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Abstract

Figures and Tables

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Introduction

The early practitioners of stable isotope geochemistry recognised that the three isotopes of oxygen followed mass-dependent rules, such that fractionation in ¹⁷O/¹⁶O was approximately half that of ¹⁸O/¹⁶O for both equilibrium and kinetic processes (Craig, 1957

Craig, H. (1957) Isotopic standards for carbon and oxygen and correction factors for mass-spectrometric analysis of carbon dioxide. Geochimica et Cosmochimica Acta 12, 133-149.

). Measuring the ¹⁷O/¹⁶O ratios therefore provided no additional information to the ¹⁸O/¹⁶O values alone. Mass-independent fractionations have since been found in primitive meteorites (Clayton et al., 1973

Clayton, R.N., Grossman, L., Mayeda, T.K. (1973) A component of primitive nuclear composition in carbonaceous meteorites. Science 182, 485-488.

) and many atmospheric components such as O₃, CO₂, H₂O₂ which are explained by photochemical processes (Thiemens, 2006

Thiemens, M.H. (2006) History and application of mass-independent isotope effects. Annual Review of Earth and Planetary Sciences 34, 217-262.

).

With improved precision, it is now recognised that there are small, but non-zero deviations from a simple best fit line in δ¹⁷O - δ¹⁸O space that are related to mass-dependent processes (Luz and Barkan, 2010

Luz, B., Barkan, E. (2010) Variations of ¹⁷O/¹⁶O and ¹⁸O/¹⁶O in meteoric waters. Geochimica et Cosmochimica Acta 74, 6276-6286.

; Pack and Herwartz, 2014

Pack, A., Herwartz, D. (2014) The triple oxygen isotope composition of the Earth mantle and Δ¹⁷O variations in terrestrial rocks. Earth and Planetary Science Letters 390, 138-145.

). As more data are collected, general trends are being observed. Here we compile the bulk of published, and our own unpublished, high precision triple oxygen isotope data and categorise distinct trends in δ′¹⁸O – Δ′¹⁷O space for different processes.

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The Terrestrial Fractionation Line and Relevant Notation

A fit through δ¹⁸O - δ¹⁷O values of terrestrial materials defines the ‘Terrestrial Fractionation Line’ (TFL) with a slope of ~½. The general expression for the TFL is

δ′¹⁷O = λ_TFL δ′¹⁸O + γ_TFL

where λ_TFL is the best fit slope and γ_TFL is the y-intercept of the best fit line. Equation 1 and all data in this study are presented in the linearised notation given by δ' (see Miller, 2002

Miller, M.F. (2002) Isotopic fractionation and the quantification of ¹⁷O anomalies in the oxygen three-isotope system: an appraisal and geochemical significance. Geochimica et Cosmochimica Acta 66, 1881-1889.

and Supplementary Information). There is no ‘correct’ or unique TFL, as different equilibrium or kinetic processes result in slightly different triple isotope fractionations. For example, meteoric waters fall on a trend that does not exactly overlap with the trend defined by most rocks and minerals (Luz and Barkan, 2010

Luz, B., Barkan, E. (2010) Variations of ¹⁷O/¹⁶O and ¹⁸O/¹⁶O in meteoric waters. Geochimica et Cosmochimica Acta 74, 6276-6286.

; Pack and Herwartz, 2014

Pack, A., Herwartz, D. (2014) The triple oxygen isotope composition of the Earth mantle and Δ¹⁷O variations in terrestrial rocks. Earth and Planetary Science Letters 390, 138-145.

; Pack et al., 2016

Pack, A., Tanaka, R., Hering, M., Sengupta, S., Peters, S., Nakamura, E. (2016) The oxygen isotope composition of San Carlos olivine on the VSMOW2-SLAP2 scale. Rapid Communications in Mass Spectrometry 30, 1495-1504.

). A δ′¹⁷O - δ′¹⁸O plot of published data from natural samples is shown in Figure S-1. Virtually all data plot exactly on the same line at the resolution of the figure.

