C Israel

M Boyet

R Doucelance

P Bonnand

P Frossard

D Auclair

A Bouvier

Formation of the Ce-Nd mantle array: crustal extraction vs. recycling by subduction

Keywords: 138 Ce/ 142 Ce, rare earth elements, chondritic bulk silicate Earth, silicate reservoirs, mantle array, ocean island basalts

We present new measurements of 138 Ce/ 142 Ce and 143 Nd/ 144 Nd isotopic ratios in terrestrial and extraterrestrial samples. The mean value obtained from nine chondrites defines the 138 Ce/ 142 Ce ratio of the chondritic uniform reservoir (CHUR) as 0.02256577 ± 66 (2sd). MORBs and OIBs define the mantle array in the εNd vs. εCe diagram to be εNd = -7.3 (± 0.5) × εCe + 0.4 (± 0.3). From MORB measurements, we derive the isotopic composition of the depleted MORB mantle (DMM) to be εCe = -1.1 ± 0.6 (2sd). Both CHUR and a modelled early-depleted mantle reservoir plot on the mantle array.

Thus, the precise determination of the mantle array does not further constrain the La/Ce and Sm/Nd ratios of the bulk silicate Earth (BSE; i.e., primitive mantle). The composition of 1.8 Ga upper continental crust obtained from aeolian sediments is εCe = 1.8 ± 0.3 (2sd; εNd = -11.2), and that of its 2.2 Ga equivalent is εCe = 2.3 ± 0.3 (2sd; εNd = -17). Binary mixing models between depleted (DMM) and enriched (upper crust or mafic crust composition) components do not reproduce the linear Ce-Nd mantle array but plots close to the island arc basalt data. When the bulk Ce isotopic composition of the continental crust is calculated from the range of accepted Nd isotope values and a mass-balance budget of the BSE, the mixing curves are closer to the mantle array. However the calculated Ce isotopic composition for the bulk crust is always less radiogenic than measurements. Adjusting the Ce-Nd isotopic composition or the Ce/Nd ratio of the end-members to fully linearise the mixing curve leads to unrealistic values never measured in terrestrial samples. We propose a recycling model to reconstruct the mantle array with the participation of both oceanic crust and sediments in the mantle through time.

Cerium is a redox sensitive element, making the La-Ce and Sm-Nd systematics an ideal combination to investigate sediment recycling through time. In this recycling model, the most extreme EM-like signatures require the involvement of oceanic sediments that formed under reduced conditions before the Great Oxygenation Event at 2.4 Ga, and which are devoid of Ce elemental anomalies.

Introduction

Long-lived isotope systematics are remarkable tracers of the long-term evolution of the different terrestrial reservoirs. Radiometric systems based on refractory lithophile elements are the most likely to provide robust information on the bulk silicate Earth (BSE) because they were not lost during Earth's accretion or segregated into the core during its differentiation. Indeed, rare earth elements (REEs) have high condensation temperatures and remain strictly lithophile at the conditions of Earth's core formation [START_REF] Bouhifd | Superchondritic Sm/Nd ratio of the Earth: Impact of Earth's core formation[END_REF]. The REE concentrations of the primitive mantle (PM) are assumed to be equivalent to those of the BSE, and their ratios should be chondritic if chondrites are the Earth's main building blocks. [START_REF] Boyet | 142Nd evidence for early (> 4.53 Ga) global differentiation of the silicate Earth[END_REF] identified a systematic offset between the 142 Nd/ 144 Nd ratios of modern terrestrial rocks and chondrites resulting in an active debate on the refractory lithophile element composition of the PM (see [START_REF] Caro | Super-chondritic Sm/Nd ratios in Mars, the Earth and the Moon[END_REF][START_REF] Jackson | Major and trace element composition of the high 3He/4He mantle: Implications for the composition of a nonchonditic Earth[END_REF]O'Neill and Palme, (1984). However, new results from chondrites and mantle-derived samples lead to a different observation. The mantle array passes directly through the CHUR composition in the Ce-Nd isotopic diagram (Willig and Stracke, 2019). Our new results first confirm this trend. Moreover we show that a modelled reservoir depleted in incompatible elements (and characterised by a depleted REE pattern; see early-depleted reservoir in [START_REF] Boyet | 142Nd evidence for early (> 4.53 Ga) global differentiation of the silicate Earth[END_REF] that would be formed early in the Solar System's history also plots on the mantle array.

The mantle array must reflect the formation of the major silicate reservoirs and their interactions during Earth's history. Important questions have been addressed by coupling Lu-Hf and Sm-Nd isotope systematics; for example, arc lavas do not follow the Hf-Nd mantle array, which reflects the elevated 176 Hf/ 177 Hf signature measured in most oceanic sediments [START_REF] Carpentier | The "zircon effect" as recorded by the chemical and Hf isotopic compositions of Lesser Antilles forearc sediments[END_REF]. Also, the presence of pelagic sediments in the source of the Hawaiian hotspot was first identified from Hf-Nd isotopic measurements [START_REF] Blichert-Toft | Hf Isotope Evidence for Pelagic Sediments in the Source of Hawaiian Basalts[END_REF]. Cerium is a redox sensitive element, making the La-Ce and Sm-Nd systematics an ideal combination to investigate sediment recycling through time. Indeed, most documented modern forearc sediments are depleted in Ce relative to neighbouring elements [START_REF] Plank | The chemical composition of subducting sediments[END_REF]. Before the Great Oxygenation Event (GOE), however, all REEs should have behaved similarly and no Ce fractionation is expected to have occurred during that time. Coupling Ce and Nd isotopic measurements will thus provide additional constraints on the nature of sediments recycled into the deep mantle and sampled via hotspot volcanism. Chauvel et al. (2008) explained the Hf-Nd mantle array by the recycling of oceanic crust and sediments into the mantle. Here, we present similar models in Ce-Nd isotope diagrams for the first time.

Sample selection

We measured the Ce and Nd isotopic compositions of four ordinary chondrites, six enstatite chondrites, one carbonaceous chondrite, seven MORBs, 51 OIBs, one intraplate continental volcanism occurrence (Ethiopia), and six loess samples. To include all mantle end-members, we selected rocks with extreme Nd-Sr-Pb-He compositions. OIB samples were selected from 13 locations covering the Atlantic (Iceland, São Miguel (Azores archipelago), Cape Verde, Saint Helena, Tristan Da Cunha), Pacific (Hawaii, MacDonald seamount, Rurutu and Tubuai Islands (Austral archipelago), Fangataufa (Tuamotu archipelago), Tahaa Island (Society archipelago)), and Indian Oceans (Heard, Kerguelen, Reunion and Saint-Paul Island (French Southern and Antarctic Lands)). MORB samples are unaltered glasses collected on the Pacific ridge (Bellot et al., 2015) and the Southwest Indian Ridge. The Pacific MORBs have similar REE patterns and do not show the Dupal anomaly (Sr and Pb isotopic anomalies in MORBs and OIBs erupted around 30° S). We used loesses from western Europe (wind-transported periglacial deposits), China and Tajikistan (sediments originating in northwestern Mongolia and the Karakum (Turkmenistan) and Kyzylkum deserts (Kazakhstan and Uzbekistan), respectively), and the Sahara Desert (dusts blown to Southern France; [START_REF] Chauvel | Constraints from loess on the Hf-Nd isotopic composition of the upper continental crust[END_REF] and references therein; Supplementary data 1, Figs S1-4).

Analytical procedures

Dissolution and chromatography protocols

All samples were entirely processed at the Laboratoire Magmas et Volcans (LMV, Clermont-Ferrand, France), except three chondrites (NWA 8007, NWA 10854, and Adrar Bous) that were dissolved at the University of Western Ontario (UWO). Mantle-derived and loess samples were dissolved using the following protocol. We used 50 to 300 mg of sample depending on the REE concentration and the quantity of powder available. Powders were digested in a 3:1 mixture of HF (65%) and HNO3 (48%) that was maintained at 75 °C on a hot plate for 48 h. Once dried, the samples were dissolved a second time in 6 M HCl. The dissolution protocol was slightly different for chondrites. Oudiyat Sbaa, Yilmia, Pillistfer, Agen, Sahara 97158, and Saint-Séverin were dissolved in a 10:1 mixture of HF (65%) and HNO3 (48%) in PFA-Savillex beakers placed on a hot plate at 110 °C for seven days. Fluorides were broken down in a second step using concentrated HClO4. Allende, Sahara 97072, Adrar Bous, NWA 8007, and NWA 10854 were dissolved in Parr bombs using the same acid mixtures (48 hours at 180 °C in HF-HNO3, or seven days at 150 °C, followed by HClO4 treatment). Once dried, all chondrite samples were dissolved in 6 M HCl for two to five days on a hot plate at 110 °C.

All sample solutions were then separated into two aliquots for trace element and isotopic dilution (5-10%) and Ce-Nd isotopic analyses (90-95%). Ce and Nd were chemically separated following the procedure reported in detail by [START_REF] Bonnand | Radiogenic and stable Ce isotope measurements by thermal ionisation mass spectrometry[END_REF]modified from Tazoe et al., 2007 andBellot et al., 2015 and summarised here. REEs (including Ba) were first separated from the matrix using AG50W-X8 resin. An additional step using AG1-X8 resin (200-400 mesh) was performed on the meteorites to remove Fe. Then, Ce was separated from the trivalent REEs using an oxidation technique (NaBrO3) on Ln-Spec resin, and purified in a final step using AG50W-X8 resin to remove any residual Ba. The remaining REE fraction was processed using Ln-Spec resin (25-50 mesh) and Nd was collected in 0.25 M HCl. Total procedural blanks for Ce and Nd were 0.4 ± 1.7 ng (2sd, n = 12) and 0.02 ± 0.05 ng (2sd, n = 7), respectively, and were always negligible relative to the quantities collected from the samples.

