Thank you Dr. Serov. I applied these values but I gained positive values for TCHUR and negative values for TDM. How to interpret these negative values?Thanks.

Yes. The non isotopic ratios of Sm/Nd are > 0.3. But now is it possible to use these T(CHUR) or T(DM) only for an age comparison? To say which sample is older or younger? If I had two T(CHUR) or T(DM) for two lithology, why I cannot subtract them to gain the age difference of samples? Thank you. Nargess

Hi Nargess,

The most up to date reference for CHUR is

Bouvier A., Vervoort J. D., and Patchett P. J., 2008. The Lu–Hf and Sm–Nd isotopic composition of CHUR: Constraints from unequilibrated chondrites and implications for the bulk composition of terrestrial planets. Earth and Planetary Science Letters, v. 273, p. 48-57.

My suggestion, if you want to understand why your samples have positive values for TCHUR and negative values for TDM is to calculate the Nd isotope evolution from 4.56 Ga to the present day for CHUR, BSE and DM, Then plot Nd isotopes vs time with your samples.

Note that the BSE is now considered to have a different initial Nd isotope composition to CHUR. See

Jackson and Carlson 2012. Homogeneous superchondritic 142Nd/144Nd in the mid-ocean ridge basalt and ocean island basalt mantle

And reference therein

Hi Nargess,

yes, this is the problem with ANY model age, in that it depends on both your sample and the model source you are comparing it to. Obviously you have mafic or ultramafic samples with very high Sm/Nd (and hence 147Sm/144Nd). In that case the model ages you calculate will be very sensitive to firstly the choice of reservoirs, and the references suggested by others in this discussion are all the best and most up to date. As you point out, it is how to actually interpret these values you are getting, and whether you can actually use the data (ages) calculated.

In essence it depends on what you want. In general we use these ages not, of course, as ages of the rock, but the time it was last in isotopic equilibrium with that reservoir: ie, the time at which we think it was extracted from that portion of the Earth. In that sense, I don't think many people would argue that there is a large, truly chondritic reservoir still inside the Earth that is regularly sourcing large amounts of magmatism on the modern Earth, so T CHUR is not likely to be particularly meaningful for geological applications rocks of Proterozoic or younger ages.

TDM is derived from the evolution of the Depleted Mantle which is the cumulative residue of the upper convecting mantle after extraction of the continents and MORB. Indeed, one isotopic approximation of the DM is to plot the Nd isotopic value of MORB through time, therefore tracking its evolution. What happens when one does this is that we see that there is no "single" DM reservoir, and we need to use a two stage evolution as discussed above. However, I digress- I simply want to illustrate what your data may be telling you, and I attach a graphic that I prepared for other purposes that can outline what your data are saying.

Since the DM reservoir is itself evolving through time as a function of its own Sm/Nd (and hence 147Sm/144Nd) ratio, if your samples have a similar Sm/Nd ratio to the reservoir, then they will define a line that, when you back calculate, will never cross the DM evolution (pale blue line in the figure). In fact it doesn't matter what the present day epsNd value of your sample is, if it has a very high Sm/Nd ratio it will form a sub parallel array with the DM evolution and hence give meaningless ages. Therefore you will not be able to either calculate a TDM or compare it with any of your other samples.

Another case is where your sample has a positive modern day epsNd, but a low Sm/Nd (and hence 147Sm/144Nd) and hence will evolve to give you a TDM, but no TCHUR (since it will never cross the CHUR evolution (dark blue line on figure).

Finally, I have included the "normal" case, say that of Continental crust (CC) which is negative at the present day and will project back to gave both a TCHUR and an TDM- with TCHUR always being younger than TDM. In this case you can start to compare potential sources, extraction ages and mixing, but these all assume a near or below chondritic Sm/Nd (and 147Sm/144Nd) ratio.

I have a pile more examples if you need/are interested, but I think your issue is not the choice of reservoirs, but the Sm/Nd ratio of you samples, rendering model age calculations meaningless.

The final thing you could try is to see whether they plot on an isochron diagram, hence testing whether your ultramafic samples were all derived from a source of the same age, but at different times. I have seen the is for some komatiites and high Mg dolerites which are clearly not of the same magma batch, but are still isochronous.

cheers, and sorry for the long exposition!

