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4He ratio in the Earth’s mantle reservoirs for the first 2 Ga
Earth and Planetary Science Letters 188 (2001) 211^219 www.elsevier.com/locate/epsl
Concurrent evolution of 3 He/4 He ratio in the Earth's mantle reservoirs for the ¢rst 2 Ga Akihiro Seta *, Takuya Matsumoto, Jun-ichi Matsuda Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan Received 28 August 2000; received in revised form 8 January 2001; accepted 9 March 2001
Abstract The differences in 3 He/4 He ratios between mid-oceanic ridge basalts (MORBs) and ocean island basalts (OIBs) require the existence of at least two distinct mantle reservoirs that have been preserved over long periods of the Earth's history. However, it is unclear how the 3 He/4 He ratios have evolved in the mantle over time, and when these reservoirs acquired their present-day signatures. Here we report the results of our model calculation for helium evolution in the mantle, and show that, from the time of the Earth's formation to the Late Archean (V2 Ga), the 3 He/4 He ratios in both the MORB and OIB mantle reservoirs evolved in a rather homogeneous fashion. In contrast to previous models, our model suggests that the distinction in 3 He/4 He ratios between the MORB-type source and the plume-type source is a relatively recent characteristic of the Earth's mantle. ß 2001 Elsevier Science B.V. All rights reserved. Keywords: mantle; models; helium; argon; isotope ratios
1. Introduction The discovery that primordial 3 He is being degassed from the Earth's interior [1] to the atmosphere reveals that terrestrial degassing is an ongoing process. Helium and other noble gas isotopes trace the Earth's degassing history and permit characterization of volatile reservoirs in the Earth's mantle. For example, an excess of 129 Xe in mantle-derived samples relative to the atmospheric composition suggests that early extensive
* Corresponding author. Tel.: +81-6-6850-5497; Fax: +81-6-6850-5480; E-mail: [email protected]
outgassing from the Earth's mantle to the atmosphere occurred before all live-129 I became extinct [2]. We now have su¤cient analytical data on mantle-derived rocks and £uids to conclude that the present-day mantle is comprised of at least two distinct domains, which evolved essentially as separate reservoirs with di¡erent time-integrated radioactive parent to primordial noble gas ratios (e.g. U+Th/3 He, 40 K/36 Ar). One reservoir is sampled by mid-oceanic ridge basalts (MORBs) and has a quite uniform 3 He/4 He ratio of 1.1U1035 (e.g. [3]). The other reservoir is sampled by mantle plumes, and has variable 3 He/4 He ratios, with maximum ratios of up to 4.7U1035 (as in Loihi basalts [4]). These distinct isotopic ratios in MORBs and ocean island basalts (OIBs) indicate that degassing of the Earth's mantle did not occur in a homogeneous fashion.
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Instead, the mantle source for MORBs was degassed of its primordial 3 He more signi¢cantly than the OIB source. Thus, the MORB source is commonly designated the `degassed' mantle, and the OIB source the `less-degassed' mantle. In general, the isotopic systematics of other noble gas isotopes (i.e. 21 Ne/22 Ne, 40 Ar/36 Ar ratios) can also be explained by the presence of these two distinct mantle reservoirs. However, as the ratios observed in MORBs and OIBs are recent mantle signatures, how noble gas isotopic ratios have evolved in the mantle through the Earth's history is essentially unknown. This makes it di¤cult to interpret the signi¢cance of high 3 He/4 He ratios observed in older samples such as in diamond (3 He/4 He ratios up to 2U1035 [5^8]) and in Archean komatiites (V5U1035 [9]). Recently, we constructed a new model for the evolution of noble gas isotopic compositions in the atmosphere^mantle system [10], based on the notion that the OIB source mantle had experienced more extensive degassing [11] than had previously been considered (e.g. [12]). In our model, the degassing £ows of noble gases from the mantle are represented by their concentrations in the mass £ows from mantle reservoirs to the surface, following the model of Porcelli and Wasserburg [13,14]. However, our model is unique in that the mass £ows are modeled as having decreased exponentially as a function of time over the history of the Earth. This assumption is in contrast to the steady-state £ow model employed in Porcelli and Wasserburg [13,14]. The validity of our model calculation is supported by its ability to predict that the Earth's primordial 3 He/36 Ar ratio was in cosmic abundance [10], which is indeed consistent with the notion made independently based on He^ Ne isotope observations in oceanic basalts [4,15]. In our continuing e¡ort to further develop a model to describe noble gases in the Earth^atmosphere system, we have expanded our model to include the time-dependent evolution of 3 He/4 He ratios in di¡erent mantle reservoirs. As noted above, such estimates have great implications for bettering our understanding of the dynamics of mantle evolution, and for interpreting the noble gas isotopic ratios observed in terrestrial samples.
2. The model Before presenting results of the model calculation on 3 He/4 He evolution in mantle reservoirs, we brie£y outline here the underlying ideas of our previous model on the mantle degassing [10] (for this model calculation, some more details are given in the Appendix). The model assumes that the present Earth has three separate noble gas reservoirs with distinct di¡erentiation histories that originated from an isotopically homogeneous primitive Earth (Fig. 1). These are: (i) the degassed mantle (with the noble gas isotope characteristics of MORBs) ; (ii) the less-degassed mantle (as sampled by some plume-related intraplate volcanism); and (iii) the surface reservoir (atmosphere and oceanic and continental crust). Mass £ows through the following paths were assumed to control transfer of elements among those three reservoirs (Fig. 1); (i) from the degassed mantle to the oceanic crust, (ii) from the less-degassed mantle to the oceanic crust, (iii) from the degassed mantle to the continental crust, and (iv) the recycling of oceanic crust back in the mantle. The ¢rst
Fig. 1. A schematic diagram of the mantle reservoirs and mass £ows assumed in the Osaka model.
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and second paths correspond to the magmatism at spreading centers and plume-related volcanic activity, respectively. Simultaneous and complete outgassing of noble gases was assumed for the mass £ows to the oceanic crust. The third path involves the selective uptake of radioactive parents, such as U, Th and K, from the depleted mantle to the continental crust with the conceptual extraction factor x [10] (see Appendix). Noble gas recycling into the mantle was not considered in the last path because of the suggested existence of a subduction barrier for all the noble gases except for xenon [16] and only solid elements were assumed to be recycled into the mantle with extraction factor r [10] (see Appendix). For the solid elements, mantle-derived material exchanges between the degassed reservoir including the oceanic crust and the less-degassed reservoir. In our model, `degassed' and `less-degassed' reservoirs will be equated to the `depleted' and `lessdepleted' reservoirs in reference to the solid elements. As noted earlier, the above mass £ows are assumed to have decreased as an exponential function of time so as to simulate the extensive outgassing early in the Earth's history. For example, the following equations describe the mass £ows from the depleted mantle and the less-depleted ç Dout and mantle to the surface reservoir (M ç MLout ) decrease as a function of the decrement factors LD and LL , respectively [10]:
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We estimated the values of LD , LL , and x by using the representative 3 He/4 He and 40 Ar/36 Ar ratios in the MORB and OIB source mantle reservoirs. The planetary 3 He/4 He ratio (1.42U1034 [17]) was used for the initial helium composition of the Earth, because 3 He in the present-day solar wind composition is elevated owing to production of 3 He by deuterium burning in the Sun [18]. For the present calculation, we used 3 He/4 He ratios of 1.1U1035 and 4.7U1035 for the representative compositions in the MORB and OIB source reservoirs, respectively. We also assumed 40 Ar/36 Ar ratios of 6U104 [19] and 3U103 [11] for the lower limit of the values in the MORB and OIB source reservoirs, respectively. The extraction factor x was estimated from the present 40 K concentration in the continental crust (3.6U1016 atoms/g [20]) and in the depleted reservoir (1.8U1014 atoms/g [21]). The values of LL , LD and x that satisfy the above conditions are 1.32^1.34U1039 , 2.60^ 3.32U10310 and 40^274, respectively. Note that these values are slightly di¡erent from those reported by Kamijo et al. [10]. This is because we used updated noble gas isotopic ratios from recent empirical studies (see Appendix). The decrement factors obtained from the model suggest that the mass £ows from the depleted and less-depleted reservoirs to the surface reservoir have decreased by factors of 1/4 and 1/400, respectively, compared with the initial mass £ow during the Earth's history.
