G 3. AN ELECTRONIC JOURNAL OF THE EARTH SCIENCES Published by AGU and the Geochemical Society

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1 Geosystems G 3 N ELETRONI JOURNL OF THE ERTH SIENES Published by GU and the Geochemical Society rticle Volume 4, Number 2 0 December , doi:0.029/2002g ISSN: onstraints on the 232 Th/ 238 U ratio (K) of the continental crust D. Paul Department of Geological Sciences, ornell University, Ithaca, New York 4850, US Now at Max-Planck-Institut für hemie, Mainz, Germany 5528 (dpaul@mpch-mainz.mpg.de) W. M. White and D. L. Turcotte Department of Geological Sciences, ornell University, Ithaca, New York 4850, US (white@geology.geo.cornell.edu) [] This study examines constraints on the 232 Th/ 238 U ratio of the continental crust (k ) imposed by heat flow, Th-U systematics and Pb isotope ratios. The 232 Th/ 238 U ratio of the depleted upper mantle (k UM )as sampled by mid-ocean ridge basalt is well-constrained to be 2.5 ± 0.. The 232 Th/ 238 U ratio of the lower mantle (k LM ) can be constrained as follows. Oceanic island basalts (OIB) have average k of If OIB are derived from mantle plumes and if plumes are representative of the lower mantle, then k LM lternatively, if the lower mantle is primitive, then k LM is similar to the chondritic 232 Th/ 238 U ratio of k S = 4 ± 0.2. Mass balance calculations assuming k UM = 2.5, and k LM 4 with heat production constraints suggest that k is in the range 5 6. Further support for k substantially greater than 4 comes from the Pb isotopic composition of the continental crust. We estimate the 208 Pb/ 204 Pb of the lower continental crust to be to and the 208 Pb*/ 206 Pb* ratio of the total continental crust to be.046 to.059, which corresponds to a time-integrated 232 Th/ 238 U ratio (k (Pb) ) of four-reservoir (upper and lower continental crust, depleted upper mantle, and primitive lower mantle) forward transport model of Pb isotope evolution that reproduces the difference in k UM and k UM(Pb) values in the depleted mantle suggests that to achieve a k (Pb) of 4.25, the present 232 Th/ 238 U ratio in the crust (k ) must be 5. Thus several lines of evidence converge on a value k of around 5 or slightly higher. omponents: 0,205 words, 9 figures, 6 tables. Keywords: ontinental crust composition; Th/U ratio; Pb isotope evolution. Index Terms: 020 Geochemistry: omposition of the crust; 00 Geochemistry: hemical evolution; 040 Geochemistry: Isotopic composition/chemistry. Received 6 December 2002; Revised 9 October 2003; ccepted 2 October 2003; Published 0 December Paul, D., W. M. White, and D. L. Turcotte, onstraints on the 232 Th/ 238 U ratio (k) of the continental crust, Geochem. Geophys. Geosyst., 4(2), 02, doi:0.029/2002g000497, Introduction [2] The composition of the continental crust is of great interest because it provides a key constraint on models of crustal evolution. It also provides a key constraint on the structure and composition of the Earth s mantle [e.g., DePaolo, 980; O Nions et al., 979; llègre et al., 983a, 983b]. lthough the composition of the continental crust is sometimes considered well established, certain aspects of the canonical crustal composition need more careful consideration. In particular, estimates of 232 Th/ 238 U in the continental crust (k ) show a surprisingly wide range. Rudnick and Fountain [995] and Taylor and McLennan [995] estimated k < 4.0, while Gao et al. [997] opyright 2003 by the merican Geophysical Union of 7

2 estimated k = 6., more than 50% higher. This large uncertainty is disturbing for several reasons. First, the distribution of refractory lithophile elements such as U and Th is often used as a benchmark for estimating the distribution of other elements, which must therefore be even more uncertain. Second, since U and Th provide most of the energy to drive convection and tectonic activity in the Earth, uncertainty in their distribution translates into an uncertainty in the distribution of energy sources in the Earth. Finally, Pb isotope ratios provide constraints on internal processes within and the chemical evolution of the Earth, but these constraints are best interpreted if the behavior and distribution of the parent elements, U and Th, are known. [3] The abundance and distribution of the heat producing elements in the Earth can be constrained in a number of ways. One of these is the assumption that the Earth formed from a pre-solar nebula of chondritic composition. Since the relative abundances of refractory lithophile elements (such as U and Th) in primitive meteors are approximately uniform, it seems reasonable to assume that such elements are also present in the Earth in chondritic relative abundances [e.g., McDonough and Sun, 995]. This assumption, if correct, constrains the 232 Th/ 238 U ratio of the bulk silicate Earth (k S )tobe 4.0 ± 0.2 [llègre et al., 986; McDonough and Sun, 995; Rocholl and Jochum, 993]. The element K, however, is not a refractory element, and its abundance in the Earth is clearly lower than predicted by a strictly chondritic model of Earth s composition. [4] The abundances of the decay products, i.e., the radiogenic isotopes of Pb and r, and intermediate daughters of U, provide additional constraint on the abundances of the heat producing elements. For example, the gof 40 r in the atmosphere, essentially all of which is radiogenic, implies a concentration of K in the bulk silicate Earth of 8 ppm [Turekian, 959] if the Earth is fully degassed, and more if it is not. Similarly, ratios of radiogenic 208 Pb, produced by decay of 232 Th, to radiogenic 206 Pb, produced by decay of 238 U are close to in most terrestrial rocks, which is broadly consistent with a terrestrial 232 Th/ 238 U ratio (k) of about 4, as inferred from the chondritic model. Intermediate decay products of 238 U, most particularly 230 Th, in volcanic rocks provide additional useful constraints on k in the mantle sources of those rocks. [5] Heat flow from the Earth s interior is an independent observation that provides a final constraint on the distribution of the heat-producing elements. Some fraction of the total heat flow through the Earth s surface is due to secular cooling of the Earth; the remainder originates in the Earth s interior through the radioactive decay of U, Th, and K. Thus global heat flow, which is well known, constrains the terrestrial inventory of radioactive elements and ultimately can be used to constrain the Th/U ratio in the continental crust. The K/U ratio, though not known precisely, appears to have a limited variability in the Earth [Wasserburg et al., 964; Jochum et al., 983]. Hence the major unknowns are the concentrations of U, Th, and the masses of the various reservoirs, in particular the masses of mantle reservoirs and the distribution of U between them. [6] In the case of Th and U, the heat producing nature of these elements plus the well-constrained value of 232 Th/ 238 U ratio in the depleted upper mantle (k UM ) can be used to constrain the relative size of the source of mid-ocean ridge basalts (MORB), the upper depleted mantle [Turcotte et al., 200]. The results obtained by Turcotte et al. [200] suggest the mass fraction m (ratio of the mass of the depleted upper mantle to that of the whole mantle) of the depleted upper mantle reservoir is about 45% of the whole mantle. In this model, the remainder of the mantle is approximately primitive in composition and mantle Urey numbers, Ur (ratio of radiogenic heat production to total heat flow), are in the range of Such a model is consistent with the layered mantle structure postulated by Kellogg et al. [999], with compositional stratification at a deeper depth of 700 km. Turcotte et al. [200] concluded that whole mantle convection is only possible if U, Th, and K concentrations have been substantially underestimated in the depleted mantle or if a substantial fraction of the subcrustal heat 2of7

