Triple oxygen isotope constraints on the origin of ocean island basalts

Xiaobin Cao·Huiming Bao,·Caihong Gao·Yun Liu·Fang Huang·Yongbo Peng·Yining Zhang

Abstract Understanding the origin of ocean island basalts(OIB)has important bearings on Earth’s deep mantle.Although it is widely accepted that subducted oceanic crust,as a consequence of plate tectonics,contributes material to OIB’s formation,its exact fraction in OIB’s mantle source remains ambiguous largely due to uncertainties associated with existing geochemical proxies.Here we show,through theoretical calculation,that unlike many known proxies,triple oxygen isotope compositions(i.e.Δ17O)in olivine samples are not affected by crystallization and partial melting.This unique feature,therefore,allows olivineΔ17O valuesto identify subducted oceanic crusts in OIB’s mantle source.Furthermore,the fractions of subducted ocean sediments and hydrothermally altered oceanic crust in OIB’s mantle source can be quantif ied using their characteristicΔ17O values.Based on published Δ17O data,we estimated the fraction of subducted oceanic crust to beashigh as22.3%in certain OIB,but the affected region in the respective mantle plume is likely to be limited.

Keywords Triple oxygen isotope·Helium isotope·Ocean island basalts·Mantle plume·Mantle heterogeneity·Crustal recycling

1 Introduction

Earth is highly evolved and differentiated into different layers(Hofmann 1988).The surface layers of the Earth prevent us from directly observing its deep mantle.Ocean island basalts(OIB)are thought to originate from partial melting of deep mantle(White 2010),and therefore providing information on deep mantle’s composition,evolution,and theinteraction between themantleand thesurface layers(Hofmann 1997).

Theisotopecompositionsof Sr,Nd,Pb,Hf,Os,H,O,S,Si,Mg,Ca,and trace elements have been used to study the origins and evolutions of OIB(Cabral et al.2013;Delavault et al.2016;Hofmann 2014;Huang et al.2011;Loewen et al.2019;Pringle et al.2016;Wang et al.2003,2016).These studies have concluded that subducted oceanic crust,in addition to primitive mantle,has contributed materials to OIB’s mantle source.However,the observed variation of Sr,Nd,Pb,Hf isotopes and trace elements can be alternatively explained by the variation of oceanic lithosphere thickness(Niu et al.2011).Isotope fractionations during subduction(John et al.2012),partial melting(Wang et al.2016;Zhu et al.2018),and fractional crystallization(Wang et al.2003)cannot be unambiguously ruled out for the observed variation of stable isotopes.

To understand subducted oceanic crust’s role in OIB’s origin,it is important to quantify its fraction at the mantle source(Sobolev et al.2007).Although sulfur mass-independent fractionation(S-MIF)found in Mangaia and Pitcairn islands show that oceanic sediments can survive in subducted oceanic crust(Cabral et al.2013;Delavault et al.2016),it cannot be used to determine its exact fraction in OIB’s mantle source owing to large variation of sulfur isotope compositions in subducted oceanic crust(Farquhar et al.2000).In addition,S-MIFsignature is only useful for subducted oceanic crusts around or before the great oxidation event(Farquhar et al.2000).

In this study,we propose that the triple oxygen isotope compositions(Δ17O)in olivine are exempted from these uncertainties and can serve as a unique tool to resolve OIB’s origin.HereΔ17O≡δ17O′-0.5305×δ18O′(ref.Bao et al.2016;Pack and Herwartz 2014),δxO′-=ln(1+δxO),δxO=xR/xRref-1,xR=xO/16O,ref isthe reference material for oxygen isotope measurements,and x is 17 or 18.Our working hypothesis is that high-temperature processes(e.g.＞1000°C)cannot shift olivine’s Δ17O away from that of primitive mantle,but the addition of subducted oceanic crust to OIB’s mantle source will because subducted oceanic sediments and hydrothermally altered oceanic crust have respectively negative and positiveΔ17O values,relative to that of the primitive mantle,due to their interactions with ocean water(Pack and Herwartz 2014;Sengupta and Pack 2018;Sharp et al.2018)(Fig.1).We will test this hypothesis by(1)theoretically calculating triple oxygen isotope relationships for related olivine-mineral pairs(i.e.theθvalues),with a special interest in high temperatures relevant to olivine formation;and(2)examining publishedΔ17O values in OIB’s olivine sampled worldwide.

