On April 9, David Tyler (d.tyler@mmu.ac.uk) posted the following about Rb-Sr
dating methods and criticisms of it. I was in the middle of putting together
a reply (it was taking a while because it had a low priority) when I saw Glenn
Morton's (GRMorton@gnn.com) post today (April 22) addressing this issue.
Anyway, I thought I'd toss out what I had put together in the way of comments
as well even though I wasn't totally finished. I'll try to be careful to
distinguish between what Tyler said, what Morton said, and what I say...
David Tyler wrote:
> ABSTRACT: A look at presuppositions in historical geology - with reference
> to the use of isochrons in radiometric dating (and a brief comment on the
> work of Steve Austin).
>
> I had written: "Your comment presupposes that the presuppositions of these
> radiometric dating methods are valid. But if the isotopic data is better
> understood in terms of geochemical or non-radiogenic geophysical causes, the
> data is not meaningful in a chronological sense".
>
> Bill Hamilton wrote on 28th March:
> "What do you mean by this? Do you have references? I am not a geologist,
> but I understand radioactive decay and I have read a few references on
> radiometric dating methods and the rules geologists use to qualify samples
> to reduce the possibility of errors. As nearly as I can tell, their science
> is sound."
>
> In my original post to Steve, I illustrated my point with two examples: the
> theoretical distinction between "normal" and "abnormal" lead isotopes (which
> is hard to defend), and alternative explanations of isochrons. I will pick
> up on the latter to develop the argument, basing it on Rb/Sr dating. In
> what follows, I am not throwing stones at geochronologists - their
> methodology is sound GIVEN THEIR PREMISES. What we are looking at is an
> alternative framework for interpretation - one that is open to the idea that
> the isotopic ratios are not necessarily caused by the passage of time. (I
> should add that I last looked seriously at this subject about 10 years ago -
> but I'm not aware of significant developments over the last decade).
I'm glad you admit that their methodology is sound. I don't think your
following comments effectively criticize the premises, only point out a
few well-know limitations of the Rb-Sr dating method.
David Tyler wrote:
> 1. Isochrons are not a sign of closed systems.
>
> The thought sometimes expressed is that BECAUSE a straight line is produced,
> the data must be "reliable" and the conclusions "accurate". This is of
> significance because both Sr and Rb isotope values are quite variable in
> igneous rocks. Can we be sure that the system is closed and isotope
> migration has not occurred?
The standard explanation of Rb-Sr dating claims that if the data falls on
a straight line (isochron), then it's reliable and indicates either the
original age of the sample or the age of isotopic resetting by a metamorphic
event (these must be distinguished by fieldwork and examination of the
fabrics, mineral assemblages, and geochemistry of your samples). It is
pretty impressive when results from several different minerals and whole
rock samples falls on an EXACT straight line for some analyses considering
that Rb and Sr are incorporated differently into each mineral in the rock
(see, for an example of an excellent isochron, figure 5.11a for a lunar mare
basalt in Dalrymple, 1991, p. 232).
David Tyler wrote:
> It is common to identify metamorphic or deformation events which disturb or
> reset the isotopic ratios. However, it is generally assumed that the system
> is closed outside these events - so that the dates obtained are dates of the
> disturbances.
Well, if the data form an isochron, it's assumed that the system has been
closed since isotopic resetting.
David Tyler wrote:
> Matsua (1974) has shown that "a linear isochron can be obtained even for an
> open system". "Such open systems likely exist in Nature. Hence, we must be
> very careful to conclude the age on the basis of an isochron".
Glenn Morton wrote:
> Matsuda linearizes his equations by an assumption that the diffusion
> equation can be replaced by a simple first order rate equation. In my
> mind this is questionable. A diffusion is not a linear process, most of
> the diffusion occurring early decreasing linear and decays
> exponentially. His assumption is wrong and thus produces a red herring.
Matsuda showed that if we assume that 87Rb, *87Sr (radiogenic Sr), 87Sr,
and 86Sr are removed from the system according to some functions f(t) (for
87Rb), g(t) (for *87Sr), and h(t) (for 87Sr & 86Sr), than we might obtain
a "virtual isochron" which would not correspond to the age isochron unless
f(t), g(t), and h(t) are constants equal to zero (i.e. no loss).
