¹⁴⁷Sm-¹⁴³Nd systematics of Earth are inconsistent with a superchondritic Sm/Nd ratio

Abstract

The relationship between the compositions of the Earth and chondritic meteorites is at the center of many important debates. A basic assumption in most models for the Earth’s composition is that the refractory elements are present in chondritic proportions relative to each other. This assumption is now challenged by recent ¹⁴²Nd/¹⁴⁴Nd ratio studies suggesting that the bulk silicate Earth (BSE) might have an Sm/Nd ratio 6% higher than chondrites (i.e., the BSE is superchondritic). This has led to the proposal that the present-day ¹⁴³Nd/¹⁴⁴Nd ratio of BSE is similar to that of some deep mantle plumes rather than chondrites. Our reexamination of the long-lived ¹⁴⁷Sm-¹⁴³Nd isotope systematics of the depleted mantle and the continental crust shows that the BSE, reconstructed using the depleted mantle and continental crust, has ¹⁴³Nd/¹⁴⁴Nd and Sm/Nd ratios close to chondritic values. The small difference in the ratio of ¹⁴²Nd/¹⁴⁴Nd between ordinary chondrites and the Earth must be due to a process different from mantle-crust differentiation, such as incomplete mixing of distinct nucleosynthetic components in the solar nebula.

Reliable estimates of the compositions of the bulk silicate Earth (BSE) and depleted mantle (DM), which is the source of midocean ridge basalts (MORBs), are important in determining the degree of mantle processing and the thermal evolution of our planet. Chondritic meteorites have provided the most accurate basis for estimating the compositions of the Sun and planets (1). However, the Earth’s chemical composition is overall not chondritic; it has long been known that Earth is depleted in volatile elements (e.g., K) relative to chondrites (2). The assumption that the refractory elements (e.g., rare earth elements) in the Earth are present in chondritic proportions relative to each other is the basis for most estimates of the compositions of the BSE and DM (1, 3–6). This assumption has recently been challenged by several ¹⁴²Nd/¹⁴⁴Nd studies. Specifically, the ¹⁴²Nd/¹⁴⁴Nd of the Earth is ∼20 ppm higher than that of the ordinary chondrites (7–9). There are three ways to produce the observed ¹⁴²Nd difference between the Earth and chondrites (10): (i) nucleosynthetic anomalies due to variations of either initial ¹⁴⁶Sm/¹⁴⁴Sm or initial ¹⁴²Nd/¹⁴⁴Nd ratios in the solar system (11, 12); (ii) difference in the Sm/Nd ratio between the BSE and chondrites (8, 13–15); and (iii) the BSE has a chondritic Sm/Nd ratio, but an early formed reservoir with a low ¹⁴²Nd/¹⁴⁴Nd ratio is hidden at the base of the mantle (7) or was eroded from the Earth by impacts (16), such that the accessible portion of the BSE has a high ¹⁴²Nd/¹⁴⁴Nd ratio.

Because of the short life (<200 Ma) of the oceanic crust, the extraction of the continental crust (CC) is the only major process depleting the Earth’s mantle. Consequently, the DM is complementary to the CC (3, 4). The sum of the CC and DM is the BSE in cases i and ii, and it is the accessible portion of the BSE in case iii, referred to as the “early depleted reservoir” (EDR) by Boyet and Carlson (7). These three scenarios have different implications for the composition of the BSE. In case i, the BSE and the chondritic reservoir have essentially the same Sm/Nd ratio (at a ±1% level). In case ii, the sum of the CC and DM is the BSE (8, 13–15), and it has a superchondritic Sm/Nd ratio (∼6% higher than the chondritic value). In case iii, the sum of the CC and DM is the accessible portion of the BSE (7, 16), and it also has a superchondritic Sm/Nd ratio. Such a superchondritic Sm/Nd ratio leads to a present-day ε_Nd of ∼+7 for CC + DM (7, 8, 13). Here, ε_Nd is the deviation of a sample’s ¹⁴³Nd/¹⁴⁴Nd ratio from the chondritic value (17) in parts per 10⁴.

