The bulk composition of the silicate portion of the Earth (BSE) has long been assumed to be tied to chondrites, in which refractory, lithophile elements like Sm and Nd exist in chondritic relative abundances. However, the 142Nd/144Nd ratios of modern terrestrial samples are 18 ± 5 ppm higher than the ordinary-chondrite reservoir, and this challenges the traditional BSE model. Here we investigate a hypothesis that this terrestrial 142Nd excess is related to a Sm/Nd ratio 6% higher than chondritic. This Sm/Nd ratio yields a superchondritic 143Nd/144Nd (∼0.5130) similar to that identified in the highest 3He/4He mantle reservoir, and we argue that this reservoir represents the BSE composition for lithophile elements. We develop a compositional model for BSE in which the elevated Sm/Nd requires a shift of 143Nd/144Nd from 0.51263 (chondritic) to 0.51300. The new BSE composition is depleted in highly incompatible elements, including K, relative to the chondrite-based BSE, and offers a solution the “missing” 40Ar paradox. This BSE compositional model requires that >83% of the mantle is depleted to form continental crust. It also implies a ∼30% reduction in BSE U, Th and K, and therefore in the current rate of radiogenic heating and, thus, a proportional increase in the heat flow delivered to surface by plate tectonics. We explore thermal history models including effects related to a newly recognized evolution in the style of plate tectonics over Earth history: The lower radiogenic heat production may delay the onset of core convection and dynamo action to as late as 3.5 Gyr.
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 The Earth's mantle preserves a history of the long-term evolution and differentiation of the planet. For example, mid-ocean ridge basalts (MORB) exhibit geochemical signatures of incompatible element depletion, and indicate that much of the upper mantle has experienced melt removal over geologic time [Gast, 1968; Hofmann, 1988; Salters and Stracke, 2004; Workman and Hart, 2005; Boyet and Carlson, 2006]. The mantle is “re-enriched” when crust, both oceanic and continental, are subducted into the mantle, and the geochemistry of basalts erupted at some oceanic hotspots record the return of these subducted components, as well as deeply seated primitive components, in regions of mantle upwelling and melting [Zindler and Hart, 1986; Hofmann, 1997; White, 2010]. These enriched and depleted mantle reservoirs are mixed, thereby complicating much of the geochemical history recorded in the mantle [e.g., Brandenburg et al., 2008; van Keken et al., 2004]. While much of the mantle has been processed at mid-ocean ridges and subduction zones, fundamental questions remain: Are there domains in the mantle that have survived, relatively undisturbed since accretion, that might shed light on the composition of the earliest Earth? If so, what are their compositions?
 Helium is an important tracer for primitive material residing in the Earth's mantle. Helium has two stable isotopes: 3He, which is of primordial origin in the mantle, and 4He, which has both radiogenic (resulting primarily from U and Th decay) and primordial components in the Earth's mantle. Lavas with high 3He/4He have long been thought to represent melts of relatively undegassed regions of the mantle with low (Th+U)/He ratios, which are conducive to preserving high 3He/4He over geologic time [e.g., Kurz et al., 1982, 1983; Farley et al., 1992; Stuart et al., 2003; Class and Goldstein, 2005]. Lavas with the highest terrestrial mantle 3He/4He globally, from Baffin Island [Stuart et al., 2003] and West Greenland [Graham et al., 1998], exhibit Pb-isotopic compositions that lie near the geochron, the locus of data in Pb-isotopic space that have had undisturbed U/Pb ratios for ∼4.5 Ga [Jackson et al., 2010; Jackson and Carlson, 2011]. This observation is consistent with the high 3He/4He mantle being the oldest accessible terrestrial mantle reservoir. This interpretation is supported by the discovery that the high 3He/4He mantle sampled by the Iceland hotspot (which sourced Baffin Island lavas at ∼62 Ma) [Storey et al., 1998] has 129Xe/130Xe isotopic compositions distinct from the depleted MORB mantle (DMM), which requires formation and separation of the DMM and high 3He/4He reservoirs within ∼100 Ma following accretion [Mukhopadhyay, 2012]. In contrast to the primitive He and Pb isotopic compositions in the highest 3He/4He lavas, their 143Nd/144Nd isotopic compositions are higher than chondritic [e.g., Hart et al., 1992; Hanan and Graham, 1996], with values closer to the average 143Nd/144Nd of the MORB mantle (0.51313) [Su, 2003] than chondritic (0.51263) [Bouvier et al., 2008]. If the bulk silicate Earth (BSE) originated by accretion of chondrites, or planetesimals that descended from chondritic precursors, then the superchondritic 143Nd/144Nd and 176Hf/177Hf ratios in high 3He/4He lavas [e.g., Caro and Bourdon, 2010; Jackson et al., 2010] suggest a history of depletion by melt extraction, a process that increases the Lu/Hf and Sm/Nd ratios in the melt-depleted residue. The association of primitive noble gas isotopic signatures in a mantle reservoir with distinctly nonchondritic refractory element radiogenic isotopic signatures is a paradox that has been the subject of considerable discussion [e.g., Kurz et al., 1982; Hart et al., 1992; Class and Goldstein, 2005; Parman et al., 2005; Caro et al., 2008; Carlson and Boyet, 2008; Gonnermann and Mukhopadhyay, 2009; Caro and Bourdon, 2010; Jackson et al., 2010; Jackson and Carlson, 2011].
 A recent landmark discovery provides a possible solution to this helium paradox. Boyet and Carlson  (BC05 hereafter) found small, but significant differences (18 ± 5 ppm) [Carlson and Boyet, 2008] in 142Nd/144Nd between modern terrestrial samples and ordinary (O) and carbonaceous (C)-chondrites. This difference is important because, if the Earth has chondritic ratios of Sm/Nd, then the Earth is predicted to have 142Nd/144Nd and 143Nd/144Nd identical to chondrites. BC05 suggest that the 142Nd excess in terrestrial samples relative to O and C-chondrites is the result of 146Sm decay, and that the accessible silicate Earth has superchondritic Sm/Nd and 143Nd/144Nd (0.5130 ± 0.0001). This value matches the 143Nd/144Nd ratios measured in high 3He/4He lavas, and has lead to the idea that the high 3He/4He reservoir may reflect the lithophile element composition of a nonchondritic BSE [Caro et al., 2008; Jackson et al., 2010] from which most of the continental crust and all known oceanic lavas were derived [Jackson and Carlson, 2012]. In this paper, chondrite-based models for BSE are those models in which only the refractory lithophile elements (like Sm and Nd) exist in chondritic relative abundances, while ratios of other elements (e.g., volatile element/refractory element, siderophile element/lithophile element, etc.) may not. The term “nonchondritic Earth,” as used here, implies that even the refractory lithophile elements fail to exhibit chondritic relative abundances.
 An alternative model for the 142Nd excess in terrestrial samples relative to O and C-chondrites suggests that it is the result of Earth's accreting from a nucleosynthetically heterogeneous early solar nebula [Ranen and Jacobsen, 2006; Kleine et al., 2013], a view challenged by recent high-precision measurements of Ba, Sm, Nd, and Sr isotopes in chondrites [Andreasen and Sharma, 2006, 2007; Carlson et al., 2007; Carlson and Boyet, 2008; Qin et al., 2011]. While some enstatite (E)-chondrites have been found to exhibit 142Nd/144Nd similar to the Earth [Gannoun et al., 2011], their 143Nd/144Nd is similar to O and C-chondrites and does not provide a solution to the paradox of superchondritic 143Nd/144Nd in terrestrial lavas with primitive 3He/4He, and we do not explore an E-chondrite model for the Earth [e.g., Javoy et al., 2010]. However, we note that the community cannot, at present, rule out an E-chondrite model for the BSE or demonstrate the Earth accreted from E-chondrites, and this will no doubt continue to be a source of discussion.