3 Geosystems G 3 paul et al.: constraints on the 232 th/ 238 u ratio 0.029/2002G Table. verage U, and Th omposition of the Bulk ontinental rust Reference, ppm flow originates in boundary layers or in the core. None of these possibilities seems likely. [7] Here we use heat flow, mass balance and Pb isotope ratios to better constrain the value of k. We conclude that k is significantly higher than the values of 3.87 and 3.97 estimated by Taylor and McLennan [995] and Rudnick and Fountain [995] respectively. Estimates of Shaw et al. [986] and Wedepohl [995] of about 5 are more likely to be correct. 2. Observational onstraints on the 232 Th/ 238 U Ratio Th/ 238 U Ratio of the ontinental rust Th, ppm 232 Th/ 238 U, k Gao et al. [997] Haack [983] Rudnick and Fountain [995] Shaw et al. [986] Taylor and McLennan [995] Weaver and Tarney [984] Wedepohl [995] verage [8] The concentrations of U and Th in the bulk continental crust as estimated by various authors are listed in Table. These estimates are obtained using a number of geochemical, geophysical, geological, and petrological constraints. Estimates of the ratio of these elements in the crust, k, vary more widely than one might expect, from 3.87 to This is a surprisingly large uncertainty, given the chemical similarity of these elements and their importance in heat production and Pb isotope evolution. Estimates of k by Taylor and McLennan [995] and Rudnick and Fountain [995] are both less than 4, which is less than the current best estimate for bulk silicate Earth. If these estimates are correct, mass balance considerations would then require that the value of k in the mantle be greater than 4. Most of the other estimates of k are in the range 4 < k < 7, which imply mantle k values of less than 4. The average k for all the estimates is 5.03, which is close to the values proposed by both Shaw et al. [986] and Wedepohl [995]. [9] Shaw et al. [986] estimated k of 5.04, a value derived from their earlier estimates [e.g., Shaw et al., 967, 976] based on analyses of anadian Shield composites from surface exposures of low- through high-grade metamorphic rocks. n empirical approach by Weaver and Tarney [984], incorporating both geophysical and isotopic constraints, gives k of Haack [983] found that the value of k = 6.7 is best satisfied by the observed continental heat flow. Taylor and McLennan [995] give k = 3.87, a value carried over from their early estimates [e.g., Taylor and McLennan, 985]. Taylor and McLennan s [985] model takes into account the heat flow data, tectonics (the andesite model ), and the continental growth history. The so-called andesite model assumes that the bulk continental crust is equivalent in composition to that of average island arc volcanic rocks. Their model bulk crust composition is derived from a mixture of 75% rchean bimodal (basalts on the one hand and felsic trondhjemites, tonalites, and granites on the other) igneous suites and 25% post-rchean andesitic compositions, and neglects any new additions of material due to basaltic underplating. Their estimate was based on a mean continental radiogenic surface heat flow of 23 mw.m 2. [0] Others have estimated the composition of the continental crust using seismic models along with the analyses of amphibolite- to granulite-grade terrains and xenoliths. Seismic models utilize the refraction seismic data in order to model the seismic velocity (mainly V p ) structure of the continents [hristensen and Mooney, 995; Rudnick and Fountain, 995; Wedepohl, 995; Gao et al., 997]. While the estimate of k by hristensen and Mooney [995] is essentially similar to that of Taylor and McLennan [995], that of Rudnick and Fountain [995] is slightly higher (k = 3.97) nevertheless less than 4. Wedepohl [995] utilized a 3000 km long refraction seismic profile through western Europe along with the analyses of anadian Shield data [Shaw et al., 967, 976] and the data on felsic granulite terrains and mafic xenoliths compiled by Rudnick and Presper [990]. He estimated 3of7