Trace element concentrations and Ce and Nd isotopic measurements

We determined trace element abundances for all samples except NWA 8007, NWA 10854, and Adrar Bous by inductively coupled plasma mass spectrometry (ICP-MS) using the Agilent 7500 quadrupole instrument in normal mode (no collision cell) at LMV. These 3 meteorites were analysed using a Thermo iCAP quadrupole ICP-MS in collision cell mode with He flux at UWO. Concentrations were calculated using an external calibration (CMS reference material standard, Inorganic Ventures). We analysed certified rock standard BHVO-2 (or BCR-2 at UWO) together with our samples to assess the accuracy of our analytical protocol.

We performed Ce isotopic analyses in static mode with double Re filaments on a ThermoScientific TM Triton Plus TIMS at LMV. Ce isotopes were measured as CeO + oxides using the procedure described in [START_REF] Bonnand | Radiogenic and stable Ce isotope measurements by thermal ionisation mass spectrometry[END_REF]. A typical run comprised 27 blocks with 20 cycles of 8 s integration time each, and a baseline measurement (deflected ion beams) of 60 s. Matrix rotation of the amplifiers was not active because the 10 11 , 10 12 , and 10 13 Ω resistors were used simultaneously. All corrections (oxygen, mass discrimination using 136 Ce/ 142 Ce = 0.01688, and tailing effect) were performed offline. All reported uncertainties are 2 standard deviations. During the course of the study, the value of the tailing correction was ΔεCe = 0.77 ± 0.18 (n = 151). Repeated measurements of our CeLMV synthetic reference material gave 138 Ce/ 142 Ce = 0.02257063 ± 54 (24 ppm; n = 31). 138 Ce/ 142 Ce ratios measured for rock reference standards BCR-2 and BHVO-2 were equal to 0.02256684 ± 48 (21 ppm; n = 9) and 0.02256453 ± 99 (44 ppm; n = 7), respectively (see Supplementary data 2 for details on the total reproducibility of measurements). The mean 134 Ba 16 O signal was 0.000003 ± 0.000010 V (n = 139), and the maximum reached 1 × 10 -5 V, which has no significant effect on the 138 Ce/ 142 Ce and 136 Ce/ 142 Ce ratios. Ce isotopic compositions of loess samples were measured on the same TIMS but using the two-line acquisition method of 360 cycles (Bellot et al., 2015).

We performed Nd isotopic analyses in static mode with double Re filaments using a ThermoScientific TM Triton TIMS at LMV. A typical run comprised 18 blocks of 10 cycles, allowing a full rotation of the amplifier system. Mass discrimination was corrected using 146 Nd/ 144 Nd = 0.7219. Repeated measurements of the JNdi-1 standard and the two rock reference standards BCR-2 and BHVO-2 gave 143 Nd/ 144 Nd = 0.512099 ± 4 (7 ppm; n = 16), 0.512623 ± 8 (17 ppm; n = 3) and 0.512973 ± 3 (6 ppm; n = 3), respectively. The Sm contribution measured at mass 147 was negligible in all analyses.

Results

Measured Ce and Nd isotopic compositions are reported in Table 1 and2, and details for individual runs (number of cycles, mean intensity, tailing value) are given in Supplementary data 2.

Chondrites

Chondrites define a small range of 138 Ce/ 142 Ce ratios between 0.02256522 and 0.02256633, excluding the two EL6 samples (Yilmia and Pillistfer) that show lower values (0.02256251 and 0.02256272, respectively). Enstatite, ordinary, and carbonaceous chondrites have indistinguishable average values within errors (Fig. 1A). The two EL6 samples plot on the 4.568 Ga isochron in the 138 Ce/ 142 Ce vs. La/Ce diagram (Fig. 1B) suggesting that their La/Ce ratios were modified early in the history of the Solar System, in agreement with previous conclusions [START_REF] Barrat | The lithophile trace elements in enstatite chondrites[END_REF][START_REF] Boyet | Enstatite chondrites EL3 as building blocks for the Earth: The debate over the 146 Sm-142 Nd systematics[END_REF]. Consequently, we define the Ce isotopic composition of CHUR as the mean value of the other nine (i.e., unmodified) chondrite samples: 138 Ce/ 142 CeCHUR = 0.02256577 ± 66 (29 ppm).

To compare our CHUR value with the most recent estimates of Bellot et al. (2015) and Willig and Stracke (2019), we have normalised these previous data using a common reference material ( 138 Ce/ 142 CeCeLMV/ 138 Ce/ 142 CeCeAMES = 0.02257053/0.02257426, [START_REF] Bonnand | Radiogenic and stable Ce isotope measurements by thermal ionisation mass spectrometry[END_REF]. The normalised CHUR value of Willig and Stracke (2019) is thus 138 Ce/ 142 Ce = 0.02256644 ± 53 (using 136 Ce/ 142 Ce = 0.01688), consistent with our estimate within errors. In contrast, the normalised CHUR value of Bellot et al. (2015) is significantly distinct from our value (Fig 1A). Combining the normalised data of Willig and Stracke (2019) with our measurements to calculate a mean chondritic 138 Ce/ 142 Ce ratio increases the uncertainty from 29 to 39 ppm because their chondrite measurements were systematically 30 ppm more radiogenic than ours. This deviation exists also for MORB and OIB data and it is highlighted when data are reported in a 143 Nd/ 144 Nd vs. 138 Ce/ 142 Ce isotope diagram. Thus, to compare these different datasets, we henceforth strictly use the epsilon notation (Fig. 1B). In the future, to achieve better interlaboratory reliability, chondrites should be measured under similar analytical conditions (see Supplementary Fig. S5).

Ce-Nd isotopic compositions of terrestrial samples

The Ce and Nd isotopic compositions of terrestrial samples measured in this study are reported in a eNd vs. εCe diagram (Fig. 2) and compared with recent MORB and OIB data from the literature. MORB samples have the least radiogenic Ce ratios and the most radiogenic Nd ratios, with εCe and eNd values ranging from -1.19 to -0.71 and from 8.85 to 10.42, respectively. Pacific MORBs have slightly lower Ce isotopic ratios than Indian ones. OIB samples define larger compositional ranges with εCe and εNd values ranging from -1.44 to 0.43 and from -2.49 to 10.42, respectively. Enriched mantle (EM1 and EM2)-like OIBs (Heard, Gough, Kerguelen, Tristan Da Cunha, São Miguel, and Tahaa) have the highest Ce isotopic ratios. Samples from Iceland and two samples from Hawaii plot in the MORB field. Other OIBs, including those with HIMU affinity (Saint-Helena), have compositions intermediate between Iceland samples and those with EM affinities, forming a continuum between these two end-members.

The seven samples from Ethiopia have subchondritic eCe values and plot along the OIB trend. The entire range of MORB eCe values is relatively large (1 unit) compared to OIBs (1.5 units) considering the dispersion of eNd values (3 units for MORBs and 12 units for OIBs).

Loess samples have εCe and eNd values ranging from 1.6 to 2.0 and from -13.52 to -9.73, respectively, with average values of εCe = 1.8 ± 0.3 and εNd = -11.2 ± 3.0. Our samples represent a sub-sampling of those analysed by [START_REF] Chauvel | Constraints from loess on the Hf-Nd isotopic composition of the upper continental crust[END_REF], who determined a mean εNd value of -10.3 ± 2.3, consistent with our results.

Discussion

5.1. Definition of the Ce-Nd mantle array [START_REF] Dickin | Cerium isotope geochemistry of ocean island basalts[END_REF] was the first to present coupled Ce and Nd isotopic measurements of OIB samples and define the Ce-Nd mantle array. Recently, Willig and Stracke (2019) published new high-precision measurements of MORBs and OIBs and refined the εCe-εNd correlation. We extended their results by analysing 66 new mantle-derived samples. The regression line calculated from all samples presented in Figure 2 (n = 134) gives the following equation for the mantle array: εNd = -7.3 (± 0.5) × εCe + 0.4 (± 0.3), using Isoplot â and considering errors of 0.25 for eCe and 0.10 for eNd. In agreement with Willig and Stracke (2019), the mantle array intercepts the chondritic composition. However, we will show in the following section that a chondritic intercept for the mantle array does not prove that these mantlederived samples come from a source with a chondritic light REE (LREE) pattern.

Chondritic vs. non-chondritic REE composition of the primitive mantle

A non-chondritic REE composition of the primitive mantle was initially proposed to explain the radiogenic eNd values measured in Eoarchean samples (e.g., [START_REF] Chase | Stored mafic/ultramafic crust and early Archean mantle depletion[END_REF]. High-precision isotopic measurements of the short-lived 146 Sm-142 Nd systematics in both terrestrial samples and chondrites have strongly revived the debate on the nature of the REE composition of the PM [START_REF] Boyet | 142Nd evidence for early (> 4.53 Ga) global differentiation of the silicate Earth[END_REF]. Most 142 Nd/ 144 Nd variations measured in the different chondrite groups are now attributed to initial isotopic heterogeneities of nucleosynthetic origin within the solar nebula during planetary accretion [START_REF] Bouvier | Primitive Solar System materials and Earth share a common initial 142Nd abundance[END_REF][START_REF] Burkhardt | A nucleosynthetic origin for the Earth's anomalous 142Nd composition[END_REF][START_REF] Carlson | Chondrite Barium, Neodymium, and Samarium Isotopic Heterogeneity and Early Earth Differentiation[END_REF]. However, in terms of non-radiogenic Nd isotope compositions, enstatite chondrites are the closest to the Earth and, on average, are depleted in 142 Nd by 10 ppm relative to terrestrial samples [START_REF] Boyet | Enstatite chondrites EL3 as building blocks for the Earth: The debate over the 146 Sm-142 Nd systematics[END_REF][START_REF] Dauphas | The isotopic nature of the Earth's accreting material through time[END_REF] with the exception of the EL3 sub-group. Carbonaceous chondrites may have been involved during the last stage of Earth's accretion, and, because they are depleted in 142 Nd by 32 ppm relative to terrestrial samples, they may have further contributed to the difference between terrestrial and EC values [START_REF] Boyet | Enstatite chondrites EL3 as building blocks for the Earth: The debate over the 146 Sm-142 Nd systematics[END_REF]. None of the current meteorite groups available for analysis and mixing models satisfy the isotopic and elemental composition of the Earth, and call for unknown end-members or fractionation processes. Thus, it is still possible that some of the observed difference between terrestrial and chondritic 142 Nd abundances was produced by the decay of 146 Sm in a superchondritic Sm/Nd reservoir.

