Extensive crustal extraction in Earth’s early history inferred from molybdenum isotopes

Estimates of the volume of the earliest crust based on zircon ages and radiogenic isotopes remain equivocal. Stable isotope systems, such as molybdenum, have the potential to provide further constraints but remain underused due to the lack of complementarity between mantle and crustal reservoirs. Here we present molybdenum isotope data for Archaean komatiites and Phanerozoic komatiites and picrites and demonstrate that their mantle sources all possess subchondritic signatures complementary to the superchondritic continental crust. These results confirm that the present-day degree of mantle depletion was achieved by 3.5 billion years ago and that Earth has been in a steady state with respect to molybdenum recycling. Mass balance modelling shows that this early mantle depletion requires the extraction of a far greater volume of mafic-dominated protocrust than previously thought, more than twice the volume of the continental crust today, implying rapid crustal growth and destruction in the first billion years of Earth’s history. Steady-state chemical differentiation between Earth’s mantle and crust was reached 3.5 billion years ago, following vigorous crustal recycling, according to mass balance modelling of molybdenum isotopes measured in mantle-derived volcanic rocks.


FIRST PARAGRAPH 1
Estimates of the volume of the earliest crust based on zircon ages and radiogenic isotopes 2 remain equivocal. Stable isotope systems, such as molybdenum, have the potential to provide 3 further constraints but remain underused, due to the lack of complementarity between mantle 4 and crustal reservoirs. Here we present molybdenum isotope data for Archean komatiites and 5 Phanerozoic komatiites and picrites and demonstrate that their mantle sources all possess sub-6 chondritic signatures complementary to the super-chondritic continental crust. These results 7 confirm that the present-day degree of mantle depletion was achieved by 3.5 billion years ago 8 and that the Earth has been in a steady state with respect to molybdenum recycling. Mass 9 balance modelling shows that this early mantle depletion requires the extraction of a far greater 10 volume of mafic-dominated proto-crust than previous thought, more than twice the volume of 11 the continental crust today, implying rapid crustal growth and destruction in the first billion 12 years of Earth's history. 13 and implicitly consider both crust extraction and recycling 3,9 . The complementarity of the 23 crustal and mantle reservoirs for long-lived radiogenic isotopes (Sr-Nd-Hf) has long been 24 established, with time-dependent models requiring that only ~25-50% of the mantle's mass 25 underwent melt extraction to balance the present-day compositions of the depleted mantle and 26 crust 7,8,10 . Estimating crustal growth from a mantle-depletion perspective using time-invariant 27 proxies provides an alternative approach 4 . As stable isotope ratios are time-independent, they 28 fit this criteria and can be used to put quantitative constraints on differentiation processes 29 occurring in the early Earth. However, this approach is hindered by the lack of resolvable 30 isotopic variation in samples representative of the depleted mantle and crust for many non-31 traditional stable isotope systems. Phanerozoic Baffin Island picrites possess variable δ 98 Mo from −0.13 to −0.32‰, which at first 87 glance suggests a lighter mantle δ 98 Mo (Fig. 1). However, the Baffin Island picrites represent 88 a special case of disequilibrium olivine accumulation 26 and after this is corrected the 89 composition of the parental melt is calculated as δ 98 Mo = −0.210 ±0.010‰ (Table S2; Figs.  90 S3-5), within error of depleted MORB 22 , the Gorgona komatiites, and three Archean komatiite 91 localities that span 800 Ma. These data thus demonstrate that the Mo isotope composition of 92 the accessible mantle has changed little over the last 3.5 Ga. The data for magmatic rocks are 93 further augmented by mantle xenoliths enabling us to calculate the average composition of the 94 depleted mantle as δ 98 Mo = −0.204 ±0.008‰ (Table S3). 