Something I think David Tyler should have mentioned is that there was a
rebuttal to Matsuda's (1974) paper a couple of months later by Levsky (1975)
who pointed out something implied in Matsuda's equations but not explicitely
stated. For a "virtual isochron" to form, the transport coefficients must be
equal for all specimens corresponding to each of the data points on the
isochron.
In other words, if I have fifteen samples of either whole rock or mineral
separates, then a virtual isochron would form if, and only if, there was loss
and the transport coefficients for these losses were identical in each of the
samples. In other words, f(t), g(t), and h(t) are the same for plagioclase
as they are for ilmenite, and they are for biotite, as they are for the whole
rock, etc. Is that reasonable?
In Matsuda's reply to Levsky's rebuttal, he discussed two cases. One
for the mineral isochron method (where several different minerals are used
to make up the isochron) and one for the whole rock isochron method.
Matsuda admitted, for the mineral isochron method, that "many conditions
should be satisfied to conform a linear isochron in the mineral isochron
method. Except for a very special case, the point for each mineral will
disperse for the open system." His special cases (no outside *Sr, only *Sr
leaches out, and the rock is soaked in water) were such that they would not
apply to most terrestrial samples and would NEVER apply to samples like lunar
Mare basalts which have been successfully dated by the Rb-Sr method.
Dalrymple (1991, p. 108) gives a hypothetical example of why "the results
are unpredictable in detail, but the isotopic ratios for a system that has
been disturbed almost invariably do not fall on a straight line."
"To see why, consider an oversimplified example that involves only the loss
of 87Sr from our hypothetical rock... Mineral R is high in Rb and low in Sr
because a Rb atom is chemically and physically more compatible with the
particular chemistry and crystal structure of that mineral than is a Sr atom.
This means that s 87Sr atom resulting from the decay of 87Rb may find itself
at a location within the crystal at which it is less firmly bound than either
the original 87Rb or a 87Sr atom incorporated into the crystal when it formed.
When the crystal is reheated, therefore, radiogenic 87Sr atoms may be lost
more easily than either 86Sr or 87Rb atoms. The same will not necessarily be
true for mineral P, in which Sr is a more natural constituent. The ease with
which radiogenic 87Sr is lost from minerals P, Q, and R will be a function of
many factors, such as chemical composition, crystal structure, and crystal
defects, most of which are not directly related to the ratio 87Sr/86Sr. Thus
the movement of compositions from P', Q', and R' to P", Q", and R" will not
fall on a line except by a highly unlikely coincidence."
To be fair, Matsuda still defended his idea of a "virtual isochron" as
being a possibility for the whole rock isochrom method but I think this
also falls prey to the above criticism by Dalrymple in that the Rb and Sr
will not be identically incorporated into the same minerals from different
whole rock samples, even those from which are comagmatic. This is especially
true since whole rock samples often show a spread in Rb and Sr values (i.e.
the further apart your data points are, the better your chance of getting
the slope of the line accurately).
David Tyler wrote:
> Sometimes, an identifiable disturbance is found which correlates with the
> resultant date - and the interpretation placed on the data is not only
> consistent but considered meaningful. But is this optimism justified? Field
> and Raheim (1979) published their data regarding "A geologically meaningless
> Rb-Sr total rock isochron". Although the rock suites used showed "evidence
> of only minor secondary alteration effects", they had to conclude that "An
> isochron so produced is geologically meaningless, that is, the apparent age
> is unrelated to any geological event".
Glenn Morton wrote:
> But they state, "The only petrographically visible effects of this
> superimposed low-grade event are (1) partial, and often variable, alteration
> of orthopyroxenes to chlorite and/or serpentine, (2) minor corrosion of
> pre-existing biotite, and (3) incipient turbidity within some
> plagioclases. These mineral alterations were initiated along narrow (<1mm )
> irregularly spaced cracks which facilitated the open system behaviour."
> p. 498
>
> The low level event was petrologically observable and so did not lead to
> an acceptance of an anomalous date. It would appear to me that the system
> worked as it was supposed to.
Exactly. One can't just grab a rock and isotopically date it. One has to
do careful field and petrologic studies in order to determine if there is
evidence for alteration and resetting due to loss of isotopes. That's the
lesson from this paper. They weren't "fooled" by these isochrons because
they carefully looked at the rocks from which they were derived.