_ Dout t M _ Dout 0Wexp 3 L D Wt M
1
_ Lout t M _ Lout 0Wexp 3 L L Wt M
2
3. Temporal variations of 3 He and 4 He amounts in the mantle reservoirs
The abundance of non-radiogenic noble gas isotopes in the reservoirs at a given time can be constrained as the sum of mass £ows into and out of each reservoir, provided that the initial and present-day concentrations and decrement factors (LD and LL ) are known. In the case of the concentrations of radiogenic isotopes such as 4 He and 40 Ar in each reservoir, time-dependent production and net transfer of parent isotopes need to be considered. Thus, the values of LD , LL , x, and the initial and present concentrations of noble gases in each reservoir need to be constrained.
By using the parameters estimated above, temporal variations of 3 He contents in the degassed and less-degassed reservoirs are calculated (Fig. 2a). Because there is no signi¢cant production of 3 He in the mantle, the amount of 3 He is a¡ected only by mantle degassing. As the decrement factor of the mass £ow from the degassed mantle to the surface is smaller than that from the less-degassed mantle, the degassed mantle has lost s 99.8% of its initial 3 He over 4.5 Ga. The model calculation suggests that the present-day less-degassed mantle has also lost a signi¢cant fraction of its primor-
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Fig. 2. Estimated temporal variation in amounts of (a) 3 He, (b) 238 U and (c) 4 He in the less-degassed and degassed mantle reservoirs (solid and shaded curves, respectively). The width of curves at a given time represents the upper and lower limits derived from the present-day concentration of 40 K in the continental crust and in the depleted mantle (see text and Appendix). The broken lines in (b) show the amounts of 238 U decreased only by the radioactive decay in each reservoir assuming a closed system. The paired broken curves in (c) show ranges of radiogenic 4 He produced in the less-degassed and the degassed mantle reservoirs. C
dial 3 He ( s 87%), but it still has a few hundred times more primordial 3 He than that in the degassed reservoir. The amount of primordial 4 He in the mantle reservoirs at a given time, on the other hand, can be obtained from that of 3 He (Fig. 2a) and the assumed primordial 3 He/4 He ratio of 1.42U1034 [17]. To model the amount of the total 4 He in the mantle, we need to consider the e¡ect of radiogenic production from U and Th decay, in addition to the degassing of a primordial component. The amount of U in each reservoir is a¡ected by U extraction from the mantle to crust, recycling into the mantle through subduction and, of course, by radioactive decay. These three processes had been taken into account for the calculation as described in the Appendix. Resultant curves for 238 U amounts in each reservoir over the history of the Earth are presented in Fig. 2b as an example. To clarify the in£uences of the mass £ows on the U content in each reservoir, we also calculated the case for the simple radiogenic decay in each reservoir (broken lines) assuming a closed system. The evolution of U content in our model is very similar to that in the closed system model for the less-degassed reservoir, but is very di¡erent for the degassed reservoir. This is because the mass of degassed reservoir is about 1/3 of the less-degassed reservoir. Especially, in the ¢rst 500 Ma, the e¡ect of the mass £ow is considerably large in comparison to the mass of the degassed reservoir ç Lout (0)V8U1018 g/yr is almost 400 times as (M large as the present one). As a result, the amount of U in the degassed mantle is about 1/10 of that in the less-degassed reservoir over 4.5 Ga. By constraining the behavior of U and other
radioactive parents through time, the total 4 He budget in each mantle reservoir can be estimated as functions of time. As shown in the ¢eld bounded by the dotted curves in Fig. 2c, produc-
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tion of radiogenic 4 He shows a dramatic increase in the ¢rst several hundred million years of the Earth's history. However, in this period, the absolute abundance of radiogenic 4 He in the degassed reservoir is signi¢cantly smaller than that of the primordial 4 He still remaining there. This is because the subduction of oceanic crust to the less-degassed reservoir removes signi¢cant amounts of parent nuclides from the degassed reservoir owing to the large mass £ow in the early history of the Earth. Thus, the total amount of 4 He in the degassed mantle reservoir follows a similar path that is de¢ned by a primordial 3 He until the radiogenic 4 He becomes signi¢cant. As shown in Fig. 2c, the radiogenic 4 He appeared to become dominant in the degassed mantle reservoir after a lapse of about 2 Ga since the formation of the Earth. The calculation suggests that about 90% of total 4 He in the present-day degassed reservoir is of radiogenic origin. The radiogenic 4 He in the less-degassed mantle, on the other hand, amounts to about 70% of the total 4 He amount. Its temporal variation is suggested to follow a somewhat di¡erent trend than that in the degassed reservoir. Due to the less active degassing after the ¢rst 1 Ga and its less-depleted ( = more production of radiogenic helium) character, the total budget of 4 He in the less-degassed reservoir showed some increase after it experienced rapid degassing in the ¢rst 1 Ga (Fig. 2c). 4. Temporal variations of 3 He/4 He ratio in the mantle and its implications The temporal variations in the amounts of 3 He and 4 He in the mantle reservoirs allow us to calculate the changes in 3 He/4 He ratios in the mantle over the last 4.5 Ga. Fig. 3 shows how the 3 He/4 He ratios have evolved in each reservoir from the initial, assumed planetary, ratio to the present ratios. The most interesting point to be noted is the concurrent change in 3 He/4 He ratios in both mantle reservoirs in the ¢rst 2 Ga, followed by a rather abrupt separation of the two evolution curves. This abrupt change corresponds to the change in the major component of 4 He in
215
Fig. 3. Temporal variation of the helium isotopic ratio (3 He/ 4 He) in each reservoir. A shaded curve shows the evolution in the degassed mantle and the solid curve shows the evolution in the less-degassed mantle. The upper limit is calculated from the present concentration of 40 K in the depleted mantle. The lower limit is calculated from the concentration of 40 K in continental crust at present. The right axis shows the 3 He/4 He ratio ( = R) as R/Ra (Ra is the atmospheric ratio, 1.4U1036 ). The broken curves show the simple closed system evolution of 3 He/4 He ratio in each mantle reservoir. In the closed system, the degassed and less-degassed reservoirs are assumed to have initial U/3 He ratios as 19 000 and 3200, respectively. All curves were obtained by ¢xing the initial and present 3 He/4 He ratios in the degassed and less-degassed reservoirs (1.42U1034 , 1.10U1035 and 4.67U1035 , respectively). The open circle is the datum of Archean komatiite [9].