To attempt to constrain the REE composition of the PM, we consider a 10 ppm increase in radiogenic 142 Nd that corresponds to the difference between modern terrestrial samples and either EC values having a terrestrial mean 142 Nd/ 144 Nd 10 ppm higher than that of the continental crust, or an Earth made with 90% of EL3 chondrites + 10% carbonaceous chondrites [START_REF] Boyet | Enstatite chondrites EL3 as building blocks for the Earth: The debate over the 146 Sm-142 Nd systematics[END_REF]. This excess 142 Nd would have been produced in a high-Sm/Nd reservoir. Assuming this reservoir formed 4.568 Ga, this corresponds to a 3.6% increase of the BSE Sm/Nd ratio relative to the chondritic value. Modelled Sm/Nd ratios in early-differentiated reservoirs have been discussed in a large number of publications (e.g. [START_REF] Boyet | 142Nd evidence for early (> 4.53 Ga) global differentiation of the silicate Earth[END_REF][START_REF] Caro | Super-chondritic Sm/Nd ratios in Mars, the Earth and the Moon[END_REF] and can goes up to 5% higher if this early-differentiated reservoir formed 4.5 Ga. Here we use the terms "early depleted reservoir" (EDR) and "early enriched reservoir" (EER) as defined by [START_REF] Boyet | 142Nd evidence for early (> 4.53 Ga) global differentiation of the silicate Earth[END_REF]: the EDR has a chondrite-normalised REE pattern that is depleted in LREEs relative to heavy REEs and thus a superchondritic Sm/Nd ratio, whereas the complementary EER has a subchondritic Sm/Nd ratio. The EER may exist in the lower mantle [START_REF] Boyet | 142Nd evidence for early (> 4.53 Ga) global differentiation of the silicate Earth[END_REF] or may correspond to embryonic crust lost by collisional erosion during Earth's accretion [START_REF] O'neill | Collisional erosion and the non-chondritic composition of the terrestrial planets[END_REF].

We calculate the REE composition of the EDR by the method developed by [START_REF] Jackson | Major and trace element composition of the high 3He/4He mantle: Implications for the composition of a nonchonditic Earth[END_REF], which is based on three different isotopic systematics ( 146 Sm-142 Nd, 147 Sm-143 Nd, and 176 Lu-176 Hf) and invariant elemental ratios (e.g., Sm/Hf). CHUR REE elemental ratios needed for this calculation were obtained from a large and recent database of ordinary, enstatite, and carbonaceous chondrites (Barrat et al., 2012[START_REF] Barrat | The lithophile trace elements in enstatite chondrites[END_REF][START_REF] Boyet | Enstatite chondrites EL3 as building blocks for the Earth: The debate over the 146 Sm-142 Nd systematics[END_REF][START_REF] Braukmüller | The chemical composition of carbonaceous chondrites: Implications for volatile element depletion, complementarity and alteration[END_REF][START_REF] Dauphas | Thulium anomalies and rare earth element patterns in meteorites and Earth: Nebular fractionation and the nugget effect[END_REF][START_REF] Pourmand | A novel extraction chromatography and MC-ICP-MS technique for rapid analysis of REE, Sc and Y: Revising CI-chondrite and Post-Archean Australian Shale (PAAS) abundances[END_REF]. We selected the least thermally metamorphosed fall samples (types 1-4, n = 42), and outliers (Orgueil and Kelly) were removed. The mean La/Ce ratio thus calculated for CHUR is 0.387 ± 0.022 (n = 39), similar to the value we obtained from our smaller sample set (La/CeCHUR = 0.390 ± 0.022). The CHUR Sm/Nd ratio determined from the same database of chondrite samples is 0.324 ± 0.014, consistent with the value proposed by [START_REF] Bouvier | The Lu-Hf and Sm-Nd isotopic composition of CHUR: Constraints from unequilibrated chondrites and implications for the bulk composition of terrestrial planets[END_REF]. Lastly, we used the Lu/Hf ratio of CHUR (0.236) calculated from the average 176 Lu/ 177 Hf value determined by [START_REF] Bouvier | The Lu-Hf and Sm-Nd isotopic composition of CHUR: Constraints from unequilibrated chondrites and implications for the bulk composition of terrestrial planets[END_REF].

The calculated REE pattern for an EDR is presented in Figure 3. For a 3.6% increase of the Sm/Nd ratio of the BSE, the modelled EDR has eCe = -0.4 and eNd = 4.1. This reservoir plots very close to the mantle array in the eNd vs. εCe diagram, and shows Ce-Nd isotopic compositions similar to those measured in several OIBs (Fig. 4). A large-scale silicate differentiation event early in the Solar System's evolution does not produce any offset in the Ce-Nd isotopic composition of the EDR relative to the mantle array. Thus, defining the Ce-Nd mantle array does not resolve the long-standing debate over the chondritic vs. EDR-like REE composition of the PM.

Crustal extraction mass-balance calculations

Mantle melting and subsequent extraction of the crust has contributed to the depletion of the mantle in incompatible elements. Crustal growth models are widely discussed and several authors have proposed rapid continental growth early in Earth's history despite the scarce geological record of the Earth's first billion years [START_REF] Belousova | The growth of the continental crust: Constraints from zircon Hf-isotope data[END_REF][START_REF] Dhuime | A Change in the Geodynamics of Continental Growth 3 Billion Years Ago[END_REF]. Geochemical signatures in mantle-derived samples linked to this process are particularly difficult to decipher because surface material is continuously reintegrated into the mantle via subduction. In this section, to investigate the production of the various mantle reservoirs, we attempt to recreate the Ce-Nd mantle array via mass-balance mixing calculations between the depleted MORB mantle (DMM) and continental crust (CC). We first simplify our approach by assuming that the CC was extracted from the PM in a single differentiation step (i.e., DMM + CC = BSE). Since we have not resolved the chondritic vs. EDR-like composition of the PM, we explore both bulk compositions and compare their modelled Ce-Nd mixing curves to the mantle array. Distinct scenarios proposed that oceanic crust formation was the dominant process of mantle depletion with continents formed later by reworking in subduction zones (e.g., [START_REF] Jones | Origins of the terrestrial Hf-Nd mantle array: Evidence from a combined geodynamical-geochemical approach[END_REF].

Furthermore, isotopic studies of rocks from the Nuvvuaggituq Supracrustal Belt and the neighbouring Hudson Bay terrane show that the Archean felsic crust formed by reworking of Hadean mafic crust [START_REF] O'neil | Chapter 16 -The Nuvvuagittuq Greenstone Belt: A Glimpse of Earth's Earliest Crust[END_REF][START_REF] O'neil | Building Archean cratons from Hadean mafic crust[END_REF]. From these observations, we choose to calculate the Ce-Nd isotopic composition of such an enriched reservoir and compare it to the global dataset to evaluate the effect of primitive mafic crustal extraction on the mantle.

End-members

Depleted MORB Mantle

The DMM end-member isotopic composition is commonly calculated from MORB samples. Our measurements and literature data are plotted in the eNd vs. εCe diagram (Fig. 2). The average of 48 MORB measurements gives εCeDMM = -1.1 ± 0.6 and εNdDMM = 9.7 ± 2.3. This mean Nd isotopic composition is consistent with previously proposed values of 9.2 and 9.8 based on a more complete dataset [START_REF] Salters | Composition of the depleted mantle[END_REF][START_REF] Salters | Composition of the depleted mantle[END_REF][START_REF] Workman | Major and trace element composition of the depleted MORB mantle (DMM)[END_REF]Hart, 2005, respectively). Restricting the MORB samples to those that do not show the Dupal anomaly (i.e., North Atlantic and Pacific MORBs) gives an identical result (εCe = -1.2 ± 0.6, n = 33).

