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Chapter 6
greater complexity of the U-Pb system. Figure 6.07 also shows the relationship between 208 Pb/ 204 Pb and (^206) Pb/ 204 Pb. The two ratios are reasonably well correlated, implying U and Th have behaved rather similarly. Since slopes on 207 Pb/ 204 Pb – 206 Pb/ 204 Pb plots are proportional to time, we can associate an age with the overall slope of the array in Figure 6.06. The slope corresponds to an age of about 1.68 Ga (White, 2010). Exactly what this age means, if indeed it is meaningful at all, is unclear. The array in figure 6. can be interpreted as a mixing line between components at each end, in which case the age is only the minimum time that the two components must have been isolated. Alternatively, the age may date a single differentiation event, or represent the average age of a series of differentiation events, with the latter case being the most likely. Sm-Nd, Lu-Hf, and Rb-Sr all appear to be behaving in a generally coherent manner in the mantle, but one or all of U, Th, and Pb appear to behave 'anomalously'. Pb isotope ratios generally show only poor correlations with other isotope ratios, for example 206 Pb/ 204 Pb vs. 87 Sr/ 86 Sr shown in Figure 6.08. We know that the 207 Pb/ 204 Pb and 206 Pb/ 204 Pb ratios provide information about the time-integrated U/Pb ra-
Figure 6.08. 87 Sr/^86 Sr vs. 206 Pb/^204 Pb ratios of the suboceanic mantle as sampled by oceanic basalts.
Chapter 6
tio, or μ, and 208 Pb/ 204 Pb provides information about time-integrated Th/Pb. The Pb isotope system can also provide information about the time-integrated Th/U ratio, or κ. This is done as follows. We can write two equations:
208 Pb * = 232 Th ( e! 232 t " 1) 6.
and 206 Pb * = 238 U ( e^!^238 t^ " 1) 6.
where the asterisks denotes the radiogenic component. Dividing 6.04 by 6.05, we obtain:
208 Pb *
206
Pb *
232 Th
238
U
( e^ "^232 t^ # 1)
( e
" 238 t
Thus the ratio of radiogenic 208 Pb to radiogenic 206 Pb is proportional to the time-integrated value of κ. This ratio may be computed as: 208
Pb *
206
Pb *
208
Pb /
204
Pb! (
208
Pb /
204
Pb ) i
206
Pb /
204
Pb! (
206
Pb /
204
Pb ) i
where the subscript i denotes the initial ratio. By substituting a value for time in equation 6.06, and picking appropriate initial values for equation 6.07, we can calculate the time-integrated value of κ over that time. For example, picking t = 4.56 Ga and initial ratios equal to Canyon Diablo, we calculate the time-averaged κ over the past 4.56 Ga. Now let's see how 208 Pb/ 206 Pb, and hence κ relates to other isotope ratios, and hence other parent- daughter ratios. Figure 6.09 shows εNd plotted against 208 Pb/ 206 Pb. We can see that the two are rea- sonably well correlated, implying the fractionations of Sm from Nd and U from Th in the mantle have been closely related. From this, we conclude that the lack of correlation of ‘first-order’ Pb isotope ratios with Sr, Nd, and Hf isotope ratios is due to ‘anomalous’ behavior of Pb. We have seen that there are systematic differences in isotopic composition between MORB and OIB. Thus, there are at least two major reservoirs in the mantle – although deducing the physical relation- ship between these reservoirs is more problematic. The conventional interpretation is that MORB are derived from the uppermost mantle, which we can see is the most depleted of the reservoirs sampled by oceanic volcanism. Oceanic islands are thought to be surface manifestations of mantle plumes, which rise from, and therefore 'sample', the deeper mantle. A standard interpretation would thus be of a layered mantle. However, this interpretation encounters the difficulty that there is little or no geo- physical evidence for a layered mantle. Seismic tomography, in particular, has imaged subducted oce- anic lithosphere extending to near the core-mantle boundary, suggesting free communication between deep and shallow mantle. Furthermore, there is no convincing evidence of reflections or seismic veloc- ity discontinuities that would be expected from a boundary between distinct and isolated mantle lay- ers, with the possible exception of the D’’ region occupying the lowermost 200 km of the mantle. The magma flux of mantle plumes is, however, small compared to the magmatic flux at mid-ocean ridges. Thus the volume required of a plume reservoir could be quite small, perhaps no bigger than the seismi- cally distinct D’’ layer at the base of the mantle The idea of early enriched and depleted reservoirs in the mantle, derived from the non-chondritic na- ture of the terrestrial 142 Nd/ 144 Nd ratio, encounters similar problems. The hypothesis of Boyet and Carlson (2005) effectively requires that the early enriched reservoir remain isolated, not just for a couple of billion years, but throughout Earth’s history. As we noted in the previous chapter, such a reservoir would contain a significant fraction of the Earth’s radiogenic heat production, and it seems particularly unlikely that such an energy-rich reservoir would remain isolated. The difficulty in associating ‘reser- voirs’ deduced from isotope geochemistry with physical features in the mantle remains one of the most pressing problems in understanding the Earth’s deep interior.