the degassed mantle. Before 2 Ga, the amount of 4 He in the degassed reservoir is largely controlled by the amount of a primordial component. Note that, in the ¢rst 2 Ga of the Earth's history, the radiogenic 4 He contributes only 6 1/100 to 1/2 of total 4 He in the degassed reservoir (Fig. 2c) due to a rapid extraction of U and Th from the degassed reservoir (Fig. 2b) and their long half-lives. Thus, the degassed reservoir maintained its high 3 He/4 He ratio for a rather extended period of time than that anticipated from the simple closed system evolution (Fig. 3 and [9]) and a ¢rst-order degassing process [12]. After the 2 Ga, the contribution of radiogenic 4 He to the total 4 He budget in the degassed reservoir becomes more and more signi¢cant (Fig. 2c). Accordingly, a decrease in
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3
He/4 He is accelerated towards the present-day value, whereas the 3 He/4 He ratios in the less-degassed reservoir decreased following a path similar to that de¢ned by the closed system evolution. Our model suggests that the 3 He/4 He ratio of the degassed mantle was signi¢cantly di¡erent in the past. This further suggests that some caution should be taken when interpreting 3 He/4 He ratios from ancient mantle-derived samples. For example, very high 3 He/4 He ratios of V5U1035 observed in some Archean komatiites were taken as evidence for a plume origin for the parent magma of the komatiites [9]. However, as shown in Fig. 3, the model results suggest that a plumerelated (less-degassed) component is not necessarily required for the komatiite source, as the 3 He/ 4 He ratio is also similar to that in the Archean degassed mantle. In addition, mantle xenoliths derived from the continental lithospheric mantle are estimated to have formed 0.5^2.0 Ga ago (e.g. [22]). The mantle 3 He/4 He ratios during this time interval are calculated to be as high as 1.4^ 4.0U1035 . However, none of the continental xenoliths analyzed so far shows such high 3 He/4 He
ratios. Instead the 3 He/4 He ratios are either MORB-like or lower (e.g. [23^25]). In this respect, our model suggests that the helium trapped in xenoliths is unlikely to have been trapped during the formation of the continental lithosphere. It is possible that the helium was instead recently trapped in the xenoliths, and was ultimately derived from the present-day degassed mantle source by metasomatism [23,24], or by £uid injection from the xenolith's host basalts [25]. As discussed above, although we assumed the existence of two separate mantle reservoirs with signi¢cantly di¡erent degassing histories, there is a possibility that the entire Earth's mantle had quite uniform 3 He/4 He ratios during the ¢rst 2 Ga of Earth's history. Compositional criteria used to infer the origin of recent mantle samples (MORBs and OIBs) certainly cannot be applied to ancient samples. Any samples with an age greater than 500 Ma could have plume-like 3 He/4 He ratios ( s 10 Ra), even though they are originated from the degassed mantle reservoir. Acknowledgements The authors thank Eleanor Dixon, by whom the manuscript was greatly improved both in its contents and in English. Thanks are also due to Koich Kamijo for his help in developing the computer source codes for this project. Don Porcelli and Manuel Moreira are thanked for careful and insightful reviews. Alex N. Halliday is also thanked for his helpful advice as a handling editor. The paper has been greatly improved through their comments. This work was partly supported by Grants-in-Aid from the Japan Society for the Promotion of Science (12740306).[AH] Appendix
Fig. 4. A £ow chart of the model calculation.
We will describe here a £ow of the model calculation in more details. A simpli¢ed £ow chart of the calculation is given in Fig. 4 and a list of all notations used in this paper is given in Table 1. As noted in the main body of the paper, we
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Table 1 Notation and constraint values in our model i
NR CR V PrR MD ML ç Dout M ç Lout M ç pcc M LD LL x N
r
Abundance of isotope i N in reservoir R Concentration of isotope N in reservoir R Decay constant of nuclides Production rate of radiogenic nuclides in the reservoir R Mass of the degassed reservoir Mass of the less-degassed reservoir Mass £ow from degassed reservoir to the surface Mass £ow from less-degassed reservoir to the surface Formation rate of the continental crust Decrement factor of mass £ow from degassed reservoir Decrement factor of mass £ow from less-degassed reservoir Extraction factor of K, U and Th for the continental crust formation Extraction factor of K, U and Th for the oceanic crust formation
atoms atoms/g /yr atoms/yr 1U1027 g [13] 3U1027 g [13] 7U1017 g/yr [26] 2U1016 g/yr [13] 4.4U1015 g/yr [10] /yr /yr dimensionless dimensionless This study
3
He/4 HeL (T) 3 He/4 HeD (T) 40 Ar/36 ArL (T) 40 Ar/36 ArD (T) 40 Ar/36 Aratm (T) K/U Th/U
The The The The The
present-day 3 He/4 He ratio in the less-degassed reservoir present-day 3 He/4 He ratio in the degassed reservoir present-day 40 Ar/36 Ar ratio in the less-degassed reservoir present-day 40 Ar/36 Ar ratio in the degassed reservoir present-day 40 Ar/36 Ar ratio in the atmosphere
expanded the model developed by Kamijo et al. [10] to obtain the evolutions of 3 He/4 He ratios in mantle reservoirs. An important assumption in [10] is that amounts of noble gases and radiogenic parents in reservoirs are controlled by the mass £ows, which decreased as an exponential function of time. Such an assumption is expressed as Eqs. 1 and 2 in the main text for mass £ows from the less-degassed and the degassed mantle reservoirs to the surface with respective decrement factors (LL and LD ). The present-day mass £ows from the less-degassed and the degassed mantle reserç Lout (T) and M ç Dout (T) where T = 4.5 Ga voirs (M since the formation of the Earth) are required for calculating the initial mass £ows by using Eqs. 1 and 2. We adopted the same values for ç Lout (T) = 2U1015 the present-day mass £ows (M 17 ç g/yr and MDout (T) = 7U10 g/yr) as were applied in [10]. As will be noted later, LL and LD are treated as unknown parameters to be determined by solving the following equations to satisfy some empirical analytical data from representative mantle-derived samples. The amounts of non-radiogenic isotope (N) in
Kamijo et al. [10]