Bruce

Hi Bruce. It is a perfect exposition. Thank you, Nargess

Hi Nargess,

First a little background about the TUR/TCHUR, and TDM model ages. When the TUR model was first proposed, the idea was that this model gives the total crustal age of an igneous rock, that is, the time when the precursors of the rock were first extracted from the mantle. Fortunately for the authors, the examples they selected did give the total crustal age of the rocks. However, it was found out later that in many cases the model age was far younger than the expected age, and the TUR and TCHUR ages for the same rock were quite different. They had no explanation for that. That was the time when the TDM and many other similar models came into vogue. It was thought that the TUR model does not yield the expected age because the precursors of the rock have not been derived from a chondritic reservoir but were derived either from an enriched or a depleted reservoir. Therefore, in order to get the right model age one has to use the correct parameters of the reservoir from which the rocks were derived. They thought that as the mantle is depleted , therefore, one has to use the parameters of the depleted mantle to get the right age. By extending the same argument, many other modified models such as TMix, and TMORB and several others came into being. That is where the problem lies in their thinking. A common sense answer to this would be if a person knows so much about the mantle reservoir from where the rock was derived that he can figure out its present day parameters then how come he does not know much about the rock itself. So by using their argument virtually every rock comes from a unique reservoir because after some amount of magma is retrieved from a reservoir that reservoir is altered forever relative to its original state. So by that logic we should have unique parameters for every rock.

However, I presented a paper in the AGU conference in the Spring 1992 meeting held in Ottawa which is published as an abstract. The title of the paper was “Is the concept of the TDM and the other similar total crustal age models a paradox?”: EOS Trans. AGU, 73 (14), p. 376, 1992.

In this paper I have shown why the rocks do not always yield the correct Total Crustal model age of the rock. The TUR model in fact is not a model for getting the Total Crustal age but rather a model which yields the time of the last fractionation event. When the magma is extracted from its source reservoir its parent and daughter isotopes are fractionated. The TUR model dates this fractionation event. So if a rock has a complex metamorphic history, and in subsequent events the Rb/Sr or Sm/Nd ratio is not changed, the TUR model would continue to yield the same model age. If however, in a subsequent event the parent and daughter isotopes are fractionated, the model would yield the age of the last fractionation event. Its previous history would be lost. Now the question is how much fractionation is required to reset the model age. I had shown that the degree of fractionation required for resetting the model age increases progressively with younger age. I call this the Coefficient of Fractionation. Thus the Coefficient of Fractionation is very small for much older rocks, say of Archean age, but for younger rocks of about a few hundred million years, the Coefficient of Fractionation has to be several hundred percent. After a rock passes beyond the threshold of the Coefficient of Fractionation then no matter to what extent it is fractionated, the model would yield the correct time of the fractionation event. Now in those cases where the rock does not pass beyond the Coefficient of Fraction, the model age would lie anywhere between the time of its extraction from the mantle (First fractionation event) and the latest fractionation event, or between the penultimate fractionation event and the last fractionation event. In such cases this model age would be meaningless. Further if in a petrogentic event the parent /daughter ratio decreases, in other words if there is a negative fractionation, in that case the model age may be much higher than the expected age, and would be meaningless.

Thus basically, this model age depends on the degree of fractionation of parent daughter isotopes. So it is important to understand the extent of fractionation in the derived rock. Now the question is, why in some cases the model TUR and TCHUR ages for the same rock are quite different. As we know that the Rare Earths behave quite differently from the Rb and Sr trace elements, and thus the fractionation of the two parent/daughter pairs may be quite different in the same rock. A petrogenetic event may lead to higher Rb/Sr ratio and lower Sm/Nd ratio, or one of them may cross the coefficient of fractionation whereas the other may not. So in such a case the model ages by two systems may be quite different.

One may ask, if the model dates the last fractionation event then what this model age signifies. First of all the model age should generally be higher than the metamorphic age because the model age dates the time when the fractionation occurred whereas the metamorphism-date dates the time when the rock cooled below the blocking temperature after the radiogenic isotopes were homogenized. So in case of a sheared rock in which shearing is accompanied by fractionation, the model age should indicate the beginning of shearing when the fractionation occurred and the metamorphic age would indicate the time after the rocks were uplifted to a point where they cooled below their blocking temperature. In case of mylonites or ductiley sheared rocks the difference between the two dates may be quite significant because the ductile shearing takes place at great depths, and the rate of shearing also is very slow. I also presented a paper in the AGU conference about such rocks, and showed the difference between two dates due to the time taken in shearing and the uplift of the rocks to their blocking temperatures. The title of the paper is “Tectonic significance of the high initial 87Sr/86Sr ratio in the ultramylonites formed from the I-type quartz-monzodiorites (Corbin gneiss) in the Blue Ridge of Georgia (ABSTRACT)”: EOS Trans. 67 (16), Spring Meeting Suppl., p. 401, 1986. In my opinion, the difference in the two dates could be used to calculate the rate of shearing, and uplift rates.

The TDM date or a date given by any other such modified model is meaningless and has no geological significance at all. Also another reason for their insignificance is the fact that mantle is not depleted/enriched. The mantle appears to be depleted or sometimes enriched because of the fractionation of radiogenic isotopes. The mantle by and large is homogenous and undepleted. Most of the material which has been derived from the mantle has gone back to the mantle. Whatever is left behind is miniscule in comparison to the total volume of the mantle. In my view not only radiogenic isotopes of 87Sr, but all radiogenic isotopes from the lightest to the heaviest are fractionated with respect to their non-radiogenic counterparts; and this fractionation gives the perception of a depleted or an enriched mantle. Please see my paper “Characterizing source reservoirs of igneous rocks: A new perspective. Fractionation of radiogenic isotopes: A new tool for petrogenesis. Chemie der Erde, 72 (2012) 323-332.”