95 These results place several new constraints on the evolution of Earth's mantle, notably: 96 1) the Mo isotope composition of the accessible mantle is unambiguously sub-chondritic (an 97 analysis of variance test confirms that the mantle samples are a resolvably different population 98 to chondritic meteorites at the 99% significance level; p-value <0.001); 2) the formation of this 99 reservoir must have occurred before ~3.5 Ga, 3) it must have had a substantial volume (magmas 100 generated at a range of melting depths are affected); and 4) no resolvable temporal variations 101 are observed with Archean komatiites ranging in age from 3.5−2.7 Ga having identical δ 98 Mo 102 to Cretaceous Gorgona komatiites, Paleogene Baffin Island picrites and modern MORB (an 103 analysis of variance test confirms that the means of these populations are identical; p-value 104 ~0.42). Together these constraints demonstrate that from a Mo isotope perspective most of the 105 present-day depletion of the mantle must have been completed by the Paleoarchean. This 106 finding is in agreement with independent constraints on the temporal chemical evolution of 107 continental basalts, which indicates a nearly constant amount of mantle depletion since ~3.8 108 Ga 31 . However, the amount of mantle depletion, and hence the volume of early continental 109 crust produced and subsequently destroyed, remain under-constrained 3,9 . Nonetheless, most 110 studies agree that 30−50% melt depletion of the whole mantle can reproduce most of the 7 radiogenic and incompatible element signatures of the crust and depleted mantle, assuming 112 they represent complementary reservoirs 7,8,10 . This has significant implications for the growth 113 of early crust given that the proto-crust and depleted mantle should chemically complement 114 each other, if no other processes have perturbed the system. We explore this further below. 115

COMPOSITION OF THE SILICATE EARTH 116
Due to the refractory nature of Mo in the solar nebula, we assume that the proto-Earth inherited 117 the δ 98 Mo of chondritic meteorites (Fig. 2). Soon after accretion, core formation occurred (≈ 118 34 Ma 32 ) resulting in the efficient removal of the highly siderophile elements into the Fe-Ni 119 metal core, including 95% of the Earth's original Mo 33 (Table S5). The near quantitative 120 removal of Mo to the core means isotope ratios in the metallic phase are unlikely to be 121 fractionated from those in bulk chondrites, as observed in iron meteorites 11 . Early experimental 122 work suggested this sequestration of Mo may have been associated with a small but resolvable 123 isotopic fractionation of the silicate portion of the planet 34 . However, recent metal-silicate 124 experiments which incorporate the effect of Mo valence state 16  added volatiles, including significant sulfur, which may have been sequestered to the outer core 130 in the "Hadean matte" (<1% of core mass; this sulfide-enriched phase is expected to have 131 preferentially incorporated isotopically light Mo 35,36 ); or 2) late accretion: since geochemical 132 modelling suggests that all of the Mo in Earth's mantle was added during the last 10% of 133 accretion 37 , with N-body simulations require only ~1% of the Earth's mass was accreted 134 following the Moon-forming impact 38 . Ultimately, due to the chondritic composition of the 8 new materials these processes will not significantly change the δ 98 Mo of the BSE, which should 136 be around δ 98 Mo ≈ −0.154 ‰. Therefore, the only remaining global-scale mechanism that can 137 modify the Earth's Mo isotope budget and account for the Earth's super-chondritic crust and 138 sub-chondritic mantle is the extraction of the crust (Fig. 2). Furthermore, the presence of 139 positive Nb anomalies and radiogenic Nd isotope compositions in some komatiite suites 140 suggest that their source regions have previously undergone melt extraction 23,39 . 141

EXTRACTION OF AN ISOTOPICALLY HEAVY CRUST 142