Chapter 6 Spring 2011
BALANCING MANTLE AND CRUST The crust of the Earth is relatively enriched in incompatible elements. This is true of both the oceanic and continental crust, although the continental crust is much more incompatible element-enriched than the oceanic crust. This is entirely consistent with our hypothesis that the crust was created through partial melting of the mantle. We can then ask, from what fraction of the mantle have these incompati- ble elements been extracted to account for their abundance in the crust? Since its ephemeral, on average only 60 million years old, let’s ignore the ocean crust for the moment and just focus on continental crust. We have seen that MORB have “depleted” Nd, Sr and Hf isotopic compositions — let’s assume that the MORB source is residual mantle remaining after extraction of the continental crust. How much undepleted mantle would remain? This is essentially a problem mass balance among a number of reservoirs, so we begin by writing a series of mass balance equations. The first is mass of the reservoirs:
M j = 1
j
where Mj is the mass of reservoir j as a fraction of the total mass of the system, in this case the silicate Earth. We can also write a mass balance equation for any element i as:
M jC^ ij^ = C 0^ i
j
where Co is the concentration in the silicate Earth. For an isotope ratio, R , of element i , or for an elemental ratio of which element i is the denominator, the mass balance equation is:
M jCj^ i^ Rj^ i
j
! =^ C 0
i R
0
i 6.
Our problem assumes the existence of 3 reservoirs: the continental crust, the mantle depleted by crust formation, and the undepleted, or primitive, mantle. These mass balance equations can be combined to solve for the mass ratio of continental crust to depleted mantle:
M DM
MCC
CCC^ i
C 0
i
Rcc
i
! RDM
i ( )
R 0
i
! RDM
i!^1 6.1^2
where the subscripts DM and CC refer to depleted mantle and continental crust respectively. A number of solutions to the mass balance equations are possible, but we choose this form because it does not contain the concentration term for the depleted mantle. We can judge the isotopic composition of man- tle sources because the magmas they produce have the same isotopic composition, but this is not true of elemental concentrations. Once we have solved for the mass of depleted mantle, however, it is straight- forward to solve for the depleted mantle concentration term:
CD^ i^ M =
C 0
i ( M (^) DM + MCC )! MCCCCC i
M DM
Another difficulty arises with the isotopic composition of the continental crust, which is not well known. On the other hand, there are a number of estimates of elemental composition of the continental crust based on compilations of data, as well as on the age of the crust. With some assumptions, how- ever, we can combine the information that we do have to arrive at an estimate of the volume of mantle depleted by crust formation. The Nd isotope system is perhaps best suited for this question since 142 Nd/^144 Nd ratios constrain the Nd isotopic composition of the Earth and, being a refractory lithophile element, its concentration in the
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bulk silicate Earth is also constrained (though not precisely). The Nd concentration and the Sm/Nd ra- tio of the continental crust are also better constrained than many other elements. The Sm/Nd ratio and (^143) Nd/ (^144) Nd of the crust are related through isotopic evolution, specifically:
143 Nd / 144 Nd = ( 143 Nd / 144 Nd )
147 Sm / 144 Nd ( e! t " 1 ) 6.
Because the half-life of 147 Sm is long compared to the age of the Earth and because we do not need the level of precision necessary for geochronology, we can linearize this equation as:
143 Nd / 144 Nd = 143 Nd / 144 Nd
147 Sm / 144 Nd! t 6.
Let’s assume for simplicity that the some fraction of silicate Earth differentiated in a single event into a continental crust and depleted mantle at some time T. This is certainly not the case, as we shall see, but because of the linearity of the equation 6. 15 , even if the crust formed through similar events over a range of times, our approach is still valid if T is the average age of the crust. At time T , the continental crust and depleted mantle both had the same isotopic composition as undepleted mantle; i.e., the com- position of the undepleted mantle becomes the initial ratio in version of 6.14 written for depleted man- tle and continental crust. For the continental crust:
(^143 Nd /^144 Nd ) CC = (^143 Nd /^144 Nd )^ TPM^ + (^147 Sm /^144 Nd ) CC! T 6.
where the superscript T denotes the value at time T. We can calculate that value from the present-day (^143) Nd/ (^144) Nd and 147 Sm/ (^144) Nd of primitive mantle. Substituting, we have:
(^143 Nd /^144 Nd ) CC = (^143 Nd /^144 Nd ) PM + ⎡⎣ (^147 Sm /^144 Nd ) CC − (^147 Sm /^144 Nd ) PM ⎤⎦ λ T 6.
The value thus calculated can then be used in equation 6.12 to calculate the mass fraction of depleted mantle. Figure 6.10 shows the mass fraction of the depleted mantle as a function of the ratio of the con- centration of Nd in the crust to the bulk silicate Earth; i.e., the enrichment of Nd in the continental crust. It assumes that the average age of the crust is 2.0 Ga and that its 147 Sm/^144 Nd ratio is 0.1228. If the εNd of the Earth is around +6.9, as suggested by Caro and Bourdon (2010), then the mantle depleted by crust extraction occupies at least 75% of the entire mantle and possibly all of it. This is quite a different picture of the mantle from the one that has prevailed for the last 30 years or so derived from assumption that the Earth has chondritic Sm/Nd and therefore εNd = 0. Mass balance cal- culations such as those of Jacobsen and Wasserburg (1979), O’Nions et al. (1979) and DePaolo (1980) concluded that the mass of the depleted mantle is was only 25% to 50 % the total mass of the mantle, and therefore that a large “primitive mantle” reservoir existed. The lower end of this range corre- sponds to the mass fraction of mantle above the 660 km seismic discontinuity. This coincidence led to models of the mantle in which a depleted reservoir occupied the upper mantle, the region above the 660 km discontinuity, and the region below it, the lower mantle, consisted of primitive mantle. Main- taining two distinct reservoirs for the age of the Earth in turn implied that convection in the mantle was layered and that the 660 km discontinuity represented a boundary to mass transport. Eventually, how- ever, new evidence from other branches of earth science raised questions about this model. Experimen- tal studies revealed that increase in seismic velocity at 660 km depth resulted from a phase change re- sulting from a fundamental change in silicate structure, and that while the phase change might retard mass transport across the boundary, it probably did not prohibit it. The development of seismic tomo- graphy in the 1990’s confirmed that subducting lithosphere did, at least sometimes, pass through the 660 km discontinuity into the lower mantle, and in some cases could be traced nearly to the core-mantle boundary. Thus isotope geochemistry, which seemed to support two layered convection in the mantle, was at odds with geophysics, which favored whole mantle convection. This conflict is resolved is the Earth is non-chondritic and has a high εNd. Any surviving “primitive mantle” reservoir would be small; most of the mantle likely consists of the kind of depleted mantle that produces MORB. This accords with the observation that no mantle or mantle-derived materials having εNd = 0 and other chemical and isotopic characteristics expected of primitive mantle have been identified.