4 a value of k = Seismic models give higher concentrations of U and Th in the continental crust (also predict a more felsic crust) compared to the estimates of Taylor and McLennan [995] Th/ 238 U Ratio in the Depleted Upper Mantle [] NMORB (Normal Mid-Ocean Ridge Basalt) provide evidence for the existence of a relatively well-mixed, incompatible element-depleted upper mantle reservoir that we will refer to as the depleted upper mantle (by use of the word upper, we do not imply that this reservoir is necessarily restricted to the region above the 660-km seismic discontinuity). The present-day 232 Th/ 238 U ratio in the depleted upper mantle (k UM ) can be estimated both from direct measurements of the concentrations of Th and U in NMORB [Jochum et al., 983; Newman et al., 983; White, 993], and from the measurement of 232 Th/ 230 Th activity ratio in NMORB [k = (l 230Th /l 232Th l 238U )( 232 Th/ 230 Th)] [llègre and ondomines, 982; Newman et al., 983; Ben Othman and llègre, 990; O Nions and McKenzie, 993; Bourdon et al., 996]. Both approaches yield similar values for k UM = 2.5 ± 0.. On the other hand, the time-integrated 232 Th/ 238 U ratio (k Pb ) can be estimated from the ratio of 208 Pb*/ 206 Pb* where the asterisk represents the radiogenic contribution only [k Pb = ( 208 Pb*/ 206 Pb* exp (l 238 t) )/exp (l 232 t) ); t is the age of the Earth]. For the NMORB these measurements give k UM(Pb) = 3.8 ± 0.2 [Galer and O Nions, 985], which is much closer to the accepted bulk silicate Earth value k S = 4.0 ± 0.2 [McDonough and Sun, 995; Rocholl and Jochum, 993] Th/ 238 U Ratio in the Lower Mantle [2] For the purposes of this paper, we define lower mantle as the region below the depleted upper mantle reservoir; its upper bound could be below the 660-km seismic discontinuity. The value of k in this reservoir (k LM ) is not so easily constrained as in the depleted upper mantle reservoir. We consider three possibilities: (a) the lower mantle is primitive (b) mantle plumes provide a representative sample of lower mantle, and (c) lower mantle is represented by those plumes having the most extreme compositions. [3]. strong case can be made from K-r systematics that roughly half of the Earth s mantle has not been degassed since very early in Earth s history [llègre et al., 996]. This leads to the hypothesis that the lower mantle is primitive, i.e., chemically unprocessed since the Earth s formation. Because both U and Th are refractory lithophile elements, they should be present in the bulk silicate Earth and primitive mantle in the same relative proportions as in chondrites. We take the value of k in the bulk silicate Earth (k S ) to be 4.0 ± 0.2 [McDonough and Sun, 995; Rocholl and Jochum, 993]. Thus in this case, k in the lower mantle is 4.0 (k LM =4). [4] 2. Ocean Island Basalts (OIB) are thought to be produced by partial melting in mantle plumes. It is likely that the plume material originates, at least in part, in the lower mantle. If so, then OIB compositions can be used to constrain the composition of the lower mantle. We extracted 4 high quality Th and U analyses of OIB published over the last decade from the online GEORO database maintained by the Max-Planck-Institut für hemie in Mainz, Germany. summary of this compilation is given in Table 2, and the frequency distribution of 232 Th/ 238 U in OIB is shown in Figure a. s may be seen in Table 2, k in OIB ranges from 2.8 (Umu volcanic field) to 4.70 (Heard Is, Indian Ocean), i.e., from well below to well above the chondritic value. This variability most likely reflects the heterogeneous nature of OIB sources, which has already been well established from isotopic studies. The average value of k in the OIB is 3.78, remarkably close to the chondritic value, but much higher than the upper mantle value. [5] To the extent that U and Th partition differently between melt and the solid residue, k in OIB may not necessarily reflect the value of k in OIB sources. Indeed, studies of 230 Th/ 238 U ratios in young OIB and determinations of partition coefficients in mantle minerals [e.g., LaTourette and Burnett, 992; Beattie, 993; Salters and Longhi, 999] indicate that the 232 Th/ 238 U ratio in a basalt 4of7

5 [6] 3. If OIB sources are mixtures of incompatible element-depleted upper mantle, and weakly incompatible element-enriched plumes from the lower mantle, then the lower mantle k could be higher than the average of OIB sources, i.e., higher than the value of 3.4 deduced above. s an extreme possibility, we consider the scenario that most plumes are diluted by depleted upper mantle material and only the most incompatible elementenriched OIB are representative of pure lower mantle. The highest values of k occur in Heard Island lavas. ssuming, as discussed above, that magmatic processes are responsible for a 0% increase in k, the 4.70 value found in Heard lavas would correspond to a k of 4.23 in the source. This value (k LM = 4.2) will be used for the third possibility mentioned above. 3. Mass Balance and Heat Flow onstraints 3.. Heat Flow [7] Following Rudnick and Fountain [995] we assume that the mean continental heat flow (q R ) Figure. Histogram of (a) 232 Th/ 238 U ratio, and (b) K/U ratio in oceanic island basalts (OIB). Results shown encompass data from Table 2. will generally be higher than its source because Th is slightly more incompatible than U. In some cases the 230 Th/ 238 U in basalt can be as much as 30% higher than in its source, but on average 230 Th/ 238 U ratio during OIB production is only 0 20% enriched over the equilibrium source ratio [Hemond et al., 988; Hemond et al., 994; Sims et al., 999]. Some of this enrichment, particularly the more extreme values, likely reflects in-growth and subsequent extraction of 230 Th from the melt residue during dynamic melting [e.g., Elliot, 997], so we assume 0% increase in the Th/U ratio in the melt over that of the source. Using this value, the average k of 3.78 in OIB would correspond to an average k for OIB sources of Hence we assume that if mantle plumes are representative of the lower mantle, then k LM 3.4. Table 2. OIB Island/hain verage 232 Th/ 238 U(k) and K/U Ratios in Number 232 Th/ 238 U, k K/U ustral-ook ,920 zores ,568 anary Island ,690 ape Verde Island ,073 aroline Island ,920 omoros Island ,348 Easter Sea Mt ,028 Galapagos ,893 Hawaii ,784 Heard ,730 Iceland ,564 Jan Mayen ,082 Kerguelen ,626 Macquarie Island ,273 Marion Island Marquesas 8 4.9,306 Mascarene Island ,027 Medeira rchepelago ,300 Pitcarin-Gambier ,340 Revillagigedo Island ,33 Samoan Island ,762 Society Island ,075 St. Helena ,823 Tristan da unha 6 4.2,294 Umu volcanic field 6 2.8,370 verage ,047 5of7