To better visualise subtle deviations from the TFL reference line, the Δ′¹⁷O value has been introduced. The Δ′¹⁷O term is defined as

Δ′¹⁷O = δ′¹⁷O - λ_RL δ′¹⁸O + γ_RL

λ_RL is the reference line slope and γ_RL is the y intercept. In this study, δ′¹⁷O and δ′¹⁸O values from different publications are normalised to VSMOW (rocks and minerals) and VSMOW/SLAP2 scale (waters; SLAP2 from Schoenemann et al., 2013

Schoenemann, S.W., Schauer, A.J., Steig, E.J. (2013) Measurement of SLAP2 and GISP δ¹⁷O and proposed VSMOW-SLAP normalization for δ¹⁷O and ¹⁷Oexcess. Rapid Communications in Mass Spectrometry 27, 582-590.

) and derived Δ′¹⁷O to a reference line with slope 0.528 (λ_RL) and zero intercept (γ_RL = 0). Rock samples are normalised to the VSMOW scale with the Δ′¹⁷O value of the broadly adopted San Carlos Olivine standard (SCO) having δ′¹⁸O and Δ′¹⁷O values of 5.4 ‰ and -0.05 ‰ relative to a λ_RL = 0.528 and γ_RL = 0 (Sharp et al., 2016

Sharp, Z.D., Gibbons, J.A., Maltsev, O., Atudorei, V., Pack, A., Sengupta, S., Shock, E.L., Knauth, L.P. (2016) A calibration of the triple oxygen isotope fractionation in the SiO2 - H2O system and applications to natural samples. Geochimica et Cosmochimica Acta 186, 105-119.

). See Pack et al. (2016)

Pack, A., Tanaka, R., Hering, M., Sengupta, S., Peters, S., Nakamura, E. (2016) The oxygen isotope composition of San Carlos olivine on the VSMOW2-SLAP2 scale. Rapid Communications in Mass Spectrometry 30, 1495-1504.

for details of normalisation.

Small variations in Δ′¹⁷O become apparent in a Δ′¹⁷O vs. δ′¹⁸O plot (Fig. 1). Waters have positive Δ′¹⁷O values, while rock samples have negative Δ′¹⁷O values that tend to decrease with increasing δ′¹⁸O. Hydrothermally altered samples have the lowest δ′¹⁸O values of any rock samples.

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Characteristic Δ′¹⁷O - δ′¹⁸O Fields and Trends

A number of generalisations can be made from the data shown in Figure 1. A clear separation in the Δ′¹⁷O values between waters and rocks is immediately apparent. The mantle has a very tight range of Δ′¹⁷O values of -0.03 to -0.07 ‰, with most samples plotting at -0.05 ± 0.01 ‰. The 0.04 spread in Δ′¹⁷O in mantle samples is due to mantle metasomatism or alteration and in some cases analytical error. True variability within pristine mantle is likely much smaller and is centered on Δ′¹⁷O = -0.05 ‰.

The δ′¹⁸O values of more evolved high silica igneous rocks are higher than the typical mantle value of ~5.4 ‰, but the Δ′¹⁷O values remain relatively constant. This is because 1) the shift in δ′¹⁸O is small and 2) the associated high-T θ value (where θ = ln(α¹⁷O) / ln(α¹⁸O); see Supplementary Information) for minerals and melts is close to the reference slope value of 0.528, thereby moving more siliceous samples to higher δ′¹⁸O, but constant Δ′¹⁷O values.

Meteoric waters
Meteoric water data vary greatly in Δ′¹⁷O - δ′¹⁸O space (Fig. 2). Samples with δ¹⁸O values between -55 and -15 ‰ have an average Δ′¹⁷O value of 0.041 ± 0.006 and fall on a line with slope λ = 0.528. The offset in Δ′¹⁷O relative to the value of 0 ‰ for the ocean is related to the kinetic fractionation associated by transport of vapour from the saturated layer into the free, undersaturated atmosphere (Luz and Barkan, 2010

Luz, B., Barkan, E. (2010) Variations of ¹⁷O/¹⁶O and ¹⁸O/¹⁶O in meteoric waters. Geochimica et Cosmochimica Acta 74, 6276-6286.