David Tyler wrote:
> Bell and Blenkinsop (1978) address the problem of open systems: "The
> susceptibility of fine-grained, volcanic rocks to open-system behaviour
> during regional metamorphic activity has long been suspected in Rb/Sr
> geochronology". Their paper not only confirms suspicions, but relates Rb/Sr
> ratios to bulk chemical composition. Their paper discusses the problem of
> getting any meaningful information from the analyses.
Glenn Morton wrote:
> Wait a minute here. The classical evidence for open system behavior is a
> non-linear isochron. Samples that fall off a straight line indicate that
> the system is open. Bell and Blenkinsop's figure 2 clearly shows that
> there is a kink in the isochron data. They related this kink to the
> chemical composition of the rocks. They state,
>
> "The evidence that we present here shows that not only can open-system
> behaviour occur, but that it is partly a function of bulk chemical
> composition." p. 532
>
> The isochron method relies on the concept that the rocks came from the
> same magma melt. I would question this in the Bell and Blenkinsop data.
> The samples he has fall into two groups, one group has silica content
> between 44 and 69% while the second group has greater than 70% silica.
> The K2O values are also quite different as is the iron ratios. Given this
> chemical difference in the two sets of samples one might question whether
> or not the material came from the same magma melt although Bell and
> Blenkinsop don't. They ascribe different behavior to the two different
> chemical compositions.
>
> Once again, the isochron system detected open system behavior and so no
> one was fooled.
Bell and Blenkinsop (1978) collected samples from volcanic rocks in northern
Newfoundland. The rocks have been metamorphosed from sub-greenschist up
through amphibolite facies as you move from south to north across the area
(i.e. lower-grade metamorphism in the south, higher-grade in the north). They
found that you couldn't draw a unique isochron through their data, rather two
separate isochrons (with different slopes) fit the data better (and 2 of the
16 data points were excluded because they didn't fall on the isochrons!). The
older (520 Ma) group of data fall very close to the true age of the rocks
(given their stratigraphic relationships) and are distinguished from the
younger group of data (385 Ma) by differences in bulk chemistry. This data
thus exhibits open system behavior. They offered three explanations for this
data and favored one that called for metamorphic resetting around 390 Ma which
preferentially affected the more silicic members of the volcanic succession.
They call upon other Ar/Ar and U/Pb studies in the area to support their
conclusions.
The conclusions of this paper are that:
1. Drawing a single isochron through all of the data would have yielded a
ficticious age somewhere between the ages of formation and metamorphism.
That's true but the isochron would also have a large uncertainty which
would justify it being used very cautiously. After all, the fact that
the data didn't line on a good single isochron suggested to them that
they were looking at a metamorphic overprint.
2. Determining the bulk chemistries of the rocks allowed them to show that
there was indeed evidence for metamorphic remobilization of Rb and Sr
(open system behavior) in the more silicic members of the volcanic rocks.
My conclusion. Rb-Sr dating can't be done in isolation from careful field
geologic and geochemical studies. But, geologists doing Rb-Sr dating already
know this.
David Tyler wrote:
> Are meaningless isochrons the norm or the exception? Are premises relevant
> here?
We have to distinguish between inapproprate samples for Rb-Sr dating
(meaning they show evidence of having been open to Rb and/or Sr migration)
and sample which appear appropriate yet yield ficticious isochrons (which
may be more difficult to identify).
I think it's clear that meaningless isochrons are the rare exception and
that the premises underlying Rb-Sr dating are sound.
David Tyler wrote:
> 2. Isochrons can be produced by the mixing of source materials.
>
> Suppose that a two-phase model of rock magma be considered. This is not a
> way-out suggestion as bimodality is not unusual in igneous terrains. Whilst
> models of magma evolution are less complex, most will agree that there are
> many unknowns between generation and emplacement. In our two phases, we have
> differences in the Rb and Sr contents.
> The resultant rocks produced from these magmas will yield isochrons which are
> unrelated to age. The isochron is a geochemical signature, not a mark of the
> passage of time. The theory for this seems to be well-recognised in the
> literature, but I have not got a reference to the mathematical derivation to
> report.
Faure (1986), in a standard textbook of isotope geology, has an entire chapter
devoted to "Isotope Systematics of Two-Component Mixtures."
David Tyler wrote:
> Dupre et al (1982) discuss isotopic variations on the island of Terceira.