 Here we explore the implications for 146Sm decay driving the 142Nd/144Nd difference between Earth and O and C-chondrites. If the difference is the result of 146Sm decay, then the accessible Earth (i.e., crustal and upper mantle rocks and MORB and hotspot lavas) [e.g., Jackson and Carlson, 2012] did not have chondritic relative abundances of the refractory lithophile elements, including Sm/Nd, during the first ∼20 million years (using the 146Sm half-life [68 Ma] from Kinoshita et al. ) after accretion (BC05). Instead, the observation of constant superchondritic 142Nd/144Nd in all modern terrestrial mantle reservoirs requires that they descend from a parental reservoir that has a Sm/Nd ratio ∼4.5–7.9% higher than chondrites [e.g., Jackson and Carlson, 2012], but the origin of this reservoir is debated. In an attempt to preserve the chondrite model for BSE in light of the new 142Nd result, BC05 suggest that an early (ca., <30 Ma following accretion, where they assumed a 103 Ma half-life for 146Sm) differentiation event of a chondritic Earth resulted in two reservoirs: an early depleted reservoir (EDR) with Sm/Nd 4.5–7.9% higher than chondrites from which all modern terrestrial mantle reservoirs descend, and a complementary early enriched reservoir (EER) hidden in the deep mantle with characteristics similar to that proposed by Labrosse et al. . To-date, however, all measured modern MORB and hotspot lavas have the same 142Nd/144Nd as the terrestrial standard [e.g., Boyet and Carlson, 2006; Caro et al., 2006; Andreasen et al., 2008; Murphy et al., 2010; Jackson and Carlson, 2012]. There is no observational evidence from geochemistry for an EER, but its existence cannot be excluded. However, to avoid the requirement of a hidden EER at the bottom of the mantle, O'Neill and Palme  suggest that the mantle began with a chondritic composition that underwent early catastrophic differentiation and loss of early-formed enriched crust by impact erosion. Alternatively, impact erosion-induced loss of enriched crust from the planetesimals that accreted to make up the Earth could generate a BSE composition with superchondritic Sm/Nd. In the impact erosion model, the residual BSE (or the impact-eroded planetesimals that accreted to form the Earth), depleted in the highly incompatible elements by early loss of enriched crust to space, hosts a bulk superchondritic Sm/Nd ratio and is compositionally identical to BC05's EDR (but the BC05 EER has been lost to space instead of the deep mantle).
 This early-formed, depleted reservoir with superchondritic 142Nd/144Nd and 143Nd/144Nd has been argued to be the most primitive surviving reservoir in the Earth's mantle and host to high 3He/4He [Carlson and Boyet, 2008; Caro et al., 2008; Caro and Bourdon, 2010; Jackson et al., 2010; Jackson and Carlson, 2011]. Lavas with the highest terrestrial mantle 3He/4He have superchondritic 143Nd/144Nd ratios that generally fall within the range of values predicted for the EDR (i.e., 0.5130 ± 0.0001). Importantly, like all modern terrestrial mantle-derived lavas measured to-date, lavas with high 3He/4He have 142Nd/144Nd that is 18 ± 5 ppm higher than O and C-chondrites [Andreasen et al., 2008; Murphy et al., 2010; Jackson and Carlson, 2012]. Therefore, we adopt the recent hypothesis that the mantle reservoir with high 3He/4He was formed by early melt extraction from O or C-chondrite precursors and is the parental reservoir from which all accessible modern terrestrial mantle reservoirs were derived [Carlson and Boyet, 2008; Caro et al., 2008; Caro and Bourdon, 2010; Jackson et al., 2010; Jackson and Carlson, 2012].
 Taking the high 3He/4He mantle to be the most primitive accessible terrestrial mantle reservoir, we develop a major and trace element compositional model for this reservoir that is consistent with Nd-isotopic constraints, which require early formation of the high 3He/4He mantle and a Sm/Nd ratio that is 4.5–7.9% higher than chondritic. Therefore, our model for the high 3He/4He mantle provides a lithophile element composition for either a nonchondritic BSE (if BSE is not chondritic owing to early loss of enriched material to space), or the EDR (if BSE is chondritic and enriched material is hidden in the deep mantle). This manuscript is meant to complement the work of Caro and Bourdon , and the new compositional model for the high 3He/4He mantle provides a major and trace element composition for a nonchondritic BSE that is based on the composition of high 3He/4He lavas, called Super-Chondritic Earth Model (SCHEM).
2. Estimating the Lithophile Element Composition of a Nonchondritic BSE by Constructing the Trace Element Budget of the High 3He/4He Mantle
2.1. Calculating the 147Sm-143Nd, 176Lu-176Hf, and 87Rb-87Sr of the high 3He/4He mantle
 At the foundation of our trace element model is the assumption that a nonchondritic BSE has a Sm/Nd ratio 4.5–7.9% higher than chondritic, which is necessary to generate the 18 ± 5 ppm difference in 142Nd/144Nd between chondrites and modern terrestrial mantle-derived lavas by 146Sm decay. The uncertainty in 142Nd/144Nd, from 13 to 23 ppm higher than chondritic, results in uncertainty in the Sm/Nd ratio, which propagates into uncertainty in the 143Nd/144Nd ratio. Therefore, assuming an initial 143Nd/144Nd that is chondritic and closed-system evolution for 4.567 Ga, the range of possible Sm/Nd ratios will generate a range of present-day 143Nd/144Nd values of 0.5130 ± 0.0001 (ε143Nd = 7.1 ± 2.0). This range of 143Nd/144Nd values for a nonchondritic BSE is similar to the range of values identified in the highest 3He/4He lavas globally [Stuart et al., 2003; Jackson et al., 2007; Starkey et al., 2009], and we argue that the lithophile element composition of the high 3He/4He mantle represents the composition of a nonchondritic BSE.
Caro and Bourdon  use the superchondritic 147Sm/144Nd and 143Nd/144Nd of the high 3He/4He mantle to estimate its 176Lu/176Hf and 87Rb/87Sr ratios. The lithophile, incompatible behavior of Sm-Nd, Lu-Hf, and Rb-Sr systems during melting and subsequent magmatic differentiation cause the isotopic systematics of 143Nd/144Nd, 176Hf/177Hf, and 87Sr/86Sr to exhibit correlated variations in crustal and mantle-derived samples [e.g., Allègre et al., 1979; DePaolo and Wasserburg, 1979; DePaolo, 1980; Patchett et al., 1981; Salters and Hart, 1991; Vervoort et al., 1999; Chauvel et al., 2008; Bouvier et al., 2008; Caro and Bourdon, 2010]. Consequently, a key assumption for evaluating the Sr and Hf isotopic composition of BSE is that the correlated global isotopic data—which form “mantle arrays” in 143Nd/144Nd versus 176Hf/177Hf and 143Nd/144Nd vs. 87Sr/86Sr isotopic spaces—pass through BSE (Figure 1). Therefore, if the composition of a nonchondritic BSE is known for any one of these three isotopic systems (e.g., 143Nd/144Nd), then its composition can be estimated for the other two isotopic systems (87Sr/86Sr and 176Hf/177Hf) using the mantle array. In a plot of ε143Nd versus ε176Hf, the range of Nd-isotopic compositions for nonchondritic BSE (ε143Nd = 7.1 ± 2.0) intersects the mantle array over a range of ε176Hf values (ε176Hf = 12.6 ± 3.1), and these are the Hf-isotope values used for modeling the trace element composition of a nonchondritic BSE (Figure 1 and Table 1). In 87Sr/86Sr versus 143Nd/144Nd isotopic space, the range of 143Nd/144Nd values for a nonchondritic BSE intersects the mantle array over a range of 87Sr/86Sr values (0.7030 ± 0.0004) (Table 1). The 143Nd/144Nd, 176Hf/177Hf, and 87Sr/86Sr isotopic values selected for a nonchondritic BSE in Table 1 are similar to those presented for SCHEM by Caro and Bourdon .
Table 1. 147Sm-143Nd, 176Lu/176Hf, 87Rb/86Sr for the Nonchondritic BSE, Which Represents the High 3He/4He Mantle Compositiona
Chondrite-Based BSE (CHUR)
High 3He/4He Mantle (This Study)
High 3He/4He Mantle enriched (This Study)
High 3He/4He Mantle depleted (This Study)
CHUR is Chondrite Uniform Reservoir. Many of the values for the nonchondritic BSE in this table are adopted from Caro and Bourdon's  estimates for SCHEM or are similar to their values. The 143Nd/144Nd and 176Hf/177Hf values for CHUR are from Bouvier et al. , where the CHUR 143Nd/144Nd value is similar to the Jacobsen and Wasserburg [1980b] value. DMM compositions are from Workman and Hart  (WH05), Salters and Stracke  (SS04), and Boyet and Carlson  (BC06). Following Caro and Bourdon , the ε176Hf of the nonchondritic BSE is calculated from its ε143Nd by using the equation for the mantle array from Chauvel et al. : ε176Hf=1.59*ε143Nd + 1.28. The table also provides enriched and depleted bounds about an average nonchondritic BSE composition. These enriched and depleted estimates are generated from the uncertainty on the difference in 142Nd/144Nd (and hence difference in Sm/Nd) between Earth and O-chondrites.