Chapter 6 Spring 2011
We should note that the existence of multiple reservoirs in the mantle does not necessarily invalidate the mass balance models discussed above if the mass of the various OIB reservoirs is insignificant. Since the volume of OIB is small compared to MORB, this is certainly a possibility. Mass balance mod- els also neglect the mass of the subcontinental mantle lithosphere. Although significant parts of the subcontinental lithosphere appear highly incompatible element enriched, it is probably not a significant reservoir of incompatible elements. A different view of the mantle has been taken in papers by Galer and O’Nions (1985) and White (1993). The models we have discussed thus far assume that isotope ratios in mantle reservoirs reflect the time-integrated values of parent-daughter ratios in those reservoirs. Indeed, we devoted some time to the concept of time-integrated parent-daughter ratios in the previous lecture. Wasn’t this, after all, what Gast said, that (among other things) an isotope ratio reflects the time-integrated parent-daughter ratio? Indeed, what did Gast say? He said “ The isotopic composition of a particular sample of strontium... may be the result of time spent in a number of such environments. In any case, the isotopic composition is the time- integrated result of the Rb/Sr ratios in all past such environments. ” If for example, a sample of Sr from the depleted upper mantle (we’ll adopt the acronym DUM*^ for this reservoir) had spent the past 4.55 Ga in
- (^) You may get the impression that to really succeed in mantle isotope geochemistry you need to be good at thinking
Figure 6.11. Five reservoir types of White (1985) and the components of Zindler and Hart (1986). They are essentially identical, except for Hawaii and PREMA (prevalent mantle). Other Zindler and Hart acronyms stand for high-μ (HIMU), enriched mantle I and II (EM I and EM II), and depleted MORB mantle (DMM).
Chapter 6 Spring 2011
that reservoir, its isotopic composition should indeed reflect the time-integrated Rb/Sr in that reservoir. But suppose that sample of Sr had spend only the last few hundred million years in the DUM? Its iso- topic composition will be more of a reflection of the Rb/Sr ratios in the previous environments than in DUM. This is exactly the point made by Galer and O’Nions. We have seen in previous lectures that the time integrated Th/U ratio is recorded by the 208 Pb/^206 Pb ratio. Galer and O’Nions (1985) found that the average 208 Pb/^206 Pb in MORB corresponded to a time- integrated Th/U ratio of about 3.75. The chondritic Th/U ratio, according to several compilations, is about 3.9. Since Th and U are both refractory elements, this should be the ratio of the bulk Earth as well. The present-day Th/U ratio of the mantle source of a basalt can be deduced from Th isotope sys- tematics, as we have seen. According to the compilation made by Galer and O’Nions, κ in DUM, based on Th isotope ratios in MORB, is about 2.5. That the present ratio is lower than the chondritic one makes perfect sense because Th is more incompatible than U, so we would expect this ratio to be low in
up acronyms. As near as I can tell, this is true. This acronym is due to Claude Allegre.
Figure 6.12. Five reservoir types of White (1985) and the components of Zindler and Hart (1986) in a plot of εNd vs. 87 Sr/^86 Sr.
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of the islands in the South Atlantic and Indian Oceans (Schilling, 1985). These variations can be seen in Figure 6.14. Other variations along the ridge, however, cannot be directly related to mantle plumes. Is there evidence for for larger scale geochemical provinces in the mantle, comparable to say tectonic provinces of the continents? The answer is again yes. Perhaps the first such 'province' to be identified was the Indian Ocean geochemical province. Data published as early as the early 1970's suggested MORB from the Indian Ocean were distinct from those of the Pacific and the Atlantic, having higher (^87) Sr/ (^86) Sr ratios. However, the scarcity and poor quality of data on Indian Ocean MORB left the issue in doubt for more than a decade. It was resolved with a flood of data on Indian Ocean MORB, beginning with a paper by Dupré and Allègre (1983). Dupré and Allègre found Indian Ocean MORB has higher (^87) Sr/ (^86) Sr ratios but lower 206 Pb/ (^204) Pb ratios compared to MORB from other oceans. They also have high (^207) Pb/ (^204) Pb and 208 Pb/ (^204) Pb ratios for a given value of 206 Pb/ (^204) Pb than other MORB. This is can be seen in Figure 6.07. Furthermore, these characteristics seem to be shared by many of the oceanic islands in the Indian Ocean. Subsequent work that showed Indian Ocean MORB have low εNd as well. Finally, MORB from the Pacific Ocean can be distinguished from Atlantic MORB by having lower 87 Sr/^86 Sr ra- tios for a given εNd. Hart (1984) noticed that oceanic basalts with high 207 Pb/^204 Pb and 208 Pb/^204 Pb ratios for a given value
Figure 6.14. Variation of Sr and Pb isotope ratios with angular distance along the mid-ocean ridge system. The “0” point is the location of the northernmost sample site of the Gakkel Ridge at 85.64˚N, 85.05 E. From White and Klein (in press).
