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Downloaded by guest on September 30, 2021 a Keller Brenhin ancient C. on silica crustal Constraining www.pnas.org/cgi/doi/10.1073/pnas.2009431117 that processes same very the by limited however, is, nental life. of and dawn deeply tectonics, the physiography, is at planet the composition our of of crustal climate inference ancient our to Earth’s connected of Consequently, 19–21). question (10, the the during climate possibly equable and relatively since and conti- ) well- felsic thus (and posits less crust view refs. nental uniformitarian a (e.g., more mid-Archean second (presumably) the The and in 13–18). sometime tectonics, until climate plate regulated no “majority predominantly features crust, the Earth as mafic growth, characterized crust (12) continental emerged. of Moorbath view” have what models first, to the member In end 11), with conceptual (10, crust competing latter continental subse- two Earth’s the the of on growth of consensus and any reaction formation produced of quent the absence directly the to In have Crystal- . due itself produce (9). crust, not ocean 8) felsic could (7, magma a primordial Ga that a 4.51 of wake, to lization its prior in Moon left, of likely formation accre- in planetary culminating energetic tion since crust, continental) (henceforth down 6). (5, draws oceans weathering surface whose crust subaerial atmospheric forming sur- Earth’s by at face liquid turn, stabilize In and felsic (3) buoyant, viscosity, differentiation those temperature, magmatic during solidus relationships altering whereby phase by system production magmas exis- the feedback felsic catalyzes the a of the that to to suggested water due ocean anomaly been is of subduction long crust the continental has is of it crust tence context, continental this sil- felsic other In of the (1–4). crusts while the oceanic to planets, the composition higher- two, icate in a these analogous more Of and is continents. crust oceans, the comprising the type underlying silica variety basaltic crust—a A crust Archean.continental early the least with at model since a silica by crustal explained constant parsimoniously nearly most find are we data ter- complications, the from these that inferred for content Accounting sediments. silica rigenous crustal of latter the estimates while from undermines abundances, silica element crustal infer incompatible to or efforts compatible complicates former We the oxi- investigated. that fully driven find been biologically not the have the atmosphere as Earth’s and of such mantle dation effects Earth’s of biases, cooling sampling introduced secular and composition from preservation crustal Apart crustal present. early by at conti- assessing than Hadean in mafic a and more complications proposed slightly Archean effi- only have which were an Others in nents lacking view climate. consequently and uniformitarian regulate years tectonics more and to billion plate crust, mechanism 2 modern subaerial cient to of of lack 1 paucity a first a implying the history, rel- over a Earth crust of of dawn growth planetary the the mafic involves at paradigm atively planet longstanding our One the life. of of understanding of climate our and on to tectonics, critical crust physiography, is continental Earth Albar Archean Francis of by and composition reviewed Hadean 2020; the 15, May quantifying review for Accurately (sent 2020 21, July Harrison, Mark T. by Contributed 90095 CA Angeles, Los eateto at cecs atot olg,Hnvr H075 and 03755; NH Hanover, College, Dartmouth Sciences, Earth of Department u blt odtrieteps opsto fteconti- the of composition past the determine to ability Our felsic first Earth’s of age maximum the to limit hard a is There w opstoal n opooial itnttpsof types distinct morphologically possesses and Earth system, compositionally solar our two of planets the among lone CO | lt tectonics plate 2 hspeetn uaa rehuels of loss greenhouse runaway preventing thus , a,1 n .Mr Harrison Mark T. and | Archean | Hadean b,1 b eateto at,Paeay n pc cecs nvriyo California, of University Sciences, Space and Planetary, Earth, of Department is ulse uut1,2020. 17, August published First 1 the under Published interest.y competing no declare University.y authors Yale The J.K., and System; Lyon of and paper. University y F.A., the C.B.K. Reviewers: wrote T.M.H. research; and performed C.B.K. and C.B.K. data; research; analyzed T.M.H. designed C.B.K. contributions: Author Gyr. 4 past the continental over preserved in increase concentrations incompatible brief, element in while 38); decrease (37, concentrations Schoene element and is compatible Keller by elements length trace some this at incompatible discussed of and generalization compatible straightforward to rather phenomenon sys- The element 36). decreasing (35, including major This MgO notably changing basalts, 34). mantle-derived in (33, of high-degree results Archean tematics fraction the by melt since abundance produced peridotite) declining declining mantle magmas the as of of magmas, (magnesian melting context mantle the komatiites con- in in of observable noted fraction been primary melt long declining The has the 32). radio- is (31, 46 declining sequence about production exponentially be heat to by estimated genic compounded today heat, (31), of terawatts loss ongoing Earth’s of driven hydrosphere, changing . and oxygenic radically atmosphere by the primarily Earth’s 2) of and state mantle oxidation Earth’s the the 1) of and than (30): cooling (29) crust appreciated secular radioactive sampling less weakly incomplete of even preservation by preferential been introduced have biases that first-order factors two by (26–28). felsic to (15–18) While mafic reached the from nonetheless (25). results, of have divergent estimates young crust widely recent Archean geologically known, Earth’s of well is Moon composition is our crust challenge or Earth’s first-order (23) this of like most worlds (24), compar- quiescent In currently 22). to ref. of (e.g., ison birth magma mantle-derived the from accompanying crust new metamorphism to and crust and assimilation felsic subduction–erosion; and the ancient of subduction of sediment by return and mantle slow rain, the the wind, hydrosphere; the by active erosion an habitable: planet our make owo orsodnemyb drse.Eal belrdrmuheuo tmark. or [email protected] Email: [email protected]. addressed. be may correspondence whom To atr eut netmtsmc lsrt h opsto of composition the crust. to continental closer modern much estimates these in for results Accounting factors composition. for crustal methods ancient previous estimating some oxi- compromise atmospheric that significantly and find cooling dation) We (mantle Earth. processes early geologic stable two climatically less atmosphere, a the to in such exposed resulting crust, poorly be oceanic 2 likely to modern would 1 Like crust history. mafic first thin- Earth the was for of silica that years in billion crust lower ancient significantly and an denser, ner, propose models many continental crust, modern to relative However, weathering. main- and atmospheric sion wherein is process climate feedback CO negative habitable a Earth’s by tained timescales, geologic On Significance eua atecoigi ieyepce saconsequence a as expected widely is cooling mantle Secular explained be may results divergent these that suggest We 2 scnue yrato ihslct ok uigero- during rocks with reaction by consumed is PNAS NSlicense.y PNAS | y etme ,2020 1, September d n u Korenaga) Jun and ede ` | o.117 vol. | o 35 no. | 21101–21107

EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES The second factor, the oxygenation of Earth’s atmosphere and hydrosphere, is mediated primarily by biological factors: oxy- A 0-1 Ga genic photosynthesis. For much of Earth’s early history, before 12 1-2 Ga 2-3 Ga 2,450 Ma, atmospheric oxygen is thought to have been less 3-4 Ga than 10−5 of the modern partial pressure, as indicated by mass- independent sulfur isotope fractionation driven by atmospheric photochemical reactions that occur only in the absence of oxy- 8 gen (39, 40). The path of subsequent oxygenation is less clear, but is thought to have reached comparatively modern, breath-

able levels by no later than 400 Ma (41–43). The effects of this MgO (wt. %) 4 oxygenation on the and phase relations of exposed crust and sediment have been widely considered in other con- texts (e.g., refs. 44 and 45), yet many estimates of Archean crustal 0 composition rely critically on redox-sensitive trace element ratios 45 50 55 60 65 70 75 in terrigenous sediments (e.g., refs. 16–18). B Secular Variation as a Function of Silica Content 4 To further explore the difficulties posed by secular cooling for some previous estimates of Archean crustal composition, we employ the dataset and weighted bootstrap resampling approach 3 of Keller and Schoene (37, 38). This weighted bootstrap resam- pling approach attempts to reduce sampling bias by assigning to