Fig.1 A cartoon depicting the rationale of our hypothesis.The Δ17O values presented in this f igure are relative to the primitive mantle value

2 Methods

Density functional theory has been used to estimate the oxygen isotope fractionation factor18αamong different silicate minerals(Meheut et al.2009;Qin et al.2016).Forsterite,clinoenstatite,diopside,enstatite,spinel,and pyrope are selected asmineral representativesof the mantle(McDonough and Rudnick 1998).Although other minerals,e.g.ilmenite and magnetite,may be involved in basalt melt evolution,they are not considered here due to their accessory nature.Volatile components,e.g.H2O,CO2,and SO2,are not discussed here either,because their role in changing the oxygen isotope compositions of basalt melts is limited(e.g.＜0.3‰)(Eiler 2001).

Starkey et al.(2016)presented a systematic investigation ofΔ17O in olivine samples,and Greenwood et al.(2018)recalibrated their original data and presented additional measurement details.We therefore focus on the Δ17O data documented in Greenwood et al.’s paper.

2.1 Density functional theory(DFT)calculations

The equilibrium triple oxygen isotope relationshipθ between two different minerals can be calculated by Cao and Liu(2011)and Hayles et al.(2018):

where κ≡ln17β/ln18β,18αa-b≡18βa/18βb,β is the equilibrium isotope fractionation between the mineral in question and the oxygen atom in ideal gas state,18αa-bis the equilibrium isotope fractionation between‘a’and‘b’,and‘a’and‘b’refer to two different minerals.

Theβvalues can be estimated by partition function ratios.Taking18βfor olivine as an example,there are 4 oxygen sites in one silica tetrahedral structure unit,and each of them correspondsto apartition function ratio,then,

where f(Si16O318Oi)is the partition function ratio of Si16-O318Oito Si16O4,and‘i’refers to the i th site.The partition function ratio can be calculated by Bigeleisen and Mayer(1947)and Urey(1947),

where N isthe number of atomsin the unit cell for olivine;ujisequal to hcωj/kbT,in which h is the Planck constant,c the speed of light,ωjthe j th normal vibration mode,kbthe Boltzmann constant,and T temperature in Kelvin.The terms with star(*)refer to the isotopologues Si16O318Oi.

The vibrational frequencies for each mineral were calculated within DFT,and the Perdew–Burke–Ernzerhof(PBE)exchange correlation functional(Perdew et al.1996)was employed.The projector augmented wave(PAW)pseudopotentials were used for all elements with a cut off energy of 600 eV.Brillouin-zone integrations were done on a grid of 3×3×3 k-point centered at Gamma.The unit cell was used for structure optimization,and then the unit cell or super cell was constructed for vibrational frequency calculation.The Hessian matrix was determined by density functional perturbation theory(DFPT)at the Gamma point.All DFT calculations were carried out by Vienna Ab initio Simulation Package(VASP)(Kresse and Furthmu¨ller 1996).

2.2 Recalibrating publishedΔ17O data to the primitive mantle scale

In this study,olivine samples with high3He/4He ratio from Ofu Island were chosen as the representative of theΔ17O in the primitive mantle,since the mantle source of these olivine samples has shown no contamination from crust materials(Jackson et al.2007).Although Ofu lavamay not result from primitive chondritic materials directly,its Δ17O will equal to that of the primitive mantle as long as no crust contamination hasbeen added to itsmantle source,because differentiation at high temperatures does not change theΔ17O(See Sect.4).