Now one may ask that those rocks which have very complex metamorphic history is it possible to get a total crustal age of such a rock. I think it is still possible, however I have not discussed it yet in any of my papers. May be I would do it at some later date.

Now with regard to your question what Sm and Nd values are best for computing the TCHUR model age, I do not agree with some of the suggestions given here. However, I would answer that in my next post.

Satya Gargi

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I had stated earlier that I would come back at a later date with my preferred Sm-Nd isotopic parameters. But before I discuss that further, I want to make some further comments about the TCHUR crustal age model because it has some bearing on the ensuing discussion.

I have noticed many versions of the equation for the model total crustal age, and some of which are not correct. However, the correct equation for this model (Cf. DePaolo and Wasserburg, 1976b) is given below:

TCHUR = 1/λ ln [1+ {(143Nd/144Nd)meas – (ICHUR (0))} / {(147Sm /144Ndmeas) – (147Sm /144NdCHUR)}]

The above equation can be derived from the radioactivity equation for determining the age of a rock. In fact the above equation is also the equation for the age of the earth. For example if in this equation we replace the measured isotopic ratios of the sample with those of the bulk earth at the time of its formation, it will give us the age of the earth. This equation also shows that if for example, the rock magma at the time of its extraction from the mantle was not fractionated, that is, its isotopic make up was exactly similar to that of the undifferentiated mantle then its measured isotopic composition would be similar to that of the present-day bulk earth/(ICHUR (0)), and its TCHUR date in that case would be infinity. Therefore, for this equation to work, the rock must be fractionated at the time of its extraction from the mantle. Thus anytime the isotopic evolution of the bulk earth deviates from its normal course because of a certain petrogenetic event such as extraction of magma, metamorphism / metasomatism, or shearing - this equation dates that event. If, however, the metamorphism or shearing is not accompanied by the fractionation of parent/daughter isotopes, it would not reset the model age, and the equation would still yield the time of the penultimate fractionation event. Therefore, it would be more appropriate to call it a fractionation age model instead of the total crustal age model. In those cases where this model does not yield the expected date, it could be due to several reasons. It could be that the igneous rock may have had a complex history of magmatism, metamorphism and deformation, and some of those events may have again fractionated the parent-daughter isotope ratio. Or, if the fractionation had not crossed the threshold of fractionation required for resetting the date, it would then yield an erroneous date – the date could lie anywhere between the penultimate and ultimate fractionation events. The degree of fractionation required for resetting the fractionation age increases with decreasing age. So for a rock only a few hundred million years old the degree of fractionation required is very high – by several hundred percent. It was this problem that led to the proliferation of so many crustal age models such as TDM, TMORB, TMix and several others in which the isotopic parameters of CHUR were replaced with those of the purported reservoirs the rocks were derived from. This is a totally fallacious concept and is based on the erroneous assumption that the isotopic parameters of the reservoir from which the rock was derived are required to get the expected total crustal date. Also the acronym CHUR for the imaginary reservoir having the isotopic characteristics of the chondrites is highly misleading and has further enhanced this misconception. It has caused a great confusion, and gives the impression that in order to get the correct date the isotopic parameters of the reservoir the rock was derived from, are required. Therefore, it would be preferable to use the term bulk earth (BE) or solar nebula instead of CHUR. As the bulk earth at the time of its formation, inherited the isotopic evolution of the solar nebula unchanged, and as the chondrites are the most primitive and undifferentiated planetary objects, and are considered as the best representatives of the solar nebula, the acronym CHUR in this equation simply means the present-day isotopic parameters of the bulk earth/solar nebula. Above all no such exclusive reservoir exists anywhere in the mantle or the earth, or ever existed at any time in the solar nebula. The ultimate reservoir of course is the solar nebula from which all the planets and meteorites were derived by cold homogeneous accretion. Thus the bulk earth at the time of its formation was chondritic, and the mantle is still chondritic (Gargi, 2012). The extraction of the enriched crustal material from the mantle could not have caused the kind of depletion observed in the mantle derived rocks because it is so miniscule in comparison to the total volume of the mantle. This kind of depletion would require a massive depletion of the order of 30-35% at the time of the formation of the earth. However, if the extraction of continental rocks did cause some minor depletion, it should have been compensated by the extraction of the depleted oceanic crust from the mantle. The apparent depletion or enrichment we see in the mantle derived rocks is the result of magmatic differentiation (Schilling, 1971), and fractionation of radiogenic isotopes (Gargi, 2012).