6 attributed to radiogenic heat production in the continental crust is 37 mw.m 2, and the total radiogenic heat production in the continental crust Q R = W (see Turcotte et al. [200] for a detailed discussion of heat flow). The radiogenic heat production in the continental crust (Q R ) is attributed to the amount of U, Th, and K present in the crust, and is given by Q R ¼ ð H U þ Th H Th þ H K ÞM ðþ where, Th, and are the mean concentrations of U, Th, and K in the continental crust and H stands for the heat production per unit mass of HPE; H U = Wkg, H Th = W kg, and H K = Wkg. M refer to the mass of the continental crust (M = kg). We assume that the Th/U ratio in the crust (k )is unknown. Following Wasserburg et al. [964] and Jochum et al. [983], we assume that the K/U ratio in the crust is 2,500 (we will argue below that this same ratio applies to the mantle as well). Thus equation can be rewritten as function of the U concentration ( ), k, and the K/U ratio ( / ) of the continental crust. Q R ¼ H U þ k H Th þ K H K M [8] s is often done [e.g., DePaolo, 980; O Nions et al., 979; llègre et al., 996; Turcotte et al., 200] we assume a two-layered mantle: a depleted upper mantle reservoir and a lower mantle reservoir. We define m, the mass fraction of the upper mantle as m ¼ M UM M M where M UM is the mass of the upper deleted mantle, and M M is the mass of the whole mantle (M M = kg). For instance, a value of m 0.25 would correspond to a depleted mantle reservoir that is restricted to the upper mantle above the 660-km seismic discontinuity. The parameter m is a variable in our calculations. [9] In the two-layer mantle model, the radiogenic heat production in the mantle, Q MR, can be ð2þ ð3þ expressed as a function of the U concentration, k, and the K/U ratio: Q MR ¼ UM H U þ k UM H Th þ K H K mm M þ LM H U þ k LM H Th þ K H K ð mþm M ð4þ where UM, and LM are the mean concentrations of U in the upper and lower mantle respectively. In our calculations k UM is treated as a variable whose value is fixed by observation (k UM = 2.5), whereas results will be obtained for a range of values for k LM. [20] Jochum et al. [983] found that the average K/U ratio in MORB was 2,700, very similar to the terrestrial value proposed by Wasserburg et al. [964]. We extracted K and U abundances for ocean island basalts from the Mainz GEORO database. The observed K/U ratios are summarized in Table 2, and the frequency distribution is presented in Figure b. We did filter the data roughly for weathering/alteration and analytical quality. While it is possible, and perhaps likely, that some of the variation observed is still due to these factors, we note that the K/U ratio varies even in high quality data obtained on fresh rocks [e.g., Newsom et al., 986]). While average values for individual island chains vary by a factor of 3 (from 20,33 in Revillagigedo Island to 6,073 in the ape Verde Island), the mean value of all chains of,047 is remarkably similar to the K/U ratio of Wasserburg et al. [964]. Thus while the K/U ratio apparently can vary, the similarity of this ratio in the continental crust, in MORB, and in OIB to Wasserburg s estimate of the terrestrial value suggests that the value of 2,500 is a valid one. We therefore assume a K/U of 2,500 in all reservoirs. However, we show later that our estimates of k are only very weakly dependent the K/U ratio. ssuming a value as low as 0,000 would have almost no influence on the result. [2] Following Turcotte et al. [200], we take the total heat flow from the convecting mantle to be Q M = W. The heat loss from the mantle is well constrained and has an error of <0%. However, some fraction of this heat loss is due to secular cooling of the mantle and core 6of7

7 rather than radioactive decay. The Urey number, Ur, is defined to be the fraction of the mantle heat loss attributed to radioactive decay: Ur ¼ Q MR Q M Since Q M is known and Q MR is a function of mantle U concentrations (equation 4), Ur is also a function of mantle U concentration. Using the bulk silicate Earth U concentration of McDonough and Sun [995] and adjusting for the crustal U abundances of Wedepohl [995], Rudnick and Fountain [995], and Taylor and McLennan [995] yields respectively Urey numbers of 0.28, 0.34, and 0.42, which imply very substantial secular cooling of the Earth. In contrast, geophysical approaches such as parameterized convection calculations suggest a value of Ur in the range [see Turcotte et al., 200, references therein]. onsequently, Turcotte et al. [200] preferred a higher bulk silicate Earth U. Their preferred U concentration of 26.6 ppb corresponds to Urey numbers of 0.5 and 0.56 for the crustal U abundances of Rudnick and Fountain [995] and Taylor and McLennan [995] respectively. In our calculations, we will consider a range of Urey numbers, which in turn correspond to a range of bulk silicate Earth U concentrations Mass Balance [22] n entirely independent constraint comes from the assumption that the Th/U ratio of the Earth is chondritic, i.e., that k S = 4. This requires that: ð5þ k M þ k UM UM mm M þ k LM LM ð mþm M ¼ 4 M þ UM mm M þ LM ð mþm M ð6þ and that M þ UM mm M þ LM ð mþm M ¼ BSE ðm þ M M Þ where BSE represent the concentration of uranium in the bulk silicate Earth. In simple terms, equation (6) states that the sum of total ð7þ thorium divided by the sum of total uranium in crust + upper mantle + lower mantle reservoirs is equal to the bulk silicate Earth kappa k S = 4. Equation (7) states that sum of total uranium in crust + upper mantle + lower mantle reservoirs is equal to the total uranium in the bulk silicate Earth. [23] If we assume that the lower mantle is primitive, i.e., that both LM = BSE and k LM = k S, then the lower mantle as well as the upper mantle + continental crust must have U and Th concentrations equal to bulk silicate Earth. In this case, equation (6) simplifies to: k M þ k UM UM mm M M þ UM mm M ¼ 4 ð8þ Furthermore, the concentration of U in the continental crust plus upper mantle must be same as that of bulk silicate Earth in this case, so that equation (7) simplifies to: M þ UM mm M ¼ BSE ðm þ mm M Þ ¼ LM ðm þ mm M Þ [24] If the lower mantle is not primitive, the problem is less constrained as equations (8) and (9) do not hold and assumptions must be made for the U concentration and value of k in the lower mantle. Hence we consider two working hypotheses that allow k LM to vary yet simplify the situation somewhat. In first, which we call the approximately primitive lower mantle solution or Model I, we assume that k LM differs from that of the bulk silicate Earth, whereas the concentration of U in the lower mantle is that of primitive mantle. In essence, we assume that any variation in k LM is due to a variation in the Th concentration. In this case, when k LM 6¼ 4, equation (9), the mass balance for U, still holds, although equation (8) does not. Equations (2), (4), (5), (6), and (9), can be combined to find expressions for the four unknowns, k, UM, and LM in terms of parameters that are either known or constrained from observations (e.g., Q R, Ur, k LM ) or variables of the model (m, k LM ): ð9þ 7of7