Once this was done,we used their averagedδ17O and δ18O to recalibrate the published data.The original data can be found in Greenwood et al.(2018),and the correspondingδ′17Or,δ′18Or,andΔ17OPMwere calculated by

whereδ′xOrandδxOorepresent the recalibrated and originalδvalues for the corresponding measurements,respectively;δxOofu-avgrefersto theaveragedδvaluesfor a set of olivine samples with high3He/4He ratio from Ofu Island;‘x’refers to 17 or 18;the subscript‘‘PM’’in Δ17OPMrefer to aΔ17O value with respect to that of the primitive mantle.

3 Results

The calculatedθvalues were presented in Fig.2 and Table S1,and the recalibratedΔ17OPMvalues were given in Fig.3 and Table S2.These results show that the equilibriumθvalues for the related mineral pairs range from 0.5300 to 0.5303 at temperatures from 1000°C to 1300°C(Fig.2),and the recalibratedΔ17OPMvalues for published olivine data range from-13.8 ppm to 15.0 ppm(Fig.3).The observed variation ofΔ17OPMwill be explored below.

Fig.2 Calculated equilibrium triple oxygen isotope relationshipsθeq for different olivine-mineral pairs at different temperatures above 1000°C.The 0.5305 line is our reference line.The largest difference between the calculatedθeq and 0.5305 is 0.0005,which corresponds to a variation of less than 0.5 ppm in theΔ17OPM at this temperature range.Fo,Cen,Di,En,Spl,and Prp refer to Forsterite,Clinoenstatite,Diopside,Enstatite,Spinel,and Pyrope,respectively

4 Discussion

4.1 Partial melting and fractional crystallization cannot fractionateΔ17OPM values measurably in olivine

The largest vibrational frequency for these mantle related minerals is about 1100 cm-1(ref.Lin 2004),which corresponds to a u value(≡hcωj/kbT)less than 1.24 at 1000°C and above.High temperature approximation for isotope effect calculation is applicable in this case(Bigeleisen and Mayer 1947).Therefore,the equilibriumθvalues should be close to their high temperature limit,i.e.0.5305(Cao and Liu 2011;Young et al.2002).Our calculatedθvalues are consistent with this theoretical estimation.

It is known that the pressure can affect the18O isotope fractionation(Polyakov and Kharlashina 1994).However,the inf luence of pressure on theθvalue is expected to be small.For example,although the largest vibrational frequency for forsterite can increase from 960 cm-1at 0 GPa to 1180 cm-1at 50 GPa(Durben et al.1993),the corresponding increase of u value is less than 0.25 at 1000°C and above.Therefore,the increase of pressure does not affect the applicability of high temperature approximation for isotope effect calculation at these high temperatures(Bigeleisen and Mayer 1947).

Fig.3 RecalibratedΔ17OPM value and 3He/4He ratio(number close to the data symbol)for olivine samples separated from basalts fromdifferent locations.All 3He/4He ratiosare reported relativeto the atmospheric one(i.e.R/Ra).The error bar is given by 1×SEM(i.e.one standard error of the mean).The original oxygenisotope data are from reference(Greenwood et al.2018)and the original 3He/4He ratios from references(Ellam and Stuart 2004;Garapic´et al.2015;Jackson et al.2007;Kurz et al.2004;Starkey et al.2009).Different colors represent different olivine samples as detailed in Table S2

Anharmonic correction can also inf luence oxygen isotope fractionation,its contribution to the equilibriumθis expected to be small(Cao and Liu 2011;Hayles et al.2017).The nuclear volume effect and the Diagonal Born–Oppenheimer Correction arealso estimated to benegligible for oxygen isotopes at these high temperatures following established approaches(Yang and Liu 2015;Zhang and Liu 2018).

In addition,our calculatedθvalues are consistent with f ield observations(Pack et al.2016).Therefore,the values ofθfor partial melting and fractional crystallization processesassociated with olivineformation areestimated to be about 0.5302±0.0001.

Given the limited18O isotope fractionation associated with partial melting and fractional crystallization(i.e.around 1‰or less)(Eiler 2001),the above range ofθ values can only contribute to a change in theΔ17OPMof less than 0.5 ppm.Therefore,partial melting and fractional crystallization processes cannot fractionate Δ17OPMmeasurably.