4.67U1035 [4] 4.2U1035 1.10U1035 (e.g. [3]) s 3.0U103 [11] s 6U104 [19] s 1U104 295.5 296 12 700 [21] 3.9 ([21] reference therein)
the less-degassed and the degassed reservoirs are described as: dN L t _ Lout t 3N C L WM dt _ Lout 0exp 3 L L Wt 3N C L W M
A1
dN D t _ Dout t3N C D WM _ pcc t 3N C D W M dt _ Dout 0exp 3 L D Wt3N C D WM _ pcc t 3N C D W M A2 where N CR denotes the concentration of isotope N in reservoir R. In our model, noble gases are assumed not to be recycled into the mantle by subduction of the oceanic crust. A mass £ow to ç pcc ) is assumed to form the continental crust (M have been derived only from the depleted mantle reservoir, and obtained by dividing a total mass (2U1025 g [12]) of the continental crust by 4.5 Ga. The di¡erential equations for the radiogenic
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isotopes (4 He and
40
Ar) were written as:
dN L t _ Lout t PrL t 3 N C L WM dt
A3
dN D t _ Dout t3N C D WM _ pcc t PrD t 3N C D W M dt A4 PrL (t) and PrD (t) are terms describing production of radiogenic isotopes in less-degassed and degassed reservoirs at a given time t, and are written as:
satisfy the observation (see Fig. 4). With these two new parameters, the di¡erential equations of the radiogenic parents (N) can be written as: dN cc t _ pcc 3V WN cc t xWN C D WM dt dN D t dt _ Lout 3xWN C D WM _ pcc 3V WN D t3 rWN C D 3N C L WM A8 dN L t _ Lout 3V WN L t rWN C D 3N C L WM dt
PrR t 8V 238U W238 UR t 7V 235U W235 UR t 6V 232Th W232 ThR t
A5
PrR t V e W40 KR t
A6
where V denotes the respective decay constant of the parents. In order to solve Eqs. A3 and A4, we need to know how the amounts of K, U and Th in each mantle reservoir vary with time. In contrast to gaseous noble gases for which the bulk partitioning into the melt phase (thus, into the mass £ows in the case of this model) is expected upon melt^solid partitioning, the behavior of radioactive parents should be treated di¡erently as those applied for noble gases. Therefore, two new parameters, x and r, are introduced in [10]. The parameter x re£ects the extraction of radioactive parents by the continental crust formation. The parameter r represents the enrichment factor of the radioactive parents in the oceanic crust at the subduction £ow. The r must be larger than one due to the incompatibility of K. Kamijo et al. [10] estimated r to be 2 comparing the K2 O concentration in the oceanic crust with that in the upper mantle. As this estimation may be oversimpli¢ed, we estimated the e¡ect of uncertainty of r to the result of our calculation. Even if r is about 10, the concurrent evolution of helium isotopic ratio is retained with a somewhat longer period (up to about 2.5 Ga). The parameter x is the ratio of the concentration of radiogenic parents in the continental crust to that in the degassed reservoir which will be determined during the calculation to
A7
A9
The ¢rst terms of the right side of Eqs. A7^A9 describe the decrease of N in each reservoir due to ç Lout , in Eqs. A8 its decay. The next terms, with M and A9 can be regarded as representing the material mixing or exchange between the degassed and less-degassed reservoirs by the recycling of the oceanic crust (note that the mass £ow recycled into the less-degassed mantle from the reservoir which consists of oceanic crust and depleted mantle is balanced with the mass £ow out of the lessdegassed mantle (see Fig. 2 of [10]) to keep the volume of each reservoir constant). The ¢nal ç pcc represent the selective uptake of terms with M radioactive parents from the degassed reservoir to the continental crust. As noted above, the decrement factor L is one of the most important parameters that controls the mass £ows among the assumed mantle reservoirs. As shown in Fig. 4, L is started from an independent variable. The parameter x is, then, expressed as a function of L by using the present-day concentrations of U and Th. Concentrations of U in the crust and the depleted reservoir give upper and lower limits for all parameters. At this stage, all parameters are expressed as functions of LL . These functions can be solved from the observed 40 Ar/36 Ar ratios in the atmosphere and the mantle. Then, all parameters can uniquely be obtained. The obtained values for the parameters are slightly di¡erent from what was estimated in [10]. This is because we used some
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updated values for values for the present-day noble gas isotopic ratios. However, this change did not a¡ect the results of ours and [10] to a signi¢cant extent. References [1] H. Craig, W.B. Clarke, M.A. Beg, Excess 3 He in deep water on the East Paci¢c Rise, Earth Planet. Sci. Lett. 26 (1975) 125^132. [2] T. Staudacher, C.J. Alle©gre, Terrestrial xenology, Earth Planet. Sci. Lett. 60 (1982) 389^406. [3] D.R. Hilton, K. Hammerschmidt, G. Loock, H. Friedrichsen, Helium and argon isotope systematics of the central Lau Basin and Valu Fa Ridge: Evidence of crust/mantle interactions in a back-arc basin, Geochim. Cosmochim. Acta 57 (1993) 2819^2841. [4] M. Honda, I. McDougall, D.B. Patterson, A. Doulgeris, D.A. Clague, Noble gases in submarine pillow basalt glasses from Loihi and Kilauea, Hawaii: a solar component in the Earth, Geochim. Cosmochim. Acta 57 (1993) 859^874. [5] M. Honda, J.H. Reynolds, E. Roedder, S. Epstein, Noble gases in diamonds: occurences of solarlike helium and neon, J. Geophys. Res. 92 (1987) 12507^12521. [6] M. Ozima, S. Zashu, Solar-type Ne in Zaire cubic diamonds, Geochim. Cosmochim. Acta 52 (1988) 19^25. [7] M. Ozima, S. Zashu, Noble gas state of the ancient mantle as deduced from noble gases in coated diamonds, Earth Planet. Sci. Lett. 105 (1991) 13^27. [8] N. Wada, J. Matsuda, A noble gas study of cubic diamonds from Zaire: Constraints on their mantle source, Geochim. Cosmochim. Acta 62 (1998) 2335^2345. [9] D. Richard, B. Marty, M. Chaussidon, N. Arndt, Helium isotopic evidence for a lower mantle component in depleted Archean komatiite, Science 273 (1996) 93^95. [10] K. Kamijo, K. Hashizume, J. Matsuda, Noble gas constraints on the evolution of the atmosphere^mantle system, Geochim. Cosmochim. Acta 62 (1998) 2311^2321. [11] J. Matsuda, B. Marty, The 40 Ar/36 Ar ratio of the undepleted mantle; a reevaluation, Geophys. Res. Lett. 22 (1995) 1937^1940. [12] C.J. Alle©gre, T. Staudacher, P. Sarda, Rare gas systematics: formation of the atmosphere, evolution and structure of the Earth's mantle, Earth Planet. Sci. Lett. 81 (1987) 127^150.