ε143Nd (versus CHUR)
100 × ε142Nd (versus ordinary chondrites) (ppm)
18 ± 5 ppm
18 ± 5 ppm
18 ± 5 ppm
ε176Hf (versus CHUR)
2.2. Constructing the “Backbone” of the High 3He/4He Mantle Spidergram: Toward a Composition of a Nonchondritic BSE
 Armed with estimates for the Nd, Hf and Sr isotopic compositions of a nonchondritic BSE, it is possible to calculate the present-day parent-daughter ratios of these three isotopic systems assuming closed-system isotopic evolution for 4.567 Ga, an age that is consistent with Pb [Jackson et al., 2010] and Xe [Mukhopadhyay, 2012] isotopic measurements on high 3He/4He lavas from Baffin Island and the associated Iceland hotspot. We follow Caro and Bourdon  and Jackson et al.  and assume that the initial Nd, Hf, and Sr isotopic compositions and associated parent-daughter ratios of BSE (or the planetesimals that differentiated before accreting to form the Earth) were chondritic. The parent-daughter ratios required to generate the present-day isotopic compositions of the nonchondritic BSE result in Sm/Nd (0.3441 instead of the chondritic value of 0.324), Lu/Hf (0.266 instead of 0.237) and Rb/Sr (0.0211 instead of 0.029) ratios that are different from that predicted by the chondrite-based model for BSE (Table 1).
 The three isotopically constrained parent-daughter ratios bracket the entire spidergram: The Rb/Sr ratio brackets the portion of the spidergram occupied by trace elements that are most incompatible during mantle melting, the Sm/Nd ratio brackets the moderately incompatible elements, and the Lu/Hf ratio brackets the least incompatible elements. These three segments of the spidergram can be “linked” together using canonical ratios derived from measurement of oceanic lavas (Figure 2). Incompatible trace elements that have the same partition coefficients during mantle melting exhibit reasonably constant ratios in oceanic lavas independent of the absolute concentrations in the lavas (as long as the degree of melting is much larger than the bulk partition coefficient), and these canonical ratios are considered to reflect the mantle source of the lavas [Hofmann, 2003]. A number of ratios are employed in this study to construct the spidergram of the nonchondritic BSE mantle, and the ratios are relatively constant in oceanic lavas: Sm/Hf [Chauvel and Blichert-Toft, 2001], Sr/Nd [Sun and McDonough, 1989], La/Th [Willbold and Stracke, 2006], Ba/Rb [Hofmann and White, 1983], Ba/Th [Salters and Stracke, 2004], Nb/U [e.g., Hofmann et al., 1986], and K/U [e.g., Jochum et al., 1983]. We use the trace element compilation on ocean island basalts (OIBs) from Willbold and Stracke  to determine average trace element ratios and their associated uncertainty, and we exclude lavas with <10 wt% MgO to avoid fractionation of the trace element ratios during magmatic evolution (Table 2). High3He/4He ratios are associated with OIB and not with MORB, so a trace element compilation based on OIB [Willbold and Stracke, 2006] (Table 2) is used to define the spidergram of the high 3He/4He mantle that is here assumed to reflect the nonchondritic BSE. Additionally, the canonical ratios that we employ are broadly similar in all OIB, and should therefore also reflect the ratios in the subset of OIB with high 3He/4He (and thus the ratios in the nonchondritic BSE). Therefore, using trace element ratios in OIBs from Table 2, the Sr/Nd ratio (15.3) can be used to link the Rb-Sr and Sm-Nd sections of the spidergram for the high 3He/4He mantle, and the Sm/Hf ratio (1.44) links the Sm-Nd and Lu-Hf sections, thereby providing the “backbone” of the nonchondritic BSE spidergram from Rb to Lu (Figure 2).
Table 2. Trace Element Ratios in Global OIBs Used to Construct the Nonchondritic BSE Mantle Source for high 3He/4He lavasa
Mean (All MgO)
±1σ (Standard Deviation, %)
Mean (MgO > 10 wt%)
±1σ (Standard Deviation, %)
WH83 = Hofmann and White , A09= Arevalo et al. , H05 = Hofmann , G13 = Gale et al. . Unless indicated otherwise, all canonical ratios are calculated using OIB data compiled in Willbold and Stracke . Average values are provided for the entire OIB data set from Willbold and Stracke  and for the subset of samples that have >10 wt% MgO (to ensure that extensive crystal fractionation does not modify the trace element ratios). The subset of trace element data from OIBs with MgO > 10 wt% are used in Table 3. Two estimates for K/U from Arevalo et al.  are given, one for OIB and the other for MORB. The elements used to bracket the calculated elemental anomalies (Ti/Ti*, Y/Y*, Zr/Zr*, Eu/Eu*) are provided in parenthesis.
This is an average of samples from 269 ridge segments; thousands of samples were used to calculate the ridge-segment mean values.
 However, the fit in Figure 3 provides no constraints on the shape of the REE spidergram for the elements more incompatible than Nd: La, Ce and Pr. In order to estimate this part of the spidergram we first identify terrestrial peridotite samples with Sm/Nd (0.344) and Lu/Nd (0.0634) ratios, ratios of the three REEs determined using isotopic constraints, that approach the ratios calculated for nonchondritic BSE calculated in Table 3. Next, we compare the normalized median REE values from this subset of peridotite samples with the polynomial fit through Sm, Nd and Lu to evaluate whether the La, Ce, and Pr in our model spidergram are qualitatively similar for these elements in peridotites.
Table 3. Trace Element Composition of the Nonchondritic BSE, Which Also Represents the High 3He/4He Mantle Compositiona
Chondritic Earth [MS95] (ppm)
DMM [WH05] (ppm)
DMM [SS04] (ppm)
DMM [BC06] (ppm)
High 3He/4He Mantle Average (This Study) (ppm)
High 3He/4He Mantle Upper Limit (This Study) (ppm)
High 3He/4He Mantle Lower Limit (This Study) (ppm)
The upper and lower limits on the nonchondritic BSE (high 3He/4He mantle) composition are calculated by taking into account two separate sources of uncertainty: (1) The uncertainty on the Lu concentration, which anchors the nonchondritic BSE spidergram, is ±5.5%, and this uncertainty is propagated through the entire spidergram, (2) The range in isotopic compositions for the nonchondritic BSE (given in Table 1) give rise to a range in parent-daughter ratios (the upper limit uses the “enriched” nonchondritic BSE values from Table 1, and the lower limit uses the “depleted” nonchondritic BSE values). Note that the canonical ratios from Table 2 are not varied when calculating the upper and lower compositional limits. The K and Ti concentrations are calculated independently of the concentrations shown in Table 4.
 We select the subset of peridotites from the MS95 database that have Sm/Nd (0.344 ± 0.034) and Lu/Nd (0.0634 ± 0.0190) ratios most similar to the values for nonchondritic BSE (Table 3). A larger or smaller range of Sm/Nd and Lu/Nd values could be permitted, but the selected range provides a reasonable number (n = 20) of peridotites. From this set of 20 peridotites, we exclude peridotites enriched in incompatible elements by metasomatic processes. Peridotites with (La/Yb)N > 2 [Lyubetskaya and Korenaga, 2007] or peridotite with high La/Ce [(La/Ce)Nz = 1.25] (where N signifies normalization to the chondrite-based BSE composition from MS95) are removed, leaving 18 peridotites for consideration. There are only seven REEs that have been analyzed in all 18 peridotites. The shape of the REE spidergram formed by the median normalized concentrations of the seven REEs in the 18 peridotites is in good agreement with the relative abundances of Sm, Nd and Lu for the nonchondritic BSE REE spidergram in Figure 3 (the absolute abundances are different, but the relative abundances are similar). Critically, the relative normalized abundances of the three REEs extrapolated from the polynomial, La and Ce, also agree with the relative normalized median values for La and Ce obtained from the peridotites. Therefore, we apply the polynomial fit through Sm, Nd, and Lu to extrapolate the compositions of the other 11 naturally occurring REE's, including La, Ce and Pr, to obtain a plausible REE spidergram for the nonchondritic BSE (Figure 3). The averaged peridotite spidergram is shown only to demonstrate that the REE pattern for the high 3He/4He mantle composition is not an impossible pattern in terrestrial rocks, and we emphasize that our new BSE composition does not rely on peridotite compositions.
 During melting or solidification Y is partitioned into the melt phase in approximately the same way as most heavy REEs. To estimate the relative abundance of Y, we then assume that it has a normalized abundance intermediate between Ho and Er. We use the OIB database of Willbold and Stracke  to calculate the average Y-anomaly, or Y/Y* [where Y/Y* = YN/√(HoN·ErN)] for the least evolved lavas and obtain a mean Y/Y* value of 1.03 (Table 2) (Figure 2).
 We use a similar method to incorporate Zr and Ti into the nonchondritic BSE spidergram. Zr/Zr* [Zr/Zr* = YN/√(SmN·NdN)] is 0.90 in the OIB database (Table 2). We place Zr between Sm and Nd so that Zr in the spidergram has a Zr/Zr* value of 0.90 (Figure 2). The relative abundance of Ti in the nonchondritic BSE spidergram is given by Ti/Ti* [where Ti/Ti* = TiN/√(GdN·EuN)], which is 1.06 in the OIB database (Figure 2 and Table 2). By excluding lavas with MgO < 10 wt%, we avoid effects related to Eu fractionation in the filtered data set (Table 2).