Continental Crust

The CC is a low-mass reservoir containing 20-70% of the PM's incompatible element budget. The difficulty in constraining the CC composition stems from its nature. With a mean age of 1.8-2.4 Ga [START_REF] Chauvel | Constraints from loess on the Hf-Nd isotopic composition of the upper continental crust[END_REF][START_REF] Taylor | The geochemical evolution of the continental crust[END_REF] and an average thickness of about 40 km, it is much older and thicker than the present-day oceanic crust. The major-and trace-element compositions of the upper, middle, and lower crust are based on numerous rock samples from which global compositions were obtained (Rudnick and Gao, 2003, and references therein), though the isotopic composition of the bulk CC is largely under-constrained; very few data are available for Ce, and εNd values generally vary between -21 and -10. Based on loess measurements, [START_REF] Chauvel | Constraints from loess on the Hf-Nd isotopic composition of the upper continental crust[END_REF] proposed a model age of 1.8 Ga for the UCC and a εNd value of -10. On the other hand, [START_REF] Goldstein | Nd and Sr isotopic systematics of river water suspended material: implications for crustal evolution[END_REF] considered suspended materials in rivers (εNd = -11, TDM = 1.6 Ga) but corrected their mean value for the preferential erosion of young terranes (εNd = -17 recalculated at 2.1 Ga). Similarly, [START_REF] Hawkesworth | Earth's Continental Lithosphere Through Time[END_REF] discussed the erosional bias based on the proportions of young and old source rocks and proposed a bulk CC εNd value of -12. Other studies consider that the upper and bulk crusts have distinct isotope signature; Allègre and Lewin (1989) calculated a εNd value of -21 from DMM-bulk CC mass-balance equations, whereas Jacobsen and Wasserburg (1980) obtained a slightly higher value with a similar approach (εNd = -14).

To date, CC rocks analysed for Ce and Nd isotopes are mainly ~2 Ga granites and gneisses (see Supplementary Fig. S6 for details). Combining all published Ce-Nd measurements gives average values of eCe = 2.8 and eNd = -19 (Fig. 4). This is slightly different from the sole published estimate for the CC (εCe = 1.3 and εNd = -14; Tanaka et al., 1987), which was calculated by regression from five crustal rock measurements (eCe = -0.112 × eNd) anchored to the mean eNd value of aeolian sediments and particulates in rivers (eNd = -11.4; [START_REF] Goldstein | A Sm-Nd isotopic study of atmospheric dusts and particulates from major river systems[END_REF]. Our loess average is εCe = 1.8 and εNd = -11.2, relatively close to Tanaka et al.'s (1987) value.

Mafic crust

Results obtained on the 146 Sm-142 Nd short-lived systematics suggest that the oldest mafic crust preserved at the Earth's surface is the ~4.3 Ga Nuvvuagittuq Supracrustal Belt in northern Quebec [START_REF] O'neil | Neodymium-142 Evidence for Hadean Mafic Crust[END_REF]. Even if this age is debated, the neighbouring Hudson Bay terrane shows that the Archean felsic crust formed by reworking of an Hadean mafic crust [START_REF] O'neil | Chapter 16 -The Nuvvuagittuq Greenstone Belt: A Glimpse of Earth's Earliest Crust[END_REF][START_REF] O'neil | Building Archean cratons from Hadean mafic crust[END_REF].

We chose sample PC-162 (La/Ce = 0.49 and Sm/Nd = 0.27) as representative of the Archean mafic crust to model its Ce and Nd isotopic compositions. This and other samples from the enriched low-Ti group [START_REF] O'neil | Implications of the Nuvvuagittuq Greenstone Belt for the Formation of Earth's Early Crust[END_REF] are enriched in LREEs by 10 to 80 times the chondritic reference, whereas rocks from the depleted low-Ti and high-Ti units show lower LREE enrichments (<20 times). Furthermore, PC-162 is one of the most REE-depleted samples among those of the enriched low-Ti group that do not show any evidence of metamorphic disturbance [START_REF] O'neil | Formation age and metamorphic history of the Nuvvuagittuq Greenstone Belt[END_REF], and thus its REE contents correspond to a reasonable crustal extraction rate: that is, more enriched compositions reflect increased depletion of the mantle during extraction of the crust. The Ce-Nd isotopic compositions of the modelled mafic end-member are reported in Figure 4; they are identical (eCe = 3.8 and eNd = -17.3) for a crust formed at 4.3 Ga, irrespective of the PM considered (CHUR or EDR). The EER calculated by [START_REF] Carlson | Composition of the Earth's interior: the importance of early events[END_REF] has similar La/Ce and Sm/Nd ratios of 0.47 and 0.28, respectively, producing presentday isotopic compositions of eCe = 3 and eNd = -13.5 if this reservoir formed 4.3 Ga. Both these models plot to the right of the mantle array (Fig. 4).

Model parameters and mixing hyperbolas

Our mass-balance models consider DMM-CC complementarity for chondritic and early-depleted PM compositions. We aim to determine the εCe value of the CC using four-successive calculation steps (Supplementary material). 1) We calculate the mass fraction of Nd in the CC relative to the total amount in the crust and DMM (the sialic index; e.g., Allègre and Lewin, 1989) based on the DMM, CHUR/EDR (Table 3), and CC εNd values. As the range of published CC isotopic values is large, we do not set a precise εNd value in the mass-balance model, but consider all possibilities between εNd = -10 and -21.

2) We calculate the mass fraction of CC using the Nd contents of the BSE (as determined in section 5.2 with REE patterns anchored to a Lu content of 68 ppb; [START_REF] Mcdonough | The composition of the Earth[END_REF] and CC (Rudnick and Gao, 2003). The Ce/Nd ratio is set to 1.28 for a chondritic BSE and to 1.22 for the EDR model (Table 3). Importantly, the Lu value chosen to anchor the REE pattern of the BSE has no consequence on the final εCe value. 3) The Ce sialic index is calculated using the Ce contents of the BSE (see step 2) and CC (Rudnick and Gao, 2003). 4) The εCe value of the CC is calculated from the Ce sialic index and the εCe values of the DMM and CHUR/EDR (Table 3): εCeCC varies from 0.2 to 1 in the chondritic case and from 0.4 to 1.2 in the EDR case. All CCs are represented as orange or green lines at the lower end of the mixing curves in Figure 4 (chondritic or EDR model, respectively) and all calculated DMM-CC mixing hyperbolas are plotted in the form of a coloured field. Their curvature is a function of the Ce/Nd ratios of both end-members.

In the upper left of the εNd vs. εCe diagram, the DMM-CC mixing hyperbolas overlap and pass through both the CHUR and EDR compositions. However, they do not fully overlap the data points defining the mantle array. The Ce-Nd isotopic compositions calculated for the CC are always less radiogenic in cerium than the mean values estimated from measurements, which might question the relevance of the published data used to estimate the isotopic composition of the bulk CC. Most of the samples are upper crust (e.g., loess) samples. If the observed difference reflects heterogeneities within the crustal reservoir, the lower and middle crust should be characterised by negative eCe values to adjust the mass balance budget within the continental crust (Willig and Stracke, 2019). However, [START_REF] Vervoort | Hf-Nd isotopic evolution of the lower crust[END_REF] suggested that lower crustal xenoliths have eHf-eNd values close to the mantle array.

The mass fraction of depleted mantle relative to the whole mantle can be calculated in the case of the mass balance calculations for the entire range of εNdCC considered. It varies from 14 to 33% and from 28 to 64% (±20%) for the CHUR and EDR bulk compositions, respectively (Fig. 5). As mentioned in section 5.3.1, a more depleted initial composition implies that a larger volume of the mantle was depleted by crustal extraction [START_REF] Boyet | A new geochemical model for the Earth's mantle inferred from 146Sm-142Nd systematics[END_REF]. For comparison, Allègre and Lewin (1989) calculated the mass fraction of depleted mantle to be comprised between 32 and 40% using a chondritic BSE.

The mixing curve joining the DMM and a 4.3 Ga early mafic crust is also reported in Figure 4. The Ce/Nd ratio of this mafic crust is 1.9, only slightly different from the mean value of 2.15 determined for the CC by Rudnick and Gao (2003). Thus, the DMM-mafic crust mixing hyperbola has a curvature close to that of the DMM-CC mixing curve. Again, such a mixing scenario seems unlikely to reproduce the mantle array.

What parameters can bring the DMM-CC mixing model closer to the mantle array?

To superimpose the DMM-CC mixing curve on the mantle array, Willig and Stracke (2019) proposed using a more depleted isotopic composition for the DMM end-member (see their Figure 5). However, for a likely CC Nd isotopic composition, such a DMM-CC hyperbola requires DMM Ce-Nd isotopic ratios very different from those measured in MORB samples. For example, to fully reproduce the mantle array, the εCe and εNd values of the DMM should be approximately -10 and +40, respectively, if we set the εNd value of the bulk CC to -17 (in the case of a chondritic BSE). Such compositions have never been measured in MORBs or peridotites.

Several authors have proposed loess samples to be a good approximation of the upper crust because these clastic rocks sample large surface areas and have relatively uniform Nd and Hf isotopic compositions (e.g., [START_REF] Chauvel | Constraints from loess on the Hf-Nd isotopic composition of the upper continental crust[END_REF]. Because the lower crust appears to have Hf-Nd isotopic ratios similar to those of the upper crust [START_REF] Vervoort | Hf-Nd isotopic evolution of the lower crust[END_REF], we also calculated the εCe-εNd mixing hyperbola between the DMM end-member and a loess-like component. Its curvature is a function of the Ce/Nd ratios of both end-members. The mean Ce/Nd value calculated from our loess samples (2.38 ± 0.30) is similar within errors to the value of 2.33 determined for the upper crust by Rudnick and Gao (2003) and to that of the global subducting sediment reservoir that represents the bulk composition of trench sediments [START_REF] Plank | The chemical composition of subducting sediments[END_REF]. However, this result is more than twice the Ce/Nd ratios of 1.08 and 0.95 determined for the DMM by [START_REF] Salters | Composition of the depleted mantle[END_REF] and [START_REF] Workman | Major and trace element composition of the depleted MORB mantle (DMM)[END_REF], respectively. Consequently, considering the Ce-Nd isotopic composition of loess as representative of the CC moves the DMM-CC mixing curve further from the mantle array (Fig. 4).