The sub-chondritic mantle δ 98 Mo signature may be the result of partial melting 22 13 into cumulates in the lower crust. incompatible 27 than Mo 4+ , residues of melting will have lower Mo 6+ /∑Mo than melt in addition 160 to higher mean co-ordination number, and hence will display lighter δ 98 Mo consistent with the 161 sense of fractionation observed in the komatiites measured here (Fig. 1)   Filled symbols are data analysed herein with hollow symbols data taken from Greber et al. 17 Table S3). 263 differentiation. Earth accretes from chondritic meteorites thus the bulk Earth initial δ 98 Mo 265 will be chondritic. During core formation 95 % of Earth's Mo is sequestered into the core 266 trapping isotopically light Mo in the metal phase, possibly making the residual BSE heavier. 267 Subsequent extraction of Earth's isotopically heavy crust prior to 3.5 Ga resulted in a bulk 268 mantle that is lighter than the building blocks of Earth. Earth's earliest crust was more mafic 269 than modern crust and therefore had a different Mo concentration and isotopic composition. 270      Subsequent extraction of Earth's isotopically heavy crust prior to 3.5 Ga resulted in a bulk 471 mantle that is lighter than the building blocks of Earth. Earth's earliest crust was more mafic 472 than modern crust and therefore had a different Mo concentration and isotopic composition. 473  and an additional Parr bomb digestion step was undertaken to completely dissolve any 503 refractory minerals. 2) Alternatively, carius tubes digestions were undertaken on some 504 Baffin Island samples whereby ~1.0 g of sample powder was double spiked and mixed 505 with 9 mL of reverse Aqua Regia (4:5 HCl-HNO3), the tubes were subsequently sealed 506 and heated to 220˚C for >72 hours. Following cooling the carius tubes were opened and 507 the supernatant and all undissolved silicate material was removed, using multiple rinses 508 with MQ H2O. This material was then further processed with a conventional HF-HNO3 509 hotplate digestion, to dissolve the refractory silicate portion. 510 A leaching experiment was undertaken on two of the Baffin Island picrites (PI-37, PI-511 43; Table S5). A second aliquot of the same sample powder was sealed in a carius tube with 512 cooling the Aqua Regia supernatant was removed (henceforth the leachate; predominantly 514 chromite and any sulfides present) and the remaining residual material (henceforth the 515 residue; predominantly silicates) was then rinsed three times with MQ H2O. The residue was 516 then dried for reweighing and subsequently digested using conventional HF-HNO3 digestion 517 as described above. When fully dissolved the concentration of Mo in the two splits was 518 obtained and the samples were spiked using the 97 Mo− 100 Mo double spike and then refluxed 519 several times in concentrated HNO3 to equilibrate the spike and sample. 520 Chemical separation of Mo was achieved using anion exchange (AG1-x8) 521 chromatography following the procedure described by Willbold, et al. 53  were also processed through the complete chemical separation procedure twice to ensure the 532 complete removal of Fe and Ru that can provide isobaric interferences during mass 533 spectrometry. Total Mo procedural blanks calculated following double-spike deconvolution 534 range from 0.18 to 0.30 ng (n = 7) and are considered negligible. 535

Mass Spectrometry 537
Molybdenum isotope compositions were measured using a Thermo-Finnigan Neptune multi-538 collector induction coupled plasma mass spectrometers (MC-ICP-MS). Samples were 539 introduced using an Aridus II desolvating nebuliser and a low uptake rate Cetac35 nebuliser 540 (aspiration rate 25-35 µlmin -1 ). All measurements were made in low resolution using X-cones, 541 and static collection mode with the simultaneous measurement of 9 isotopes 91 Zr, 92  Data reduction was carried out using the Isospike plugin 56 for Iolite 57 which is underpinned 553 by the double spike deconvolution equations of Rudge, et al. 52 . Baseline subtraction was 554 undertaken using the 60 s of acid blank that immediately preceded a sample, with direct isobaric 555 interferences from Zr on 92 Mo, 94 Mo and 96 Mo and Ru on 96 Mo, 98 Mo and 100 Mo mass 556 fractionation corrected iteratively using the beta-factors calculated following the initial 557 deconvolution. In addition to using the double spike to correct for instrumental mass 558 fractionation, a secondary correction for within run mass spectrometer drift was applied using 559 IsoSpike. The Mo isotope compositions of the unknowns were corrected using linear 560 interpolation by adjusting the composition of the bracketing analyses of the primary standard 561 NIST3134, run at least every two unknowns, to 0‰. 