2.4. Filling in the Backbone of the Nonchondritic BSE: The Highly Incompatible Elements—U, Th, K, Ba, Nb—and Pb
 The most highly incompatible elements, the elements with compatibilities between Rb and La, and Pb (which has a compatibility between Ce and Nd) [Hofmann, 2003], still remain to be incorporated into the nonchondritic BSE spidergram. These elements are integrated into the spidergram using canonical (Ba/Rb, Nb/U, K/U, La/Th, Ba/Th) and isotopically constrained (Th/U, U/Pb) ratios.
 We suggest two similar approaches for estimating the abundances of U, Th, K, Pb, Ba, Nb and Pb in the nonchondritic BSE spidergram. The first integrates these elements into the spidergram sequentially from “left to right,” starting with Rb, which is already included in the backbone of the spidergram in section 'Constructing the “Backbone” of the High 3He/4He Mantle Spidergram: Toward a Composition of a Nonchondritic BSE', and continuing to the less incompatible trace elements. Using the canonical Ba/Rb ratio in OIBs (13.4; Table 2), Ba is added to the right of Rb on the spidergram. Ba/Th is approximately constant in oceanic lavas [e.g., Willbold and Stracke, 2006], with a value of 80.2 (Table 2), and this ratio permits insertion of Th to the right of Ba on the spidergram (Figure 2).
 We then calculate the relative abundance of U by pairing Th with the estimated Th/U ratio (3.9) of the nonchondritic BSE (Figure 2), which is required to generate the Pb-isotopic composition of much of the global OIB array, including high 3He/4He lavas, on a 4.50 Ga geochron [Jackson et al., 2010].
 We estimate the U/Pb ratio from isotopic constraints, and combine this ratio with our estimate for the relative abundance of U to insert Pb into the nonchondritic BSE spidergram. We select a 238U/204Pb (µ = 8.5) ratio that places the nonchondritic BSE on a 4.5 Ga geochron where it intersects the OIB array in 207Pb/204Pb versus 206Pb/204Pb isotopic space. The U/Pb ratio (∼0.136; Figure 2) is the same as used by MS95. Although often considered to be a canonical ratio, we do not use the Ce/Pb ratio is OIBs to constrain the relative Pb abundance in the nonchondritic BSE. The Ce/Pb ratio in the spidergram (∼12; Table 3) is approximately half the canonical ratio in OIBs (∼25) [Hofmann et al., 1986]. Because it is chalcophile, Pb can be strongly influenced by the presence of sulfides in the mantle source, and as a result the Ce/Pb ratio of the mantle source of high 3He/4He OIBs (here argued to be ∼12) may differ from the melt (∼25) [Hart and Gaetani, 2006].
 In addition to Pb, two other elements, K and Nb, are anchored to U in the spidergram (Figure 2). To constrain the relative abundance of Nb we use the canonical Nb/U ratio observed in OIBs, which is about 46.8–50.8 (Table 2), and is similar to Hofmann's  value of 52 for “nonenriched mantle-type” samples. These Nb/U ratios generate a positive Nb anomaly in the nonchondritic BSE spidergram, which is consistent with earlier observations of “nonenriched mantle-type” OIBs in general and Nb-enrichment in high 3He/4He OIBs in particular [Jackson et al., 2008].
 The canonical K/U ratio is used to incorporate K by anchoring its value to U (Figure 2). The K/U ratio is relatively constant in oceanic lavas [e.g., Wasserburg et al., 1964; Arevalo et al., 2009] and continental crust [Jochum et al., 1983; Palme and O'Neil, 2003; Lyubetskaya and Korenaga, 2007], and this ratio therefore reflects the composition of BSE. We adopt the most recent K/U estimate (11,900) for OIBs [Arevalo et al., 2009], which is somewhat higher than the average OIB K/U value of 10,322 from Willbold and Stracke  (Table 2). However, there appears to be variability in the oceanic mantle, as suggested by the K/U ratio of 19,000 proposed for the MORB mantle [Arevalo et al., 2009]. We note that the value of 19,000 is significantly higher than a recent estimate for the K/U of the MORB mantle of 13,207 [Gale et al., 2013], and we adopt the lower K/U ratio for MORB, which is based on a much larger data set, as the upper limit for the K/U of the oceanic mantle. The lower limit is given by the K/U ratio (10,322) from the Willbold and Stracke  data set (Table 2). As a check for the internal consistency of the K/U ratio in the spidergram, we note that the K/U ratio of 11,900 results in a K/La ratio for the nonchondritic BSE of 357 (Table 3), which is within the range of accepted values for the canonical K/La ratio (330 ± 30) in oceanic lavas that is though to reflect the mantle source ratio [O'Neill and Palme, 1998; Palme and O'Neil, 2003; Lyubetskaya and Korenaga, 2007].
 It is difficult to assess the uncertainty associated with the relative abundances of the most incompabile elements in the nonchondritic BSE spidergram (see section 'Estimating Uncertainty in the Nonchondritic BSE Composition'). However, the internal consistency of our method can be examined by employing a different trace element ratio to construct this portion of the spidergram (Figure 2). Having integrated the most incompatible elements from “left to right,” we suggest a second, complementary method that integrates the most incompatible elements from “right to left” and utilizes a different ratio, La/Th, that is relatively constant in OIBs (La/Th = 8.4 ± 1.2, 1σ standard deviation of the mean; Table 2) and thought to reflect the ratio in the OIB mantle [Willbold and Stracke, 2006]. The La/Th ratio bridges the section of the spidergram from the light REEs to Th. The Ba/Th ratio (80.2) provides the relative abundance of Ba. Rb is already included in the backbone of the spidergram (section 'Constructing the “Backbone” of the High 3He/4He Mantle Spidergram: Toward a Composition of a Nonchondritic BSE'), and a Ba/Rb ratio does not need to be estimated to incorporate Rb. Instead, the Ba/Rb ratio that results from this alternative “right to left” method (13.6) can be used to evaluate the internal consistency of our overall approach for estimating the abundances of the most incompatible elements from “right to left,” and is similar to the average OIB Ba/Rb ratio of 13.4 in Table 2. The remaining highly incompatible elements are integrated into the nonchondritic BSE spidergram using the same ratios and assumptions as above: U (from Th/U), Pb (U/Pb), Nb (Nb/U), and K (K/U). The resulting K/La value for the nonchondritic BSE (363) is similar to the range of accepted K/La values (330 ± 30) in oceanic lavas. This right-to-left spidergram construction yields a pattern that is quite similar to the spidergram architecture generated by construction from left-to-right (Figure 2, Panel E).
2.5. Anchoring the Nonchondritic BSE Spidergram to Lutetium (Lu)
 Lu is incompatible during melting. Therefore, if the nonchondritic BSE acquired its super-chondritic Sm/Nd ratio and incompatible element depletion by extraction of early enriched crust from an originally chondrite-based BSE similar to MS95, then the abundance of Lu in a nonchondritic BSE must be lower than its abundance in chondrite-based estimates for BSE. On the other hand, DMM has experienced greater melt depletion than the nonchondritic BSE, as evidenced by the combination of higher Sm/Nd ratios and 143Nd/144Nd ratios in DMM (Table 1). Therefore, the nonchondritic BSE must have higher Lu abundances than DMM. For the nonchondritic BSE, we adopt a Lu concentration of 0.064 ppm (Table 3), which is the average of Lu concentration estimates for the chondrite-based BSE composition from MS95 and estimates of DMM (using an average of the Lu concentrations from Workman and Hart  and Salters and Stracke ). In this way, the Lu concentration of the nonchondritic BSE is tightly bracketed, and is within 5.5% of the Lu concentrations of the upper bound (i.e., the chondrite-based BSE) or the lower bound (DMM).
 We note that, in contrast to our approach of anchoring the new BSE composition to Lu, O'Neill and Palme  anchor their nonchondritic BSE composition to a K abundance that provides a possible solution to the missing Ar paradox. Their approach results in highly incompatible elements being ∼50% lower than MS95 values, while our approach yields values that are only ∼30% lower. We consider the estimate for K concentration in a nonchondritic BSE to be more fraught with error than the estimate for Lu, and we argue that Lu offers a more robust anchor for the trace element concentrations of a nonchondritic BSE.