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[13] D. Porcelli, G.J. Wasserburg, Mass transfer of xenon through a steady-state upper mantle, Geochim. Cosmochim. Acta 59 (1995) 1991^2007. [14] D. Porcelli, G.J. Wasserburg, Mass transfer of helium, neon, argon and xenon through a steady-state upper mantle, Geochim. Cosmochim. Acta 59 (1995) 4921^4937. [15] M. Honda, I. McDougall, D.B. Patterson, A. Doulgeris, D.A. Clague, Possible solar noble gas component in Hawaiian basalts, Nature 349 (1991) 149^151. [16] J. Matsuda, K. Matsubara, Noble gases in silica and their implication for the terrestrial `missing' Xe, Geophys. Res. Lett. 16 (1989) 81^84. [17] J.H. Reynolds, U. Frick, J.M. Niel, D.L. Phinney, Raregas-rich separates from carbonaceous chondrites, Geochim. Cosmochim. Acta 42 (1978) 1775^1797. [18] M. Ozima, F.A. Podosek, Noble Gas Geochemistry, Cambridge University Press, 1983, 367 pp. [19] P. Burnard, D. Graham, G. Turner, Vesicle-speci¢c noble gas analysis of `popping rock': Implications for primordial noble gases in Earth, Science 276 (1997) 568^571. [20] R.K. O'Nions, S.R. Carter, N.M. Evensen, P.J. Hamilton, Upper mantle geochemistry, Sea 7 (1981) 49^71. [21] K.P. Jochum, A.W. Hofmann, E. Ito, H.M. Seufert, W.M. White, K, U and Th in mid-ocean ridge basalt glasses and heat production, K/U and K/Rb in the mantle, Nature 306 (1983) 431^436. [22] M. Handler, V. Bennett, T. Esat, The persistence of o¡cratonic lithospheric mantle: Os isotopic systematics of variably metasomatised southeast Australian xenoliths, Earth Planet. Sci. Lett. 151 (1997) 61^75. [23] T. Matsumoto, M. Honda, I. McDougall, S.Y. O'Reilly, Noble gases in anhydrous lherzolites from the Newer Volcanics, southeastern Australia: A MORB-like reservoir in the subcontinental mantle, Geochim. Cosmochim. Acta 62 (1998) 2521^2533. [24] T. Matsumoto, M. Honda, I. McDougall, S.Y. O'Reilly, M. Norman, G. Yaxley, Noble gases in pyroxenites and metasomatised peridotites from the Newer Volcanics, southeastern Australia: implications for mantle metasomatism, Chem. Geol. 168 (2000) 49^73. [25] T.J. Dunai, H. Baur, Helium, neon, argon systematics of the European subcontinental mantle: Implications for its geochemical evolution, Geochim. Cosmochim. Acta 59 (1995) 2767^2783. [26] J.A. Crisp, Rates of magma emplacement and volcanic activity, J. Volcanol. Geotherm. Res. 20 (1984) 177^211.
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Concurrent evolution of 3 He/4 He ratio in the Earth's mantle reservoirs for the ¢rst 2 Ga Akihiro Seta *, Takuya Matsumoto, Jun-ichi Matsuda Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan Received 28 August 2000; received in revised form 8 January 2001; accepted 9 March 2001
Abstract The differences in 3 He/4 He ratios between mid-oceanic ridge basalts (MORBs) and ocean island basalts (OIBs) require the existence of at least two distinct mantle reservoirs that have been preserved over long periods of the Earth's history. However, it is unclear how the 3 He/4 He ratios have evolved in the mantle over time, and when these reservoirs acquired their present-day signatures. Here we report the results of our model calculation for helium evolution in the mantle, and show that, from the time of the Earth's formation to the Late Archean (V2 Ga), the 3 He/4 He ratios in both the MORB and OIB mantle reservoirs evolved in a rather homogeneous fashion. In contrast to previous models, our model suggests that the distinction in 3 He/4 He ratios between the MORB-type source and the plume-type source is a relatively recent characteristic of the Earth's mantle. ß 2001 Elsevier Science B.V. All rights reserved. Keywords: mantle; models; helium; argon; isotope ratios
1. Introduction The discovery that primordial 3 He is being degassed from the Earth's interior [1] to the atmosphere reveals that terrestrial degassing is an ongoing process. Helium and other noble gas isotopes trace the Earth's degassing history and permit characterization of volatile reservoirs in the Earth's mantle. For example, an excess of 129 Xe in mantle-derived samples relative to the atmospheric composition suggests that early extensive
* Corresponding author. Tel.: +81-6-6850-5497; Fax: +81-6-6850-5480; E-mail: [email protected]
outgassing from the Earth's mantle to the atmosphere occurred before all live-129 I became extinct [2]. We now have su¤cient analytical data on mantle-derived rocks and £uids to conclude that the present-day mantle is comprised of at least two distinct domains, which evolved essentially as separate reservoirs with di¡erent time-integrated radioactive parent to primordial noble gas ratios (e.g. U+Th/3 He, 40 K/36 Ar). One reservoir is sampled by mid-oceanic ridge basalts (MORBs) and has a quite uniform 3 He/4 He ratio of 1.1U1035 (e.g. [3]). The other reservoir is sampled by mantle plumes, and has variable 3 He/4 He ratios, with maximum ratios of up to 4.7U1035 (as in Loihi basalts [4]). These distinct isotopic ratios in MORBs and ocean island basalts (OIBs) indicate that degassing of the Earth's mantle did not occur in a homogeneous fashion.
0012-821X / 01 / $ ^ see front matter ß 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 2 - 8 2 1 X ( 0 1 ) 0 0 3 0 7 - 7
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Instead, the mantle source for MORBs was degassed of its primordial 3 He more signi¢cantly than the OIB source. Thus, the MORB source is commonly designated the `degassed' mantle, and the OIB source the `less-degassed' mantle. In general, the isotopic systematics of other noble gas isotopes (i.e. 21 Ne/22 Ne, 40 Ar/36 Ar ratios) can also be explained by the presence of these two distinct mantle reservoirs. However, as the ratios observed in MORBs and OIBs are recent mantle signatures, how noble gas isotopic ratios have evolved in the mantle through the Earth's history is essentially unknown. This makes it di¤cult to interpret the signi¢cance of high 3 He/4 He ratios observed in older samples such as in diamond (3 He/4 He ratios up to 2U1035 [5^8]) and in Archean komatiites (V5U1035 [9]). Recently, we constructed a new model for the evolution of noble gas isotopic compositions in the atmosphere^mantle system [10], based on the notion that the OIB source mantle had experienced more extensive degassing [11] than had previously been considered (e.g. [12]). In our model, the degassing £ows of noble gases from the mantle are represented by their concentrations in the mass £ows from mantle reservoirs to the surface, following the model of Porcelli and Wasserburg [13,14]. However, our model is unique in that the mass £ows are modeled as having decreased exponentially as a function of time over the history of the Earth. This assumption is in contrast to the steady-state £ow model employed in Porcelli and Wasserburg [13,14]. The validity of our model calculation is supported by its ability to predict that the Earth's primordial 3 He/36 Ar ratio was in cosmic abundance [10], which is indeed consistent with the notion made independently based on He^ Ne isotope observations in oceanic basalts [4,15]. In our continuing e¡ort to further develop a model to describe noble gases in the Earth^atmosphere system, we have expanded our model to include the time-dependent evolution of 3 He/4 He ratios in di¡erent mantle reservoirs. As noted above, such estimates have great implications for bettering our understanding of the dynamics of mantle evolution, and for interpreting the noble gas isotopic ratios observed in terrestrial samples.
2. The model Before presenting results of the model calculation on 3 He/4 He evolution in mantle reservoirs, we brie£y outline here the underlying ideas of our previous model on the mantle degassing [10] (for this model calculation, some more details are given in the Appendix). The model assumes that the present Earth has three separate noble gas reservoirs with distinct di¡erentiation histories that originated from an isotopically homogeneous primitive Earth (Fig. 1). These are: (i) the degassed mantle (with the noble gas isotope characteristics of MORBs) ; (ii) the less-degassed mantle (as sampled by some plume-related intraplate volcanism); and (iii) the surface reservoir (atmosphere and oceanic and continental crust). Mass £ows through the following paths were assumed to control transfer of elements among those three reservoirs (Fig. 1); (i) from the degassed mantle to the oceanic crust, (ii) from the less-degassed mantle to the oceanic crust, (iii) from the degassed mantle to the continental crust, and (iv) the recycling of oceanic crust back in the mantle. The ¢rst
Fig. 1. A schematic diagram of the mantle reservoirs and mass £ows assumed in the Osaka model.