Further, if in this equation, isotopic parameters of any other reservoir are substituted for the bulk earth parameters, then the equation no longer can be considered as the equation for dating the time of the fractionation event because the assumed parameters are not the result of normal isotopic evolution but of magmatic differentiation. Also if their logic of using the isotopic parameters of the reservoir the rock is derived from is taken further, it would require different parameters for every rock derived from the mantle because each rock of the same age with different initial isotopic ratios should have come from a different reservoir. Also the problem of not getting the expected total crustal age because of later metamorphism, shearing, or some other reason cannot be resolved by changing the isotopic parameters in the equation for the model age. There are other ways to resolve that problem, and I will come to that at a later date.

References Cited

DePaolo, D.J. and Wasserburg, G. J., 1976b. Inferences about magma sources and mantle structure from variations of 143Nd/144Nd. Geophys. Res. Lett. 3, 743-746.

Schilling, J.G., 1971. Sea-floor evolution: rare-earth evidence, Phil. Trans. Roy. Soc. Lond. A. 268, 663-706.

Gargi, S.P., 2012. Characterizing source reservoirs of igneous rocks: A new perspective. Fractionation of radiogenic isotopes: A new tool for petrogenesis. Chemie der Erde 72, 323-332.

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The preferred or the best Sm-Nd isotopic parameters!

The question - what are the best or the most appropriate Sm-Nd isotopic parameters for the bulk earth cannot be answered in isolation from the Rb-Sr isotopic parameters as the latter are partly derived from the former, and the two isotopic systems thus are interrelated. Therefore, the important point here is not just how precisely the isotopic ratios have been measured but how they have been determined – that is, by what method and from what source material, and how well they satisfy the internal as well as external constraints.

The chondritic meteorites, of all the meteorites, are the most primitive and undifferentiated planetary objects. Therefore, these are regarded as the best representatives of the solar nebula. Their importance also lies in the fact that these are the only primitive planetary objects and of the same age as the earth on which we can lay our hands and analyze them. So it is natural to use chondritic meteorites to define the Sm-Nd isotopic evolution of the solar nebula. However, most of the chondrites were subjected to severe shocks and brecciation (Cf. Minster et al., 1982) soon after they were formed; also many of the chondrites show signs of secondary alteration by the action of water (Ebihara et al., 1982; Macdougal et al., 1984) which has disturbed their isotopic system. Because of this, they do not yield well defined Rb-Sr or Sm-Nd isochrons. The achondrites, on the other hand are highly differentiated objects, but they yield very precise isochrons both for Rb-Sr and Sm-Nd systems. As the Sm/Nd ratio of achondrite Juvinas (0.3072) (Lugmair et al., 1975c) is comparable to that of the chondrites (0.3081) (Masuda et al., 1973; Masuda, 1975; Nakamura, 1974), and their Sm–Nd isochron age also is very similar to that of the Earth (Lugmair, 1974), the isotopic characteristics of Juvinas, therefore, could be used to define the isotopic parameters of the Solar System/bulk earth.

DePaolo and Wasserburg (1976a, 1976b) showed that initial Nd isotopic ratios of old intrusive continental rocks of various lithologies, mostly silicic rocks, ranging in age from 3.8 Gyrs to 1.00 Gyrs and young continental basalts ( zero age) with few exceptions fall within error (~5%) on the chondritic evolution line. They considered this as indicating that continental silicic rocks throughout the geologic history were derived from a single uniform widespread reservoir having REE characteristics of ordinary chondrites. They termed this reservoir as chondritic uniform reservoir, CHUR, which in their opinion most probably resides in the mantle. They consider CHUR an important reservoir and representative of the bulk Earth, and whose Sm-Nd isotopic characteristics closely approximate that of the Juvinas achondrite.

DePaolo and Wasserburg (1976a, 1976b) claim to use the isotopic characteristics of the achondrite Juvinas for defining the Sm-Nd isotopic parameters of CHUR. However, they used the values of 0.1936 for the 147Sm/144Nd ratio, 0.50598±10 for the initial ratio (IJUV) and 0.511836 for the present day 143Nd/144Nd ratio (ICHUR(0)). They stressed that these values are based on the isotopic characteristics of Juvinas (Lugmair, 1974, pers. comm. to them, Lugmair et al., 1975b). They further contended that this ICHUR(0) value is much lower than, and differs significantly from what was reported by Lugmair (1974); and is considered as the best revised estimate for the 143Nd/144Nd ratio (ICHUR(0)) of the Juvinas as per the personal communication of Lugmair (1974) to them.