A BSE with a ε_Nd of +7 is critical to the claim that some basalts sample the primitive mantle (PM) (14, 15). Specifically, lavas from some large igneous provinces (LIPs), such as Baffin Island or West Greenland, which cluster around the 4.5-Ga Geochron in a ²⁰⁷Pb/²⁰⁴Pb-²⁰⁶Pb/²⁰⁴Pb plot, have a ε_Nd of ∼+7. Moreover, Baffin Island picrites with a ε_Nd of ∼+7 have the highest terrestrial ³He/⁴He ratio, up to 50-fold the ratio of air (R/Ra) (18). Because high ³He/⁴He ratios are often taken as evidence for sampling a PM reservoir, it was concluded that these LIP lavas sample pure PM and do not incorporate any other mantle reservoirs (14, 15). In this scenario, PM has a superchondritic present-day ε_Nd of ∼+7. However, the high ³He/⁴He ratios of 30- to 50-fold R/Ra associated with a ε_Nd of ∼+7 could also result from mixing between PM and recycled slabs (19).

Extinct ¹⁴⁶Sm-¹⁴²Nd System

Subsequent to the publication of Boyet and Carlson (7), several studies have revealed a ε¹⁴²Nd variation of 0.5 ε-units in chondrites, as well as possible correlations of the ε¹⁴²Nd variation with nucleosynthetic anomalies in ¹³⁵Ba, ¹⁴⁴Sm, and ¹⁴⁸Nd (9, 11, 12, 20) (Fig. 1). Specifically, Earth and some enstatite chondrites have a similar ε¹⁴²Nd, whereas ordinary chondrites have ε¹⁴²Nd ∼0.2 ε-units lower than that of the Earth, and carbonaceous chondrites have the lowest ε¹⁴²Nd (up to 0.5 ε-units lower than that of the Earth) (figure 1 of ref. 9). In addition to the ¹⁴²Nd similarity, Earth and enstatite chondrites have the same isotopic compositions of O, Ca, Ti, and Cr, which are elements that show substantial isotopic variation among different chondrite groups (21, 22). Jacobsen and Wasserburg (17) showed that chondrites have a very homogeneous ¹⁴⁷Sm/¹⁴⁴Nd ratio (0.1932–0.2000), which was later confirmed by Boyet and Carlson (7). This amount of Sm/Nd variation leads to ∼0.1 ε-units ε¹⁴²Nd variation. In addition, ε¹⁴²Nd is correlated with ε¹⁴⁴Sm [a proton-process (p-process) only isotope], ε¹⁴⁸Nd [a rapid neutron capture process (r-process) dominated isotope], and ε¹³⁵Ba in chondrites, and the Earth plots on the chondrite trends, overlapping with enstatite chondrites (Fig. 1). The ε¹⁴²Nd variation of 0.5 ε-units in chondrites is most likely of a nucleosynthetic origin (11, 12), resulting from small variations in the distribution of different nucleosynthetic components in the solar nebula. To summarize, there are sub–ε-level nucleosynthetic anomalies in Ba, Nd, and Sm isotopes in chondrites, implying that the chondritic reservoir is not homogeneous at this level. Consequently, it is inappropriate to claim that Earth and the chondritic reservoir have an ∼0.2 ε-units ε¹⁴²Nd difference.

Fig. 1.

Variations in ¹⁴⁴Sm/¹⁵²Sm (or ¹⁴⁴Sm/¹⁵⁴Sm), ¹⁴⁸Nd/¹⁴⁴Nd, and ¹³⁵Ba/¹³⁶Ba vs. ¹⁴²Nd/¹⁴⁴Nd for chondrites. Isotopic ratios are expressed using ε-notation (parts per 10,000) relative to the Earth. ¹⁴⁴Sm is a pure p-process isotope, and ¹⁴⁸Nd is an r-process dominated isotope. The error bars for the Earth are taken as 5 ppm, which represents the best analytical uncertainty currently available in these isotopic measurements. The Earth plots within the chondrite trends. These trends imply a nucleosynthetic origin for the ¹⁴²Nd variation in chondrites. The ∼0.5 ε-units ε¹⁴²Nd variation in chondrites does not allow a statement that the Earth and the chondritic reference point have an ∼0.2 ε-units difference in ε¹⁴²Nd (7). Similar plots have also been presented elsewhere (9, 35) showing correlations among these isotopic anomalies. Data are taken from refs. 7, 9, 12, and 20.

Because there are multiple pathways for producing a ε¹⁴²Nd variation (10) and the chondritic reservoir is not homogeneous, ε¹⁴²Nd is not suitable for investigating whether the BSE, or the sum of the CC and DM, has a superchondritic Sm/Nd ratio.