O (wt. %) 2

each sample a resampling probability that is inversely related 2 to spatiotemporal sample density (37, 38). However, more crit- K ical to the results than any improvement in evenness is simply 1 the ability to accurately represent each measured value (be it age, silica, K2O, etc.) as a distribution rather than as a sin- gle value. We accomplish this numerically, by adding Gaussian 0 noise with appropriate variance to each sample in each resam- 45 50 55 60 65 70 75 pling step—but an analogous result can be equally obtained C by Gaussian kernel methods as in Pt´aˇcek et al. (28). As in 1.2 Keller and Schoene (37, 38), the dataset includes data pre- viously compiled by EarthChem (49) (including contributions from NAVDAT and GEOROC), Condie and O’Neill (50), and Moyen (51). 0.8 Since many studies rely upon trace element ratios as prox- ies to infer major element concentrations of the Archean crust (15–18), it is critical to understand the relationship between such

Median Rb / Sr 0.4 ratios and SiO2 if we wish to infer Archean crustal silica con- tent in this way. To quantify such relationships, and any potential variation therein over time, we calculate the mean (for single ele- ments), median (for ratios), and 95% credible interval thereof 0 45 50 55 60 65 70 75 for several elements and ratios binned as a function of SiO2, for four age intervals: 0 Ga to 1 Ga, 1 Ga to 2 Ga, 2 Ga to 3 Ga, and D 1.5 3 Ga to 4 Ga. While perhaps less obvious than in sedimentary rocks, dia- 1 genetic and metasomatic processes, broadly defined, remain serious obstacles in the igneous record as well. Archean seafloor magmatic rocks, for instance, are commonly silicified, dramati- 0.5 (Cr / U)

cally altering both major and trace element compositions (52). Δ While we focus here on continental crust, not oceanic, we by no 0 means warrant our calculations to be free of bias from metaso- matic alteration and weathering. Rather, we aim to show that, Median even in the most benign scenario in which such effects are min- -0.5 imal, the use of trace element proxies to infer major element concentrations through time is fraught. -1 As seen in Fig. 1, the relationship between major and trace ele- 45 50 55 60 65 70 75 ment concentrations with SiO2 has not been constant through SiO2 (wt. %) time. For instance, MgO abundance has consistently decreased Fig. 1. Variations in MgO, K O, Rb/Sr, and Cr/U as a function of SiO for four as a function of time at constant SiO2 (Fig. 1A), with the most sig- 2 2 gigayear-long time intervals between 0 Ga and 4 Ga, plotted as the mean nificant changes occurring at low silica. Conversely, K2O content has dramatically increased as a function of time for preserved (MgO and K2O) and median (Rb/Sr and Cr/U) along with the 95% credi- ble interval thereof, determined using the dataset and weighted bootstrap continental igneous rocks of every SiO2 from to granite resampling approach of Keller and Schoene (37, 38). (Fig. 1B). Similarly dramatic variations through time at con- stant silica are observed in a range of significant trace element ratios. In particular, as illustrated in Fig. 1C, Rb/Sr ratios were observed in Cr/U, this time with higher values in the Archean dramatically lower at a given SiO2 in the Archean, especially (Fig. 1D) as shown here in the ∆ (Cr/U) notation (∆(Cr/U) = at the felsic end of the spectrum. Similarly large variations are log (Cr/U)/ log (Cr/U)PAAS, where PAAS is Post-Archean

21102 | www.pnas.org/cgi/doi/10.1073/pnas.2009431117 Keller and Harrison Downloaded by guest on September 30, 2021 Downloaded by guest on September 30, 2021 elradHarrison and Keller bin silica each for compositions (taking average recombining the simply average) by calculated weighted aver- is a bin model time reference each constant-silica for the age present Finally, the for Ma. between interval 3,900 interest time and of 100-Ma each variable for compositional bin silica each each of value average the 55% to into compositions 43 SiO observed bins: the compositional separate three first we herein, shown modern the mafic, in of observed that crust. as proportions hypothesis compositions relative intermediate null same and a felsic, the conceptual on featured a based crust model Archean as more model—or, reference silica. consider, reference a we silica crustal specifically, crustal point, Archean constant a this for framework, illustrate proxies further element To trace of accuracy nearly the remained and differentiation—has crust, the crustal constant. to for mantle the point from starting flux mass primary the sent time, over extent melting the mantle in changes dramatic despite between say, extents melting GPa for 2 percent at % mantle wt primitive 0.15 of “pyrolite” and melting (48) equilibrium isobaric Sun of and case McDonough the magma for 2 on Fig. influence in melt- illustrated little mantle calc-alkaline of remarkably extent has to the silica, ing contrast higher to magmas In drives which rapidly crystallization, inaccurate. fractional hydrous highly by descrip- driven a differentiation be such reality, would In felsic.” tion “more mafic” melts “more lower-degree be and to melts melting if higher-degree is, consider partial that qualitatively we opposed, that we diametrically assumption are if crystallization an fractional counterintuitive and with seem problem may the silica, approach Ga. constant 0 to at Ga 1 centrations from than con- Ga 1 the granitic to and Ga time, on granodioritic 2 for circa time; over compositions higher of markedly increase Rb/Sr function broadly and higher a both as while monotonic trary, trends always such Notably, not (17). Mezger are and Smit of ) Australian and McDonough of composition H % pyrolite wt 0.15 alphaMELTS and the GPa pMELTS-mode 2 and at (48) using Sun 47) calculated (46, melting simulations mantle from result 2. Fig.