). Samples from the Vostok ice core (pale blue points in Fig. 2) are fit with a higher λ value of 0.5309 ± 0.0001, which is attributed loosely to variable humidity and wind speed at the ocean source and supersaturation conditions during condensation in extremely cold environments (Landais et al., 2008

Landais, A., Barkan, E., Luz, B. (2008) Record of δ¹⁸O and ¹⁷O-excess in ice from Vostok Antarctica during the last 150,000 years. Geophysical Research Letters 35, doi: 10.1029/2007GL032096.

) or direct condensation as ‘diamond dust’ (Miller, 2018

Miller, M.F. (2018) Precipitation regime influence on oxygen triple-isotope distributions in Antarctic precipitation and ice cores. Earth and Planetary Science Letters 481, 316-327.

). For δ′¹⁸O values greater than -20 ‰, the Δ′¹⁷O values of meteoric waters show the reverse trend, decreasing with increasing δ′¹⁸O. Rain re-evaporation and mixing have been explained as the principle driving force towards the low Δ′¹⁷O values (Landais et al., 2010

Landais, A., Risi, C., Bony, S., Vimeux, F., Descroix, L., Falourd, S., Bouygues, A. (2010) Combined measurements of ¹⁷O_excess and d-excess in African monsoon precipitation: Implications for evaluating convective parameterizations. Earth and Planetary Science Letters 298, 104-112.

; Risi et al., 2013

Risi, C., Landais, A., Winkler, R., Vimeux, F. (2013) Can we determine what controls the spatio-temporal distribution of d-excess and ¹⁷O-excess in precipitation using the LMDZ general circulation model. Climate of the Past 9, 2173-2193.

; Li et al., 2015

Li, S., Levin, N.E., Chesson, L.A. (2015) Continental scale variation in ¹⁷O-excess of meteoric waters in the United States. Geochimica et Cosmochimica Acta 164, 110-126.

).

The best fit line to meteoric water samples with a δ′¹⁸O value greater than -20 ‰ is

δ′¹⁷O = 0.52654 (±0.00036) δ′¹⁸O + 0.014 (±0.003).

Most waters outside of extreme polar regions have δ¹⁸O values that are greater than ‑20 ‰, so that Equation 3 is a rough fit to the Global Meteoric Water Line for waters from non-polar sample regions.

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Low temperature sediments
A compilation of data from low temperature sediments shows decreasing Δ′¹⁷O values with increasing δ′¹⁸O (Fig. 3). This trend is explained by the temperature effect on the equilibrium fractionation between minerals and seawater. The triple isotope equilibrium θ value decreases with decreasing temperature, (Cao and Liu, 2011

Cao, X., Liu, Y. (2011) Equilibrium mass-dependent fractionation relationships for triple oxygen isotopes. Geochimica et Cosmochimica Acta 75, 7435-7445.

; Sharp et al., 2016

Sharp, Z.D., Gibbons, J.A., Maltsev, O., Atudorei, V., Pack, A., Sengupta, S., Shock, E.L., Knauth, L.P. (2016) A calibration of the triple oxygen isotope fractionation in the SiO2 - H2O system and applications to natural samples. Geochimica et Cosmochimica Acta 186, 105-119.

). The curved line in Figure 3 is the equation governing the Δ′¹⁷O - δ′¹⁸O values of silica in equilibrium with ocean water as a function of temperature (Sharp et al., 2016

Sharp, Z.D., Gibbons, J.A., Maltsev, O., Atudorei, V., Pack, A., Sengupta, S., Shock, E.L., Knauth, L.P. (2016) A calibration of the triple oxygen isotope fractionation in the SiO2 - H2O system and applications to natural samples. Geochimica et Cosmochimica Acta 186, 105-119.