8 0 H U UrQ M ðð mþm M ðk LM 4ÞþM ðk UM 4ÞþmM M ðk UM 4ÞÞ þq R ð4h Th k UM ðm þ ð mþm M þ mm M ÞþH U ð4m þ 4mM M 0 UrQ M ðð mþ M M ðk LM 4Þ þm ðk UM 4Þ þð mþm M ð4 k LM þ k UM ÞÞÞ þ H K þmm M ðk UM 4ÞÞ þq R ð4m þ 4mM M Þ B þð mþm ð4 k k ¼ LM þ k UM ÞÞ Q R H K ðm þ ð mþm M þ mm M ÞþH Th UrQ M 0 ð mþm M ðk LM 4Þ B þm ðk UM þ Q R þmm M ðk UM 4Þ ðh U ðm þ ð mþm M þ mm M Þ þh Th ðð mþm M k LM þ ðm þ mm M Þk UM ÞÞ 0 ð0þ Q R H K ðm þ ð mþm M þ mm M ÞþH Th UrQ M 0 ð mþm M ð 4 þ k LM ÞþM ð 4 þ k UM þ mm M ð 4 þ k UM Þ þq R ðh U ðm þ ð mþm M þ mm M Þ þh ¼ Th ðð mþm M k LM þ ðm þ mm M Þk UM ÞÞ H K þ 4H Th þ H U M ðm þ ð mþm M þ mm M Þ H K þ H U þ H Th k UM 0 H K ð Q R ð mþm M þ ðm þ mm M ÞUrQ M Þ Q R ð mþm M ðh U þ H Th k LM Þ þurq M ðh U ðm þ mm M ÞþH Th ð4m þ 4 ð mþm M þ4mm UM ¼ M ð mþm M k LM ÞÞ H K þ 4H Th þ H U mm M ðm þ ð mþm M þ mm M Þ K H K þ H U þ H Thk UM 0 Q R þ UrQ M LM ¼ H K þ 4H Th þ H U ðm þ M M Þ ðþ ð2þ ð3þ The case where the lower mantle is exactly primitive is considered as a subset of the solutions to Model I. We point out that this set of equations is not physically valid over the entire parameter range, since certain combinations of parameters can yield negative U concentrations. For example, for k LM =4,Ur =0.6,UM becomes negative for m less than about [25] In the second case, which we will refer to as non-primitive lower mantle solution or Model II, neither equations (8) nor (9) hold and instead the four equations (2), (4), (5) and (6) are combined to solve for three unknown variables, k, LM as functions of K/U ratio, k UM, Ur, m, k LM, and UM. The solutions obtained for Model II are: 0 4H Th Q R k LM þ H U 4Q R þ UrQ M ðk LM 4Þ 2UM 2H Th þ H K mm M ðk LM k UM Þ þum HU 2 mm Mðk UM k LM Þ þum HK 2 2 K mm M ðk UM k LM Þþ H K B ð 4Q R þ UrQ M ðk LM þ4 k ¼ UUM H Th mm M ðk UM k LM ÞÞ H U ðq R þ UM H Th mm M ðk UM k LM ÞÞ þh K ðq R þ UM H Th mm M ðk UM k LM ÞÞ þ H Th ðurq M ðk LM 4ÞþQ R k LM þ 4UM H Th mm M ðk UM k LM ÞÞ ð4þ 0 UrQ M UM mm M H U þ H K þ H Th k UM LM ¼ U ð mþm M H U þ H K þ H Th k LM ð5þ 0 H U ðq R þ UM H Th mm M ðk UM k LM ÞÞ þ H K ðq R þ UM H Th mm M ðk UM k LM ÞÞ þ H Th ðurq M ðk LM 4ÞþQ R k LM þ 4 ¼ UUM H Th mm M ðk UM k LM ÞÞ 4H Th þ H U þ H K M H U þ H K þ H Th k LM ð6þ 8of7

9 Table 3. Parameter Values Used in the Model Parameters Value Mass of the continental crust, M,kg Mass of the mantle, M M, kg Mass fraction of upper depleted mantle, m variable Global surface heat loss from convecting mantle, Q M,W Mean continental radiogenic surface 37 heat flow, q R,mW.m 2 Radiogenic heat production in the continental crust, Q R,W Radiogenic heat production in the variable mantle, Q MR,W Urey ratio, ratio of radiogenic to total heat variable production in mantle, Ur K/U ratio of the bulk silicate Earth 2, Th/ 238 U ratio in the depleted upper 2.5 mantle, k UM 232 Th/ 238 U ratio in the bulk silicate Earth, k S 4.0 [26] n important aspect of the non-chondritic model is that k LM is not fixed, hence its value must be obtained from other observations. ssuming oceanic island basalts are at least partially derived from material rising from the deep mantle, they provide independent observations about lower mantle composition. Hence a limiting assumption would be that k LM is equal to that of the average OIB source, either with or without correcting for an assumed fractionation between Th and U during melting. This leads to estimates of k LM of 3.5 and 3.8 respectively. nother assumption might be that the lower mantle is represented not by the mean, but by the extreme OIB composition, which would be Heard Island, which, after a correction for 0% fractionation, leads to k LM = Solutions to Mass Balance Equations [27] Utilizing equation 0 for Model I and equation 4 for Model II, and assumptions outlined above (For Model I, we assume that k LM differs from that of the bulk silicate Earth, whereas the concentration of U in the lower mantle is that of primitive mantle; and for Model II, we assume two scenarios; one where k LM is equal to that of the average OIB source, and in the other the lower mantle is represented not by the mean, but by the extreme OIB composition), we now obtain solutions for a range of values of k in the continental crust. summary of assumed values for the parameters in these equations is given in Table 3. Solutions for four different values of the Urey numbers, Ur = 0.34, 0.5, 0.6, and 0.8 are considered along with a range of values for m and a value for the K/U ratio of 2,500. [28] First we will describe the results for Model I. Figure 2 illustrates the dependence of k on Ur for different m = 0.25, 0.45, 0.65, and (whole mantle convection) when k UM = 2.5, k LM = 4.0, and K/U = 2,500. In general, k decreases with decreasing Ur ratio, and for a particular value of Ur, k increases with m. For the case m =, whole mantle convection, when Ur = 0.3, k becomes 7.8, an improbably high value for the continental crust. For m = 0.65, k has a minimum value of 5.3 when Ur is 0.3, and rises to 7 for Ur = 0.5 and. for Ur = 0.8. These values for Ur > 0.5 are well above the estimates of k summarized and Table. s Turcotte et al. [200] argued, such high values seem to excluded the possibility of a depleted upper mantle reservoir as large as m For m = 0.25, UM becomes negative when Ur < 0.6, limiting k > 4.03 in this case. value of k as low as 4.0 is thus possible for m = 0.25 only if k LM >4. [29] For approximately primitive lower mantle, we consider the possibility that although the U concentration of the lower mantle equals that of bulk Figure 2. Dependence of k on Ur in Model I. Results shown are for depleted upper mantle mass fractions (m) 0.25, 0.45, 0.65 and, when k LM =4,k UM = 2.5 and K/U = 2,500. Note that k < 4 (for m = 0.25) when Ur < 0.6, which results in negative U concentration in depleted upper mantle, a direct consequence of mass balance assuming a primitive lower mantle with k LM =4. 9of7