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and second paths correspond to the magmatism at spreading centers and plume-related volcanic activity, respectively. Simultaneous and complete outgassing of noble gases was assumed for the mass £ows to the oceanic crust. The third path involves the selective uptake of radioactive parents, such as U, Th and K, from the depleted mantle to the continental crust with the conceptual extraction factor x [10] (see Appendix). Noble gas recycling into the mantle was not considered in the last path because of the suggested existence of a subduction barrier for all the noble gases except for xenon [16] and only solid elements were assumed to be recycled into the mantle with extraction factor r [10] (see Appendix). For the solid elements, mantle-derived material exchanges between the degassed reservoir including the oceanic crust and the less-degassed reservoir. In our model, `degassed' and `less-degassed' reservoirs will be equated to the `depleted' and `lessdepleted' reservoirs in reference to the solid elements. As noted earlier, the above mass £ows are assumed to have decreased as an exponential function of time so as to simulate the extensive outgassing early in the Earth's history. For example, the following equations describe the mass £ows from the depleted mantle and the less-depleted ç Dout and mantle to the surface reservoir (M ç MLout ) decrease as a function of the decrement factors LD and LL , respectively [10]:
213
We estimated the values of LD , LL , and x by using the representative 3 He/4 He and 40 Ar/36 Ar ratios in the MORB and OIB source mantle reservoirs. The planetary 3 He/4 He ratio (1.42U1034 [17]) was used for the initial helium composition of the Earth, because 3 He in the present-day solar wind composition is elevated owing to production of 3 He by deuterium burning in the Sun [18]. For the present calculation, we used 3 He/4 He ratios of 1.1U1035 and 4.7U1035 for the representative compositions in the MORB and OIB source reservoirs, respectively. We also assumed 40 Ar/36 Ar ratios of 6U104 [19] and 3U103 [11] for the lower limit of the values in the MORB and OIB source reservoirs, respectively. The extraction factor x was estimated from the present 40 K concentration in the continental crust (3.6U1016 atoms/g [20]) and in the depleted reservoir (1.8U1014 atoms/g [21]). The values of LL , LD and x that satisfy the above conditions are 1.32^1.34U1039 , 2.60^ 3.32U10310 and 40^274, respectively. Note that these values are slightly di¡erent from those reported by Kamijo et al. [10]. This is because we used updated noble gas isotopic ratios from recent empirical studies (see Appendix). The decrement factors obtained from the model suggest that the mass £ows from the depleted and less-depleted reservoirs to the surface reservoir have decreased by factors of 1/4 and 1/400, respectively, compared with the initial mass £ow during the Earth's history.
_ Dout t M _ Dout 0Wexp 3 L D Wt M
1
_ Lout t M _ Lout 0Wexp 3 L L Wt M
2
3. Temporal variations of 3 He and 4 He amounts in the mantle reservoirs
The abundance of non-radiogenic noble gas isotopes in the reservoirs at a given time can be constrained as the sum of mass £ows into and out of each reservoir, provided that the initial and present-day concentrations and decrement factors (LD and LL ) are known. In the case of the concentrations of radiogenic isotopes such as 4 He and 40 Ar in each reservoir, time-dependent production and net transfer of parent isotopes need to be considered. Thus, the values of LD , LL , x, and the initial and present concentrations of noble gases in each reservoir need to be constrained.
By using the parameters estimated above, temporal variations of 3 He contents in the degassed and less-degassed reservoirs are calculated (Fig. 2a). Because there is no signi¢cant production of 3 He in the mantle, the amount of 3 He is a¡ected only by mantle degassing. As the decrement factor of the mass £ow from the degassed mantle to the surface is smaller than that from the less-degassed mantle, the degassed mantle has lost s 99.8% of its initial 3 He over 4.5 Ga. The model calculation suggests that the present-day less-degassed mantle has also lost a signi¢cant fraction of its primor-
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Fig. 2. Estimated temporal variation in amounts of (a) 3 He, (b) 238 U and (c) 4 He in the less-degassed and degassed mantle reservoirs (solid and shaded curves, respectively). The width of curves at a given time represents the upper and lower limits derived from the present-day concentration of 40 K in the continental crust and in the depleted mantle (see text and Appendix). The broken lines in (b) show the amounts of 238 U decreased only by the radioactive decay in each reservoir assuming a closed system. The paired broken curves in (c) show ranges of radiogenic 4 He produced in the less-degassed and the degassed mantle reservoirs. C
dial 3 He ( s 87%), but it still has a few hundred times more primordial 3 He than that in the degassed reservoir. The amount of primordial 4 He in the mantle reservoirs at a given time, on the other hand, can be obtained from that of 3 He (Fig. 2a) and the assumed primordial 3 He/4 He ratio of 1.42U1034 [17]. To model the amount of the total 4 He in the mantle, we need to consider the e¡ect of radiogenic production from U and Th decay, in addition to the degassing of a primordial component. The amount of U in each reservoir is a¡ected by U extraction from the mantle to crust, recycling into the mantle through subduction and, of course, by radioactive decay. These three processes had been taken into account for the calculation as described in the Appendix. Resultant curves for 238 U amounts in each reservoir over the history of the Earth are presented in Fig. 2b as an example. To clarify the in£uences of the mass £ows on the U content in each reservoir, we also calculated the case for the simple radiogenic decay in each reservoir (broken lines) assuming a closed system. The evolution of U content in our model is very similar to that in the closed system model for the less-degassed reservoir, but is very di¡erent for the degassed reservoir. This is because the mass of degassed reservoir is about 1/3 of the less-degassed reservoir. Especially, in the ¢rst 500 Ma, the e¡ect of the mass £ow is considerably large in comparison to the mass of the degassed reservoir ç Lout (0)V8U1018 g/yr is almost 400 times as (M large as the present one). As a result, the amount of U in the degassed mantle is about 1/10 of that in the less-degassed reservoir over 4.5 Ga. By constraining the behavior of U and other
radioactive parents through time, the total 4 He budget in each mantle reservoir can be estimated as functions of time. As shown in the ¢eld bounded by the dotted curves in Fig. 2c, produc-
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tion of radiogenic 4 He shows a dramatic increase in the ¢rst several hundred million years of the Earth's history. However, in this period, the absolute abundance of radiogenic 4 He in the degassed reservoir is signi¢cantly smaller than that of the primordial 4 He still remaining there. This is because the subduction of oceanic crust to the less-degassed reservoir removes signi¢cant amounts of parent nuclides from the degassed reservoir owing to the large mass £ow in the early history of the Earth. Thus, the total amount of 4 He in the degassed mantle reservoir follows a similar path that is de¢ned by a primordial 3 He until the radiogenic 4 He becomes signi¢cant. As shown in Fig. 2c, the radiogenic 4 He appeared to become dominant in the degassed mantle reservoir after a lapse of about 2 Ga since the formation of the Earth. The calculation suggests that about 90% of total 4 He in the present-day degassed reservoir is of radiogenic origin. The radiogenic 4 He in the less-degassed mantle, on the other hand, amounts to about 70% of the total 4 He amount. Its temporal variation is suggested to follow a somewhat di¡erent trend than that in the degassed reservoir. Due to the less active degassing after the ¢rst 1 Ga and its less-depleted ( = more production of radiogenic helium) character, the total budget of 4 He in the less-degassed reservoir showed some increase after it experienced rapid degassing in the ¢rst 1 Ga (Fig. 2c). 4. Temporal variations of 3 He/4 He ratio in the mantle and its implications The temporal variations in the amounts of 3 He and 4 He in the mantle reservoirs allow us to calculate the changes in 3 He/4 He ratios in the mantle over the last 4.5 Ga. Fig. 3 shows how the 3 He/4 He ratios have evolved in each reservoir from the initial, assumed planetary, ratio to the present ratios. The most interesting point to be noted is the concurrent change in 3 He/4 He ratios in both mantle reservoirs in the ¢rst 2 Ga, followed by a rather abrupt separation of the two evolution curves. This abrupt change corresponds to the change in the major component of 4 He in
215
Fig. 3. Temporal variation of the helium isotopic ratio (3 He/ 4 He) in each reservoir. A shaded curve shows the evolution in the degassed mantle and the solid curve shows the evolution in the less-degassed mantle. The upper limit is calculated from the present concentration of 40 K in the depleted mantle. The lower limit is calculated from the concentration of 40 K in continental crust at present. The right axis shows the 3 He/4 He ratio ( = R) as R/Ra (Ra is the atmospheric ratio, 1.4U1036 ). The broken curves show the simple closed system evolution of 3 He/4 He ratio in each mantle reservoir. In the closed system, the degassed and less-degassed reservoirs are assumed to have initial U/3 He ratios as 19 000 and 3200, respectively. All curves were obtained by ¢xing the initial and present 3 He/4 He ratios in the degassed and less-degassed reservoirs (1.42U1034 , 1.10U1035 and 4.67U1035 , respectively). The open circle is the datum of Archean komatiite [9].