Long-Lived ¹⁴⁷Sm-¹⁴³Nd System

The long-lived ¹⁴⁷Sm-¹⁴³Nd system is not very sensitive to small nucleosynthetic anomalies between chondrites and the Earth because of much larger ¹⁴³Nd variation due to radioactive decay (many ε units, compared with sub–ε-level variations in ¹⁴²Nd/¹⁴⁴Nd). Therefore, we use the ¹⁴⁷Sm-¹⁴³Nd isotopic system in MORBs and the CC to test whether the BSE could have a superchondritic ¹⁴⁷Sm/¹⁴⁴Nd ratio with a present-day ε_Nd of +7 or higher. That the DM is complementary to the CC is widely used in literature to support both the chondritic Earth model and superchondritic Earth models (SCHEM) (3–6, 13, 23); consequently, the BSE composition can be reconstructed by summing the CC and DM. In a ¹⁴³Nd/¹⁴⁴Nd vs. ¹⁴⁷Sm/¹⁴⁴Nd plot, the CC, BSE, and DM should all plot on a common isochron, with the CC-BSE and DM-BSE tie-lines having the same slopes. Their slopes give the Sm-Nd model age of the CC in the simple case of a single continent formation event; that is, the age of the CC calculated from the resulting mantle depletion is equivalent to the age of the CC calculated from its ¹⁴⁷Sm-¹⁴³Nd isotopic composition. This single-event age is very close to the mean age of the CC for a more realistic model of forming the CC by a continuous process of melt-extraction over Earth history. If CC recycling is important (24), this single-event Sm-Nd model age could be many hundred million years younger than the average age of the CC (4). Nevertheless, if the ¹⁴⁷Sm/¹⁴⁴Nd and ¹⁴³Nd/¹⁴⁴Nd ratios of the DM and CC could be determined independently, they would provide a simple test of whether the BSE has a superchondritic ¹⁴⁷Sm/¹⁴⁴Nd ratio.

The ¹⁴⁷Sm/¹⁴⁴Nd ratio of the DM has previously been estimated by assuming either a chondritic (5, 6) or a superchondritic (13) BSE composition and a mean age of CC extraction (4, 25) that depleted the mantle (1.5–2.2 Ga). Boyet and Carlson (7, 23) offered a slightly different view of how the DM was generated. They started with a chondritic BSE, but global silicate differentiation within the first 30 Ma generated an EDR (7) with a superchondritic ¹⁴⁷Sm/¹⁴⁴Nd ratio (ε_Nd of ∼+7.5) and an early crust [early enriched reservoir (EER)] with a subchondritic ¹⁴⁷Sm/¹⁴⁴Nd ratio. The EER was hidden at the base of the mantle after its formation and is inaccessible to mantle volcanism. In this scenario, the EDR is the accessible portion of the Earth, from which the CC was extracted to form the DM. A ¹⁴⁷Sm/¹⁴⁴Nd ratio of 0.229–0.249 for the DM was inferred using a chondritic BSE (5, 6), and a ¹⁴⁷Sm/¹⁴⁴Nd ratio of 0.217–0.222 for the DM was inferred if the BSE or the accessible portion of the BSE is superchondritic (13, 23).

We note that Boyet and Carlson (7) used a t_1/2 of 103 Ma for ¹⁴⁶Sm, which has been redetermined to be 68 Ma (26). Using this more recently measured t_1/2, the early silicate differentiation in the model of Boyet and Carlson (7) has to occur within 20 Ma after the formation of the solar system (i.e., before Earth was fully accreted).

Estimating the ¹⁴⁷Sm/¹⁴⁴Nd Ratio of the DM

Testing whether the Earth has a chondritic or superchondritic ¹⁴⁷Sm/¹⁴⁴Nd ratio requires the ¹⁴⁷Sm/¹⁴⁴Nd of the DM to be estimated independent of the BSE composition.