562 The long-term stability of the mass spectrometer over a two-year period was confirmed 563 by repeated measurement of the in-house standard Romil which has an average δ 98 Mo of 0.045 564 ± 0.027‰ (2 s.d.; n = 327). Long-term accuracy was tested by repeated analyses of 565 international standard solutions Open University (-0.341 ± 0.032‰, n = 58) and Bern (-0.242 566 ± 0.029‰, n = 73), which are within error of previous determinations 40, 55,58 . The 567 reproducibility of analyses was further evaluated using a range of US Geological Survey rock 568 standards. A range of first generation rock standards (BCR-1, BHVO-1, and AGV-1) were 569 analysed here (see Table S1), multiple digestions (n = 3-5) reproduce to better than 0.031‰, 570 however, both BCR-1 and BHVO-1 have lower Mo concentrations and distinctly different 571 δ 98 Mo than there second generation counterparts (i.e. BHVO-2) 11,59,60 , which suggests that 572 these samples were contaminated with Mo during preparation of the second aliquot as 573 suggested previously 18,53 . Two separate digestions of low Mo (~30 ng/g) standard BIR-1 yield 574 an average δ 98 Mo of -0.133 ±0.062‰, which is within error of the previous estimate 53 . 575 Replicate digestions of the high mass, low Mo (30-75 ng/g) Baffin Island and komatiite 576 samples herein generally reproduce to better than ±0.10‰, with two samples having 577 significantly larger 2 s.d. (the statistics are poor with only two replicates) although their total 578 range in δ 98 Mo is <0.14‰. Therefore, we conservatively consider ± 0.07‰ as the long-term 579 reproducibility of the measurements herein (the average 2 s.d. variability on the replicates 580 herein is ± 0.068‰; n = 14). 581

Mass balance calculations 583
The distribution of δ 98 Mo between the depleted mantle and crust after differentiation can be 584 estimated using isotopic and elemental mass balance (e.g. 18 ). For the present-day it is possible 585 to calculate the mass of depleted mantle relative the total mantle using Nd isotopes because the 586 mass of the present-day crust is well known, with previous studies suggesting that 30-50 % of 587 whole mantle has been depleted 7,8,10,61 . Whereas for the early Earth these parameters remain 588 poorly constrained and we need to make assumptions about crustal or mantle masses to 589 undertake geochemical modelling. In this study, we measured Archean and Mesozoic primary 590 magmas and found that have identical sub-chondritic Mo isotope compositions, therefore we 591 conclude that the Paleoarchean mantle that produced the Barberton komatiites was equally 592 depleted as the present-day mantle that produced the Gorgona komatiites. Since, present-day 593 mantle depletion is the result of crust formation, it is logical to correlate that mantle depletion 594 on the early Earth is also consequence of crust extraction. Given the range of present-day 595 estimates of mantle depletion, by assuming at least 30 % mantle depletion had occurred by the 596 Paleoarchean we can make inferences about the minimum volume of >3.5 Ga old crust that 597 existed using mass modelling 598 The equations presented here are similar to those used previously 62 . Here we consider 599 that Mo of a portion of the bulk silicate Earth (BSE) has been accessed for crust formation and 600 is distributed among two reservoirs; a depleted mantle (DM) and a proto-crust (C) (see Fig.  601 S8). Given that at present-day that only 30-50 % of whole mantle has been depleted 7,8,10,61 , in 602 the early Earth the mass of mantle sampled will be less than that of whole BSE, i.e. mDM << 603 mBSE, and mDM = mBSE only if the whole BSE mass has been used for crust extraction, which is 604 probably not the case 7

(C) 616