2.6. Bracketing the Major Element Composition of a Nonchondritic BSE
 In the same way that the Lu concentration of a nonchondritic BSE should not be lower than the Lu concentration in DMM, or higher than the Lu concentration in a chondrite-based BSE composition, the major element composition of the nonchondritic BSE must also be bracketed by DMM and a chondrite-based BSE. Compatible elements, such as Mg, will have lower concentrations in nonchondritic BSE than in DMM, but higher concentrations than in a chondrite-base BSE. Incompatible elements, such as K, will have higher concentrations in the nonchondritic BSE than in DMM, but lower concentration than in a chondrite-based BSE. For most of the major elements, there is little variability between estimates for the major element composition of DMM and chondrite-based estimates for BSE. This owes to the fact that relatively little melt (from 1.5–2% [Salters and Stracke, 2004] to 2–3% [Workman and Hart, 2005]) is extracted from a chondrite-based BSE to generate DMM. (Even less melt would be extracted from a chondrite-based BSE to generate the nonchondritic BSE). Such a small amount of melt extraction has only a minor affect on the abundances of most major elements (which are either compatible or slightly incompatible) in the residual peridotite, excluding K, which is highly incompatible. Therefore, a simple average of the major element abundances in DMM and BSE is sufficient to bracket the major element abundances of the nonchondritic Earth, particularly for the compatible or moderately incompatible elements, where the difference in the abundance of an element between DMM and BSE is generally small (Table 4). For example, the SiO2 concentration of the chondrite-based BSE is 45.0 wt% and the average concentration of SiO2 in DMM is 44.8 wt% (Table 4) are quite similar, so the SiO2 abundance of the nonchondritic BSE is tightly bracketed at 44.9 ± 0.1%. The goal of this study is to provide a first-order estimate that brackets the major element composition of the nonchondritic BSE, and future work may permit a more precise estimate.
Table 4. Bracketing the Major Element Composition of a Nonchondritic BSE, Which Represents the High 3He/4He Mantlea
Chondritic Earth [MS95] (wt%)
DMM [WH05] (wt%)
DMM [SS04] (wt%)
Nonchondritic BSE High 3He/4He Mantle (This study) (wt%)
Bracketing Range (wt%)
The concentration of a major element in the nonchondritic BSE is estimated to lie between the average concentration of a given element in chondrite-based compositional estimates for BSE [e.g., McDonough and Sun, 1995] and DMM (where DMM is the average of the compositions from Workman and Hart  and Salters and Stracke ). See section 'Bracketing the Major Element Composition of a Nonchondritic BSE' of the text for explanation. For a given element, the average concentration of the chondrite-based BSE and DMM concentratios is taken to be the concentration for the nonchondritic BSE. The uncertainty on a given elemental concentration is simply the absolute difference between the concentration in the nonchondritic BSE and the two bracketing reservoirs, DMM and the chondrite-based BSE. Workman and Hart  provided two estimates for the Na2O concentratio in DMM. The estimate that more closely matches the Na2O concentraion in Salters and Stracke  is shown in parenthesis. Concentrations of Ti and K in this table are 1000 ± 200 and 150 ± 90 ppm, respectively. The Ti and K values shown in this table (using methods outlined in section 'Bracketing the Major Element Composition of a Nonchondritic BSE' of the text) are calculated independently of the values shown in Table 3 (which uses methods outlined in sections 'Calculating the 147Sm-143Nd, 176Lu-176Hf, and 87Rb-87Sr of the high 3He/4He mantle' through 'Anchoring the Nonchondritic BSE Spidergram to Lutetium (Lu)' of the text). Within uncertainty, the two estimates for Ti and K in the nonchondritic BSE agree. Mg# = molar ratio of MgO/(MgO + FeO) * 100.
 Major (Table 4) and trace (Table 3) element concentrations in the nonchondritic BSE are calculated using independent methods. As a check for internal consistency between the independently calculated major and trace elements, we employ a known relationship between CaO (wt.%) and Lu (ppm) concentrations in peridotites, where Lu = 0.0172 × CaO + 0.0032 [Salters and Stracke, 2004]. Using the Lu concentration in the nonchondritic BSE of 0.064 ppm (section 'Anchoring the Nonchondritic BSE Spidergram to Lutetium (Lu)' and Table 3), the calculated CaO abundance in is 3.53 wt%, which lies within the uncertainty of the nonchondritic BSE CaO abundance (3.44 ± 0.11 wt%) in Table 4. Additionally, we present independently determined estimates for K and Ti for the nonchondritic BSE in Table 3 (166 and 1118 ppm, respectively) and Table 4 (150 ± 90 and 1000 ± 200 ppm, respectively). We note that, within uncertainties, the two independent estimates for the K and Ti abundances are in agreement. We consider the estimate for K and Ti in Table 3 to be more robust, as the estimate in Table 4 is based on simple bracketing arguments, but we emphasize that all estimates for the K abundance in the Earth are highly uncertain. Nonetheless, these observations demonstrate broad internal consistency between our independent methods for estimating for major and trace element abundances in the nonchondritic BSE.
3. Estimating Uncertainty in the Nonchondritic BSE Composition
Salters and Stracke  constructed a trace element source for DMM using a similar approach of “cascading” elemental ratios that we use to calculate the nonchondritic BSE, and they discussed the difficulties associated with estimating uncertainties for each of the elements. They noted that, owing to the use of canonical and isotopically constrained ratios to construct a mantle source, the concentrations of each trace element is linked to the abundances of other elements, and so must be the uncertainties. For example, the Sm abundance is linked to the estimated Lu abundance through a canonical ratio (Sm/Hf) and an isotopically constrained ratio (Lu/Hf). The Sm/Hf ratio has a 1σ deviation of 20% (Table 2). In addition to being dependent on uncertainties associated with the Sm/Hf ratio, the possible range of concentrations for Sm in the nonchondritic BSE is also tied to the uncertainty in Lu/Hf (±2.6%), and to the uncertainty in Lu (±5.5%). To estimate the uncertainties in the concentrations of Sm, or any other trace element, the uncertainties that accumulate with each canonical or isotopically constrained ratio “upstream” of Sm must be added.
Salters and Stracke  did not propagate uncertainties in their DMM estimate. Instead, they provided a mantle source estimate that they considered to be “most reasonable” that is based on mean trace element ratios and follows a clear set of criteria that can be tested. They provided a Microsoft Excel™ worksheet that provides full access to the relationships used to calculate the elemental concentrations. Following this precedent, we also provide a Microsoft Excel worksheet (Table S1, supporting information)1 that allows the reader to follow our calculations in a step-by-step manner. With this spreadsheet, the reader can evaluate the sensitivity of the nonchondritic BSE to different trace element ratios and evaluate how changing a particular ratio will impact the concentrations of other “dependent” elements downstream.
4. Melting the Nonchondritic BSE Composition to Make High 3He/4He Lavas
Jackson et al.  suggested that the highest 3He/4He lavas erupted globally (up to 50 Ra, ratio to atmospheric), from the Baffin Island flood basalt [Stuart et al., 2003; Starkey et al., 2009], are melts of an early-formed depleted mantle reservoir with high 3He/4He, which we argue represents the lithophile element composition of a nonchondritic BSE. We explore whether melts of the nonchondritic BSE calculated here (Table 3) can yield trace element patterns that resemble the highest 3He/4He lavas from Baffin Island. We select the highest 3He/4He lava (DUR8 from Starkey et al., 2009) from Baffin Island and correct the trace element abundances for olivine fractionation by adding equilibrium olivine until the lava is in equilibrium with Fo90 olivine (see method in Jackson et al. ). This generates an estimate of the trace element composition of the primary melt in equilibrium with the Baffin Island mantle, with the exception of K and Rb, which have been mobilized during weathering [Jackson et al., 2010].
 We compare the primary melt trace element composition of DUR8 to two different trace element compositions calculated using simple melting models of the nonchondritic BSE (Table 3). The two calculated melts were generated using two nonmodal aggregated fractional melting models that have different trace element partition coefficients and mineral and melt modes. The melt models are outlined in Jackson et al.  (which refers to melt models 1 and 2). Both melting models generate trace element patterns that are similar to the highest 3He/4He Baffin Island lava when the degree of melting is ∼14% (the two melt models require somewhat different contribution from melt in the garnet and spinel stability fields; see Figure 5). This is within the range of melting previously suggested for lavas associate with this large igneous province [Herzberg and Gazel, 2009].
 Of note is that Rb and K exhibit higher concentrations in the melt models than the olivine fractionation-corrected DUR8 lava, and we attribute this difference to alkali loss from weathering of DUR8 [Jackson et al., 2010]. In summary, simple melt models of the nonchondritic BSE calculated here broadly reproduce the trace element patterns observed in the highest 3He/4He Baffin Island lava.
5. Geodynamic Implications for a Nonchondritic BSE
5.1. A Solution to the Earth's “Missing Ar”
40Ar is the radiogenic decay product of 40K (T1/2 = 1.3 Ga). The existing 40Ar in the atmosphere and solid Earth is almost entirely a result of 40K decay, and therefore Earth's 40Ar is directly related to the Earth's K abundance. However, the absolute abundance of K is unknown because K is a volatile element that was partly lost from the Earth during accretion (e.g., MS95). Therefore, to constrain the 40Ar budget of the Earth, we must first reliably estimate the K abundance of the Earth.