the degassed mantle. Before 2 Ga, the amount of 4 He in the degassed reservoir is largely controlled by the amount of a primordial component. Note that, in the ¢rst 2 Ga of the Earth's history, the radiogenic 4 He contributes only 6 1/100 to 1/2 of total 4 He in the degassed reservoir (Fig. 2c) due to a rapid extraction of U and Th from the degassed reservoir (Fig. 2b) and their long half-lives. Thus, the degassed reservoir maintained its high 3 He/4 He ratio for a rather extended period of time than that anticipated from the simple closed system evolution (Fig. 3 and [9]) and a ¢rst-order degassing process [12]. After the 2 Ga, the contribution of radiogenic 4 He to the total 4 He budget in the degassed reservoir becomes more and more signi¢cant (Fig. 2c). Accordingly, a decrease in
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3
He/4 He is accelerated towards the present-day value, whereas the 3 He/4 He ratios in the less-degassed reservoir decreased following a path similar to that de¢ned by the closed system evolution. Our model suggests that the 3 He/4 He ratio of the degassed mantle was signi¢cantly di¡erent in the past. This further suggests that some caution should be taken when interpreting 3 He/4 He ratios from ancient mantle-derived samples. For example, very high 3 He/4 He ratios of V5U1035 observed in some Archean komatiites were taken as evidence for a plume origin for the parent magma of the komatiites [9]. However, as shown in Fig. 3, the model results suggest that a plumerelated (less-degassed) component is not necessarily required for the komatiite source, as the 3 He/ 4 He ratio is also similar to that in the Archean degassed mantle. In addition, mantle xenoliths derived from the continental lithospheric mantle are estimated to have formed 0.5^2.0 Ga ago (e.g. [22]). The mantle 3 He/4 He ratios during this time interval are calculated to be as high as 1.4^ 4.0U1035 . However, none of the continental xenoliths analyzed so far shows such high 3 He/4 He
ratios. Instead the 3 He/4 He ratios are either MORB-like or lower (e.g. [23^25]). In this respect, our model suggests that the helium trapped in xenoliths is unlikely to have been trapped during the formation of the continental lithosphere. It is possible that the helium was instead recently trapped in the xenoliths, and was ultimately derived from the present-day degassed mantle source by metasomatism [23,24], or by £uid injection from the xenolith's host basalts [25]. As discussed above, although we assumed the existence of two separate mantle reservoirs with signi¢cantly di¡erent degassing histories, there is a possibility that the entire Earth's mantle had quite uniform 3 He/4 He ratios during the ¢rst 2 Ga of Earth's history. Compositional criteria used to infer the origin of recent mantle samples (MORBs and OIBs) certainly cannot be applied to ancient samples. Any samples with an age greater than 500 Ma could have plume-like 3 He/4 He ratios ( s 10 Ra), even though they are originated from the degassed mantle reservoir. Acknowledgements The authors thank Eleanor Dixon, by whom the manuscript was greatly improved both in its contents and in English. Thanks are also due to Koich Kamijo for his help in developing the computer source codes for this project. Don Porcelli and Manuel Moreira are thanked for careful and insightful reviews. Alex N. Halliday is also thanked for his helpful advice as a handling editor. The paper has been greatly improved through their comments. This work was partly supported by Grants-in-Aid from the Japan Society for the Promotion of Science (12740306).[AH] Appendix
Fig. 4. A £ow chart of the model calculation.
We will describe here a £ow of the model calculation in more details. A simpli¢ed £ow chart of the calculation is given in Fig. 4 and a list of all notations used in this paper is given in Table 1. As noted in the main body of the paper, we
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217
Table 1 Notation and constraint values in our model i
NR CR V PrR MD ML ç Dout M ç Lout M ç pcc M LD LL x N
r
Abundance of isotope i N in reservoir R Concentration of isotope N in reservoir R Decay constant of nuclides Production rate of radiogenic nuclides in the reservoir R Mass of the degassed reservoir Mass of the less-degassed reservoir Mass £ow from degassed reservoir to the surface Mass £ow from less-degassed reservoir to the surface Formation rate of the continental crust Decrement factor of mass £ow from degassed reservoir Decrement factor of mass £ow from less-degassed reservoir Extraction factor of K, U and Th for the continental crust formation Extraction factor of K, U and Th for the oceanic crust formation
atoms atoms/g /yr atoms/yr 1U1027 g [13] 3U1027 g [13] 7U1017 g/yr [26] 2U1016 g/yr [13] 4.4U1015 g/yr [10] /yr /yr dimensionless dimensionless This study
3
He/4 HeL (T) 3 He/4 HeD (T) 40 Ar/36 ArL (T) 40 Ar/36 ArD (T) 40 Ar/36 Aratm (T) K/U Th/U
The The The The The
present-day 3 He/4 He ratio in the less-degassed reservoir present-day 3 He/4 He ratio in the degassed reservoir present-day 40 Ar/36 Ar ratio in the less-degassed reservoir present-day 40 Ar/36 Ar ratio in the degassed reservoir present-day 40 Ar/36 Ar ratio in the atmosphere
expanded the model developed by Kamijo et al. [10] to obtain the evolutions of 3 He/4 He ratios in mantle reservoirs. An important assumption in [10] is that amounts of noble gases and radiogenic parents in reservoirs are controlled by the mass £ows, which decreased as an exponential function of time. Such an assumption is expressed as Eqs. 1 and 2 in the main text for mass £ows from the less-degassed and the degassed mantle reservoirs to the surface with respective decrement factors (LL and LD ). The present-day mass £ows from the less-degassed and the degassed mantle reserç Lout (T) and M ç Dout (T) where T = 4.5 Ga voirs (M since the formation of the Earth) are required for calculating the initial mass £ows by using Eqs. 1 and 2. We adopted the same values for ç Lout (T) = 2U1015 the present-day mass £ows (M 17 ç g/yr and MDout (T) = 7U10 g/yr) as were applied in [10]. As will be noted later, LL and LD are treated as unknown parameters to be determined by solving the following equations to satisfy some empirical analytical data from representative mantle-derived samples. The amounts of non-radiogenic isotope (N) in
Kamijo et al. [10]
4.67U1035 [4] 4.2U1035 1.10U1035 (e.g. [3]) s 3.0U103 [11] s 6U104 [19] s 1U104 295.5 296 12 700 [21] 3.9 ([21] reference therein)