10 Figure 3. Dependence of k on k LM in Model I for a depleted upper mantle mass fraction m = Shaded region is the range for bulk silicate Earth k (k S = 4.0 ± 0.2). Solid horizontal lines refer to values of k as estimated by various authors: Gao et al. [997], Wedepohl [995], Weaver and Tarney [984], Rudnick and Fountain [995], Taylor and McLennan [995]. silicate Earth, its 232 Th/ 238 U deviates from that of the bulk silicate Earth by as much as 0%, i.e., 3.6 < k LM < 4.4. Figure 3 illustrates dependence of k on the 232 Th/ 238 U ratio of the lower mantle (k LM )form = 0.45 (the preferred value of Turcotte et al. [200]), k UM = 2.5, and K/U = 2,500, for different Ur ratios of 0.34, 0.5, 0.6, and 0.8. [30] It is evident from Figure 3 that a strictly primitive mantle (3.8 < k LM < 4.2) with Ur in the range 0.5 to 0.6, requires 4.6 < k < 7, and estimates of k of <4 [e.g., Taylor and McLennan, 995; Rudnick and Fountain, 995] are not possible for these values of the Urey number. Only the estimates of Haack [983], Shaw et al. [986], Wedepohl [995] and Gao et al. [997] fall within this range. Taylor and McLennan [995], and Rudnick and Fountain [995] values of k <4 are possible only when Ur < 0.34 and k LM > 4.2. When k LM =4;forUr = 0.34, k is 4.4 (a value preferred by Weaver and Tarney [984]); for Ur = 0.5, k is 5.7 (a value close to the preferred estimates of Shaw et al. [986] and Wedepohl [995] as well as the average of all the estimates in Table ); for Ur = 0.6, k is 5.7 (close to Gao et al. [997]); and for Ur = 0.8, k is 6.98 (close to the value preferred by Haack [983]). If we assume that the lower mantle is represented by the OIB (as discussed above) then for k LM = 3.5 and Ur = 0.34, k becomes It is clearly evident from Figure 4. Dependence of k on the depleted upper mantle mass fraction (m) in Model I (primitive lower mantle). Values of k < 4 results in negative concentration of U in the depleted upper mantle and are therefore excluded. Solid lines and references are same as Figure 3. Figure 3 that when k LM 3.8, then k is considerably higher than 4 even for a lower value of Ur. [3] Figure 4 illustrates the dependence of k on m for a primitive lower mantle k LM. Values of m in the range would correspond values of k within the range of estimates in Table for values of Urey ratio in the range k that approach the minimum value of 4.0 require m < However, such a low value of m is difficult to reconcile with Rb mass balance, as the fraction of terrestrial Rb in the continental crust appears to be greater than 25% [DePaolo, 979]. gain, values of k less than 4 are only possible in Model (primitive mantle) if the bulk silicate Earth k is less than 4. Figure 5. k as a function of K/U ratio of the bulk silicate Earth when k LM = 4, and m = It is apparent that k is only weakly dependent on the K/U ratio. 0 of 7

11 Figure 6. oncentration of U ( in ppb) in both the depleted upper mantle and lower mantle reservoirs as a function of k LM in Model I. Results are given for specific values of k UM = 2.5 and m = mantle. V. J. M. Salters and. Stracke (The composition of the depleted mantle, manuscript submitted to Geochemistry Geosystems, 2003) estimate the U concentration of the depleted mantle as 4.74 ppb. We therefore consider the most reasonable values of UM to be in the range of 3 to 8 ppm, but we consider a larger range, namely UM = 2 2 ppb. [35] Figure 7 illustrates the dependence of k on UM for m = 0.45, k UM = 2.5, K/U = 2,500, and [32] Figure 5 shows the variation in k with respect to the K/U ratio and demonstrates that k is not strongly dependent on K/U ratio. ssuming a K/U ratio for the bulk silicate Earth different than the value we chose of 2,500 would not change our results substantially. Similarly, assuming different values of K/U for the 3 different reservoirs has only a very small effect on the calculated k. [33] In Figure 6 concentrations of uranium in both the mantle reservoirs are given as a function of k LM for m = 0.45, and three values of Ur = 0.34, 0.5, and 0.6. Note that in the way we have defined Model I, the concentration of uranium in the lower mantle is dependent only on Ur. The concentration of U in the depleted upper mantle, UM, decreases with increase in k LM, and for a given value of k LM it tends to increase with higher value of Ur. [34] We now discuss the results obtained for Model II, the non-chondritic lower mantle. However, Model II requires an estimate of an additional variable, namely UM. The mean concentration of U in the NMORB is ppb [Jochum et al., 983; Hofmann, 988, 997]. ssuming that the concentrations in NMORB represent 0 times the depleted upper mantle concentration (equivalent to 0% batch melt with a solid/liquid partition coefficient ), the concentration of U in the upper mantle (UM ) can be estimated as 7 8 ppb. Zartman and Haines [988] have given a uranium concentration of 5 ppb for the depleted upper Figure 7. Dependence of k on the concentration of U in the depleted upper mantle (UM in ppb) for (a) Ur = 0.34 and for (b) Ur = 0.5 in Model II. Results are given for m = Shaded region is the range of previous estimates of UM by Jochum et al. [983], Zartman and Haines [988], and Hofmann [988, 997]. When Ur = 0.34, the BSE U concentration (BSE )is 9.6 ppb, and when Ur = 0.5, BSE = 25.4 ppb. of 7