This allows us to calculate the mass of crust generated assuming various amounts of 617 depletion of the mantle reservoir (see Fig. 4). 618 The volume of this crust can then be calculated using the following: 619  45,46 it is reasonable to assume that the crust 631 extracted prior to 3.5 Ga was more mafic than today. 632 633 Data Availability Statement 634 All data generated during this study are included in the published article (and its 635 supplementary information files). 636 51 Kerr  Comparative Zn data come from Starkey, et al. 6 and McCoy-West, et al. 9 . Shaded area represents the 95% confidence interval of the correlation. Error bars on δ 98 Mo are the average reproducibility of the Baffin Island analyses (± 0.07‰), with errors on Zn concentration assumed to be 2% and δ 66 Zn the long-term reproducibility (± 0.03‰). The correlation between Zn concentration and δ 66 Zn and the Mo isotope compositions suggests that the variability is controlled by the same process (i.e. olivine accumulation). See McCoy-West, et al. 9 for more detailed discussion of the accumulation of olvine phenocrsyts that have experienced kinetic isotope exchange based on Fe and Zn isotopes.  Table S2). The strong linear trends show this is the result of accumulation (i.e. a linear addition process) rather than magmatic differentiation (where parabolic curves would be expected).  Table S6 for further details).  Figure 4 and Tables S9 and S10. Based on values presented in Table S8.  Table S10.  9 . Trace earth element data is from Starkey, et al. 6 .  A second aliquot of the same sample powder was sealed in a carius tube with 9 mL of reverse aqua regia (4:5 HCl-HNO3) and heated to 220˚C for >72 hours. Following cooling the aqua regia supernatant was removed (henceforth the leachate; predominantly chromite and any sulfides present) and the remaining residual material (henceforth the residue; predominantly silicates) were spiked and processed separately through chemistry. Mafic crust compositions were calculated by mixing different proportions of mafic and felsic material (i.e. 75:25 is 75% mafic). Molybdenum concentration data shows that Phanerozoic granites are clearly more evolved than their Archean counterparts (see Fig. S7). The Mo concentration of the felsic endmembers were taken from the available published data in Greaney, et al. 14 29 . Model assumes that the force constant is a linear function of Mo 6+ /∑Mo for both minerals and melt and that all minerals have the same Mo 6+ /∑Mo. Modelling uses force constants calculated in Table S8.   Table 9: Results of partial melting modelling showing the change ∆ 98 Momelt-solid as a function of temperature (°C) at a constant oxygen fugacity (Mo 6+ /∑Mo = 0.95) as shown in Figure 3.  Figure S10.

Filtering for alteration and the composition of Archean komatiites
Due to their long residence in the crust the δ 98 Mo of Archean komatiites may have been modified by alteration or metamorphism due to the mobility of Mo in fluids 34,35 . Here we have used a plot of Mn/Fe 2+ versus Al/Fe 2+ to assess the extent of alteration in the komatiites (Fig. S1). This type of plot has been used previously to assess alteration in komatiites 1,2   also seen with trace element ratios or elemental concentrations (Fig. S5). Presumably when this diffusional re-equilibration is occurring for Fe and Zn, heavy Mo isotopes were also being preferentially removed from the crystals and entering the melt (all things being equal heavy isotopes prefer the strongest bonds 41 ; i.e. lowest coordination number; see Table S8). Olivines that have then undergone kinetic isotope exchange can then be extremely isotopically light.
Variable amounts of these unique olivines are then entrained in subsequent melts and due to the low concentration of Mo in the melt can possibly affect the bulk rock composition.
However, due to the very low Mo concentration (<0.51 ppb) in olivine mass balance calculations fail to reproduce the compositions of the olivine rich samples (e.g. PI-40) using olivine alone. An alternate scenario is additional Mo is hosted within chromite or sulfide inclusions within the olivines. Leaching experiments were conducted on two samples (see Table S5) and the nonsilicate (chromite or sulfide) fraction is resolvable isotopically lighter than the residual silicate  (Table S2) which is identical within error to all of the other high temperature high degree partial melts measured from 3.5 Ga to the present (Table   S3).

Estimates of the composition of Mid-ocean ridge basalts
The composition of the MORB mantle is a contentious issue in the Mo isotope scientific literature, with inconsistency between published results 21,22,42 . Initial work by Hibbert, et al. 43   For all the other parameters, we needed proxies.