the less-degassed and the degassed reservoirs are described as: dN L t _ Lout t 3N C L WM dt _ Lout 0exp 3 L L Wt 3N C L W M
A1
dN D t _ Dout t3N C D WM _ pcc t 3N C D W M dt _ Dout 0exp 3 L D Wt3N C D WM _ pcc t 3N C D W M A2 where N CR denotes the concentration of isotope N in reservoir R. In our model, noble gases are assumed not to be recycled into the mantle by subduction of the oceanic crust. A mass £ow to ç pcc ) is assumed to form the continental crust (M have been derived only from the depleted mantle reservoir, and obtained by dividing a total mass (2U1025 g [12]) of the continental crust by 4.5 Ga. The di¡erential equations for the radiogenic
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isotopes (4 He and
40
Ar) were written as:
dN L t _ Lout t PrL t 3 N C L WM dt
A3
dN D t _ Dout t3N C D WM _ pcc t PrD t 3N C D W M dt A4 PrL (t) and PrD (t) are terms describing production of radiogenic isotopes in less-degassed and degassed reservoirs at a given time t, and are written as:
satisfy the observation (see Fig. 4). With these two new parameters, the di¡erential equations of the radiogenic parents (N) can be written as: dN cc t _ pcc 3V WN cc t xWN C D WM dt dN D t dt _ Lout 3xWN C D WM _ pcc 3V WN D t3 rWN C D 3N C L WM A8 dN L t _ Lout 3V WN L t rWN C D 3N C L WM dt
PrR t 8V 238U W238 UR t 7V 235U W235 UR t 6V 232Th W232 ThR t
A5
PrR t V e W40 KR t
A6
where V denotes the respective decay constant of the parents. In order to solve Eqs. A3 and A4, we need to know how the amounts of K, U and Th in each mantle reservoir vary with time. In contrast to gaseous noble gases for which the bulk partitioning into the melt phase (thus, into the mass £ows in the case of this model) is expected upon melt^solid partitioning, the behavior of radioactive parents should be treated di¡erently as those applied for noble gases. Therefore, two new parameters, x and r, are introduced in [10]. The parameter x re£ects the extraction of radioactive parents by the continental crust formation. The parameter r represents the enrichment factor of the radioactive parents in the oceanic crust at the subduction £ow. The r must be larger than one due to the incompatibility of K. Kamijo et al. [10] estimated r to be 2 comparing the K2 O concentration in the oceanic crust with that in the upper mantle. As this estimation may be oversimpli¢ed, we estimated the e¡ect of uncertainty of r to the result of our calculation. Even if r is about 10, the concurrent evolution of helium isotopic ratio is retained with a somewhat longer period (up to about 2.5 Ga). The parameter x is the ratio of the concentration of radiogenic parents in the continental crust to that in the degassed reservoir which will be determined during the calculation to
A7
A9
The ¢rst terms of the right side of Eqs. A7^A9 describe the decrease of N in each reservoir due to ç Lout , in Eqs. A8 its decay. The next terms, with M and A9 can be regarded as representing the material mixing or exchange between the degassed and less-degassed reservoirs by the recycling of the oceanic crust (note that the mass £ow recycled into the less-degassed mantle from the reservoir which consists of oceanic crust and depleted mantle is balanced with the mass £ow out of the lessdegassed mantle (see Fig. 2 of [10]) to keep the volume of each reservoir constant). The ¢nal ç pcc represent the selective uptake of terms with M radioactive parents from the degassed reservoir to the continental crust. As noted above, the decrement factor L is one of the most important parameters that controls the mass £ows among the assumed mantle reservoirs. As shown in Fig. 4, L is started from an independent variable. The parameter x is, then, expressed as a function of L by using the present-day concentrations of U and Th. Concentrations of U in the crust and the depleted reservoir give upper and lower limits for all parameters. At this stage, all parameters are expressed as functions of LL . These functions can be solved from the observed 40 Ar/36 Ar ratios in the atmosphere and the mantle. Then, all parameters can uniquely be obtained. The obtained values for the parameters are slightly di¡erent from what was estimated in [10]. This is because we used some
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updated values for values for the present-day noble gas isotopic ratios. However, this change did not a¡ect the results of ours and [10] to a signi¢cant extent. References [1] H. Craig, W.B. Clarke, M.A. Beg, Excess 3 He in deep water on the East Paci¢c Rise, Earth Planet. Sci. Lett. 26 (1975) 125^132. [2] T. Staudacher, C.J. Alle©gre, Terrestrial xenology, Earth Planet. Sci. Lett. 60 (1982) 389^406. [3] D.R. Hilton, K. Hammerschmidt, G. Loock, H. Friedrichsen, Helium and argon isotope systematics of the central Lau Basin and Valu Fa Ridge: Evidence of crust/mantle interactions in a back-arc basin, Geochim. Cosmochim. Acta 57 (1993) 2819^2841. [4] M. Honda, I. McDougall, D.B. Patterson, A. Doulgeris, D.A. Clague, Noble gases in submarine pillow basalt glasses from Loihi and Kilauea, Hawaii: a solar component in the Earth, Geochim. Cosmochim. Acta 57 (1993) 859^874. [5] M. Honda, J.H. Reynolds, E. Roedder, S. Epstein, Noble gases in diamonds: occurences of solarlike helium and neon, J. Geophys. Res. 92 (1987) 12507^12521. [6] M. Ozima, S. Zashu, Solar-type Ne in Zaire cubic diamonds, Geochim. Cosmochim. Acta 52 (1988) 19^25. [7] M. Ozima, S. Zashu, Noble gas state of the ancient mantle as deduced from noble gases in coated diamonds, Earth Planet. Sci. Lett. 105 (1991) 13^27. [8] N. Wada, J. Matsuda, A noble gas study of cubic diamonds from Zaire: Constraints on their mantle source, Geochim. Cosmochim. Acta 62 (1998) 2335^2345. [9] D. Richard, B. Marty, M. Chaussidon, N. Arndt, Helium isotopic evidence for a lower mantle component in depleted Archean komatiite, Science 273 (1996) 93^95. [10] K. Kamijo, K. Hashizume, J. Matsuda, Noble gas constraints on the evolution of the atmosphere^mantle system, Geochim. Cosmochim. Acta 62 (1998) 2311^2321. [11] J. Matsuda, B. Marty, The 40 Ar/36 Ar ratio of the undepleted mantle; a reevaluation, Geophys. Res. Lett. 22 (1995) 1937^1940. [12] C.J. Alle©gre, T. Staudacher, P. Sarda, Rare gas systematics: formation of the atmosphere, evolution and structure of the Earth's mantle, Earth Planet. Sci. Lett. 81 (1987) 127^150.
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