Lugmair (1974) in his paper reported only the initial 143Nd/144Nd ratio (IJUV), and the age of Juvinas, which are 0.50687±10, and 4.56±0.08 Gyr, respectively. He derived these values from the internal isochron of Juvinas; and there is no reference to the Nd isotopic ratio of Juvinas. Also a very similar initial143Nd/144Nd ratio was reported from the achondritic meteorite Angra dos Reis by Lugmair and Scheinin (1976). They analyzed various mineral fractions of the meteorite and obtained an initial ratio of 0.50682 ± 0.0005, and an isochron age of 4.55 ± 0.04 Gyr. However, no reference to the initial or the present-day 143Nd/144Nd values as used by DePaolo and Wasserburg (1976a,b) is found in any of the subsequent publications (Lugmair et al., 1975a; Lugmair et al., 1975b; Lugmair et al., 1975c; Lugmair et al., 1976a, Lugmair et al., 1976 b).

The initial ratio and the measured 143Nd/144Nd ratio of Juvinas as reported by Lugmair (1974), and Lugmair et al. (1975b,c) are significantly different from those used by DePaolo and Wasserburg (1976a,b). Later, Lugmair et al. (1976a) gave revised values for the initial 143Nd/144Nd (IJUV) ratio, and the measured 143Nd/144Nd ratio by dating the bulk sample of Juvinas, which respectively are 0.50677±0.00010, and 0.512636±0.000040. They stated that these are updated values and are a little lower than the ones given earlier by Lugmair et al. (1975b,c). The value of the present-day 143Nd/144Nd ratio of Juvinas seems to be revised again as Stosch et al. (1984) used a little lower value of 0.512566 for this ratio. However, all the values for the Sm-Nd isotopic parameters obtained by dating the achondrites, Juvinas and Angra dos Reis by Lugmair and his associates are quite different from those used by DePaolo and Wasserburg (1976a,b) in their model..

Subsequently, Jacobsen and Wasserburg (1980) analysed five chondrites and the Juvinas achondrite for their 143Nd/144Nd, and 147Sm/144Nd ratios. These samples defined an isochron which indicates an initial ratio of 0.505828±9 at 4.6 Gyr. Based on this data, they suggested a new set of present-day Sm-Nd isotopic parameters for CHUR. Those values are 0.511836 for (143Nd/144Nd)CHUR(0), and 0.1967 for (147Sm/144Nd). It is noticed that the values of two of the parameters are slightly different from those used by DePaolo and Wasserburg (1976a). The value for the present-day Nd isotopic ratio is the same, whereas the value for the initial Nd isotopic ratio is slightly lower, and that for the present-day (147Sm/144Nd) ratio is slightly higher. They also stressed that they consider these parameters to be self-consistent. Jacobsen and Wasserburg (1984) analyzed five more chondrites and the achondrites Moama and Angra dos Reis for investigating their Sm-Nd isotopic systematics. They reported that the isotopic data obtained from these meteorites is consistent with the previously reported reference values for CHUR of (143Nd/144Nd)CHUR(0) = 0.511847, (147Sm/144Nd)CHUR(0) = 0.1967. However, the value of 0.511847 for the (143Nd/144Nd)CHUR(0) ratio reported here is slightly higher than the one previously reported by them (Jacobsen and Wasserburg,1980). Also this set of values for the Sm-Nd isotopic parameters for the CHUR/bulk Earth based on the analysis of chondrites by Jacobsen and Wasserburg (1980, 1984) are quite different from those derived from the achondrite Juvinas by Lugmair (1974) and Lugmair et al. (1975b, 1975c). This gives the impression that chondrites are somewhat different from the achondrites with respect to their Sm-Nd isotopic evolultion. However, this is not the case as shown by the work of Benjamin et al. (1987) on chondrites. They dated some chondrites by the Sm-Nd method of dating. They showed that chondrites define an isochron corresponding to an age of 4.55±0.45 Gyr with an initial Nd isotopic ratio of 0.5067±5, which is very much consistent with the initial ratio of Juvinas (0.506705 for a 4.56 Gyr age). Also, Amelin and Rotenberg (2004) reported almost identical results from their Sm – Nd isotopic investigation of chondrites. They analyzed 34 samples of phosphate fractions and chondrules from six ordinary chondrites and one carbonaceous chondrite for studying their Sm-Nd systematics. These samples defined an isochron which yielded a date of 4588 ± 100 Myr, and an initial 143Nd/144Nd ratio of 0.50665 ± 0.00014. They also suggested a median 147Sm/144Nd ratio of 0.1964 + 0.0003/ - 0.0007 based on the compilation of the published data of chondritic whole rock Sm – Nd analysis. From this value and the Sm – Nd isochron, they derived the present-day CHUR 143Nd/144Nd value of 0.512637 + 0.000009/ - 000021.