MORBs are partial melts of the DM; thus, we use the Sm and Nd concentrations in MORBs to estimate the average ¹⁴⁷Sm/¹⁴⁴Nd ratio of the DM. There are three scenarios: (i) the DM has a homogeneous ¹⁴⁷Sm/¹⁴⁴Nd ratio, and the ¹⁴⁷Sm/¹⁴⁴Nd ratio variations in MORBs are caused by partial melting only; (ii) ¹⁴⁷Sm/¹⁴⁴Nd ratio variations in MORBs only reflect source heterogeneity; and (iii) ¹⁴⁷Sm/¹⁴⁴Nd ratio variations in MORBs reflect both partial melting effects and source heterogeneity. Although Langmuir et al. (27) demonstrated that the majority of the elemental variations in MORBs are controlled by variable degrees of partial melting, we note that the first two scenarios represent two end-member models. Thus, we estimate the average ¹⁴⁷Sm/¹⁴⁴Nd ratio of the DM for the first two scenarios (SI Text).

If the ¹⁴⁷Sm/¹⁴⁴Nd ratio variations in MORBs are only caused by variable degrees of partial melting (scenario i), the ¹⁴⁷Sm/¹⁴⁴Nd ratio of the DM can be estimated using a method highlighted by Hofmann et al. (28). In this approach, the intercept of the MORB trend in a ¹⁴⁴Nd/¹⁴⁷Sm vs. Nd diagram is very close to the ¹⁴⁴Nd/¹⁴⁷Sm ratio of their mantle source. Available Nd and Sm concentrations for MORBs, determined by the isotope dilution method (SI Text and Datasets S1 and S2), define a positive trend in a ¹⁴⁴Nd/¹⁴⁷Sm vs. Nd plot (Fig. 2A). The ¹⁴⁷Sm/¹⁴⁴Nd ratio of the DM estimated in this way is 0.255 ± 0.010 (2σ). The Nd concentrations, but not the ¹⁴⁴Nd/¹⁴⁷Sm ratio, in MORBs may also be affected by crystal fractionation. To correct for this effect, we calculate MORB Nd concentrations at 8% (wt/wt) MgO, called Nd₈, following the method of Langmuir et al. (27). The ¹⁴⁷Sm/¹⁴⁴Nd ratio of the DM estimated from the ¹⁴⁴Nd/¹⁴⁷Sm vs. Nd₈ correlation (Fig. 2B) is 0.269 ± 0.013 (2σ).

Fig. 2.

(A) ¹⁴⁴Nd/¹⁴⁷Sm vs. Nd (parts per million) for MORB samples (blue circles) for which Sm and Nd concentrations have been determined by isotope dilution (sample selection is provided in SI Text and Datasets S1 and S2). The average compositions of MORBs from normal ridge segments (red squares) (29, 30) are shown for comparison. The solid line is a robust linear least square regression obtained using MATLAB (MathWorks), and it passes through the estimated average compositions of MORBs from normal ridge segments. It has a slope of 0.088 ± 0.013 (2σ), an intercept of 3.88 ± 0.14 (2σ), and a linear correlation coefficient R² of 0.48. The estimated ¹⁴⁷Sm/¹⁴⁴Nd ratio of the DM is 0.255 ± 0.010 (SI Text). Also shown are estimates of the chondritic ¹⁴⁷Sm/¹⁴⁴Nd ratio (0.1966) (17) and estimates of the ¹⁴⁷Sm/¹⁴⁴Nd ratio of the DM for the SCHEM (0.217–0.222) (13, 23). (B) ¹⁴⁴Nd/¹⁴⁷Sm vs. Nd₈ (in parts per million by weight) for MORB samples (blue circles) (sample selection is provided in SI Text and Datasets S1 and S2). Nd₈ values are Nd concentrations corrected to 8% (wt/wt) MgO following the method of Langmuir et al. (27) (Dataset S2). This trend has a slope of 0.120 ± 0.018 (2σ), an intercept of 3.66 ± 0.18 (2σ), and a linear correlation coefficient R² of 0.51. The estimated ¹⁴⁷Sm/¹⁴⁴Nd ratio of the DM is 0.269 ± 0.013 (SI Text).