4.2 The observed smallΔ17OPM variation is real

The observed variation ofΔ17OPMis small(Fig.3).Most of the data are even smaller than their one standard deviation(Table S2).However,we think this small variation is real due to the reasons given below.

4.2.1 Reduce the errors through careful recalibration

It isaware that accuratemineralΔ17O valuesarediff icult to determine to the ppm level in VSMOW scale(Pack et al.2016).TheΔ17O could differ by up to 50 ppm even for the same mineral measured in the same laboratory(Pack et al.2016).Thereason for thisvariability isdue to the diff iculty in measuring a mineral and VSMOW in the same laboratory(Pack et al.2016).Fortunately,this type of error can be avoided if allΔ17O values are reported directly relative to olivine mineral instead of VSMOW.This is the reason why we recalibrated the originalΔ17O values to primitive mantle scale instead of VSMOW scale.

Even a mineral and VSMOW can be measured in the same laboratory,different laboratories may obtain different Δ17O valuesfor a mineral relative to VSMOW(Pack et al.2016;Sharp et al.2016),which might be caused by the pressure baselines effect(Yeung et al.2018).Therefore,only data measured in the same laboratory,i.e.the ones from the Open University(Greenwood et al.2018),are used in this study.The systematic errors can be largely reduced in this way.

When recalibrating,we chose 0.5305 for the reference line instead of 0.5262 used by the original paper(Greenwood et al.2018),since the triple isotope relationship should be around 0.5302 during olivine formation as discussed above.Thisiscritical when studying small variation of theΔ17OPM,especially for samples with largeδ18O difference relative to the primitive mantle.

After a careful recalibration procedure,the errors associated with different laboratories,reference difference(i.e.primitive mantle vs.VSMOW),and difference of olivine formation processcan be reduced.However,this procedure cannot excludetheroleof statistic biasin thesmallΔ17OPMvariation presented in Fig.3 because some of the olivine samples are only measured 2 or 3 times(Greenwood et al.2018).MoreΔ17OPMmeasurementsare required to rule out thispotential error.Instead,here the3He/4He ratiosin these olivine samples are used to examine the inf luence of statistic bias.

4.2.2 The3He/4He ratio in olivine samples

If the small variation ofΔ17OPMis the result of poor statistics,the values ofΔ17OPMin those olivine samples from the same location should not be expected to correlate to their3He/4He ratios.However,as shown in Fig.3,an olivine sample with a higher3He/4He ratio tends to have a Δ17OPMvalue closer to zero,in contrast to other olivine samples within the same location.Note that there is no3He/4He data for San Carlos olivine.Given that these3He/4He ratios are measured by different and independent groups,this correlation should not be caused by statistic bias.In fact,this correlation is expected,as will be discussed below.

Therefore,even though the statistical errors are large,the observed small variations ofΔ17OPMvalues are probably real.

4.3 Subducted oceanic crusts cause the small Δ17OPM variation in olivine samples

Several mechanisms can cause the smallΔ17OPMvariation among olivinesamples.Onepossibility isthat theprimitive mantle is heterogeneous in theΔ17OPM.If this is the case,theolivinesamplesfrom different locationsand originsare not expected to have the sameΔ17OPM,i.e.Δ17OPM=0,even they have relatively high3He/4He ratios.However,this possibility is inconsistent with the results presented in Fig.3.In addition,the values ofΔ17OPMin basalts from the Amsterdam-St.Paul plateau and Gulf of Tadjoura are also equal to zero within the error(see Table S1),which is consistent with previous suggestion that primitive mantle hascontributed materialsto themantlesourcesof basaltsin these two regions(Dosso et al.1988;Marty et al.1993).Therefore,heterogeneity of primitive mantle may be true for some elements or isotopes,but not for theΔ17OPMof primitive mantle.