). Most marine silica samples fall on or near this curved line. Samples that have equilibrated with meteoric waters consequently plot towards lower δ′¹⁸O and, in general, higher Δ′¹⁷O values, consistent with a lighter meteoric water source. Our unpublished manganese oxide data from a deep sea nodule off Hawaii have very low Δ′¹⁷O values in relation to their δ′¹⁸O values, explained by incorporation of dissolved air O₂ into the MnO₂ structure (Δ′¹⁷O_air = -0.41 to -0.45). The low Δ′¹⁷O values support the conclusion that dissolved O₂ is directly incorporated in manganates during biogenic and abiogenic laboratory synthesis experiments (Mandernack et al., 1995

Mandernack, K.W., Fogel, M.L., Tebo, B.M., Usui, A. (1995) Oxygen isotope analyses of chemically and microbially produced manganese oxides and manganates. Geochimica et Cosmochimica Acta 59, 4409-4425.

).

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Hydrothermal mixing
A number of variables control the isotopic effect during hydrothermal alteration, including temperature, initial rock protolith and fluid compositions, and fluid/rock (F/R) ratio. Nevertheless, the δ′¹⁸O - Δ′¹⁷O field of most hydrothermally altered rock is surprisingly limited.

Hydrothermal alteration is modelled using a simple mass balance mixing equation. A fraction of water is allowed to equilibrate with a rock at a given temperature. The bulk composition is given by

δ¹⁸O_bulk = X_water (δ¹⁸O_{water initial}) + (1-X_water) (δ¹⁸O_{rock initial}) = X_water (δ¹⁸O_{water final}) + (1-X_water) (δ¹⁸O_{rock final})

The final δ¹⁸O value of the rock is determined by the additional fractionation equation

where α varies with temperature.

Mixing calculations are made using the standard delta values. Once the final isotopic compositions are determined, data are linearised for plotting on δ′¹⁸O – Δ′¹⁷O plots. In linearised plots, mixing trends plot as curved lines.

Figure 4 shows mixing trends between a typical unaltered granitoid (δ′¹⁸O = 8.5 ‰; Δ′¹⁷O = -0.05 ‰) and meteoric waters of varying composition. Fractionation factors for this example are for quartz. As fluid/rock ratios increase, the delta values of the altered rock initially move to lower δ′¹⁸O and ultimately higher Δ′¹⁷O values. An extreme example from the ‘snowball Earth’ altered samples from Karelia (Herwartz et al., 2015

Herwartz, D., Pack, A., Krylov, D., Xiao, Y., Muehlenbachs, K., Sengupta, S., Di Rocco, T. (2015) Revealing the climate of snowball Earth from Δ¹⁷O systematics of hydrothermal rocks. Proceedings of the National Academy of Sciences 112, 5337-5341.

) results in δ′¹⁸O values as low as -26 ‰, vastly expanding the hydrothermal alteration field (yellow field in Fig. 4). In more common cases where the δ¹⁸O value of meteoric water is -20 ‰ or higher, the hydrothermal alteration box is far more limited (red field in Fig. 4).

Assimilation of a high δ¹⁸O sediment by a granitoid will shift the δ′¹⁸O values higher, and the Δ′¹⁷O values lower (pale blue curve in Fig. 4). In practice, the effect will be small. Even 10 % incorporation of sediment will only move the altered rock as far as the dark blue curve.

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General Fields and Choice of λ_RL

Figure 1 shows the characteristic δ′¹⁸O – Δ′¹⁷O regions for different materials. While there is some overlap, different rock types generally plot in distinct regions following well established fractionation rules. The best fit λ value depends on which samples are considered (Fig. S-2). All data have a best fit λ = 0.5269. Waters define a λ value of 0.5281, but if the light Vostok ice core samples are excluded, the λ becomes 0.5275. Rocks have a still smaller λ value, controlled in large part by the high δ′¹⁸O – low Δ′¹⁷O sedimentary samples.