 One way to constrain K is to assume a chondritic U abundance (∼20 ppb) and then calculate the K abundance by using the global K/U ratio (∼104) measured in oceanic basalts (MS95), which is thought to broadly reflect the primitive ratio in the Earth [e.g., Jochum et al., 1983; Allègre et al., 1996]. Depending on the preferred U concentration and K/U ratio, this approach yields a primitive K abundance in the range 230–270 ppm [Jochum et al., 1983; MS95; Allègre et al., 1996]. The decay of 40K will, in turn, generate 13–15·1016 kg of 40Ar over 4.5 Ga, which is partitioned among Earth's atmosphere, crust, and mantle. The atmosphere has currently 6.6·1016 kg 40Ar [Turekian, 1959], or about one half the mass expected from a chondrite-based BSE. The continental crust and depleted mantle are unlikely to host more than a small fraction of the other half [Allègre et al., 1996]. Thus, about one half of the expected 40Ar is “missing,” a feature which defines the so-called “missing” Ar paradox [e.g., Allègre et al., 1996].
 Assuming a chondrite-based composition for the BSE, one common solution to the missing Ar paradox is to postulate the existence of a “hidden” gas-rich reservoir in the deep mantle that contains the terrestrial Ar not accounted for in shallow geochemical reservoirs. Other solutions for the missing Ar paradox include significant concentrations of Ar and K in the core [Chabot and Drake, 1999; Lodders, 1995; Gessmann and Wood, 2002], or a lower K/U ratio for BSE [Albarède, 1998; Davies, 1999], possibly as a result of a deep slab reservoir with low K/U [Lassiter, 2004], although this idea is contentious [Arevalo et al., 2009].
 Our nonchondritic BSE composition provides, however, a potentially straightforward way out of this apparent paradox: Earth simply has ∼30% less U and K than a typical chondritic model. To test this simple solution we first evaluate the 40Ar budgets of the atmosphere, continental crust and depleted mantle and obtain a lower bound for K in the Earth. (Any “missing” Ar reservoirs in the Earth would increase the total Ar and raise the minimum K in the Earth.) We compare this estimate for the lower bound for K in the Earth to the range of K concentrations suggested for a nonchondritic BSE composition shown in Table 3. If the two estimates for the K agree, then a hidden missing 40Ar reservoir is not required in the Earth. While a missing “hidden” 40Ar reservoir cannot be excluded, it is important to evaluate whether a missing reservoir is needed.
5.1.1. 40Ar in Continental Crust
 The amount of 40Ar in the continental crust is a function of its average K abundance, average age, and degassing rate overtime [Allègre et al., 1996]. Recent estimates for the 40Ar budgets in continental crust range from 0.1–0.9·1016 [Lyubetskaya and Korenaga, 2007] to 0.5–1.0·1016 kg 40Ar [Allègre et al., 1996] and to <0.87·1016 kg 40Ar [Lassiter, 2004]. We take 0.1·1016 kg to be the lower limit of 40Ar in the continental crust, and 1.0·1016 kg 40Ar to be the upper limit. While this range is large, it is clear that continental crust is not a significant reservoir for 40Ar [e.g., Allègre et al., 1996].
5.1.2. 40Ar in DMM
 The 40Ar content of DMM can be estimated using two independent methods: The flux of 40Ar from ridges, and the K content of DMM [e.g., Allègre et al., 1996]. The 40Ar flux at ridges can be constrained using ridge 3He flux. The 3He flux measured at ridges is ∼1.1·103 mol/yr [Craig et al., 1975; Farley et al., 1995]. When combined with the median MORB 3He/4He ratio (8.2 Ra) [Graham, 2002] and the 4He/40Ar ratios measured in MORB glasses (1–100) [e.g., Honda and Patterson, 1999], the 40Ar flux from ridges is constrained to be 0.039–3.9·106 kg 40Ar/yr. Assuming an oceanic crust production rate of 20 km3/yr (∼5.2·1013 kg/yr) [Lassiter, 2004], and 10% melting and complete extraction for Ar from the mantle during melting, the depleted mantle hosts 0.028–2.8·1016 kg 40Ar (assuming a depleted mantle mass of 4.0·1024 kg).
 This estimate for 40Ar in DMM has very large uncertainties owing to the variability in 4He/40Ar ratios in MORB glasses [Allègre et al., 1996; Lassiter, 2004; Lyubetskaya and Korenaga, 2007]. However, Lassiter  argues that high 4He/40Ar ratios may not accurately reflect the true ratio of the MORB mantle. This is because Ar is less soluble in melt than He, and is likely to be preferentially degassed relative to He during melting, transport and eruption. The negative correlation between 4He/40Ar and 40Ar concentrations in MORB glasses is consistent with this hypothesis [Sarda and Moreira, 2001; Lassiter, 2004; Gonnermann and Mukhopadhyay, 2007]. Therefore, the high 4He/40Ar ratios measured in degassed glasses represent an upper limit for the mantle ratio. However, the relative abundances of the noble gasses in the “popping rock” (4He/40Ar of ∼1.5) [Moreira et al., 1998] are thought to be similar to the undegassed 4He/40Ar ratio of MORB, and therefore reflect the depleted mantle ratio. Consistent with this hypothesis, the 4He/40Ar ratio of popping rock is bracketed by the production ratio of 4He/40Ar in DMM (1.5–2.7, assuming K/U from 8000 to 13,000 and Th/U of 2.5 to 4) [see Lassiter, 2004]. In summary, the lower limit for the DMM 4He/40Ar ratio, measured on popping rock with a 4He/40Ar ratio of 1.5, yields a 40Ar flux of 2.6·106 kg/yr from the ridge. This yields our preferred abundance of 40Ar in DMM (∼2.0·1016 kg) derived from the 40Ar ridge flux.
 Estimates using the K abundance of DMM provide higher DMM 40Ar abundances. The abundance of K in DMM has been estimated to be 49.8 ppm [Workman and Hart, 2005], 60 ppm [Salters and Stracke, 2004], and 68.4 ppm [Boyet and Carlson, 2006]. The lowest DMM K abundance (49.8 ppm) [Workman and Hart, 2005] generates a 40Ar budget of 2.8·1016 kg over 4.5 Ga, and the highest DMM K abundance (68.4 ppm) [Boyet and Carlson, 2006] yields 3.9·1016 kg 40Ar. The Boyet and Carlson  DMM estimate is also the only one calculated for a nonchondritic Earth. In summary, we consider the 40Ar abundance in DMM to lie between the 2.0·1016 kg, the preferred value obtained from the 40Ar ridge flux, and 3.9·1016 kg, the highest 40Ar value obtained from recent estimates of K in DMM from Boyet and Carlson, .
5.1.3. Total 40Ar Budget: Atmosphere, Crust, and Mantle
 Together, the atmosphere (6.6·1016 kg 40Ar), continental crust (0.1–1.0·1016 kg 40Ar) and depleted mantle (2.0–3.9·1016 kg 40Ar) comprise a minimum 40Ar budget for the Earth that ranges from 8.7 to 11.5·1016 kg. If we assume all of the 40Ar was generated by 40K decay over 4.5 Ga, and that little 40Ar was lost from the silicate Earth and atmosphere during this time, the BSE K concentration is estimated to be approximately 155–205 ppm. This range of K abundances estimated from the 40Ar in the atmosphere, crust and mantle overlaps with the range of values for K suggested here for a nonchondritic BSE (Table 3): When paired with a K/U ratio of 11,900, the low U concentration of a nonchondritic BSE (0.011 to 0.017 ppm, Table 3) generates a range of possible BSE K concentrations from 130 to 200 ppm (Table 3). The range of K abundances calculated from the 40Ar budget of the Earth (155–205 ppm) overlap with the range of K abundances that we estimate for a nonchondric BSE (Table 3). In summary, if BSE has a composition like the nonchondritic BSE we propose, a missing 40Ar reservoir is not required to reconcile Earth's Ar mass balance.
5.2. Continental Crust Extraction From a Nonchondritic BSE
 A basic test of our nonchondritic BSE model is that its trace element budget must permit extraction of the current volume of continental crust (Figure 6). However, our model for BSE is incompatible-element-depleted compared to the chondrite-based model for BSE. Therefore, a much larger fraction of a nonchondritic BSE must be depleted to generate continental crust. This idea is not new. In their model of a BSE that is incompatible-element-depleted relative to the chondrite-based model, Carlson and Boyet  find that between 74% (using the Taylor and McLennan  continental crust) and 96% (using the Rudnick and Gao  crust) of the mantle would have to be depleted to generate the continents. Clearly, a two-layered mantle divided at 660 km, with an upper layer composed of DMM and a lower layer composed of largely primitive material [e.g., Jacobsen and Wasserburg, 1979], is impossible if the BSE is depleted relative to the chondrite-based model. Instead, DMM must represent most of the mantle mass [Boyet and Carlson, 2006; Carlson and Boyet, 2008].