opouetecntn-iiamdlrfrnecompositions reference model constant-silica the produce To the undermine significantly effects such for, accounted not If con- element incompatible and compatible varying result, This Abundance (wt. %) 10 20 30 40 50 2 SiO 0 itreit) n 5t 8 fli) ete calculate then We (felsic). 78% to 65 and (intermediate), 04 08 100 80 60 40 20 0 oee etcmoiin safnto fpretml,ta would that melt, percent of function a as composition, melt Modeled 2

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MgO FeO K 2 2 sslightly is O nta,as Instead, . npooto otermdr abundances, modern 55% their to proportion in 5)adrpoue eewt emsin otrclr ersn greater represent colors hotter permission; abundance. with sample here reproduced and (58) 78% SiO 3. Fig. and compatible as well as MgO, content 38). as (37, silica elements such trace the incompatible elements we on influence as major well-established impact which, its on despite cooling little magmas mantle relatively mantle-derived secular of has of shown, effect direct have constant compatible a at even as while time silica through time decrease through concentrations element increase any concentrations at for available ment code calculated using of be interest hypothesis brenhinkeller/StatGeochem.jl may fig- of null ratio trends a this or reject Such in time element to silica. over order element change crustal in each of constant exceeded level for be minimum must variations the which considered the be 4; may ure Fig. in shown observed the bin. from time deviation 1-Gyr each little in surprisingly proportions refer- involves proportions, constant silica fact, of constant hypothesis in our null the such, on As based constant. model ence notably are record 3 continental Fig. preserved in the in interme- observed and compositions felsic, diate mafic, at of Indeed, proportions record. the rock timescales, distribution preserved gigayear the bimodal throughout expect this active to been producing has reason process some underlying is the there potentially that sampling, gaps temporal limited numerous to and attributable modes, two the preserved of tions the of entirety 3). (Fig. compositional record the (58); marked igneous arcs continental this throughout accreted (58), persists Keller in well-exposed bimodality by apparent a shown have readily as to is absent otherwise, young stalling but or too hydrous arcs muted record, active frequently of plutonic as is context such gap the settings this in in Consequently, magmas 57). felsic (56, contrast and eruptibility dominated well-known mafic the is of to felsic mafics) due the the granites, while intrusive of mode by differentiation basalts, by extrusive mafic (produced of (mantle-derived) mode proportion high the a modes, includes these Of (53–56). compositional name this two with phenomena larger- two gap”—the of “Daly version the scale as to referred sometimes bimodality of function a

Age (Ga) are elements minor and major of range a for results The posi- the in variations slight are there while Consequently, as rocks igneous continental of abundance the present, At 2 4 3 2 1 0 acltdadvsaie satodmninlhsormb C.B.K. by histogram two-dimensional a as visualized and calculated , SiO SiO geu hl-oksml bnac safnto faeand age of function a as abundance sample whole-rock Igneous 2 2 . 34 rm5 o65% to 55 from 23.4% , 45 PNAS SiO 50 2 | nmn etnsdsly pronounced a displays settings many in etme ,2020 1, September 55 SiO 2

(wt. %) ofis re,icmail ele- incompatible order, first To . 60 SiO 65 | 2 n 16 rm6 to 65 from 31.6% and , o.117 vol. 70 49 rm4 to 43 from −44.9% | 75 o 35 no. github.com/ | 21103