The model age of loesses is 1.8 Ga [START_REF] Chauvel | Constraints from loess on the Hf-Nd isotopic composition of the upper continental crust[END_REF], which is not widely agreed to be the mean age of the crust. An older equivalent (2.2 Ga) of these samples would have a less radiogenic Ce-Nd isotopic composition that still plots on the mantle array. Superimposing the DMM-loess mixing curve on the mantle array (i.e., to linearise the DMM-loess hyperbola) requires increasing the DMM Ce/Nd ratio towards a value identical to that of loesses. Unlike the CC reservoir, which has been calculated from a large number of measurements, the DMM remains a model based on a series of assumptions, such that its REE pattern can be questioned. Such a reservoir is represented in MORB Ce and Nd isotopic compositions as a strong long-term depleted REE element pattern, and a consistent Ce/NdDMM ratio requires the DMM to have a positive Ce elemental anomaly. Cerium anomaly generally reflects a specific behaviour of Ce 4+ relative to REE 3+ . However, such a Ce anomaly has never been measured in MORBs.

The DMM-loess mixing curve coincides with the repartition of Island Arc Basalts (IABs) from the Lesser Antilles and the Mariana Islands (Bellot et al., 2015(Bellot et al., , 2018)). The isotopic compositions of OIBs and IABs differ from those of MORBs due to the introduction of crustal material into their sources.

Although the isotopic compositions of arc lavas can be modified by post-melting reactions such as assimilation-fractional crystallisation processes (AFC), this is not the case for the Marianas and Lesser Antilles (e.g., [START_REF] Labanieh | Isotopic hyperbolas constrain sources and processes under the Lesser Antilles arc[END_REF], and their Ce-Nd isotopic compositions are well explained by the incorporation of sediments into the mantle wedge (Bellot et al., 2015(Bellot et al., , 2018)). We expect a larger incorporation of sediments in arc lavas relative to hotspot lavas since REEs are enriched in slab dehydration fluids, whereas sediments are recycled with oceanic crust into the OIB source and their signatures are consequently diluted. Indeed, OIBs and IABs are clearly distinct in the εCe-εNd diagram (Fig. 4).

Effect of recycled surface material on the mantle array

The EM1, EM2, and HIMU mantle end-members have been defined from the most extreme isotopic compositions measured in OIBs [START_REF] Zindler | Chemical geodynamics[END_REF] and are classically interpreted as representing the recycling of surface materials into the deep mantle. Chauvel et al. (2008) modelled the Hf and Nd isotopic compositions of basaltic crust and sediments recycled at different times during Earth's history and showed that the Hf-Nd mantle array required the incorporation of surface material older than 2 Ga into the OIB source. Here we apply the evolution model to the Ce-Nd systematics (see Supplementary Fig. S7): 1) the isotopic composition of recycled sediments and recycled oceanic crust (ROC) calculated back in time is assumed to be on the evolution line built between their present-day isotopic composition and the CHUR value at 4.568 Ga; 2) the actual isotopic compositions of these two reservoirs are then calculated considering the parent/daughter ratios in their source reservoirs. To this end, we consider the mean 143 Nd/ 144 Nd, 138 Ce/ 142 Ce, 147 Sm/ 144 Nd, and 138 La/ 142 Ce ratios measured in oceanic sediments in front of the Mariana trench (Sites 801 and 802, ODP Leg 129; Bellot et al., 2018) and near the Lesser Antilles arc (DSDP site 144; Bellot et al., 2015) together with those of the MORB samples plotted in Figure 2. Modern oceanic sediments are characterised by negative elemental cerium anomalies, reflecting an oxidised environment. Before the GOE, dated around 2.4 Ga (see [START_REF] Holland | Volcanic gases, black smokers, and the great oxidation event[END_REF], all REEs in sediments were necessarily trivalent under the anoxic conditions. Thus, we removed the elemental cerium anomaly from all oceanic sediments older than 2.4 Ga.

Our calculations produce important results. First, the ROC follows a positive slope in the εCe-εNd diagram, whereas the mantle array defines a negative slope (Fig. 6, see Supplementary Fig. S7 for further details). Thus, the incorporation of ROC into the mantle tends to shift the isotopic composition of OIBs toward slightly less radiogenic Ce isotopic ratios than MORBs. Second, as previously shown by Chauvel et al. (2008), the mantle array can be reproduced by mixing either a DMM-like or a FOZO-like component (FOZO is assumed to have εCe = -0.6 and εNd = 6.24; see [START_REF] Boyet | New constraints on the origin of the EM-1 component revealed by the measurement of the La-Ce isotope systematics in Gough Island lavas[END_REF] and recycled surface material (ROC and sediments have the same recycling ages). On the sole basis of Ce and Nd isotopes, it is still unclear whether the different plume sources contain surface material recycled at various time or pre-GOE material in various proportions (the two propositions being not mutually exclusive). Also, the intersections of the recycled crust-sediment mixing curves and the mantle array indicate the proportion of sediments in the recycled material (msediments / (msediments + moceanic crust)) to be between 6 and 12%; this proportion decreases for younger recycled components. This last result must be considered in parallel with the decreasing rate of crustal destruction until the present value of 3.2-5.5 km 3 yr -1 (Dhuime et al., 2018, and references therein).

Sediments formed before and after the GOE evolved to distinct Ce isotopic compositions. For a similar proportion of sediments in the recycled component (i.e., 10% sediment and 90% oceanic crust), the εCe value of a 2.5 Ga recycled component is inferior by 0.3 ε-units when we remove the Ce anomaly. More importantly, in our model, only the recycling of pre-GOE sediments can explain the most enriched isotopic compositions measured in OIBs. Corresponding samples are classified either as EM1 (samples from Tristan Da Cunha, Gough, Heard, and Kerguelen Islands) or EM2 (Tahaa Island in the Society archipelago). The Ce-Nd isotopic composition of Gough Island lavas was explained by the incorporation of subcontinental lithospheric material at shallow depths into the mantle [START_REF] Boyet | New constraints on the origin of the EM-1 component revealed by the measurement of the La-Ce isotope systematics in Gough Island lavas[END_REF]. The lack of correlation between the cerium anomalies and the Ce isotope compositions measured in Gough Island lavas proves that ancient sediments carrier of negative element cerium anomaly were not incorporated in the Gough mantle source. Moreover, mass-independent S isotopic fractionations measured in olivinehosted sulphides from other EM1 (e.g., Pitcairn) lavas similarly suggest the recycling of surface materials that existed in a reduced atmosphere before the GOE [START_REF] Cabral | Anomalous sulphur isotopes in plume lavas reveal deep mantle storage of Archaean crust[END_REF][START_REF] Delavault | Sulfur and lead isotopic evidence of relic Archean sediments in the Pitcairn mantle plume[END_REF].

Conclusions

We measured the Ce isotopic compositions of 51 OIBs, 1 intraplate continental volcanism occurrence, 7 MORBs, 6 loess samples, and 11 chondrites, enhancing the terrestrial and extra-terrestrial Ce isotopic database. We define the 138 Ce/ 142 Ce CHUR reference to be 0.02256577 ± 66. OIB and MORB samples define the mantle array as εNd = -7.3 (± 0.5) × εCe + 0.4 (± 0.3). The mantle array passes through the CHUR value and is not significantly different from a modelled early-depleted reservoir. We conclude that combining Ce and Nd isotopic measurements in mantle-derived samples does not further constrain the composition of the PM.

Mixing models between the DMM and CC end members, both estimated from sample measurements (upper, or early mafic crusts), cannot reproduce the Ce-Nd mantle array but better fit IAB data. The mantle array is better reproduced by considering bulk CCs consistent with a mass-balance budget of the BSE (Ce isotopic compositions calculated for a range of accepted Nd). But the mixing hyperbolas do not perfectly overlap the OIB samples with subchondritic Ce isotopic composition; and the calculated εCe for the bulk crust are significantly different from all crustal rocks measured so far. In all these models, linearising the mixing curves requires unrealistic Ce-Nd isotopic compositions and/or Ce/Nd ratios never measured in rock samples. Alternatively, the recycling of sediments and oceanic crust into hotspot sources, and their mixing with DMM-or FOZO-like material may explain the Ce-Nd mantle array. Our results further show that Ce-Nd isotopic compositions measured in the most enriched EMlike lavas can be reproduced by the incorporation in their source of recycled oceanic sediments that do not have any elemental Ce anomaly. Because Ce is a redox-sensitive trace element that can be used to trace the oxygenation of atmosphere (GOE at 2.4 Ga), our results suggest that some OIBs sample very deep mantle reservoirs that may preserve pre-GOE recycled surface materials, in agreement with observed S isotopic fractions in EM1 lavas. Constraining the long-term history of recycled surface material in the mantle is essential to understand the isotope signature of mantle-derived samples. The La-Ce isotope systematics offers a unique opportunity to detect changes on the chemical composition of oceanic sediments through time. Rudnick and Gao (2003), concentrations for the mafic crust are those measured in PC-162 from [START_REF] O'neil | Implications of the Nuvvuagittuq Greenstone Belt for the Formation of Earth's Early Crust[END_REF], and BSE 143 Nd/ 144 Nd ratios are from [START_REF] Bouvier | The Lu-Hf and Sm-Nd isotopic composition of CHUR: Constraints from unequilibrated chondrites and implications for the bulk composition of terrestrial planets[END_REF]. BSE range of Ce and Nd concentrations are modelled using Lu contents from [START_REF] Allègre | Chemical composition of the Earth and the volatility control on planetary genetics[END_REF], [START_REF] Lyubetskaya | Chemical composition of Earth's primitive mantle and its variance: 1. Method and results[END_REF], [START_REF] Mcdonough | The composition of the Earth[END_REF], [START_REF] Palme | Cosmochemical Estimates of Mantle Composition[END_REF] and chondritic REE ratios (see supplementary material S4 for more details). Ce/Nd of the BSE is constant and set to 1.28 (1.22 for EDR). DMM isotopic composition is the mean value of data from this study, Bellot et al., 2015, 2018[START_REF] Makishima | Ce isotope ratios of N-type MORB[END_REF]and Willig and Stracke, 2019. UCC (1.8 Ga) Ce and Nd contents and isotopic compositions are the mean values of loess data from this study. UCC (2.2 Ga) isotopic compositions are calculated by aging 1.8 Ga UCC.