 If BSE has the composition proposed in Table 3, we arrive at a similar conclusion (Figure 6). Here we estimate the mass fraction of a nonchondritic BSE that has to be depleted to generate the continents. We extract continental crustal (CC) from the nonchondritic BSE, leaving behind DMM. The mass of the mantle composed of DMM can be estimated from mass conservation [Carlson and Boyet, 2008]:
where [X] is the concentration of element X in the nonchondritic BSE, DMM, or CC, and M is the mass of the reservoir. MCC is 0.555% of BSE's mass [Galer et al., 1989], [X]CC is from Rudnick and Gao , and [X]Nonchondritic BSE is from Table 3. MDMM is varied until [X]DMM = 0, which sets the minimum mass of the mantle that must be depleted to generate the continents. Rb exhibits the greatest relative difference in concentration between continental crust and DMM and plays the limiting role when determining the minimum mass of mantle that must be depleted to generate the continents. If MDMM is less than 83% of the mass of the nonchondritic BSE, there is insufficient Rb to match the Rb in the continents. Therefore, at least 83% of a nonchondritic BSE must participate in continental crust extraction, and the entire mantle provides an upper limit for the mass of mantle that can be depleted to generate the continents.
 Using 83% of BSE as the minimum mass of DMM, equation (1) is solved to determine [X]DMM for a standard suite of incompatible trace elements. A spidergram for the composition of DMM after continental crust extraction from 83% of a nonchondritic BSE is shown in Figure 6 (open triangles). A spidergram for the composition of DMM after continental crust extraction from 99.455% of the mantle is also shown (Figure 6, open diamonds). These two spidergrams for DMM are generally more enriched than published estimates DMM, particularly for Nb (Figure 6). One explanation for this may be that the nonchondritic BSE is composed of three reservoirs, not two, including CC, DMM, and a reservoir composed of subducted slab material. Therefore, after extracting continental crust [from Rudnick and Gao, 2003] from the nonchondritic BSE, the composition of the mantle that remains is not composed of just DMM, as is often assumed [e.g., Carlson and Boyet, 2008], but instead must be composed of a combination of DMM and a subducted slab component. Thus, the overall enrichment in the calculated spidergrams (Figure 6, open diamonds and triangles), in particular Nb, relative to published estimates of DMM can be attributed to the presence of a subducted component that, together with DMM, resides in the residual mantle following continental crust extraction. If so, the calculated spidergrams in Figure 6 represent a combination of DMM and subducted slab material. It is not possible to deconvolve the relative contributions of the DMM component from the subducted slab component in the calculated spidergrams in Figure 6, as the mass of subducted material in the mantle is unknown. These mass balance arguments are also considered by Caro and Bourdon .
 We note that the excess Nb in the calculated spidergrams might be attributed to a subducted slab component, as subducted slabs may comprise a Nb-rich reservoir in the mantle [e.g., McDonough, 1991; Rudnick et al., 2000; Kamber and Collerson, 2000]. Alternatively, Nb may be concentrated in the core such that it does not contribute to BSE [Wade and Wood, 2001]. In this case, the Nb/U ratio of the nonchondritic BSE is lowered to a value (∼20) that removes much of the excess Nb in the mantle that remains following continental crust extraction (Figure 6). Such a low BSE Nb/U ratio is lower than the value of 47–51 suggested from the OIB database in Table 2, and lower than the lowest Nb/U ratio measured (47.6) on fresh Baffin Island glasses [Starkey et al., 2009]. Such a low ratio is untenable if Baffin Island lavas represent melts of a nonchondritic BSE reservoir, and we consider a low Nb/U ratios of 20 for BSE to be unlikely. Balancing the Earth's Nb budget is an old and persistent problem that also afflicts the chondritic-based model for BSE of MS95, and we introduce no new explanations for this Nb problem.
 We note that Huang et al.  argue that the 143Nd/144Nd isotope systematics of continental crust and DMM do not permit extraction from the nonchondritic BSE presented here (Table 1). However, we suggest that the uncertainties in their model are to too great to support their conclusions. The standard [Jacobsen and Wasserburg, 1980a; Huang et al., 2013] model that assumes continental crust derives only from the upper mantle predicts modern day ε143Nd values for average DMM that are about 2 to 5 ε-units lower than predicted by the nonchondritic Earth models where the DMM constitutes >70% of the mantle. However, we note that average continental crust, at the same mean age, also has an ε143Nd about 3 ε-units higher if generated from a nonchondritic BSE because of the higher ε143Nd at any given time in the nonchondritic BSE compared to the chondritic BSE undergoing continent extraction [see Jackson and Carlson, 2012, Figure 2]. The Taylor and McLennan  and Rudnick and Gao  average CC compositions differ in ε143Nd by 4 ε-units at the same mean age of 2 Ga. Thus, the uncertainty in average continental composition does not allow us to resolve which model, continental extraction from a chondritic BSE or a nonchondritic BSE, better approximates the evolution of the crust-mantle system.
 The 143Nd/144Nd evolution of DMM can also be used to constrain the evolution of the crust-mantle system. If one assumes a mean continental crust age of 2 Ga [Huang et al., 2013] and the crust is extracted from a mantle that starts with a chondritic Sm/Nd ratio that constitutes a volume equal to just the upper mantle, the present-day DMM will have an ε143Nd between +4.6 [Taylor and McLennan, 1985] and +7.5 [Rudnick and Gao, 2003]. The same approach starting from the nonchondritic BSE results in DMM ε143Nd near +9, assuming either the Taylor and McLennan  average continent composition and that DMM is 74% of the mantle, or using Rudnick and Gao  average continental crust and a DMM volume of 94% of the mantle [Carlson and Boyet, 2008]. Increasing the DMM volume to 90% using the Taylor and McLennan  crustal composition decreases the predicted DMM ε143Nd only by half an epsilon unit. Previous estimates [e.g., Salters and Stracke, 2004] of the average ε143Nd of DMM ranged to values even higher (>+9) than those predicted by the nonchondritic BSE model. However, Gale et al.  suggested that average DMM has an ε143Nd of only +8.7–8.9, a value between those predicted for DMM from a chondritic or nonchondritic starting mantle. We note that the Gale et al.  estimate includes all MORB isotope compositions, including enriched (E) MORB, in the DMM average, which includes MORB sampling recycled continental crust (which should not be included in the average DMM composition) and MORB sampling recycled oceanic crust. Recycled oceanic crust will have enriched (lower) 143Nd/144Nd than the average DMM peridotite and will also tend to contribute disproportionately more melt than the less-fertile DMM peridotite under the same melting conditions. Thus, including E-MORB sampling recycled oceanic crust will bias MORB averages to lower 143Nd/144Nd than the average upper mantle. For these reasons, we conclude that the average Nd-isotopic compositions of the DMM reservoir is not known precisely enough to exclude either the chondritic BSE or the nonchondritic BSE evolution models.
5.3. Consequences of a Nonchondritic BSE for Earth's Thermal History
 Our nonchondritic BSE model has ∼30% less K, Th, and U than the chondrite-based model for BSE of MS95 and, thus, predicts a smaller contribution from radiogenic heating to Earth's thermal history. Indeed, assuming that mantle stirring by plate tectonics carries 39 TW of cooling (i.e., global cooling less cooling of the continents) through the ocean basins [Jaupart et al., 2007], the present day ratio of radiogenic heating to this cooling, the convective Urey number (Ur), is ∼0.17, which is close to half of the preferred value of 0.33 found from a recent and exhaustive review of Earth's present-day heat budget assuming a chondritic Earth [Jaupart et al., 2007] (the full range is 0.21–0.49). It is well known that the relatively large convective heat flux implied by such a low Ur can be anathema to parameterized mantle thermal history models [Korenaga, 2008a]. For example, backward integrating classical scaling laws in which the surface heat flux carried by plate tectonics increases with internal mantle temperature will cause a “thermal catastrophe” in the form of global mantle melting within ∼1–2 Gyr [Christensen, 1985]. Clearly, the Earth did not undergo such an event and thus our non-chondritic BSE compositional model places new demands, as well as constraints, on the mechanics and heat transfer properties of mantle convection.