0 1 Relative Sample Density Sample Relative

EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES 0.04 62 0.03 60 2 0.02 NiO SiO 58 0.10 0.01 16

56 3 0

3 15 O O 2 2 0.05 Cr Al 14 4 8 13

0 3.5 6 O 2 MgO Na 3 4 0.4 8

0.3 2.5 7 2 5

O 0.2 2 6 CaO P

0.1 1.2 5 10 9 0 1.0 4

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7 FeO* 3 0.6 0.18 6

2.5 0.4 0.16 5 O

2 2 0.14 K MnO

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1 0.1 4 3 2 1 0 4 3 2 1 0 Age (Ga) Age (Ga)

Fig. 4. Major and minor element concentrations for our constant-silica reference model, built to illustrate a null hypothesis that the proportion of mafic, intermediate, and felsic magmas has remained constant over time. concentrations increase through time while compatible element concentrations decrease through time even at constant silica as a first-order effect of secular mantle cooling which, as we have shown, has relatively little impact on the silica content of mantle-derived magmas despite its well-established influence on major elements such as MgO, as well as compatible and incompatible trace elements (37, 38).

For some trace element ratios, accounting for this variation Intriguingly, while the overall trend is to increasing Rb/Sr over in trace element abundances at constant silica causes previous time (consistent with the generally greater incompatibility of models to entirely fail to reject the null hypothesis. For example, Rb), both records show declining average Rb/Sr ratio over the Dhuime et al. (15) use a compilation of 87Sr/86Sr ratios, Rb/Sr ratios, Sm/Nd model ages, and crystallization ages for igneous rocks to infer the “juvenile” Rb/Sr ratio of an assumed pro- tolith by calculating how much ingrowth of radiogenic 87Sr is required in the time between assumed extraction from the man- tle (Sm/Nd model age) and crystallization of the observed sample to produce the observed Sr isotope ratio. They then use modern relationships between Rb/Sr ratio, SiO2, and crustal thickness to argue that Earth’s continental crust transitioned from thin and mafic to thick and felsic starting around ∼3 Ga. However, as seen in Fig. 1C, the relationship between Rb/Sr and silica has been far from constant over time. In Fig. 5, we compare the esti- mated “juvenile” Rb/Sr ratios of Dhuime et al. (15) with our estimate of crustal Rb/Sr ratio in the null hypothesis case of constant crustal silica. While the model age-dependent method of Dhuime et al. (15) infers “juvenile” Rb/Sr ratios roughly a quarter of that observed in average crust, the trend matches our null hypothesis reference model within uncertainty, indicat- ing that their variations in Rb/Sr over time can be explained solely by changing Rb/Sr at constant silica over time. While this temporal covariance is unlikely to result from secondary alter- ation [which would instead introduce anticovariance between Fig. 5. Estimated “juvenile” Rb/Sr ratios of Dhuime et al. (15) (left axis) our direct average and the isotopic approach of Dhuime et al. compared to our estimate of crustal Rb/Sr for a “constant-silica” crust (right axis) whose proportions of mafic, intermediate, and felsic rocks match those (15)], we emphasize that independent (e.g., isotopic) evidence observed at present. While the model age-dependent method of Dhuime et supporting a lack of aqueous alteration would be required to al. (15) results in extremely low “juvenile” Rb/Sr ratios (roughly a quarter of ensure primary trace element preservation in large geochemical that observed in average crust), the trend observed by Dhuime et al. (15) datasets, especially for highly fluid mobile element such as Rb matches ours, indicating that the level of increase in Rb/Sr over time can be and Sr. explained solely by secular cooling without any change in crustal SiO2.