In scenario ii, where the ¹⁴⁷Sm/¹⁴⁴Nd ratio variations in MORBs only reflect source heterogeneity, the ¹⁴⁷Sm/¹⁴⁴Nd ratio of the DM is estimated using a forward partial melting model. The average ¹⁴⁷Sm/¹⁴⁴Nd ratio in MORBs from normal ridges (29, 30) is 0.212 ± 0.001 (2σ_m). Using a partial melting degree of 10%, proper mineral-melt partition coefficients (Table S1), and several types of partial melting models (Tables S2 and S3), the ¹⁴⁷Sm/¹⁴⁴Nd ratio of the DM is estimated to be 0.238–0.248 (SI Text). In this approach, the partial melting degree of 10% used for MORB generation is on the higher end (27). In addition, we only consider a spinel peridotite lithology for MORB generation, and arguments that melting of garnet peridotite or garnet pyroxenite is important in MORB generation have been made (26, 31–33). Because (Sm/Nd)_garnet/(Sm/Nd)_{clinopyroxene} > 1, including garnet in MORB generation would only increase the estimated ¹⁴⁷Sm/¹⁴⁴Nd ratio of the MORB source. Consequently, the ¹⁴⁷Sm/¹⁴⁴Nd ratio of the DM estimated in this way is the minimum value.

Because we discussed the two end-member scenarios (SI Text), we argue that the ¹⁴⁷Sm/¹⁴⁴Nd ratio of the DM is constrained between 0.238 and 0.269 (Fig. 3). The pale blue area in Fig. 3, where the ¹⁴⁷Sm/¹⁴⁴Nd = 0.211–0.227, represents the possible DM ¹⁴⁷Sm/¹⁴⁴Nd ratio range constrained by the CC composition under a SCHEM with a present-day ε_Nd of +7. The pink area, where the ¹⁴⁷Sm/¹⁴⁴Nd = 0.227–0.264, represents the possible DM ¹⁴⁷Sm/¹⁴⁴Nd ratio range constrained by the CC under a chondritic Earth model. All our estimated ¹⁴⁷Sm/¹⁴⁴Nd ratios of the DM are higher than that required for a superchondritic Earth, and agree with those required for a chondritic Earth (Fig. 3). Therefore, the result that the ¹⁴⁷Sm/¹⁴⁴Nd ratio of the DM inferred from MORB data is higher than that required by the SCHEM is robust and not dependent on model details.

Fig. 3.

¹⁴⁷Sm/¹⁴⁴Nd ratio of the DM estimated by various approaches. Details are provided in SI Text. Estimates from the literature are also included for comparison. The pale blue area, ¹⁴⁷Sm/¹⁴⁴Nd = 0.211–0.227, represents the possible range for the ¹⁴⁷Sm/¹⁴⁴Nd ratio of the DM under a SCHEM with a present-day ε_Nd of +7 and taking into account the possible ranges for the CC (see Fig. 4 legend). The pink area, ¹⁴⁷Sm/¹⁴⁴Nd = 0.227–0.264, represents the possible range for the ¹⁴⁷Sm/¹⁴⁴Nd ratio of the DM under a chondritic Earth model. All our DM estimates are higher than those required by the SCHEM but match those required by a chondritic Earth model. Therefore, the result that the ¹⁴⁷Sm/¹⁴⁴Nd ratios of the DM inferred from MORB data are higher than those required by the SCHEM is robust and not dependent on model details.

Test for a Superchondritic ¹⁴⁷Sm/¹⁴⁴Nd Ratio in the BSE

In a ¹⁴³Nd/¹⁴⁴Nd vs. ¹⁴⁷Sm/¹⁴⁴Nd plot, MORBs form a nearly horizontal trend, whereas the river water suspended loads (34), which sample large areas of the CC, form a nearly vertical trend with samples from young arc terrains plotting within the MORB field (Fig. 4A). The average ¹⁴⁷Sm/¹⁴⁴Nd and ¹⁴³Nd/¹⁴⁴Nd ratios of the CC are well constrained using Sm-Nd isotopic data from river water suspended loads (34) (Fig. 4A). The MORB ¹⁴³Nd/¹⁴⁴Nd data show limited variation, with a near-normal distribution. Our inferred plausible range of DM ¹⁴³Nd/¹⁴⁴Nd () covers the central 68% of the MORB histogram (Fig. 4A) and is typical of the MORB ¹⁴³Nd/¹⁴⁴Nd variations (29).

Fig. 4.