12 the bulk silicate Earth concentration of uranium is only a function of Ur Th/ 238 U Ratio as Inferred From Pb Isotope Ratios Figure 8. Variation in k with m in model II when UM = 7 ppb. Results are shown for two values of Ur = 0.34 and 0.5 for two specific cases i.e., when k LM <4 (k LM = 3.5), and k LM >4(k LM = 4.2). When k LM <4, k increases with increase in either m or Ur. Whereas for k LM > 4, k decreases with increase in Ur, but increases with increase in m. When k LM = 4, k is independent of Ur, but increases with increase in m, which is not shown in the figure. two specific values of Ur = 0.34 (Figure 7a) and Ur = 0.5 (Figure 7b). s may be seen, k increases with increasing UM and decreases with increasing k LM. For 3.5 k LM 4.2 and reasonable values of UM, k corresponds well with the estimates summarized in Table. However, k 4 is possible only if k LM 4.2, and UM 3.2 ppb for Ur = 0.34 and UM 4.8 ppb for Ur = 0.5. In the range UM = 5 8 ppb, k can also be less than equal to 4 only if k LM 4.2 and Ur > 0.6. [36] Figure 8 illustrates the relationship between m and k for a specific value of UM (UM =7 ppb). Results shown are for two values of Ur = 0.34 and 0.5 for two scenarios i.e., k LM < 4 (average OIB source with characteristic k LM = 3.5) and k LM > 4 (source of Heard Island basalts with k LM = 4.2). When k LM <4,k increases with increase in either m or Ur. In this case LM increases and decreases. Whereas for k LM >4,k decreases with increase in Ur (in which case both LM and increases), but increases with increase in m (LM increases and decreases). When k LM =4,k is independent of Ur, but increases with increase in m. In all the cases 4.. Pb Isotope Ratios in the ontinental rust [37] s we noted above, the time-integrated average of 232 Th/ 238 U (k Pb ) in a reservoir over the Earth history can be calculated from the Pb isotope compositions in that reservoir. Table 4 lists several estimates of the Pb isotopic composition and the corresponding k (Pb) of the continental crust. Unfortunately, none of these estimates are based on truly comprehensive evaluations; several, such as llègre and Lewin [989] and Kramers and Tolstikhin [997] are merely model values. [38] somewhat more thorough assessment of the Pb isotopic composition of the continental crust was published by Rudnick and Goldstein [990], but they did not include an estimate of the 208 Pb/ 204 Pb ratio. They kindly provided us with their compilation Pb isotope analyses of lower crustal xenoliths (S. Goldstein and R. Rudnick, Table 4. Estimated Pb Isotopic omposition and Time-Integrated k Values (k Pb ) of the ontinental rust and the Depleted Upper Mantle Reservoir/Reference 206 Pb 204 Pb 207 Pb 204 Pb 208 Pb 204 Pb k Pb ontinental rust llègre and Lewin [989] smerom and Jacobsen [993] a Ben Othman et al. [989] Kramers and Tolstikhin [997] Zartman and Doe [98] Rudnick and Goldstein [990] This work b This work c Depleted Upper Mantle Ito et al. [987] a verage isotopic composition in river water suspended load samples (n = 0) excluding Isua, whose 207 Pb/ 204 Pb ratio is unusually low. b Estimate based on smerom and Jacobsen [993] upper crustal composition and Rudnick and Goldstein [990] lower crustal composition using Pb concentrations of Rudnick and Fountain [995]. c Estimate based on smerom and Jacobsen s upper crustal composition and Rudnick and Goldstein s lower crustal composition using Pb concentrations of Wedepohl [995]. 2 of 7

13 Table 5a. 208 Pb/ 204 Pb of the Lower ontinental rust Tectonothermal age Ma Ma Ma >700 Ma >700 Ma Proportion of Total ontinental rea 9.% 34.4% 4.2% 32.3% Model I Model II 206 Pb /204 Pb a Pb/ 204 Pb a Pb/ 204 Pb a From Rudnick and Goldstein [990]. personal communication, 2002). Rudnick and Goldstein [990] averaged the analyses by tectonothermal age in bins of 0 250, , , and >700 Ma. They noted that the Pb isotopic compositions of rchean lower crust varied widely, and they therefore chose two values for the >700 Ma bin, one near the unradiogenic end of the range, the other near the lower end of the high 207 Pb/ 204 Pb granulites. These two choices correspond to their Model I and Model II respectively. They then estimated the isotopic composition of the total lower continental crust by computing a weighted average, with weighting based on the exposed area of each of these tectonothermal age bins. We treated the 208 Pb/ 204 Pb data in exactly the same way. The resulting estimate of the Pb isotopic composition of the lower crust is listed in Tables 5a and 5b. alculated values of the 208 Pb/ 204 Pb of for Model I and and for Model II correspond respectively to Rudnick and Goldstein s [990] values of 6.49 and 7.20 for 206 Pb/ 204 Pb and 5.20 and 5.55 for 207 Pb/ 204 Pb. This gives 208 Pb*/ 206 Pb* ratios of.098 and.060 for Models I and II respectively, which in turn correspond to time-integrated 232 Th/ 238 U ratios in the lower continental crust (k L(Pb) ) of 4.46 and 4.30 respectively. [39] Perhaps the best estimate of the Pb isotopic composition of the upper continental crust is the one that smerom and Jacobsen [993] derived from river sediments. Their upper continental crustal Pb corresponds to a k U(Pb) of 4.20 ( 208 Pb*/ 206 Pb* =.03). ombining the smerom and Jacobsen [993] upper crustal estimate with the mean of Model I and Model II lower crustal estimate of Rudnick and Goldstein [990] as extended in this work, and using the crustal Pb concentrations of Rudnick and Fountain [995], the entire continental crust has 206 Pb/ 204 Pb = 8.43, 207 Pb/ 204 Pb = 5.62, 208 Pb/ 204 Pb = and k (Pb) of 4.25 ( 208 Pb*/ 206 Pb* =.048). Using the crustal Pb concentrations of Wedepohl [995] instead of those of Rudnick and Fountain [995], the continental crust has 206 Pb/ 204 Pb = 7.70, 207 Pb/ 204 Pb = 5.5, 208 Pb/ 204 Pb = and k (Pb) of 4.3 ( 208 Pb*/ 206 Pb* =.059) (Table 4). If we use only the Model II Pb isotopic composition, we obtain a k (Pb) of 4.23, regardless of which set of concentrations are used. Thus the timeintegrated k of the continental crust appears to be >4.23, most likely between 4.25 and 4.3, significantly higher than that of bulk silicate Earth. On the other hand, the average Pb isotopic composition of NMORB reported by Ito et al. [987] corresponds to a k UM(Pb) of 3.8, lower than bulk silicate Earth. In this respect the depleted upper mantle and continental crust appear to be complimentary Forward Transport Model for U-Th-Pb Evolution [40] The next question is how are the time-integrated and present-day values of k in the crust related? In the depleted mantle, preferential extraction of Th as well as recycling of U and Pb from the continental crust have led to the present value of k (2.5) being much lower than the timeintegrated value (3.8). Because the k Pb of the mantle is lower than k Pb of the crust, addition of Table 5b. Total Lower rustal Models Model I Model II 206 Pb /204 Pb a Pb/ 204 Pb a Pb/ 204 Pb Pb*/ 206 Pb*.0.06 a From Rudnick and Goldstein [990]. 3 of 7