It appears that the results of Sm-Nd isotopic analysis for the chondrites from the two sets of laboratories are quite different. So what could be the reason for the results from two sets of laboratories to be so different from each other. The most likely reason for this is the inter-laboratory bias because of the different ways of carrying out analysis for Nd isotopic compositions (Faure, 1986). This inter-laboratory bias has rendered the comparison of Sm-Nd isotopic data from different laboratories very difficult. Ideally, no matter what method is used for analysis, the end result should be the same. However, it is not the case. Therefore, the important point here is which of the two sets of reference values should be considered as appropriate for the bulk earth isotopic parameters. In order for any set of Sm-Nd reference values to be considered plausible, it is very important to see how they relate to the Rb - Sr isotopic parameters; also they ought to be internally consistent. Jacobsen and Wasserburg (1980) had contended that the reference values that they have proposed for the Sm-Nd bulk earth parameters are self-consistent. However, they did not show on what basis these values were considered self-consistent. One test to check the self-consistency of the reference values, in other words, to see how they satisfy their internal constraints, involves comparing the measured Nd isotopic ratios with those computed from the other reference values as shown in the table below. This test, however, by itself should not be considered as the sole criterion for judging the plausibility of the parameters. However, it excludes those from consideration if they do not satisfy the internal constraints.

The following table shows the computed and measured Nd isotopic ratios from the data of Jacobsen and Wasserburg (1984), DePaolo and Wasserburg (1976a), Lugmair et al. (1976a) and Amelin and Rotenberg (2004)..

Table showing the difference between the measured and computed

present-day Nd isotopic ratios

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Jacobsen and DePaolo and Lugmair et Amelin and

Wasserburg (1984) Wasserburg (1976a) al. (1976a) Rotenberg (2004)

Present-day 143Nd/144Nd ratio (measured): 0.511847 0.511836 0.512636 0.512637

Initial 143Nd/144Nd ratio: 0.505828 0.50598 0.50677 0.50665

Present-day 147Sm/144Nd ratio 0.1967 0.1936 0.1936 0.1964

Decay constant: 6.54E-12 6.54E-12 6.54E-12 6.54E-12

Time elapsed: 4560000000 4560000000 4560000000 4560000000

Initial 147Sm/144Nd ratio (Computed): 0.20265441 0.19946057 0.19946057 0.202345331

143Nd/144Nd produced in 4.56 Gyr (Computed): 0.00595441 0.00586057 0.00586057 0.005945331

Present-day 143Nd/144Nd ratio (Computed): 0.511782412 0.511782412 0.51263057 0.512595331

Diff. between the comptd. and measured ratios: 0.000064588 0.000004570 0.000005430 0.000041669

The above table shows that the Nd isotopic ratios computed from the reference values proposed by Jacobsen and Wasserburg’s (1984), and Amelin and Rotenberg (2004) are much smaller than their measured ratios; whereas in the case of those proposed by Lugmair et al. (1976), and DePaolo and Wasserburg (1976a), the computed and measured ratios are quite similar. The difference between the two ratios in the former case is almost ten times greater than that in the latter. This shows that the Nd isotopic parameters proposed by Jacobsen and Wasserburg (1984), and by Amelin and Rotenberg (2004) are not internally consistent as they do not satisfy their mutual constraints. So this leaves the reference values suggested by Lugmair et al. (1976a), and by DePaolo and Wasserburg (1976a) in contention as both seem to satisfy their mutual constraints.

In fact the most important point in evaluating the aptness of the Sm-Nd isotopic parameters is their relationship with the Rb Sr isotopic parameters because the latter are derived partly from the former. So before considering any Sm Nd reference values for the bulk earth isotopic parameters, their relationship with the Rb-Sr isotopic parameters have to be evaluated first.

The Rb-Sr isotopic parameters for the bulk earth, unlike the Sm-Nd parameters, cannot be determined directly from the meteorites – chondrites or achondrites. This is because they have been subjected to differentiation and/or alteration after their accretion from the solar nebula, which has caused the fractionation of volatile elements such as Rb and Sr. As a result, Rb-Sr isotopic evolution in meteorites has deviated from their normal evolutionary course. Because of this, meteorites in general are not considered as very good representatives of the solar nebula with respect to the Rb-Sr isotopic evolution. However, it is the relationship of the Sr isotopic ratios with Nd isotopic ratios of Recent oceanic basalts which has helped in deducing the Rb-Sr isotopic parameters for the bulk earth/solar nebula. Richard et al. (1976) showed that in Recent oceanic basalts, 87Sr/86Sr isotopic ratios have an inverse correlation with their corresponding 143Nd/144Nd isotopic ratios. DePaolo and Wasserburg (1976b, 1977) showed a similar inverse correlation between initial Nd and Sr isotopic ratios of young volcanic rocks (zero age) from both oceans and continents. These rocks included MOR tholeiitic basalts, continental flood basalts, oceanic island basalts and a few other volcanics from the continent. However, on the correlation diagram, Nd isotopic ratios were shown as normalized to the present-day Nd isotopic ratio of Juvinas (0.511836) (DePaolo and Wasserburg, 1976a). According to them the strong correlation between the initial Nd and Sr isotopic ratios of young basalts indicates that the Rb-Sr and Sm-Nd fractionation events are correlative and caused by the same process. Therefore, they took the 87Sr/86Sr ratio corresponding to the present-day 143Nd/144Nd ratio of Juvinas of 0.511836 on this correlation diagram as the present-day 87Sr/86Sr ratio of the bulk Earth. They thus suggested 0.7045 as the present-day 87Sr/86Sr ratio of the bulk earth. Using this ratio and BABI (0.69899) (Pappanastassiou and Wasserburg, 1969) as the initial ratio of the bulk Earth, and the decay constant λRb of 1.39 E 11 Yr-1, they calculated the present-day Rb/Sr ratio of the unfractionated mantle/bulk Earth to be 0.029. They further estimated the present-day 87Rb/86Sr ratio of the bulk Earth to be 0.0839.