2) The [Mo] of the basalt endmember (0.155) has been model based on partial melting of the mantle by 30% (sitting in the middle of the Archean range; 18,19 ) to produce a high Mg basalt using well constrained D values; 16,29 . Due to the incompatible nature of Mo, varying the degree of melting from 20 to 40% does not substantial change this value it from 0.23 to 0.12 ppm (Fig. S9).
The partial melting model presented in Figure 3 shows that melting of a chondritic mantle reservoir to form basalt would reproduce this value with ~12 % melting at 1300 °C. This ~0.05 ‰ offset is comparable to the natural offset observed between N-MORB 21 and the accessible mantle herein.
Melting at higher temperatures or greater degrees of melting would result in a lighter melt.
Changing of the composition of the basalt to −0.12‰ results in a difference in VPCC of only 0.12 (for the 50:50 model at 30% mantle depletion), which is smaller than the already displayed error envelopes based on varying endmember composition (see Fig. 4). There is no a priori reason to assume that partial melting processes were different in the Archean than they are today. Therefore, we do not expect significant uncertainties in the crustal volume presented in this study due to the lack of exact match between our chosen proxies for Archean crust and the real Archean crust.

The effect of partial melting on Mo isotopes
Two major factors, redox and co-ordination, will control the fractionation of Mo stable isotopes during partial melting e.g. 41 . Due to the oxidised nature of the terrestrial upper mantle (≈FMQ), in partial melts of this mantle, Mo predominantly occurs as tetrahedral co-ordinated Mo 6+ (MoO4 2-) 30,55 . Furthermore, given Mo 6+ is significantly more incompatible than Mo 4+ 29 melting products will have higher Mo 6+ /∑Mo than their residue, and hence will be heavier. Co-ordination is a subordinate effect but will also result in an isotopically heavy melt, with Mo in pyroxene (octahedral; 56 ) and olivine having higher co-ordination than in the melt, with heavy isotopes preferentially moving to sites with the lowest coordination number 41 . The generation of isotopically heavy melts is consistent with the fact average global basalt (δ 98 Mo = −0.10 ± 0.04‰; 15 ), are isotopically heavier than the bulk accessible mantle we observe today (δ 98 Mo = −0.20 ± 0.01‰; see Table S3). Because Mo is highly incompatible during mantle melting DMo = 0.006-0.008 16,29 , it will be quantitatively extracted into the melt except at low degrees of melting (see Fig. S9).
Here we have constructed a non-modal batch melting to show the fractionation of Mo isotopes during partial melting based upon the general principles outlined in Sossi and O'Neill 33 (See Fig.   3). This model uses the Born-Mayer repulsion approximation to calculate force constants that has been shown to be adequate for other condensed phases 33,57,58 . The model set up and parameters used in modelling are described in Table S7 and At high degrees of melting as observed in komatiites and the Baffin Island picrites (20-40 % melting), they will remain essential unfractionated from their source region due to the complete removal of Mo from their residue ( Fig. 3; Table S9). The corollary is that any Mo remaining in the residual mantle after partial melting is isotopically lighter. At smaller degrees of melting or more reduced conditions the ∆ 98 Momelt-residue can be larger.  Fig. 3b; S10).
The work of Nicklas et al. 60,61 suggests there was a secular increase in upper mantle oxygen fugacity from 3.5 to 2.4 Ga, providing a upper bound on oxygen fugacity prior to 3.5 Ga (Using calculate a Mo 6+ /∑Mo ≈ 0.95, which is adopted in the temperature dependent modelling presented in Figure 3.
It has also been suggested based on stable isotope evidence that the Earth and Moon equilibrated during the Moon forming impact 42,62,63 . The lunar mantle has an oxygen fugacity of ca. IW-1 and thus Earth's mantle may have experienced a short period at more reduce conditions.
We have included modelling at highly reduced conditions (See Fig. S11, Table S10) because it is relevant to melting processes on other celestial bodies (e.g. Moon, Angrites), we are not advocating that the Earth's mantle is currently at these highly reduced conditions.