21104 | www.pnas.org/cgi/doi/10.1073/pnas.2009431117 Keller and Harrison Downloaded by guest on September 30, 2021 Downloaded by guest on September 30, 2021 elradHarrison and Keller lnsd h siae fGee ta.(6 n age l (16). al. et Tang and (26) al. et Mezger Greber of and estimates Smit the alongside of data shale (Cr/U) log the quantity to The compared (17). model, reference silica 6. Fig. last ntertoo lm oacmga noprtdit con- into incorporated magmas change arc a to in plume resulted of cooling ratio secular be if the might case in complication (26), this in second-order in al. variations A introduced associated et intro- extent. its complications and Greber melting cooling to mantle of mantle sensitive secular method by less duced isotope comparatively titanium be should the as such of that from diverges (16). significantly from al. but et estimated (26), Tang al. esti- MgO et the Greber the with of agrees 6B, mate broadly to Fig. model reference pro- in assumed constant-silica metamorphic seen our are and as igneous (17) Similarly, their Mezger toliths. of and those reflect Smit underesti- accurately igneous of to compositions median in appears shale in decrease model decrease the reference mate the constant-silica not 6A, the magnitude—but the for Fig. reduce in to in seen changes acts element eliminate—inferred only trace entirely silica the (17), between Mezger and relationship and proxy the Smit in variation by secular compositions sediment terrigenous (15). al. et contrast- Dhuime greatly of the approach and two North isotopic estimate whole-rock across a direct our how than is methodologies—both remarkable ing rather nonetheless phenomenon is signal degree this it global but The reproducible clear, true (59). less is a Bender bias reflects and American Anderson this by which circa noted to event first Ga, “A-type” 1.4 high-Rb with associated high-K, be may remarkable peak the this that suggest We cooling. secular ial,w a oeta oeohriooi approaches, isotopic other some that note may we Finally, from inferred Cr/U in variations the as such cases, other In ∼ aito in Variation (A) y fe ecigzenith reaching after Gyr 1 A PAAS B MgO (wt. %) h g otn forcntn-iiarfrnemodel reference constant-silica our of content MgO The (B) . (Cr / U) 10 15 20 -1 0 1 2 0 5 4 4 ∆ C/)i endb mtadMze slg(Cr/U)/ log as Mezger and Smit by defined is (Cr/U) ∆ ∆ C/)oe iea acltdfrorconstant- our for calculated as time over (Cr/U) 3 3 C/)ta ol eifre fthe if inferred be would that (Cr/U) Age (Ga) Age (Ga) 2 2 Median igneous(thisstudy) Shale (SmitandMezger) . a ept ongoing despite Ga, 1.4 ca. SiO (this study) reference model Constant-silica Greber etal.(2017) Tang etal.(2016) 1 1 2 o ntne as instance, For . ∆ 0 0 (Cr/U) etpoisfrcutlslc,icuigteC/nrtoo Tang of ratio Cr/Zn the including silica, crustal for proxies ment sedimentary in U and is Cr detrital decoupling but environments. markedly chromite 69), 66), detrital and (65, 68 which refs. absent in (e.g., ) widespread most Early still the is the in even to from be, GOE spanning to (roughly the appears period there transitional 67), a ref. scenario, optimistic (e.g., such U elements and redox-sensitive Cr of as record sedimentary the biasing sedimentary eroded. of interpretation were such they ∆ no however, which con- GOE, from the could protolith After ratios the Cr/U shale represent immobile, ceivably fluid low relatively of indicator being an Cr urani- as used detrital commonly Fe–Cr where is atmospheric the Archean, ) stabilize with only the to (along be In nite Fe chromite. would with difference system natural this insoluble a Eh; the in higher exacerbated of insol- substantially remaining limits Cr at with stability uble distinct, markedly the (UO How- are O–H–Cr) 7A, oxidized.” U system equally Fig. of not forms in are oxidized U seen and as Cr expected ever, where be may cases Cr/U in of immobile a only are “fractionation is U thus and this and Cr that reduced, both when since imply concern they limited elements, only of redox-sensitive matter are U and metals Cr native or condi- some as others. at precipitating at unavoidably (62)—soluble the but range within tions aqueous conditions Eh–pH natural marked sys- different display modern at the elements solubility only trace in crustal considering and variation estimate minor even relevant to that, O–H–x, observe employed tem we element previously several Herein, been for silica. a have (61) 7, Fig. that diagrams in (Pourbaix) show, pairs (16– we Eh–pH problem, studies of this previous of range extent in the been all, illustrate has at To sediments 18). the if terrigenous on perfunctorily, transition in only this proxies as considered of element “overshoot” impacts trace hypothesized the of a However, use (64). and Ga (63), 2 Ga as 3 late as pro- early “whiffs” as debated with may posed interval, oxidation considerable iso- gradual a of sulfur spanned process mass-independent have the of 40), basis (39, atmo- the fractionation on tope Earth’s Ma best 2,450 when perhaps at While (GOE), placed oxygenated. significantly Event became Oxidation first coincide sphere Great frequently 16–18) the refs. (e.g., with silica crustal in transitions specter the raising pH, and/or fractionation. state selective redox of of function frequently Inaus- a elements (16). as fluid-mobile al. varies such et used of Tang Co, solubility example, the and for piciously, Ni by, silica as crustal in elements estimate in soluble such to partially includes ratios or This charge-to-size soluble fluids. are aqueous ionic states, ele- low oxidation Many favored with risks. their brings those also especially it While advantages, ments, 26–28). com- has (16–18, approach the rocks an the on such of igneous upon based Archean directly estimates are than of many rather concentration crust sediments, bias, Archean terrigenous of preservation the position of avoid composition to the attempt an In in Sediments Ratios Terrigenous Element Trace and Oxygenation Atmospheric consis- entire a the reflect which over (38) be differentiation present calc-alkaline to interval. crust the of appears to continental dominance Ga the melting tent 3.8 in decompression least preserved at to basalts variation from flux in secular excluded of such strongly ratio However, (60). the time in over crust tinental qiaetdfclisapyt te eietr rc ele- trace sedimentary other to apply difficulties Equivalent that acknowledge (17) Mezger and Smit while instance, For proposed that given relevant especially are concerns Such rUi upral.I diint ueosohrprocesses other numerous to addition In supportable. is Cr/U pO PNAS 2 6,6) n ih ru ht ohUand U both that, argue might one 66), (65, | etme ,2020 1, September 2 rnnt)adC (Cr Cr and uraninite) ; | o.117 vol. | o 35 no. 2 O 3 nthe in , | 21105

EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES Cr, U Cr,Zn , S Cu, Ag ABC1.2 1.2 1.2 HCrO [-] Modern range HCrO [-] 4 of natural 4 (Becking, 1960) 1.0 1.0 1.0

0.8 0.8 0.8 (UO2)3(OH)7[-] HSOO4[-][-] Cu[2+]Cu[2+] Tenorite ] 0.6 ] 0.6 0.6 UO2[[2+]2+] CrO4[2-] CrO4[2-] CrOH[2+] CrOH[2+ 0.4 CrOH[2+] CrOH[2+ 0.4 0.4 Ag[+]Ag[+] CuOH[+]CuOH[+] SO [2-] Cr[3+]Cr[3+] UUOO2OOH[+]H[+] Cr[3+] 4 0.2 0.2 Zn[2+]Zn[2+] 0.2 Eh (V) Eh (V) Cr2O3((s)s) Eh (V) UO2[+]+ U AAg(s)g(s) 0.0 4 O CrO [3-] 0.0 CrO [3-] 0.0 Cu[+]Cu[+] 9 (s)) 4 4 Cr2O3((s)s) Cuprite

-0.2 U[4+] -0.2 -0.2

UOH[3+] UO2(s) CopperCopper -0.4 (Uraninite) -0.4 H S(aq) -0.4 U(OH) [-] 2 5 Cr(OH)4[-]

-0.6 Cr(OH) [-] -0.6 -0.6 4 HS[-] U[3+] Cr[2+] Cr[2CrCCr[Cr[2+]r[2+[2+]2+]+]] S[2-] -0.8 -0.8 -0.8 1 3 5 7 9 11 13 1 3 5 791113 1 3 5 7 9 11 13 pH pH pH

Fig. 7. Eh–pH (Pourbaix) diagrams for a range of trace and minor element pairs [(A) U and Cr; (B) S and Cr; (C) Cu and Ag], based on Lawrence Livermore National Laboratory dataset 3245r46, as computed by Takeno (61) for a solute concentration of 10−10 M at 298.15 K and 105 Pa. The natural Eh–pH range of modern near-surface waters from Becking et al. (62) is shown for context; the upper limit thereof would be markedly reduced for Archean surface water and

groundwater due to lower atmospheric pO2. The stability limits of insoluble phases (bold) are shaded. In B, while Zn alone is soluble at all Eh–pH conditions, we additionally shade the stability range of sulfide, which, if cooccurring with certain otherwise soluble metals such as Zn2+, would allow the formation of insoluble precipitates such as (in this case) sphalerite. Illustrated element pairs are especially subject to aqueous fractionation under any conditions where one is soluble and the other is not.