All`egre et al. (1979) viewed the correlation between Nd and Sr isotopic ratios of recent oceanic basalts as of geochemical significance because it could be used to deduce the present-day Sr isotopic parameters for the bulk earth. They maintained that as the earth has chondritic REE distribution, and as the Juvinas achondrite has nearly unfractionated Sm/Nd ratio, the Sr isotopic ratio corresponding to the present-day Nd isotopic ratio of the Juvinas achondrite on this relation, therefore, should closely approximate the bulk earth/planetary value. Following on this assumption, they suggested that the 87Sr/86Sr ratio of 0.70478 ± 0.00008 corresponding to the present-day 143Nd/144Nd value of 0.511836 of Juvinas achondrite (DePaolo and Wasserburg, 1976a) on this relation, should be regarded as the planetary value. They further added that this value along with the initial Sr isotopic ratio of 0.69899, and λRb of (1.42±0.01)10-11y-1 corresponds to the present-day Rb/Sr ratio of 0.031 and 87Rb/86Sr of 0.090 for the bulk earth.

Later, All`egre (1982) referred to the inverse correlation between the Sr and Nd isotopic ratios of recent oceanic island basalts and ridge basalts as the reference array for the whole earth. Further, he used the value of 0.51264 (Lugmair, 1976a) instead of 0.511836 (DePaolo and Wasserburg, 1976a; Jacobsen and Wasserburg, 1980) for the present-day 143Nd/144Nd ratio for deducing the present-day Sr isotopic ratio of the bulk earth from this correlation. This led to a slight revision of his previously suggested value of 0.70478 for this parameter. His new revised reference value for this parameter is 0.7047 ± 0.00008, which corresponds to the present-day 87Rb/86Sr ratio of 0.09 for the bulk earth.

O’Nions et al. (1979) observed that the Nd isotopic evolution in continental rocks as inferred from the initial 143Nd/144Nd ratios of Archean rocks such as Isua metavolcanics, Onverwacht lavas, Bulawayan volcanics, and Lewisian gneisses (Hamilton et al. 1977, 1978, 1979a, 1979b) is consistent with the view that the bulk Earth evolved with chondritic Sm/Nd. This observation of theirs is in accord with that of DePaolo and Wasserburg (1976a, 1976b). However, according to them, bulk Earth evolved with Sm-Nd similar to that of Angra dos Reis achondrites. Therefore, they assumed the Sm/Nd ratio of the bulk Earth to be similar to the chondritic average value of 0.308 (Nakamura et al. 1976). So according to them the initial 143Nd/144Nd ratio of the bulk Earth at the time of its formation 4.55 Gyr ago should be 0.50682 (Cf. Lugmair & Marti, 1977). Its present-day 143Nd/144Nd ratio based on these values was estimated to be 0.51262. They also showed the existence of a strong inverse relationship between the 143Nd/144Nd and 87Sr/86Sr ratios of Recent oceanic ridge basalts and oceanic island basalts, which in their view signifies that these isotopes have fractionated coherently during differentiation of the magma. Therefore, 87Sr/86Sr ratio corresponding to the present-day 143Nd/144Nd ratio on this relation should be taken as the present day bulk Earth ratio. From this relation, they thus obtained 0.7047 as the present-day Sr isotopic ratio for the bulk Earth. However, for this they used the value of 0.51265 as the present-day bulk Earth Nd isotopic ratio as against the value of 0.511836 used by DePaolo and Wasserburg (1976a, 1976b). From this they deduced the present day Rb/Sr ratio of the bulk Earth to be approximately 0.03. O’Nions et al. (1977) had earlier estimated the present-day 87Sr/86Sr and Rb/Sr ratios of 0.705, and 0.032 respectively for the bulk Earth from the inverse correlation formed by the Sr and Nd isotopic ratio of Recent oceanic basalts from the Mid Atalantic Ridge, Atlantic Islands, Reykjanes Ridge, and Iceland. However, they also noticed that the oceanic basalts from the Hawaiian Islands from the Pacific Ocean do not show any such correlation between their Sr and Nd isotopic ratios.