Alternative estimates of the composition of the bulk silicate Earth
In the main text we have assumed the Mo isotope composition of the bulk silicate Earth (BSE) is the same as the chondritic meteorites Earth accreted from (δ 98 Mo = −0.154 ± 0.013‰; 22,23 ). Here we investigate the effects of alternate scenarios on the volume of crust extraction required in the early Earth: 1) the Mo isotope composition of BSE was modified during core formation; or 2) the composition of the BSE is the same as the bulk silicate Moon.
Modification during core formation (Model 2): The near quantitative removal of Mo to the metallic core means the metallic phase is unlikely to be fractionated from bulk chondrites, as is observed in iron meteorites 23 . However, this sequestration of Mo may have been associated with a small but resolvable isotopic fractionation of the silicate portion of the planet of up to 0.3‰ 23 .
When extrapolating to temperatures more closely approximating core formation (>2000 °C 64 ) initial metal-silicate equilibration experiments 65  is based on assuming the BSE and Moon were once isotopically equilibrated as has been shown for several lithophile elements 62,63 . Using analyses of lunar samples (δ 98 Mo = −0.050 ± 0.033‰; 23 ), and assuming subsequent late accretion of 1% chondritic material results in a δ 98 Mo of −0.078‰. By using this value for the BSE and then undertaking mass balance modelling to investigate the volume of crust, generates unrealistically large volumes of crust ( Fig. S6e-f).
Namely, using TTG felsic materials for mafic crust-A (50:50 mafic-felsic rocks) and a depleted mantle comprising 30% of the mantle would require 14 times the PVCC. This value is even higher for the mafic crust-B (75:25 mafic-felsic rocks). Requiring >10 times the PVCC is highly unrealistic, considering the recycling rates and present extent of crustal volume. Therefore, for Mo it is extremely unlikely that the BSE was ever fully equilibrated with the bulk silicate Moon.

The effect of the lower crust
On the modern Earth the continental crust has a well-developed lower crust [48][49][50] . Estimates of the composition of the continental crust from molybdenites, granites and arc-related basalts are consistent with a super-chondritic δ 98 Mo from +0.05 to +0.30‰ 15,70,71 . These archives are focused on the upper continental crust (arc basalts are a record of juvenile continental crust), but do not consider the effect of possible compositional variations in the lower crust. However, given the extreme incompatibility of Mo during mantle melting DMo = 0.006-0.008 16,29 , Mo essentially becomes concentrated in the upper crust rather than any lower crustal cumulates. An additional complication would be the presence of residual sulfides, that due to its chalcophile behaviour will preferentially incorporate Mo. However, given on the modern Earth most continental crust is predominantly formed in subduction-like environments sulfide-saturation will generally be delayed (due to higher fO2, and water contents), and therefore Mo will remain in the melt phase and removed to the upper crust.
The composition and makeup of the Archean crust was not identical to modern crust [48][49][50] .
Therefore, whether the Archean crust has a well-defined lower crust similar to today or not is unknown. Instead, studies infer that the whole Archean crust was dominantly mafic and may have contained subordinate amount of granitoids 49,51,52 . We have considered this factor while carrying out the mass balance modelling by using 3 different crustal compositions: (1)  profile is largely devoid of residues formed after TTG extraction. Therefore, the crust is dominated by juvenile, melt-undepleted (meta-)basalts and granitoids. As stated above, our existing mass balance calculations consider both these components of the Archean crust as realistically as possible. Furthermore, even if some fraction of this TTG-depleted residual mass remains in the crust, it is likely to be of granulite to eclogite grade-where rutile exists 72 . It has been shown that in such cases, rutile should dominate the Mo-budget 14,76,77 . Mo-concentration within such eclogitic rutile can vary within 2-7 ppm 77 and thermodynamic phase equilibria modelling suggests that the Archean meta-basalts would have contained not more than ~0.5 volume % of rutile 78 . In that case, the net Mo concentration will not deviate much from that of average basalt, which we have already considered for the mafic component of our model crustal types. This further attest that the crustal volume range bracketed by the intermediate and dominantly-mafic crustal types potentially accounts for the variations due to any depleted lower crustal rocks.