Mantle derived olivineformed at high temperatures(e.g.1200±100°C)(Mattey et al.1994).Fresh olivine can hardly survive once it interacts with water due to serpentinization.Therefore,the common isotope alteration mechanism,i.e.f luid-rock interaction,is not a plausible mechanism for the observedΔ17OPMvariations among olivine samples.

Now let us examine the role of subducted oceanic crust and see if the observed variations of theΔ17OPMin olivine samples can be accounted for by a simple mixing.To explain the negativeΔ17OPMvalues in olivine samples from Pitcairn Island(i.e.the red diamond in Fig.3),subducted oceanic sediments had to be mixed in,while the assimilation of the modern ocean sediments is not likely.Here‘assimilation’refers to the interaction between magma and its conduit wall materials in the crust,being distinct from the mixed-in from the‘subducted’crustal materials.This conclusion is consistent with the observed S-MIF and Mg isotope signatures in basalt samples from Pitcairn(Delavault et al.2016;Wang et al.2018).Moreover,the addition of subducted oceanic crust to primitive mantle can lower the3He/4He ratio,which is consistent with the results presented in Fig.3.

Similarly,the olivine samples from Mauna Loa and Iceland(i.e.the red square and circle in Fig.3),which possess small positiveΔ17OPMvalues,should carry signatures of hydrothermally altered oceanic crusts.Although theΔ17OPMvalues alone cannot distinguish the subducted crust from the crust assimilation,previous studies on lavas from Mauna Loa(Pietruszka et al.2013)and Iceland(Kokfelt et al.2006)suggested that subducted hydrothermally altered oceanic crusts involved in the formation of these basalts.The small positiveΔ17OPMshifts is consistent with these previous studies.

Olivine samples from Baff in Island,West Greenland,and San Carlosare all associated with basaltsbeing erupted into continental crusts.TheΔ17OPMvalue of continental crust isnormally negative(Sengupta and Pack 2018),while it can reach as positive as 90 ppm when the continental crust has interacted with meteoric water(Herwartz et al.2015).Therefore,the non-zeroΔ17OPMvalues in these olivine samples can be caused either by the addition of subducted oceanic crust or by the assimilation of continental crust.TheΔ17OPMvalue alone cannot separate the two different mechanisms,and we will not discuss these non-zeroΔ17OPMvalues further here.

4.4 Estimatethe fraction of subducted oceanic crust in OIB’s mantle source using the observed Δ17OPM values

As discussed above,the smallΔ17OPMvariation in olivine samples from Pitcairn,Mauna Loa,and Iceland can be explained by the mixing between the subducted oceanic crust and the primitive mantle.To estimate the fraction of subducted oceanic crust in OIB’s mantle source,the oxygen isotope compositions for the related two reservoirs have to be determined f irst.For primitive mantle,its Δ17OPMvalue is 0.0 ppm as def ined here.For subducted ocean sediments,there are two potential representativeswe can choose.One is the shales(Bindeman et al.2018;Sengupta and Pack 2018)and the other is siliceous sediments(Pack and Herwartz 2014;Sengupta and Pack 2018).Here we use shales because their averageδ18O value is close to that of the top section of the subducting slab(Bindeman et al.2018;Gregory and Taylor 1981).If thisis thecase,theΔ17OPMvalueof subducted oceanic sediments is-132.7 ppm(see Table S2).Then the fraction of ocean sediments in the mantle sources of Pitcairn(i.e.the one with negative Δ17OPM) lavas is estimated to be 10.4±2.0%[i.e.(-13.8±2.7)/(-132.7)](Fig.4).This estimation will not be accurate if the related two reservoirs have a largeδ18O difference due to the non-linear mixing nature of theΔ17O(Herwartz et al.2015).The fraction is then re-calculated to be 10.3%when the non-linear mixing nature of theΔ17O isincluded,and the result is identical to the one determined byΔ17OPMonly within the error.Therefore,the fraction determined byΔ17OPMis good enough,and only the value ofΔ17OPMwill be used to estimate the contribution of hydrothermally altered oceanic crust below.