Figure captions

Fig. 1. A) 138 Ce/ 142 Ce ratios measured in enstatite (green squares), ordinary (red diamonds), and carbonaceous (black triangles) chondrites. Literature values are from Bellot et al. (2015, 'B et al. 15') and Willig and Stracke (2019, 'W&S19'). Data from the literature are normalised to the CeLMV reference material from this study: 138 Ce/ 142 CeCeLMV/ 138 Ce/ 142 CeCeAMES = 0.02257053/0.02257426 [START_REF] Bonnand | Radiogenic and stable Ce isotope measurements by thermal ionisation mass spectrometry[END_REF]. B) εCe ratios vs. La/Ce ratios of chondrites from Willig and Stracke (2019) and this study. Data are normalised to the CHUR reference defined in these studies. The dashed line represents the 4.568 Ga CHUR reference isochron. Literature data are in grey (Bellot et al., 2015(Bellot et al., , 2018;;[START_REF] Makishima | Ce isotope ratios of N-type MORB[END_REF]Willig and Stracke, 2019). Error bars are 2se (internal error). Literature data are reported considering the epsilon values and CHUR references measured in each study to limit any bias introduced by normalisation. The data from Tanaka et al. (1987) are not included because we do not have the corresponding CHUR reference. The mantle array is defined by regression on mantle-derived samples only. Its equation defined from 134 data is εNd = -7.3 (± 0.5) × εCe + 0.4 (± 0.3) (calculated with Isoplot â and considering errors of 0.25 and 0.10 for eCe and eNd, respectively). and an EDR model with Sm/Nd = Sm/NdBSE + 3.6% (green). The EDR REE pattern is calculated as follows. 1) The REE patterns are anchored at Lu, the least incompatible REE. 2) The early depleted εNdpresent value is calculated using the initial CHUR value [START_REF] Bouvier | The Lu-Hf and Sm-Nd isotopic composition of CHUR: Constraints from unequilibrated chondrites and implications for the bulk composition of terrestrial planets[END_REF] at 4.568 Ga and a Sm/Nd ratio 3.6% above that of the BSE. 3) The early depleted 177 Hf/ 176 Hf ratio is deduced from the Hf-Nd mantle correlation (εHfpresent = 1.59 × εNdpresent + 1.28; Chauvel et al., 2008). 4) The Lu/Hf ratio is obtained by comparison of the initial 177 Hf/ 176 HfCHUR ratio [START_REF] Bouvier | The Lu-Hf and Sm-Nd isotopic composition of CHUR: Constraints from unequilibrated chondrites and implications for the bulk composition of terrestrial planets[END_REF] and the early depleted Hf isotopic composition calculated in step 3. That is, the Hf concentration is obtained from the known Lu concentration set as the anchor point in step 1. 5) The Sm concentration is calculated from the Sm/Hf ratio, which has a constant value of 1.44 in OIBs [START_REF] Jackson | Major and trace element composition of the high 3He/4He mantle: Implications for the composition of a nonchonditic Earth[END_REF]. 6) The Nd concentration is calculated from the Sm/Nd ratio (known after steps 2 and 5). 7) The La and Ce concentrations are calculated using a binomial fit through the chondrite normalised Sm, Nd, and Lu concentrations (i.e., the equation of the La-Lu pattern is of the form y = ax 2 + bx + c, where x represents the REEs, numbered 1-15 for La-Lu). Fig. 4. εNd vs. εCe measured in mantle-derived samples (see Fig. 2, with additional data for IABs from Bellot et al., 2015Bellot et al., , 2018 and continental crust samples; see Supplementary Fig. S6). The global linear trend of the mantle array is shown as the black dashed line and intercepts the chondritic composition (εNd = 0.00, εCe = 0.07 ± 0.05 (2σ)). Large symbols represent terrestrial reservoirs. Note that mean loess corresponds to a 1.8 Ga UCC (TDM); and we represent a 2.2 Ga UCC as a modelled composition (aged loess). The mean CC value is the mean value of continental samples averaged by location. The continental crust value published in Tanaka et al. (1987) 3. Fig. 6. εNd vs. εCe measured in mantle-derived samples compared with reservoir evolution models. The present-day average compositions of the recycled oceanic crust (ROC = MORB; this study) and oceanic sediments (Bellot et al., 2015(Bellot et al., , 2018) ) are shown as large symbols. Solid lines outline the present-day isotopic compositions of these reservoirs if formed at different ages. The yellow line shows the evolution of MORBs using mean La/Ce and Sm/Nd ratios of MORBs and the MORB source. Similarly, the blue and purple lines show the evolution of oceanic sediments with chondrite-normalised REE patterns showing a Ce negative anomaly as observed in modern oceanic sediments (La/Ce = 0.57) or without a Ce anomaly (La/Ce = 0.47), representing oceanic sediments formed in reduced conditions before the GOE (~2.4 Ga), respectively. The Ce-Nd isotopic composition of the recycled material is shown by mixing curves between contemporaneous ROC and oceanic sediments (dashed lines). (Barrat et al., 2012).

Fig. S3. Rare earth element patterns of loess samples. Concentrations are normalised to the upper continental crust (Rudnick and Gao, 2003).

2. Ce isotopic ratios as a function of elemental Ce anomalies , where aN, CeN, and PrN are the La, Ce, and Pr concentrations normalised to CI chondrite (Barrat et al., 2012). One sample from the Saint-Helena hotspot has a large negative Ce anomaly (Ce/Ce* = 0.64), but its Ce isotopic composition is similar to that of other samples from the same location. This anomaly probably reflects the late alteration of the rock. Some samples from Ethiopia, Hawaii, and French Polynesia have significant positive anomalies. These anomalies reflect depletion in La (Fig. S2), and are not correlated with Ce isotopic ratios. 2) and continental crust samples [START_REF] Dickin | A Ce/Nd isotope study of crustal contamination processes affecting Palaeocene magmas in Skye, Northwest Scotland[END_REF][START_REF] Gao | Decoupled Ce-Nd isotopic systematics of the Neoproterozoic Huangling intrusive complex and its geological significance, eastern Three Gorges, South China[END_REF][START_REF] Hayashi | Origin of negative Ce anomalies in Barberton sedimentary rocks, deduced from La-Ce and Sm-Nd isotope systematics[END_REF][START_REF] Lee | Crustal evolution history of Korean Peninsula in East Asia: The significance of Nd, Ce isotopic and REE data from the Korean Precambrian gneisses[END_REF][START_REF] Lee | La-Ce and Sm-Nd isotopic systematics of early Proterozoic leucogranite with tetrad REE pattern[END_REF][START_REF] Liu | Isotopic and trace element studies for Cenozoic volcanic rocks from western China: implication for a crust-like enriched component in the mantle[END_REF][START_REF] Masuda | 138La β-decay constant estimated from geochronological studies[END_REF][START_REF] Minami | Two Archean Sm-Nd ages of 3.2 and 2.5 Ga for the Marble Bar Chert, Warrawoona Group, Pilbara Block, Western Australia[END_REF][START_REF] Shimizu | Geochemistry of Ce and Nd isotopes and REE abundances in the Amitsoq gneisses, West Greenland[END_REF][START_REF] Shimizu | Sources of iron-formations in the archean isua and malene supracrustals, West Greenland: Evidence from La-Ce and sm-nd isotopic data and REE abundances[END_REF][START_REF] Shimizu | Geochemistry of Nd and Ce isotopes and REE abundances in Precambrian orthogneiss clasts from the Kamiaso conglomerate, central Japan[END_REF]Tanaka et al., 1987;Tazoe et al., 2007). Large symbols represent reservoirs (as in Fig. 6). Note that the red square is the continental crust proposed by Tanaka et al. (1987). The black square is the mean value of all literature continental crust samples represented here (n = 94), and the open square is the mean continental crust value when samples are averaged by location (n = 16). S1: La, Ce, Sm and Nd contents, La/Ce and Sm/Nd ratios and Ce and Nd isotopic compositions of terrestrial reservoirs used in recycling models (Fig. 5 and Fig. S7). ROC, recycled oceanic crust; DMM, depleted MORB mantle; GOE, great oxygenation event. ROC and oceanic sediments isotopic and chemical compositions are based on measurements (MORB: this study, Bellot et al., 2015, 2018[START_REF] Makishima | Ce isotope ratios of N-type MORB[END_REF]and Willig and Stracke, 2019; oceanic sediments: Bellot et al., 2015Bellot et al., , 2018)). ROC and oceanic sediments sources have constant chemical ratios extrapolated from the evolution of an initial chondritic reservoir until present-day isotopic compositions measured in MORB and oceanic sediments. Pre-GOE oceanic sediments La/Ce ratio and Ce contents are corrected from Ce anomaly.

Fig. 2 .

 2 Fig. 2. εNd vs. εCe of mantle-derived samples and loesses from this study (coloured symbols). Nd

Fig. 3 .