The isotope community in this nascent field has not reached consensus on a standard reference line ‒ the λ_RL value ‒ for calculating Δ¢¹⁷O values. We suggest reporting both δ¹⁷O and δ¹⁸O on VSMOW scale. For materials with δ values departing far from zero, one may apply VSMOW/SLAP2 scaling. This ensures that data from the rock and water community remain comparable.

The meteorological community uses a λ_RL value of 0.528, as this initially had been suggested to be representative of the Global Meteoric Water Line slope (Luz and Barkan, 2010

Luz, B., Barkan, E. (2010) Variations of ¹⁷O/¹⁶O and ¹⁸O/¹⁶O in meteoric waters. Geochimica et Cosmochimica Acta 74, 6276-6286.

). With such a definition, most rocks have negative Δ¢¹⁷O values, whereas meteoric waters generally have positive values. Some studies adopt a λ_RL = 0.5305, the theoretical θ value at infinite temperature. All natural, equilibrium processes should have θ values less than this value, so that trends for all data should have a negative slope in Δ′¹⁷O - δ′¹⁸O space. In practice, some materials following complex kinetic processes have λ values higher than 0.5305, notably the Vostok ice core data (λ = 0.5309 ± 0.0002) and precipitation from Niger (Landais et al., 2010

Landais, A., Risi, C., Bony, S., Vimeux, F., Descroix, L., Falourd, S., Bouygues, A. (2010) Combined measurements of ¹⁷O_excess and d-excess in African monsoon precipitation: Implications for evaluating convective parameterizations. Earth and Planetary Science Letters 298, 104-112.

) (λ = 0.543 ± 0.004). Most processes undergo fractionation with a θ value (significantly less than 0.5305), resulting in a strong negative trend in Δ′¹⁷O as a function of δ′¹⁸O in this reference frame (Fig. S-3). The adoption of λ_RL = 0.5305 is consistent with other multiple isotope systems, where the theoretical high-T limit is used as a reference. A λ_RL = 0.528 would make the ‘rock’ data compatible with the longstanding data on meteoric waters and would not artificially skew Δ′¹⁷O to more negative values with increasing δ′¹⁸O values. This is critical as researchers combine ‘water’ and ‘rock’ data. The authors of this contribution do not agree on a suggested convention.

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Conclusions

The δ′¹⁷O - δ′¹⁸O values for all terrestrial materials not affected by photochemical effects plot on a straight line with a slope of ~½. In detail, small, purely mass-dependent variations can be resolved and displayed in Δ′¹⁷O - δ′¹⁸O space (Fig. 1). The vast majority of meteoric waters have positive Δ′¹⁷O values, while rocks have negative Δ′¹⁷O values. Low- and high-T rocks fall on distinct trends and fields that can be explained by well understood processes. It is unlikely that many data will fall to the right hand side of the seawater - silica equilibrium curve nor are many rocks expected to fall above the meteoric water line. These may be termed "forbidden" regions. Similarly, samples with Δ′¹⁷O values less than -0.10 are probably unique to low temperature sediments (or products of low temperature sediments). The distinction between the different regions outlined here will undoubtedly show more overlap as additional data are collected. Overall, however, the combined δ′¹⁸O - Δ′¹⁷O values of rocks and waters are characteristic of their formation conditions.

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Author Contributions and Acknowledgements

All authors contributed ideas and helped in writing the final manuscript. JW provided unpublished calcite isotope data. We acknowledge E. Cano for unpublished data for mantle samples and two anonymous reviewers.

Editor: Eric H. Oelkers

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References

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Supplementary Information

The Supplementary Information includes:

• Fractionation Equations
• The Terrestrial Fractionation Line and the Definition of Δ′¹⁷O
• Figures S-1 to S-3
• Supplementary Information References

Download the Supplementary Information (PDF).