TheΔ17OPMvalue for subducted hydrothermally altered oceanic crust was estimated to be 35.0 ppm(Sengupta and Pack 2018),which constrains the fractions of subducted hydrothermally altered oceanic crust in the mantle sources of Mauna Loa and Iceland lavas to be 22.3±12.9%and 7.1±6.6% [i.e.(7.8±4.5)/35 and (2.5±2.3)/35],respectively.Our determined fractions of hydrothermally altered oceanic crust for Mauna Loa and Iceland lavas are close to the previous estimates using trace elements(Pietruszkaet al.2013;Sobolev et al.2007;Wang et al.2010).

Note that theδ18O alone can also be used to constrain OIB’s origin(Eiler 2001).However,δ18O-based interpretation has extra degrees of freedom.This is because the δ18O value is not only dependent on the mixing between the subducted oceanic crust and primitive mantle but also on the18O isotope fractionation during degassing,partial melting,and fractional crystallization(Eiler 2001).For example,theδ18O value in olivine from Mauna Loa is expected to be low due to the addition of subducted hydrothermally altered oceanic crust to its mantle source,but it is not in reality(see Table S2).The18O isotope fractionation should have played a role,and additional geochemical parameters might be helpful to reconcile this inconsistency.

Fig.4 The estimated fractions of the subducted oceanic crust in OIB’s mantle source.The error bar is determined by 1×SEM value ofΔ17OPM

4.5 Subducted oceanic crusts might only exist locally in the mantle plume

Theolivine samplesfrom Hawaii plume can also have zero Δ17OPMvalues(See Fig.3).There are three possible mechanisms to interpret these zeroΔ17OPMvalues.The f irst is that the subducted hydrothermally altered oceanic crust exists locally and does not affect their entire mantle source.Thesecond oneisthat subducted oceanic crust does exist in their mantle source,but this crust barely experiences hydrothermal alterations.The third one is that the Δ17OPMvalue of part of the subducted oceanic crust is altered to be zero during subduction process.If thelast two cases were true,the3He/4He values in these olivine samples should have been low,which does not agree with the observation(see Fig.3).Furthermore,oxygen is a major element in the subducting slab and the amount of f luid derived from the slab is relatively small,and subduction process is thus not expected to change theΔ17OPMsubstantially in the subducted oceanic crust.Therefore,the f irst mechanism is the most likely scenario to interpret the zeroΔ17OPMvalues in these olivine samples.In other words,subducted oceanic crust only exists locally in the mantle plume and is not alwayssampled by the OIBs.This conclusion is consistent with earlier studies on Hawaii plume mantle source(Pietruszka et al.2013;Wang et al.2010).Local mantle chemical heterogeneity is also supported by theΔ17OPMresults determined for the olivine samples from Pitcairn (See Fig.3).Considering the observed S-MIF in Pitcairn basalts(Delavault et al.2016),theΔ17O heterogeneity generated by subducted oceanic crust can bepreserved locally in deep mantlefor billionsof years.

5 Concluding remarks

The large compositional variation observed in OIBs is generally attributed to the recycling of oceanic crust into the deep mantle.Our analysis of theΔ17OPMvalues of olivine from different locations suggests that there had existed aΔ17O-homogeneous deep mantle,but the recycling of oceanic crusts has since generatedΔ17O heterogeneities in mantle.ThoseΔ17O-heterogeneousregionsare likely to be limited spatially.With the addition ofΔ17OPMvalues of olivine,partition of trace elements,stable isotope fractionation,and variation of radiogenic isotopes can be better quantif ied.This study calls for an effort to improve high-precisionΔ17O analysis of terrestrial minerals.

AcknowledgementsWe thank Zhengrong Wang for his helpful comments.H.B.and Y.L.are grateful for funding supports from the strategic priority research program(B)of Chinese Academy of Sciences(XDB18010104)and(XDB18010100)and Chinese NSF Project(41490635).High-performance computational resources were partially provided by Louisiana State University(http://www.hpc.lsu.edu).

Compliance with ethical standards

Conf lict of interestThe authors declare no conf lict of interests.