et al. (16) (Fig. 7B) and the Cu/Ag ratio of Chen et al. (18) substrate and the deep stabilization of restitic garnet which (Fig. 7C), both of which are liable to fractionate due to weath- retards crystallization of aluminous phases from derived melts ering at different Eh–pH conditions. The situation becomes only (13–15) (cf. refs. 24 and 73). It follows from this conceptual more concerning when a fuller range of elements is considered framework that the simplest to the present felsic crust beyond the O–H–x system. For instance, while Zn alone is sol- occurred either in a monotonic fashion or during a discontinuity uble at all Eh–pH conditions, its solubility in natural low-Eh related to the discrete onset of subduction (e.g., ref. 15). conditions would depend heavily on the availability of sulfide, The composition of the continental crust has clearly changed which, if present, would allow the formation of insoluble metal over Earth history. For example, there is evidence for a progres- sulfide precipitates (in this case, sphalerite). A similarly trivial sive depletion in compatible elements (e.g., Cr) and enrichment attempt to quantify the redox dependence of an element ratio in incompatible elements (e.g., Rb). However, the early Earth such as Ni/Co would require us to evaluate, at a minimum, the mantle was almost certainly hotter than today, resulting in higher relative stability ranges of Ni and Co sulfides and sulfosalts; a degrees of mantle ; as a result, incompatible ele- more robust analysis would include the sorption of Ni and Co ment abundances were almost certainly lower than today (37, to other mineral surfaces (especially of clays) (e.g., refs. 70 and 38). By not taking this effect into account, we show, using a ref- 71), the of which may, in turn, change as a function of erence model characterized by constant proportions of mafic, O2. Indeed, the Ni/Co ratio of soils has been observed to strongly intermediate, and felsic rocks (i.e., constant SiO2), that incor- covary with proxies for the extent of oxidative weathering, such rect inferences regarding secular changes to the composition of as Ce/Ce∗ (72). Such effects appear to present a parsimonious continental crust (15) can result. Further errors are introduced explanation for the extraordinarily rapid rate of change inferred when fluid-mobile and redox-sensitive trace element ratios in from such ratios by Tang et al. (16) across the GOE, and the terrigenous sediments are used to indirectly estimate the com- contrast thereof with the relatively gradual decrease suggested position of the continental crust (e.g., refs. 16–18). Notably, our by Greber et al. (26) and our reference model. analysis of a constant-silica reference model to conclu- In brief, the use of potentially fluid-mobile trace element sions similar to several other recent reevaluations (26–28). This ratios in terrigenous sediment to infer crustal silica should be observation, especially in the context of recent results suggest- strongly resisted. Full mass balance models that include a wide ing a consistent dominance of arc-style flux melting throughout range of elements with different redox sensitivities appear to be the preserved rock record (38), presents a challenge to the more robust to such effects (e.g., refs. 27 and 28), especially if long-standing paradigm of early mafic crust, warranting further care is taken to avoid contamination of the sedimentary signal examination. by alteration and diagenesis (e.g., ref. 28). Extreme caution is nonetheless advised in any attempt to infer the composition of Data Availability. All underlying data and computational source code are primary igneous crust that involves potentially fluid-mobile trace available at GitHub, github.com/brenhinkeller/StatGeochem.jl. All study or minor elements in clastic detritus. data are included in the article and SI Appendix.

Conclusions ACKNOWLEDGMENTS. Many of the concepts herein were originally devel- oped over the course of discussion and collaboration with Patrick Boehnke, The geochemical community has long favored a view that early who declined to participate as an author of the present manuscript after terrestrial crust was broadly mafic, in part owing to misconcep- transitioning to the private sector. T.M.H. is supported through a grant from tions regarding both buoyancy on a hydrous magmatic the NSF Instrumentation and Facilities Program.

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