> they report observations "in agreement with a model of mixing between two
> different mantle components, ..." They obtained isochrons using lead
> isotopes, but stated: "These straight lines must be considered as mixing
> lines with no chronometric significance".
Glenn Morton wrote:
> But Dupre et al also say,
>
> "The whole series of samples which seems to define a common trend of
> fractional crystallization have variable isotopic ratio values and must
> therefore belong to different magmatic series." (p. 621)
>
> The lavas were emplaced on Terceira over a period of 300,000 years. In
> that time at the speed of thtle circulation (approx. 4 cm/year) the
> mantle material could have traveled 12 kilometers and this could be a
> factor in the change in isotopic composition over that time period.
Take the Rb-Sr data in Table 1 and plot them up on an Rb/Sr-Sr/Sr diagram.
They don't define a straight line. That's why they talk about mixing.
David Tyler wrote:
> Shaffer and Faure (1976) looked at strontium ratios in sediments taken from
> the Ross Sea. Their conclusions are: "The isotopic compositions of strontium
> and concentrations of rubidium and strontium as well as those of several
> detrital minerals in the <100-mesh noncarbonate fractions vary systematically
> throughout the Ross Sea. These variations can be attributed to mixing of two
> detrital components which are weathering products of old sialic rocks and
> young basaltic volcanics in Antarctica. ... Linear correlations of 87Sr/86Sr
> and 87Rb/86Sr ratios are due to mixing of two components and bear no relation
> to the age of the rocks in Antarctica or to the time of deposition of the
> sediment."
Glenn Morton wrote:
> This is detrital material and should have no bearing on age. The material
> ranges in age from Precambrian to Cretaceous. The reason is that you don't
> know where the detritus came from. The isochron method is supposed to work
> only if you have several rocks from the same magma. You can't guarantee that
> in detritus. But a xed assemblage from a lot of sources probably would give
> you a straight line. No one would attempt dating of the detritus by this
> method.
I'm confused as to why you included this paper here. This paper does not
have anything to do with magma mixing and the data does not form an true
isochron.
In this paper, Shaffer and Faure (Faure, by the way, is the author of
several standard textbooks on geochemistry and isotope geology) looked at
detrital sediments -- essentially, fine non-carbonate sand that was the
weathering product of preexisting rocks. They determined Rb and Sr
concentrations (in ppm) and 87Sr/86Sr and 87Rb/86Sr ratios for these
sediments. They determined from this data, and from mixing equations, that
the sediments were primarily derived from two source terrains (pre-Cretaceous
rocks rich in quartz and feldspar and younger Tertiary basalts).
Plotting the data from Table 1 of this paper will quickly demonstrate that
the data does not form a true isochron. While the data does exhibit a
positive linear correlation, there is also a great deal of scatter. That's
why the data was then examined for a fit to a mixing equation and plotted as
87Sr/86Sr vs. (1/Sr ppm). After the data was obtained, there was never any
question that it couldn't be used for an age determination and didn't form a
true isochron.
Reading between the lines, here's my interpretation of this paper... These
guys got some NSF money to do isotopic analyses (it's not cheap) on Antarctic
samples in order to see if they could determine the age of the source
provenance or the time of deposition of the sediments. They could not and
this was why (there is no single source and the seawater messed up their Rb
values). It's not really a very interesting paper and doesn't say a heck
of a lot but I think they had to publish something to justify the money they
received (if you want more NSF money in the future, you need to publish your
results).
Bottom line, this paper does not support your point because no true isochron
ever existed for this data and it has nothing to do with magma mixing (just
mixing of sediments from differing sources).
David Tyler wrote:
> Again I ask: if magma mixing is a mechanism for producing isochrons, why
> do we not hear more about it? Are there ways of distinguishing between
> age-related isochrons and geochemical isochrons (due to mixing)? (There is
> one method - see below). Are people even asking these questions? How far
> are premises important here?
Of course these questions have been dealt with in the geological literature.
They're not often addressed in popular-level or undergraduate-level textbooks
on isotopic dating, however, one has to dig into the primary literature.
One takes their data and plots it on a Rb-Sr plot. One examines the rocks for
evidence of alteration, metamorphism etc. One considers the position within
the overall stratigraphic framework of these rocks (Are they Precambrian? Are
they Mesozoic?). If the data falls on a straight line with a very low
deviation, there is no evidence of alteration, and the age is comparable with
the regional geologic picture, then it's an age isochron. If the data is
linearly correlated yet many points lie off a best-fit line, or one sees
evidence of alteration, then it probably reflects some mixing or loss of
isotopes from the system.