 3 Fig. 3. REE patterns normalised to a chondritic primitive mantle for a chondritic BSE model (orange)

  is calculated from 5 measurements. The 4.3 Ga mafic crust composition results from an extraction model from the depleted mantle. The red field represents the DMM-UCC mixing curves. The brown field corresponds to the DMM-4.3 Ga mafic crust mixing curves. The fields correspond to the different curves calculated using DMM Ce and Nd concentrations given by Salters and Stracke, 2004 and Workman and Hart, 2005. The orange field represents all the DMM-CC mixing curves calculated for a chondritic BSE model (bulk crust compositions shown by the bold orange line). The green field represents all the DMM-CC mixing curves calculated for an EDR model (bulk crust compositions shown by the bold green line). See details in the text and calculation parameters in Table3.

Fig. 5 .

 5 Fig. 5. Mass fraction of the depleted mantle relative to the primitive mantle (mDM/mPM, expressed in

  Fig.1

  0

  Fig.2

Fig. 4

 4 Fig.4

  Fig.5

Fig. S4 .

 S4 Fig. S4. 138 Ce/ 142 Ce vs Ce/Ce* diagram for terrestrial samples analysed in this study. Ce/Ce* represents the elemental Ce anomaly relative to the neighbouring REEs as !" !" * = !" %

  Fig. S7. Evolution models used to calculate the present (A) εNd and (B) εCe isotopic compositions of recycled MORBs (yellow) and oceanic sediments (blue) for ages of formation between 4 and 1 Ga. Solid lines connect the present-day isotopic compositions of MORBs and oceanic sediments to the initial CHUR ratio, and dashed lines represent their isotopic evolution since the reservoir formation times. MORBs are characterised by La/CeMORB = 0.34 and Sm/NdMORB = 0.33 (this study). Oceanic sediments formed after the Great Oxygenation Event are characterised by La/CeOS = 0.57 and Sm/NdOS = 0.20 (data from Bellot et al., 2015, 2018), and those that formed earlier are assumed to have La/CeOS = 0.47 (after Ce anomaly correction). MORB and oceanic sediments sources have constant chemical ratios extrapolated from the evolution of an initial chondritic reservoir until present-day composition. MORB source has La/CeMORB source = 0.36 and Sm/NdMORB source = 0.35. Oceanic sediments source has La/Cesediments source = 0.41 and Sm/NdMORB source = 0.31. Figure modified after Chauvel et al. (2008).

Table captions Table 1 .

 captions1 138 Ce/ 142 Ce and 143 Nd/ 144 Nd isotopic ratios and La/Ce and Sm/Nd ratios of whole-rock OIBs, MORBs and loesses. The Nd isotopic compositions of loess and Kerguelen samples (*) are from Chauvel et al. (2014) and unpublished data from B. Moine, respectively. Epsilon values are normalised according to the CHUR references defined for Ce in this study as εCe = &

				)*+	'(
				'( '( ./012( )*+ ),-	-18 × 10,000
				'( ),-'345
		),*	>?
	and for Nd by Bouvier et al. (2008) as εNd = &	>? >? ./012( ),* ),,	-18 × 10,000. Errors correspond to
		),,	>?	'345
	internal errors (2se).

Table 2 .

 2 138 Ce/ 142 Ce isotopic ratios and La/Ce whole-rock chondrites. Epsilon values are normalised according to the CHUR references defined for Ce in this study as εCe = &

	)*+	'(
	'( '( ./012( )*+ ),-	-18 × 10,000.
	'( ),-'345

Table 3 .

 3 Elemental and isotopic compositions of Earth's main silicate reservoirs used in our calculations: BSE, bulk silicate Earth; EDR, early depleted reservoir; DMM, depleted MORB mantle; CC, continental crust; UCC, upper continental crust; and mafic crust. Errors are errors on data averages. No errors are given for model-based isotopic compositions (EDR, aged UCC, and mafic crust). Values in italics refer to literature data: CC Ce and Nd concentrations are from

Type Sample Location Volcano 138 Ce/ 142 Ce 2se 𝜺Ce La/Ce 143 Nd/ 144 Nd 2se 𝜺Nd

	Table 1 Table 2
	Sample Chondritic BSE Sahara 97072 EDR Ethiopia 1.0-1.7 Sahara 97158 0.8-1.3 Oudiyat Sbaa 1.28 1.22 RRTO 06 E38 E39 E95 E156 E202 E266 E268 E271 Austral Islands TBA-IH MCD201 Allende Saint-Severin NWA 10854 Adrar Bous Yilmia Ce/ 142 Ce OIB Ce (µg/g) Nd (µg/g) Ce/Nd 138 0.02256577 ± 66 0.02256492 0.02256325 ± 145 Location DMM Sahara Sahara W Sahara Rututu Tubuai McDonald 0.02256514 27 -0.28 0.145 Type 138 Ce/ 142 Ce 2se 𝜺Ce La/Ce CC UCC (1.8 Ga) UCC (2.2 Ga) Mafic crust (4.3 Ga) Sm/Nd 0.02256395 20 -0.81 0.305 0.512935 2 5.95 EH3 -Find 0.02256613 0.16 0.410 43 68 68 11.2 0.220 0.02256372 14 -0.91 0.318 0.512936 2 5.96 EH3 -Find 0.02256571 -0.02 0.385 20 29 29 5.9 0.218 0.02256393 21 -0.81 0.318 0.512871 2 4.71 EH5 -Fall 0.02256633 0.25 0.371 2.15 2.33 2.33 1.9 0.273 0.02256421 16 -0.69 0.375 0.512907 2 5.40 0.190 0.02256401 20 -0.78 0.310 0.512728 2 1.92 0.257 0.02256469 16 -0.48 0.399 0.512824 1 3.78 0.199 0.02256497 16 -0.35 0.459 0.512779 1 2.90 0.209 0.02256558 18 -0.08 0.478 0.512746 2 2.26 0.02256437 19 -0.62 0.474 0.512877 2 4.81 0.02256375 20 -0.89 0.355 0.512894 2 5.15 0.512834 2 3.98 0.280 Mexico CV3 -Fall 0.02256585 0.20 0.400 0.193 France LL6 -Fall 0.02256522 -0.24 0.392 0.208 NW Africa L3 -Find 0.02256560 -0.07 0.382 0.205 Niger EL5 -Find 0.02256591 0.06 0.384 Australia 0.0225743 0.02256981 ± 68 0.02257091 EL6 -Find 0.02256251 -1.44 0.362 Pillistfer Estonia εCe 0.00 ± 0.29 -0.4 -1.1 ± 0.6 1.8 ± 0.3 2.3 3.8 EL6 -Fall 0.02256272 -1.35 0.354 Agen France 143 Nd/ 144 Nd 0.512630 ± 11 0.512842 0.513129 ± 116 0.512059 ± 155 0.511759 0.511745 H5 -Find 0.02256561 -0.07 0.393 NWA 8007 Morocco L3 -Find 0.02256554 -0.10 0.389 εNd 0.00 ± 0.21 4.1 9.7 ± 2.3 -11.2 ± 3.0 -17 -17.3
		13K	Society	Tahaa	0.02256578 14 0.00 0.361	0.512563	2 -1.30	0.261
		F107	Tuamotu		0.02256382 22 -0.86 0.440	0.512929	2 5.83	0.236
		F124			0.02256379 21 -0.87 0.443	0.512902	2 5.30	0.219
		F128		Fangataufa 0.02256456 20 -0.53 0.460	0.512923	1 5.73	0.239
		F129			0.02256415 20 -0.72 0.436	0.512951	2 6.25	0.229
		F176			0.02256400 25 -0.78 0.494	0.512902	2 5.31	0.210
		SP1	St-Paul		0.02256416 16 -0.71 0.445	0.512876	2 4.79	0.251
		1804-1	Hawaii	Loihi	0.02256428 15 -0.66 0.295	0.512934	1 5.94	0.249
		1804-21			0.02256427 20 -0.66 0.308	0.512935	2 5.96	0.240
		1804-19			0.02256435 19 -0.63 0.275	0.512940	1 6.04	0.247
		Haw-2000-04		Mauna Loa 0.02256451 20 -0.55 0.387	0.512913	1 5.52	0.282
		Haw-2000-19			0.02256483 20 -0.41 0.401	0.512838	2 4.06	0.270
		Haw-2000-13		Kohala	0.02256417 22 -0.71 0.417	0.512999	1 7.20	0.214
		Haw-2000-28		Kilauea	0.02256442 20 -0.60 0.407	0.512944	2 6.13	0.285
		Haw-2000-17		Mauna Kea 0.02256430 15 -0.65 0.414	0.513000	1 7.21	0.233
		0608-021	Reunion	Piton de la	0.02256414 19 -0.72 0.436	0.512851	2 4.32	0.236
		80-76		Fournaise	0.02256463 18 -0.50 0.446	0.512841	2 4.11	0.229
		989/036			0.02256450 19 -0.56 0.445	0.512859	2 4.46	0.242
		986/115			0.02256445 20 -0.58 0.440	0.512837	2 4.03	0.230
		070406-1			0.02256457 20 -0.53 0.429	0.512862	2 4.53	0.250
		67a	Cape Verde	Fogo	0.02256517 23 -0.26 0.459	0.512786	1 3.03	0.175
		F10			0.02256524 23 -0.23 0.475	0.512730	3 1.94	0.179
		F16			0.02256473 20 -0.46 0.466	0.512752	2 2.37	0.185
		CY-165			0.02256448 23 -0.57 0.421	0.512901	1 5.30	0.186
		SV-01		Sao Vicente 0.02256415 20 -0.72 0.456	0.512890	1 5.08	0.191
		SV-12			0.02256417 22 -0.71 0.479	0.512889	2 5.05	0.202
		S-06		Sal	0.02256442 20 -0.60 0.469	0.512862	2 4.53	0.214
		SN-09		Sao Nicolau 0.02256356 19 -0.98 0.481	0.512952	2 6.29	0.190
		ST08		Santiago	0.02256495 21 -0.36 0.486	0.512822	1 3.74	0.200
		93(07)77	Iceland	Höfudreidarm	0.02256424 22 -0.67 0.336	0.513102	1 9.20	0.188
		93(07)76		úli	0.02256377 24 -0.88 0.359	0.513077	1 8.71	0.381
		93(07)24		Asbyrgi	0.02256408 17 -0.75 0.377	0.513027	2 7.74	0.352
		93(07)23			0.02256371 22 -0.91 0.372	0.513030	2 7.81	0.285
		93(07)56		Langaviti 0.02256340 20 -1.05 0.350	0.513097	1 9.12	0.298
		ACO 95-3	Sao Miguel		0.02256559 17 -0.08 0.479	0.512733	1 2.00	0.190
		BM1962 128 (114) Tristan Da Cunha		0.02256653 19 0.34 0.448	0.512503	2 -2.47	0.178
		BM1962 128 (112)			0.02256654 18 0.34 0.489	0.512502	1 -2.49	0.178
		BM1965 P5 (8)	St-Helena		0.02256401 21 -0.78 0.741	0.512884	2 4.95	0.201
		BM1965 P5 (12)			0.02256417 18 -0.71 0.433	0.512872	2 4.73	0.208
		65001	Heard		0.02256604 20 0.12 0.456	0.512586	2 -0.87	0.203
		65151			0.02256674 22 0.43 0.468	0.512512	1 -2.31	0.198
		65171			0.02256620 21 0.19 0.545	0.512567	1 -1.23	0.188
		69230			0.02256555 22 -0.09 0.491	0.512691	3 1.19	0.184
		69244			0.02256551 18 -0.11 0.464	0.512697	2 1.30	0.196
		69254			0.02256550 20 -0.12 0.463	0.512711	2 1.57	0.195
		LVF-98-107	Kerguelen		0.02256577 23 0.00
		MPC-99-103			0.02256611 17 0.15	0.512484* 12* -2.85
		RR08-121			0.02256603 17 0.12	0.512579* 2* -0.99
	MORB Searise-1 DR05-102	MORB	Pacific Ocean 0.02256309 23 -1.19 0.310	0.513164	2 10.42 0.349
		MD23 Site 4			0.02256380 21 -0.87 0.289	0.513084	1 8.85	0.308
		Clipperton DR01			0.02256355 33 -0.98 0.343	0.513122	2 9.59	0.321
		CY82-0903			0.02256310 20 -1.18 0.391	0.513118	1 9.52	0.278
		MD34-D3		Indian Ocean 0.02256414 27 -0.72 0.297	0.513122	2 9.60	0.393
		MD34-D4			0.02256409 22 -0.74 0.372	0.513133	1 9.81	0.336
		MD34-D6			0.02256416 20 -0.71 0.411	0.513133	1 9.81	0.305
	Loess	R11	W Europe	Belgium	0.02257001 59 1.88	0.512035* 9* -11.61
		LO94		Svalbard	0.02257026 40 1.99	0.511937* 10* -13.52
		XN-4	China	Xining	0.02256952 50 1.66	0.512120* 11* -9.95
		Sahara 2900m	Sahara	Alpes, France 0.02256946 41 1.64	0.512011* 7* -12.07
		TJK3198	Tajikistan	Chashmanigar 0.02257004 46 1.89	0.512131* 8* -9.73
		TJK3165			0.02256955 32 1.68	0.512117* 9* -10.01