(A) ¹⁴³Nd/¹⁴⁴Nd vs. ¹⁴⁷Sm/¹⁴⁴Nd isotope systematics of MORBs and river water suspended loads (4, 34). The MORB data in the ¹⁴³Nd/¹⁴⁴Nd vs. ¹⁴⁷Sm/¹⁴⁴Nd diagram are only MORBs with isotope dilution Sm and Nd measurements (n = 166). (Right) Histogram of the ¹⁴³Nd/¹⁴⁴Nd ratio for unfiltered MORB samples (n = 2,485) (SI Text) is shown. There is no significant difference between the average ¹⁴³Nd/¹⁴⁴Nd ratio of the two datasets. The ¹⁴³Nd/¹⁴⁴Nd ratios of MORBs show limited variation and form a near-normal distribution with a peak at 0.51318, corresponding to a ε_Nd of 10.6. The ε_Nd is the ¹⁴³Nd/¹⁴⁴Nd deviation from the chondritic value (CHUR) in parts per 10⁴ (17). The ¹⁴³Nd/¹⁴⁴Nd ratio of the DM is inferred to be , corresponding to a ε_Nd of , and it agrees well with the previously published average ¹⁴³Nd/¹⁴⁴Nd ratio of 0.51311–0.51313 for normal (N)-MORBs (5, 29). For comparison, we also show positions for the chondritic reference values in this diagram (CHUR) (17), a SCHEM (13), an average CC (34) (¹⁴⁷Sm/¹⁴⁴Nd = 0.114 ± 0.010, ¹⁴³Nd/¹⁴⁴Nd = 0.51177 ± 0.00010), and a 4.567-Ga Geochron. (B) ¹⁴³Nd/¹⁴⁴Nd vs. ¹⁴⁷Sm/¹⁴⁴Nd systematics of major reservoirs in the Earth. The CHUR, SCHEM, and average CC are the same as in A. Our estimate of the DM in this diagram (brown box) comes from the ¹⁴⁷Sm/¹⁴⁴Nd ratio obtained based on MORB data and the Nd isotopic composition from A (¹⁴⁷Sm/¹⁴⁴Nd = 0.238–0.269, ¹⁴³Nd/¹⁴⁴Nd = 0.51304–0.51320). The possible range of the DM-CC tie-line is shown as a gray field outlined by two red lines (by taking the end-member values of DM and CC), and its intersection with the 4.567-Ga Geochron represents our estimated BSE composition (¹⁴⁷Sm/¹⁴⁴Nd = 0.183–0.204, ¹⁴³Nd/¹⁴⁴Nd = 0.51223–0.51286, and ε_Nd = −8.0 to +4.4). The CC-CHUR tie-line has a ¹⁴⁷Sm-¹⁴³Nd model age of 1.60 Ga, consistent with the average age of the CC (a detailed discussion is provided in ref. 4). Possible mantle-crust differentiation ages can be estimated by connecting the extreme values of the DM and CC (e.g., the lower right corner of the CC with the upper left corner of the DM). This leads to a mantle-crust differentiation age of 1.1–2.0 Ga, consistent with the age of the CC (4). The CHUR point lies within the possible range of intersections between the CC-DM isochron and the Geochron. The SCHEM point lies substantially above this range. Thus, there is no evidence for a SCHEM based on ¹⁴⁷Sm-¹⁴³Nd isotopic variations in the CC and MORBs.

We now test whether the Earth could have a superchondritic ¹⁴⁷Sm/¹⁴⁴Nd ratio using the ¹⁴⁷Sm/¹⁴⁴Nd and ¹⁴³Nd/¹⁴⁴Nd ratios of the DM and CC (Fig. 4B). The BSE must be at the intersection of the 4.567-Ga Geochron and the DM-CC tie-line in this diagram. Taking into account the possible DM and CC ranges, the DM-CC tie-line crosses the 4.567-Ga Geochron at a ¹⁴⁷Sm/¹⁴⁴Nd ratio of 0.183–0.204 and a ¹⁴³Nd/¹⁴⁴Nd ratio of 0.51223–0.51286 (ε_Nd = −8.0 to +4.4). The large uncertainties associated with the intersection of the DM-CC tie-line and the 4.567-Ga Geochron result from the large uncertainties in the ¹⁴⁷Sm/¹⁴⁴Nd and ¹⁴³Nd/¹⁴⁴Nd ratios of the DM and CC. This intersection overlaps with the chondritic point; however, even taking into account the large uncertainty, the SCHEM plots well above this intersection (Fig. 4B). Moreover, the CC-chondritic uniform reservoir (CHUR) tie-line passes through the possible DM range. This CC-CHUR tie-line has a ¹⁴⁷Sm-¹⁴³Nd model age of 1.60 Ga, consistent with the average age of the CC (a detailed discussion is provided in ref. 4). Therefore, the ¹⁴⁷Sm-¹⁴³Nd isotope systematics of the DM and CC, considered together, are inconsistent with a superchondritic Earth with a present-day ε_Nd of +7. Our results demonstrate that the BSE has a near-chondritic ¹⁴⁷Sm/¹⁴⁴Nd ratio.