David Tyler wrote:
> 3. The phenomenon of pseudoisochrons.
>
> According to Brooks et al (1976), "One serious consequence of the mantle
> isochron model is that crystallisation ages determined on basic igneous rocks
> by the Rb-Sr whole-rock technique can be greater than the true age by many
> hundreds of millions of years. This problem of inherited age is more serious
> for younger rocks, and there are well-documented instances of conflicts
> between stratigraphic age and Rb-Sr age in the literature." This phenomenon
> of "inherited age" is the theme of their paper.
Again, look at the 9 pseudoisochrons in Figure 1. They all show data which
is spread about the best-fit line (some of them show very large deviations).
That's why mixing is discussed.
David Tyler wrote:
> They distinguish a pseudoisochron from a simple isochron plot in the
> following way. The simple plot is of current-day values, but the
> pseudoisochron used values corrected back to the time of crystallisation of
> the magma. However, in practice, "For the most part the pseudoisochrons
> come from young volcanic terranes in which no age correction of the measured
> present-day Sr isotopic composition is necessary."
>
> The paper documents a whole series of "anomalous dates" from tertiary
> volcanics. Of particular interest are two reported by Leeman (1974).
> Hawaiites from the Western Grand Canyon have an apparent age of 1300 million
> years, and alkali basalts from the same area are dated as 1100 million
> years. I'll comment further on these below. The authors suggest three ways
> of getting pseudoisochrons: 1. Mixing of heterogeneous magmas. 2. Selective
> melting of heterogenous mantle material of the same age or different ages.
> 3. Disequilibrium melting of homogeneous mantle in which individual mineral
> phases are in isotopic disequilibrium. "Distinguishing between these
> possibilities is difficult as none of the proposed mechanisms leads to a
> uniquely identifiable compositional property in the rocks, other than that
> of Pb and Sr isotopic variation ..." "One means of evaluating
> pseudoisochrons is to determine whether they involve identifiable
> mixing-line chemistry. Rubidium- Strontium variation diagrams and plots of
> 87Sr/86Sr against 1/Sr can be used for this purpose. Examination of such
> plots for the data [used in this study] reveals that a good pseudoisochron
> is commonly accompanied by a good positive correlation between 87Sr/86Sr and
> 1/Sr, but no correlation at all between Rb and Sr. The absence of an Rb-Sr
> correlation is inconsistent with simple mixing. Thus, while we cannot
> discount mixing of heterogeneous mantle material, the data in general seem
> to preclude simple two- component magma mixing as an important factor in
> most pseudoisochrons."
>
> I do have a problem with the last point above. I would say that a
> correlation of 87Sr/86Sr and 1/Sr is indicative of mixing. Are the 87Sr
> isotopes due to radioactive decay of 87Rb, or are they dependent on the
> concentration of Sr in the rock? The positive correlations reported
> indicate that the strontium isotope concentrations are directly dependent on
> the strontium present in the rock. At the moment, I do not follow Brooks
> argument - if anyone can see the logic behind it, I will be glad to hear
> from you.
>
> The Grand Canyon lavas mentioned above are the ones studied by Steve Austin -
> some discussion took place on this last year. Austin has obtained values of
> 1.3 billion years for the Tertiary basalts of Grand Canyon: something for
> which he is using to question the appropriateness of using Rb/Sr dating. The
> important point here is that his findings are is close agreement with Leeman
> (1974). To nit-pick at possible selective use of data seems to be an unwise
> response to Austin. The argument of Brooks et al (1976) is that Austin has
> found a pseusoisochron - that conveys information about the earth's mantle
> and mechanisms of petrogenesis. At the moment, unless I can get my question
> (previous paragraph) answered, I think the magma mixing explanation is to be
> considered the most likely - which implies that the isochrons have
> geochemical, but not geochronological, information.
Glenn Morton wrote:
> This whole thing with the bad Rb/Sr dates ignores the fact that we know
> they are wrong because other radiometric dates give a more reasonable age.
