ne/22Ne and 20Ne/22Ne ratios from 14 air calibrations, which is an objective way of filtering outliers. These samples were not corrected for any 20NeH+ contribution to 21Ne.

High precision analysis of Ne isotopes within the Baker Farm and Mjaja samples was undertaken in multi-collection mode using a ThermoFisher ARGUS VI using the following procedures. Each copper tube sample was mounted on the ultra-high vacuum line attached to the MAP 215-50 mass spectrometer, and subjected to the same clean up procedure as outlined above, following which they were trapped in a 2 L stainless steel cylinder. Approximately 100 cm3 of total gas was extracted from this cylinder to the ultra-high vacuum system attached to the ARGUS VI mass spectrometer as described in previous work61. The gas was exposed to another SAES GP50 ZrAl getter (held at 250 °C) for 15 min and then a liquid nitrogen-cooled charcoal finger (held at −196 °C) for 15 min to trap any remaining active gases along with Ar, Kr and Xe. Ne was then adsorbed on charcoal using an IceOxford cryopump (−243 °C, 20 min) while He was pumped away. Pure Ne was released at −173 °C and administered into the ARGUS VI low resolution mass spectrometer. The ARGUS clean-up and analysis procedure was undertaken twice for both the Baker Farm and Mjaja samples, and the results of the individual repeat measurements are plotted on both Fig. 4 and Supplementary Fig. 3, and listed in Supplementary Table 4.

Analysis of Ne isotopes followed procedures described in previous work61. Ne isotopes were multi-collected (22Ne+– H2, 21Ne+ – Axial, 20Ne+ – L2) on 1012 Ω Faraday amplifiers. Isobaric interferences of 40Ar2+ and 44CO22+ were quantified using pre-determined singly/doubly charged ratios under measurement conditions and the in situ measurement of 40Ar2+ and 44CO22+ during analysis on the CDD detector. The contributions of 40Ar2+ to the corresponding 20Ne peak were found to be ~0.6% and 0.07% for Baker Farm and Mjaja samples, respectively. Contributions of 44CO22+ to 22Ne for Baker Farm and Mjaja were found to be 0.2% and 0.04%, respectively. The contribution of 40Ar+ and 44CO2+ to the overall uncertainty of Ne isotopic ratios was found to be below 0.01%. Other interferences (H218O+, H19F+, 65Cu3+) were found to be negligible. The 20NeH+ contribution at m/z = 21 was determined using a pre-recorded calibration curve of 22Ne – 22NeH at a constant hydrogen level, that exceeded the level of 22Ne, where 20Ne of each sample was measured61. The measurement of 22NeH occurred at m/z = 23, corrected for 46CO22+ and blank. 20NeH+ correction at m/z = 21 was found to be 0.96% (Baker Farm) and 1.94% (Mjaja). The contribution of NeH correction toward the overall uncertainty is ± 0.02%. Mass fractionation was corrected by the repeated analysis of air prior to and after analysis (n = 9) with the reproducibility of 20Ne/22Ne = 0.05% and 21Ne/22Ne = 0.11%.

Data analysis

3He/4He were corrected for minor atmospheric air contributions using the measured 4He/20Ne, following the established formula:37

$$\left( {{\,}^3\mathrm{He}/{\,}^4\mathrm{He}} \right)_c = \frac{{\left( {{\,}^3\mathrm{He}/{\,}^4\mathrm{He}} \right)_s \times \left( {{\,}^4\mathrm{He}/{\,}^{20}\mathrm{Ne}} \right)_s/\left( {{\,}^4\mathrm{He}/{\,}^{20}\mathrm{Ne}} \right)_{\mathrm{air}} - \left( {{\,}^3\mathrm{He}/{\,}^4\mathrm{He}} \right)_{\mathrm{air}}}}{{\left( {{\,}^3\mathrm{He}/{\,}^{20}\mathrm{Ne}} \right)_s/\left( {{\,}^3\mathrm{He}/{\,}^{20}\mathrm{Ne}} \right)_{\mathrm{air}} - 1}}$$

Mixing curves shown in Fig. 2 are calculated after62 using E

$$\left( {\frac{{{\,}^{13}{\mathrm{C}}}}{{{\,}^{12}{\mathrm{C}}}}} \right)_{\mathrm{Obs}} = {\mathrm{A}} \ast \left( {\frac{{{\,}^{13}{\mathrm{C}}}}{{{\,}^{12}{\mathrm{C}}}}} \right)_{\mathrm{A}} + {\mathrm{B}} \ast \left( {\frac{{{\,}^{13}{\mathrm{C}}}}{{{\,}^{12}{\mathrm{C}}}}} \right)_{\mathrm{B}} + {\mathrm{C}} \ast \left( {\frac{{{\,}^{13}{\mathrm{C}}}}{{{\,}^{12}{\mathrm{C}}}}} \right)_{\mathrm{C}}$$


$$1/\left( {\frac{{\mathrm{CO}_2}}{{{\,}^3{\mathrm{He}}}}} \right)_{\mathrm{Obs}} = {\mathrm{A}}/\left( {\frac{{\mathrm{CO}_2}}{{{\,}^3{\mathrm{He}}}}} \right)_{\mathrm{A}} + {\mathrm{B}}/\left( {\frac{{\mathrm{CO}_2}}{{{\,}^3{\mathrm{He}}}}} \right)_{\mathrm{B}} + {\mathrm{C}}/\left( {\frac{{\mathrm{CO}_2}}{{{\,}^3{\mathrm{He}}}}} \right)_{\mathrm{C}}$$

where A, B and C refer to three different components and A+B+C = 1.

The predicted δ13CCO2 produced by the acid dissolution of the Marble Delta Formation between temperatures of 10 and 100 °C, depicted on Fig. 2, was calculated from the measured Marble Delta Formation δ13Ccarb20 using established fractionation factors between δ13Ccarb and gaseous CO2, calculated according to equation [4]63, where T is the temperature in Kelvin:

$$10^3ln\alpha = - 2.988 \ast \left( {10^6/T^2} \right) + 7.6663 \ast \left( {10^3/T} \right) - 2.4612$$