Gargi (2012) came out with a novel model to characterize the source reservoirs of igneous rocks using Rb/Sr and 87Rb/86Sr ratios only. The model determines the isotopic characteristics of a source reservoir with respect to their 87Rb/86Sr as well as 87Sr/86Sr isotopic ratios at the time of their formation. However, the model also contains other relations by which the model age and the initial Sr isotopic ratio of a rock can be determined without requiring the direct input of the 87Sr/86Sr ratios, or the decay constant, λRb. The model is based on the interrelationship of Rb/Sr and 87Rb/86Sr ratios. The basic premise of the model is that these two cosmic ratios have been evolving because of the decay of 87Rb, and addition of 87Sr since the time the two elements, Rb, and Sr appeared in the universe more than 500 Gyr ago (Cf. Gargi, 1987; Cf. Gargi, 2005). The evolution of these two ratios through time is calibrated by plotting Rb/Sr against [(Rb/Sr)/(87Rb/86Sr)] of hypothetical rocks of various ages on an X-Y plot. It is important to note that for defining this model no data from actual rocks, whether terrestrial or extraterrestrial were used. Hence, this model is self-consistent, as it is not dependent on any meteoritic data. In order to define this model, however, values of certain parameters, such as the bulk earth isotopic parameters, age of the earth, and the decay constant, λRb, were presumed. How the values of these parameters were presumed would be discussed in a separate paper at a later date. However, the confirmation about these parameters as being apt and plausible comes from the fact that the model yields the age and initial ratio of well dated rocks from youngest to oldest, as well as meteorites, which match very precisely with their published results. No other set of reference values other than the ones used in this model produces such results. It is also evident from the table below that of all the models, the difference between the computed and measured present-day 87Sr/86Sr ratios is the least only in the case of Gargi’s (2012) model. Thus the reference values of the various parameters as used in his model are internally consistent, and satisfy all the internal and external constraints.

Table showing the differences between the measured and computed

present-day 87Sr/86Sr isotopic ratios

----------------------------------------------------------------------------------------------------------------------------------------

Gargi (2012) DePaolo and Wasserburg (1976b) All`egre (1982)

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Present-day 87Sr/86Sr ratio (measured) 0.704698 0.7045 0.7047

Initial 87Sr/86Sr ratio: 0.69878 0.69899 0.69898

Present-day 87Rb/86Sr ratio 0.089442 0.084 0.09

Decay constant used: 1.408E-11 1.39E-11 1.42E-11

Time elapsed: 4550000000 4550000000 4550000000

Initial 87Rb/86Sr ratio (Computed): 0.09535954 0.08948418 0.096006862

87Sr/86Sr produced in 4.55 Gyr (Computed): 0.00591754 0.00548418 0.006006862

Present-day 87Sr/86Sr ratio (Computed): 0.704697539 0.704474175 0.704986862

Diff. between the comptd. and measured ratios: 0.000000461 0.000025826 -0.000286862

___________________________________________________________________________________________________

The values of the Rb-Sr isotopic parameters for the bulk earth such as the beginning 87Sr/86Sr ratio, the present-day 87Sr/86Sr, 87Rb/86Sr, and the Rb/Sr ratios, as proposed by Gargi (2012), are 0.69878, 0.704698, 0.089442, and 0.031, respectively. Gargi’s (2012) model, and the parameters used to define the model, are consistent with the decay constant, λ for 87Rb being equal to 1.408 EXP-11/Yr, and the age of the earth to 4.55 Gyr. The reason why the measured value of the decay constant λ for 87Rb is a little too high than the one used here would be discussed later in a separate paper.

Conclusion

However, for the discussion here, the parameter of interest is the present-day 87Sr/86Sr ratio as it has been derived from the present-day 143Nd/146Nd ratio of the bulk earth. Both All`egre et al. (1982), and O’Nions et al. (1979) proposed the value of 0.7047 as the present-day 87Sr/86Sr ratio for the bulk earth. They deduced this value from the inverse correlation of 143Nd/144Nd with 87Sr/86Sr ratios of recent oceanic basalts. To derive this value, All`egre (1982) used the value of 0.51264 for the present-day 143Nd/144Nd ratio (Cf. Lugmair et al., 1976a), whereas O’Nions et al. (1979) used the value of 0.51265, which is very similar to the one used by Lugmair et al. (1976a). As the present-day Sr isotopic ratio for the bulk earth is obtained by using the present-day 143Nd/144Nd ratio suggested by Lugmair et al. (1976a), and as the latter’s reference values are internally consistent as shown earlier, it then leads to the conclusion that Lugmair et al.’s (1976a) reference values should be considered as the most apt and plausible for the Sm-Nd isotopic parameters for the bulk earth. It also shows that achondrites yield better results than chondrites for the bulk earth Sm – Nd isotopic parameters.

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