The existence of a hidden reservoir at the base of the mantle proposed to explain the observed ε¹⁴²Nd difference between the Earth and ordinary chondrites (7) is also inconsistent with the ¹⁴⁷Sm-¹⁴³Nd isotope systematics of the CC-DM system, because it requires an extremely young age for the CC. In this case, the accessible portion of the Earth (EDR), from which the CC was extracted, has a present-day ε_Nd of +8 to +12 (¹⁴³Nd/¹⁴⁴Nd = 0.51305–0.51325) (7), overlapping with present-day MORB values. Consequently, an EDR-DM tie-line has a near-zero slope, implying an unrealistically young age (approximately zero age) for the CC. Furthermore, because the EDR and DM have the same ε_Nd, there is no way to balance the low ε_Nd values in the CC. Because loss of an early crust through collisional erosion during the end stages of terrestrial accretion (16) in essence represents a reservoir hidden in space, such a scenario is also inconsistent with the ¹⁴⁷Sm-¹⁴³Nd isotope systematics and can be ruled out.

Assuming a simple CC growth model in which the CC started to grow at 4.4 Ga at a constant rate, Caro and Bourdon (13) have argued that a chondritic Earth model cannot explain the radiogenic ε_Nd in the Archean mantle. They argued instead that the positive ε_Nd found in the Archean mantle requires a superchondritic bulk Earth ¹⁴⁷Sm/¹⁴⁴Nd ratio (figure 11 of ref. 13). However, using a more realistic CC growth model in which recycling of the CC is allowed, Jacobsen (4) was able to reproduce the trend of radiogenic ε_Nd in the Archean mantle with a ¹⁴⁷Sm/¹⁴⁴Nd ratio evolution that is consistent with the updated DM estimate provided in this paper. The evolution curves in Fig. 5 were evaluated by Jacobsen (4) to be consistent with the data available in 1988. For comparison, we show the ε_Nd estimates for the average DM compiled in 2010 by Caro and Bourdon (13) and used in their modeling. We also show that the end point of the ¹⁴⁷Sm/¹⁴⁴Nd ratio evolution from Jacobsen (4) is consistent with the estimate given in this paper. Thus, we conclude that the Sm-Nd isotopic evolution of the mantle through time is consistent with a chondritic Earth and that the conclusion of Caro and Bourdon (13) is only valid for a particularly simplistic model calculation.

Fig. 5.

Model evolution of the DM ε_Nd and ¹⁴⁷Sm/¹⁴⁴Nd ratio through time. The data points are average DM compositions and Isua supracrustals from the recent compilation of Caro and Bourdon (13). The present-day DM estimates are from this study. The model curves are from Jacobsen (4) using a chondritic Earth model. The evolution of the DM ε_Nd is consistent with a chondritic Earth model with CC recycling (4) but not with a simple CC growth model without CC recycling as presented by Caro and Bourdon (13). Our estimate of the present-day DM ¹⁴⁷Sm/¹⁴⁴Nd ratio is also consistent with the model prediction of Jacobsen (4).

Conclusions

In summary, the ¹⁴⁷Sm-¹⁴³Nd isotope systematics of the CC and DM imply that the BSE has a near-chondritic ¹⁴⁷Sm/¹⁴⁴Nd ratio and are inconsistent with the BSE having a present-day ε_Nd of +7 as required by the SCHEM (7, 8, 13–15). The ∼0.5 ε-units ε¹⁴²Nd variation in the Earth and chondrities most likely results from variations in the mixing proportions of different nucleosynthetic components. Given the ∼0.5 ε-units ε¹⁴²Nd variation (7–9, 20) in bulk chondrites but ≤±2% variations in ¹⁴⁷Sm/¹⁴⁴Nd ratios (17), it seems inappropriate to attribute the ∼0.2 ε-units ε¹⁴²Nd difference between the Earth and ordinary chondrites to a 6% difference in ¹⁴⁷Sm/¹⁴⁴Nd ratios.