Table 3 Fig

 3

S2. Rare earth element patterns of OIBs, MORBs, and chondrites. Concentrations are normalised to CI chondrite values

142 Ce ratios of crustal samples from literature

  Fig. S6. 143 Nd/ 144 Nd vs 138 Ce/ 142 Ce ratios measured in mantle-derived samples (see Fig.

	Supplementary 3.
		10.00							Loess
		1.00 Sample/UCC
		0.10
				La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Yb Lu
		0.0225710								Ethiopia
										Austral Islands
		0.0225700								Society
										Fangataufa
		0.0225690								Saint-Paul
										Hawaii
		0.0225680								Reunion
	Ce Ce/ 142	0.0225670								Cape Verde Gough Heard
	138									Iceland
		0.0225660								Kerguelen
										Saint-Helena
		0.0225650								Tristan Da Cuhna
										Sao Miguel
		0.0225640								MORB
										Loess
		0.0225630								Chondrites
		0.6	0.7	0.8	0.9	1	1.1	1.2	1.3	1.4
						Ce/Ce*

138

Ce/

ROC (MORB) MORB source Oceanic sediments Oceanic sediments (Pre-GOE)

						Oceanic sediment
						source
	La (µg/g)	5 ± 5		18 ± 9	18 ± 9
	Ce (µg/g)	15 ± 12		33 ± 25	38 ± 22
	La/Ce	0.34 ± 0.10	0.36	0.57 ± 0.25	0.47 ± 0.05	0.41
	138 Ce/ 142 Ce	0.02256325 ± 145		0.02256771 ± 310	0.02256771 ± 310
	εCe	-1.1 ± 0.6		0.9 ± 1.4	0.9 ± 1.4
	Nd (µg/g)	13 ± 7		18 ± 13	18 ± 13
	Sm (µg/g)	4 ± 2		4 ± 3	4 ± 3
	Nd/Sm	0.34 ± 0.07	0.38	0.20 ± 0.03	0.20 ± 0.03	0.19
	143 Nd/ 144 Nd	0.513129 ± 116		0.512360 ± 653	0.512360 ± 653
	εNd	9.7 ± 2.3		-5.3 ± 12.7	-5.3 ± 12.7

Acknowledgments

We thank Raphael Pik, Manuel Moreira, Dan McKenzie, Pierre Schiano, Bertrand Moine, Ivan Vlastelic, Jane Barling, and Catherine Chauvel for providing OIB and loess samples. We also acknowledge Anthony Irving (University of Washington -Oudiyat Sbaa), the Western Australian Museum (Yilmia -off WAM 13197), the National History Museum (University of Tartu -Pillistfer -TUG 552-2), the Smithsonian Institution National Museum of Natural History (Allende -45NM3529), and the Muséum d'Histoire Naturelle de Paris (Agen -1479 ; Saint-Severin -2397 PE2) for providing chondrites. We thank the Geological Survey of Japan for providing the isotopic standard JNdi-1. The reference material CeLMV is available upon request. Detailed reviews by Richard W. Carlson and an anonymous reviewer are much appreciated as are the editorial handling by Rajdeep Dasgupta. We also thank K.R. Ludwig for the use of his program Isoplot â . This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant Agreement No. 682778 -ISOREE). AB thanks support from the Canada Foundation for Innovation and NSERC Discovery Grant and CRC programs. This is Laboratory of Excellence ClerVolc contribution no. XX.

Appendix A. Supplementary material

Supplementary material related to this article can be found online at XX. Supplementary data 1: Major and trace element contents measured by quadrupole ICP-MS. Supplementary data 2: Ce and Nd isotopic ratios of standard and rock samples and supplementary information.

Supplementary material: 1) Sample descriptions from trace element diagrams and Ce anomalies; 2) 138 Ce/ 142 Ce ratios from literature and example of normalisation with MORB; 3) 138 Ce/ 142 Ce ratios of crustal samples from literature; 4) mass-balance calculations; and 5) recycling models. [START_REF] Sun | Chemical and isotopic systematics of oceanic basalts: implications for mantle composition and processes[END_REF]. We prefer to use the epsilon notation when comparing data from the literature. The most rigorous method for comparison is the use of CHUR values measured under the same analytical conditions (i.e., mass spectrometer, cup configuration, analytical protocol, etc.). This choice results from the difficulty in normalising data acquired with distinct protocols. In Fig. S5, we highlight the bias observed when comparing MORB samples from different studies (Bellot et al., 2015(Bellot et al., , 2018;;Willig and Stracke, 2019) normalised using either BCR-2 or CeAMES. Isotopic compositions vary by up to 10 ppm for data from Willig and Stracke (2019) and by up to 20 ppm for data from Bellot et al. (2015Bellot et al. ( , 2018)). Bellot et al., 2015Bellot et al., , 2018 This study Supplementary 4.

Supplementary material

Mass-balance DMM-CC mixing calculations

Our single-stage differentiation model considers the continental crust (CC) and the depleted MORB mantle (DMM) to be complementary reservoirs developed from the primitive mantle (BSE).

The Nd sialic index (WNd) is defined as the amount of Nd in the continental crust relative to the total amount of Nd in the BSE (Allègre and Lewin, 1989). Its value can be obtained from the 143 Nd/ 144 Nd ratios of the BSE, DMM, and CC as: .

(1)

The Nd sialic index can also be approximated as the product of the mass fraction of continental crust (W, relative to the BSE) and the ratio of the Nd contents in the continental crust and BSE as:

Using W as obtained above, the Ce sialic index (WCe) and the Ce isotopic composition of the continental crust can be deduced from equations similar to equations ( 1) and ( 2):

The mass fraction of continental crust W also allows us to recalculate the complementary Nd and Ce contents of the DMM using mass-balance equations for the trace element concentrations: respectively, in the chondritic case and 0.6-1.1 and 0.8-1.0 ppm, respectively, in the EDR model. We obtained restricted εNdCC ranges of -13 to -21 (CHUR) and -10 to -12 (EDR) that are similar within errors to the values proposed by [START_REF] Salters | Composition of the depleted mantle[END_REF] and [START_REF] Workman | Major and trace element composition of the depleted MORB mantle (DMM)[END_REF].