14 mantle-derived Pb to the continents during continental growth will to pull k Pb to lower values than what it would be if the continents evolved as a closed system. We expect, therefore, that the timeintegrated value of k (k (Pb) ) will be lower than the present-day value, but how much lower? [4] We used a mathematical model of U, Th, and Pb transport and isotopic evolution in the Earth in an attempt to estimate what the difference between k (Pb) and present-day k is likely to be in the present continental crust under reasonable assumptions, and hence further constrain k. The model used has been described in detail elsewhere [Paul et al., 2002]; we will provide only a summary here. The model consists of 4 terrestrial reservoirs: upper continental crust (U), lower continental crust (L), depleted upper mantle (UM), lower mantle (LM), and the fluxes that occur between them. In the version of the model used here, it is explicitly assumed that the lower mantle has a composition equal to primitive mantle and that while there are fluxes out of this reservoir, there are no fluxes into it. In the initial state of the model, the mass of both crustal reservoirs is 0 and both mantle reservoirs have a primitive composition. Fluxes occur between the reservoirs representing mantle plumes, crustal production, and crustal recycling. Over time, the crustal masses grow to their present values, the mass of the depleted upper mantle increases, and the mass of the lower mantle decreases (and hence the mass fraction of the depleted upper mantle, m, increases). Mass fluxes decrease through time in proportion to the decrease in radiogenic heat production of the Earth. Both the mantle plume and crustal production fluxes contribute to the generation of U and L through time, so these fluxes are further constrained to produce the present-day mass of the two crustal reservoirs. Elemental fluxes allow for elemental fractionation (to mimic that occurring during partial melting, erosion and aqueous transport). The recycling efficiency of U increases with time to mimic the effect of the atmosphere becoming oxidizing in the early Proterozoic; recycling efficiencies of all other elements are time-invariant. [42] Recycled crustal material from both the U (through sediment subduction) and L (through lower crustal delamination and tectonic erosion) is returned to the UM. We assume that all fluxes can be described as continuous mathematical functions; that is, the evolution of the mantle and continental crust has been continuous, rather than episodic. Mathematically, the model consists of a series of first-order differential equations describing the changing abundance of each nuclide in each reservoir with time. For example the rate of change of a radiogenic nuclide such as 206 Pb contained in reservoir j can be expressed as: d 206 Pb j ¼ X Fj$i 206Pb þ l U j ð7þ dt where l 238 is the decay constant of 238 U, 238 U j is the amount of 238 U in reservoir j, and F j$i is the flux from reservoir i to the reservoir j and vice versa. The set of such differential equations for each nuclide and each reservoir are then solved over the age of the Earth (4.55 Ga) at Ma intervals using the second-order Runge-Kutta numerical algorithm to obtain the isotopic ratios and chemical abundances for the U-Th-Pb isotope system in the present terrestrial reservoirs Model Results [43] Using the model of Pb isotope evolution described above, we find that a time-integrated k (Pb) of 4.25 in the continental crust requires a the present-day value of k of 5. The larger difference between k (Pb) and k reflects the need to balance low 208 Pb/ 206 Pb lead from the mantle with radiogenic 208 Pb produced in the crust itself. Figure 9 shows the evolution of both k and k Pb in the continental crust and depleted upper mantle in the model. This particular solution where m grows from 0.25 initially to 0.42 at the present-day, yields reasonable Pb isotope ratios in the continental crust of 206 Pb/ 204 Pb = 7.33, 207 Pb/ 204 Pb = 5.35, 208 Pb/ 204 Pb = The continental crust plots to the left of the 4.55 Ga geochron whereas the depleted upper mantle plots to the right. ssuming a K/U of 2,500, our model produces W of radiogenic heat in the continental crust, and a Ur of 0.47, well within the range geophysical-based estimates. 4 of 7

15 Figure 9. Temporal evolution of the instantaneous (k Th ) 232 Th/ 238 U ratio and time-integrated value (k Pb )in the bulk continental crust and depleted upper mantle as predicted by the forward transport model. [44] This evolution shown in Figure 9 does not, of course, represent a unique solution. It was achieved by optimizing a number of free parameters, such as distribution coefficients [Paul et al., 2002], in the model so as to best reproduce the Pb isotopic composition of the mantle and crust. While not necessarily unique, we have found that the range of parameters that leads to solutions reasonably approximating the Pb isotopic composition of the Earth are few. We believe, therefore, that this solution likely approximates the actual Pb evolution of the crust. If so, the most probably value for k in the continental crust is about 5. This value, determined by forward modeling constrained by Pb isotope ratios, agrees well with the range of likely values we found from mass balance (Figures 2 7). 5. onclusions [45] k in oceanic islands range from 2.8 to 4.70, with an average of 3.78, remarkably close to the chondritic value. onsidering that some fractionation of Th from U may occur during magma genesis, this average would correspond to an average k for OIB sources of 3.4. Thus if OIB are produced by plumes coming from the lower mantle, k LM is lower than the chondritic and bulk silicate Earth values. Hence the well-established low k in the upper mantle must be balanced by k significantly greater than 4. [46] For a primitive lower mantle, Ur = 0.5, and m = 0.45, which we believe is the most likely value [Turcotte et al., 200], we estimate k to be 5.7, close to the estimates of Wedepohl [995] and Shaw et al. [986]. Estimates of k of around 4 [e.g., Rudnick and Fountain, 995; Taylor and McLennan, 995; Weaver and Tarney, 984] are only possible in the very unlikely case that k LM >4 and Ur and m are considerably lower than the generally accepted values. non-primitive lower mantle (k LM < 4), which is implied by Th/U ratios in OIB, favors higher values of k, such as the estimates of Gao et al. [997] and Haack [983]. [47] The Pb isotope ratios in the continental crust give time-integrated values of k (k (Pb) ) in the range 4.25 to Because Pb in the continental crust is derived from mantle reservoirs that have lower k than the crust does, the instantaneous value of k in the continental crust must be greater than the time-integrated value of k (Pb) in the crust. Our forward transport model that successfully reproduces the difference in instantaneous and time-integrated value of k in the mantle suggests that a present-day value of k (Pb) 4.25 in the continental crust requires a k 5 in the crust. Thus both mass balance and evolutionary modeling of Pb isotope ratios favor a value of k 5, consistent with the estimates of Shaw et al. [986] and Wedepohl [995], and significantly higher than the estimates of Rudnick and Fountain [995], Taylor and McLennan [995], and Weaver and Tarney [984]. cknowledgment [48] This research has been supported by NSF award # ER to WMW and DLT. GEORO, the online database on OIB compositions maintained by the Max-Planck-Institut für hemie, Mainz, Germany has been extremely helpful through out this research as well as on other occasions. We especially thank Steve Goldstein and Roberta Rudnick for providing their compilation of Pb isotope ratios in lower crustal xenoliths. Finally, we thank Vincent Salters for a thoughtful and thorough review. References llègre,. J., and M. ondomines, Basalt genesis and mantle structure studied through Th-isotopic geochemistry, Nature, 299, 2 24, of 7