 Thermal catastrophes are predicted where the current “mobile lid” mode of mantle convection is assumed to be a characteristic feature of the full extent of Earth history, which is almost assuredly not the case [e.g., Grigné et al., 2005; Jaupart et al., 2007; Korenaga, 2008a, 2008b; Höink et al., 2011]. Recently, Höink et al.  find that the dynamics and heat transfer properties of plate motions depend on the average wavelength of oceanic plates relative to the mantle depth (plate aspect ratio), as well as on the mantle viscosity. Each of these factors depends strongly on the interior mantle temperature and is, thus, influenced by the magnitude of radiogenic heat production implied by our BSE model. In more detail, the motions of large plates such as the Pacific are expected to be in the “mobile lid” regime driven by conventional slab-pull physics. For small plates such as the Atlantic or for the relatively high internal mantle temperatures of the geological past, however, plate motions are predicted to be predominantly in a “sluggish lid” regime. In this case, plates are driven as a result of viscous coupling to vigorous flow within the asthenosphere driven as a result of lateral temperature variations arising because of an approximately constant surface temperature and a lithospheric thickness that increases with age. An important difference to the mobile lid heat transfer mode is that the surface heat flux increases rather than decreases as the mantle cools and becomes more viscous.
 At present, Earth's mantle is predominantly in a mobile lid regime, cooled mostly by the subduction and stirring of the extensive Pacific plate. A key issue for Earth's thermal history, however, is to recognize that plate motions in both regimes coexist and that the global average surface heat flux carried by mantle flow is modulated by the relative contributions of the two modes, which will evolve in response to the mantle internal temperature [Höink et al., 2011; Crowley et al., 2011]. In particular, the sluggish lid regime is favored for hotter, low viscosity mantles and plausibly governed cooling of Earth's mantle over the first billion years of Earth history. Höink et al.  show, for example, that roughly equal contributions of cooling by mobile lid and sluggish lid modes can explain a present day mantle potential temperature in the range 1350–1400°C and Ur = 0.33 for a chondritic Earth.
 Before exploring the thermal history implications of a current Ur = 0.17 it is important to revisit the role of continents in the problem of mantle cooling. In typical thermal history calculations the major effect of continents is to reduce the surface heat flux carried by plate tectonics as well as the radiogenic heat production in the mantle, depending on the CC volume. Lenardic et al. [2011a], however, show that this approach misses the most important effect of continents, which is to insulate the mantle. Building on earlier work [Lenardic et al., 2005; Jellinek and Lenardic, 2009; Lenardic et al. 2011b], Lenardic et al. [2011a] show that continental insulation governs the interior mantle temperature, which, in turn, determines the mantle viscosity and the rate of subduction and mantle overturning. The greater is the rate of continental radiogenic heat production, the higher will be the mantle internal temperature. Indeed, Lenardic et al. [2011a] show that, the most accurate way to include the ∼7 TW currently carried through the continents [Rudnick and Gao, 2003; Jaupart et al., 2007] in thermal history models is to add this heat flow back into the mantle as additional heat production. Quantitatively, the effective present day Ur then increases from ∼0.33 to around 0.5. Applied to our model for a nonchondritic BSE, the effective Ur increases from ∼0.17 to about 0.35.
 To satisfy the constraints of a present day mantle potential temperature of 1350°C and an effective Ur = 0.35 with our nonchondritic BSE model, we take the initial mantle temperature to be in the range 1575–1800°C (1848–2073 K, which assumes a secular cooling rate of 50–100 K/Gyr) [Jaupart et al., 2007] and integrate forward in time, while varying the relative contributions of sluggish and mobile lid convective modes to the total cooling (cf. Höink et al., 2011; T. Höink et al., Earth's thermal evolution with multiple convection modes: A Monte-Carlo Approach, in press. Physics of the Earth and Planetary Interiors, 2013). To explain the present day Ur and mantle interior temperature, we require 65–80% of Earth's mantle cooling to be governed by the sluggish lid mode of convection, which is not inconsistent with expectations from modeling studies that suggest that this mode is favored over the first 1–2 Gyr of Earth history [Korenaga, 2008b; Höink et al., 2011] (Figure 7, top). In light of historical difficulties with low Ur conditions, an important inference from this thermal modeling exercise is that our nonchondritic BSE compositional model presents no dire consequences for the mantle's thermal evolution.
 A further remark is that our nonchondritic BSE model is inherently more demanding of thermal history models than traditional chondrite-based BSE compositions. If we perform similar calculations neglecting the insulating effects of continents, to satisfy the current mantle potential temperature and Ur = 0.17, we require >90% of Earth's cooling to be by sluggish lid convection. This picture is inconsistent with the results of modeling studies that suggest that mobile lid tectonic style is favored for plausible mantle thermal conditions over the last 1–2 Gyr [O'Neill et al., 2007; Korenaga, 2008b; Höink et al., 2012]. In addition, plate reconstructions and global geodynamic models suggest that mobile lid style tectonics probably governed the formation and breakup of the supercontinents Pangea, Rodinia and possibly Nuna and Kenorland over the last 1–2.5 Gyr [Li and Zhong, 2009].
 A final issue to consider briefly is the extent to which the evolution in mantle convective heat flow we require to satisfy the current effective Ur and mantle interior temperature is consistent with a predominantly thermally driven dynamo over the 1–2 billion years of Earth's evolution [Labrosse et al., 2001] (Figure 7, bottom). Taking 10 TW to be a reasonable critical core-mantle boundary heat flux for dynamo action [e.g., Buffett, 2002; Christensen and Aubert, 2006], for the very high initial mantle temperature of 1800°C, a dynamo is possible over the full extent of our thermal history calculations. However, for the more reasonable initial temperature of 1575°C, dynamo action is not possible until 3.9–3.5 Gyr and, moreover, the mantle may heat the core over the first ∼500 myr of Earth evolution. Although our model is crude, the delayed onset of dynamo action required by our nonchondritic BSE is consistent with the 3.4–3.45 Gyr dynamo age inferred from single crystal paleointensity measurements [Tarduno et al., 2010] as well as from the delivery of terrestrial nitrogen to lunar far side soils [Ozima et al., 2005].
 We draw the following conclusions from this study:
The lithophile element composition of a nonchondritic BSE is assumed to have a present-day make-up similar to the high 3He/4He mantle. The nonchondritic BSE has Sm/Nd ∼6% higher than chondritic and a present-day 143Nd/144Nd of 0.5130; it is consistent with the 142Nd/144Nd difference between Earth and the O-chondrite reservoir, and is an alternative composition to the traditional chondritic-based BSE.
 We present major and trace element concentrations for the high 3He/4He mantle, which represents the composition of the nonchondritic BSE. The concentrations of highly incompatible elements (Rb, Ba, Th, U, K, etc) are ∼30% lower than a chondrite-based BSE. There are several implications for an incompatible element depleted BSE composition:
 Continental crust must be extracted from >83% of the BSE. If <83% of a nonchondritic BSE is depleted, there is insufficient Rb to generate the continents.
Our nonchondritic BSE has a lower K concentration that permits a lower 40Ar budget in the solid Earth and atmosphere. The 40Ar in the atmosphere, continental crust and DMM may be sufficient to balance the Ar budget for our proposed low-K BSE, thus obviating the need for a “missing” 40Ar reservoir and providing a solution to the missing Ar paradox.
Melt models of the nonchondritic BSE, which is here thought to be represented by the lithophile element composition of the high 3He/4He mantle, generate trace element patterns similar to the highest 3He/4He basalt globally.
From our thermal history models, our new BSE has three key implications. First, Earth's thermal history can be readily characterized with our nonchondritic model without requiring a thermal catastrophe in the recent past. Second, for realistic initial mantle temperatures the lower rate of heat production requires that mantle convection cool the Earth in predominantly a small plate/sluggish lid mode over more than half of Earth's early evolution. That is, the classical Pacific plate-style of plate tectonics driven by slab-pull physics was not the dominant mode of mantle stirring over the first 1–2 Gyr of Earth evolution. Finally, for plausible initial mantle temperatures we expect heat transfer into the core and a delay of core convection and dynamo action until as recently as 3.5 Gyr. In summary, the lower U, Th and K concentrations calculated for a nonchondritic BSE present no dire consequences for the thermal evolution of the Earth and may provide a restrictive constraint on the age of Earth's magnetic field.
 This paper is dedicated to Karl Turekian, who introduced Jackson to the “missing” Ar problem in his first geochemistry course as an undergraduate. The course (and Karl) was inspirational, and the rest was history! We thank Rick Carlson for invaluable advice on continental crust extraction models. We also thank Stan Hart, Nobu Shimizu and Steve Shirey for discussion. Dave Graham and Bernard Bourdon provided insightful and helpful comments. We thank the “Bills” (McDonough and White) and an anonymous reviewer for comments on an earlier version of the manuscript. MGJ was supported by NSF grants OCE-1061134 and EAR-1145202. AMJ was supported by NSERC and the Canadian Institute for Advanced Research.