> The dating of the lava dam (which gives a billion years age with Rb/Sr)
> gives 1.16 Myr with K-Ar. This date also agrees with the date derived
> from stratigraphy. This always seems to be ignored. The bad Rb/Sr dates
> at Grand Canyon are always spoken of as if this is the only dating method
> applicable to them.
>
> One of the explanations given by Brooks et al is that some of the
> lithosphere has become trapped below the continent accounting for the
> problematic Rb/Sr dates. If this is correct then it is quite possible
> that the magma melt which gave rise to the Cardenas Basalt also gave rise
> to the late Cenozoic volcanism. This would explain the discrepancy
> between the K/Ar date and the Rb/Sr d
>
> I would also like to point out that Steve is quite selective in the way he
> handles contradictory evidence. He cites (p. 123 of his Grand
> Canyon:Monument to Catastrophe) a 117 million year old K/Ar date on the
> Vulcan Throne Basalt in the text but only informs the reader at the end of
> the footnote buried at the end of the chapter that olivine is not a
> suitable mineral for K/Ar ying that piece of info.
>
> He then cites the 1.2 Myr date I mention above but never discusses their
> significance. Argon being a gas is able to mostly leave the mineral when
> the lava erupts. It's date fits with local geologic evidence and Steve
> simply mentions the age and then moves on. He also cites a 10,000 year
> K/Ar date for one of the upper lavas and a 230,000 year date for another.
>
> Because of all this Brooks et al's explanation seems quite reasonable.
This is the part I haven't had time to look into in detail yet. I've been
reading up on the problems associated with dating Tertiary basalts in the
Colorado Plateau region and I'll get back to it in the near future.
I do have a question about Austin's work. Where has it been published?
I'd like to see what he's written about this and the details of his study.
David Tyler wrote:
> Even if Brooks et al are right, the number of variables involved becomes
> very large. We have a situation where the isotope variations cannot be
> interpreted without a context: "Effective use of the mantle isochron concept
> requires knowledge of actual crystallisation ages (so that the measured
> isochron can be divided into its pre- and post-crystallisation components)
> and determination of isochron parameters on rocks that have been subjected
> to minimal postmelting processes (fractional crystallisation, wall rock
> contamination, and so forth)..." The net effect is to "fit" the data into
> an accepted paradigm.
>
> Conclusion
>
> I have discussed (1) the problem of open systems, (2) the alternative
> explanation of magma mixing, and (3) pseudoisochrons. The picture emerging
> is one of paradigm-dependency. The presuppositions are essential for the
> method to deliver results. The objectivity of radiometric dating (at least
> affecting Rb/Sr dating) is an illusion. My personal conclusion (stated in a
> previous post) is that all dating methods are subject to presupposition
> problems of this kind - and that we really have no valid ways to establish a
> chronology of earth history.
Glenn Morton wrote:
> This last sentence is quite incorrect IMO. The relative chronology of earth
> history can be worked out by studying the sequence of rock layers. The
> principle of superposition is the basis of all geochronology. The rock layer
> on the bottom is the oldest. Some sedimentary rocks preserve the orbital
> cyclicities of the earth (20,000, 40,000 aes). These cyclicities allow one
> to date the time it took for those sediments to be deposited. The 13 million
> layers in Lake Gosuite of the Green River Formation preserve these types of
> cyclicities. It is believed that this deposit took about 6.5 million years
> to be deposited and it represents only 7% of the sedimentary column. It is
> also one of the most rapidly deposited formations.
Rb-Sr dating is testable against other isotopic dating methods. One can date
many types of igneous rocks with Rb-Sr, Sm-Nd, K-Ar, Ar-Ar, U-Pb, etc. All of
these methods have built-in assumptions and limitations (as does everything we
do) yet the assumptions and limitations are generally very well known and,
most importantly, the assumptions and limitations are often different for the
different methods. They are all genuinely different techniques and do provide
independant means of evaluation each other. Also, as Glenn points out,
classical stratigraphy certainly provides evidence for a very old earth.
If the earth is only a few thousand years old, the God fiddled with the
isochrons (not just one, but many) to make it look old.
References:
Bell, K. & Blenkinsop, J. 1978. Reset Rb/Sr whole-rock systems and chemical
control. Nature 273 (15 June), 532-534.
Brooks, C., James, D.E., & Hart, S.R. 1976. Ancient lithosphere: Its role
in young continental volcanism. Science 193 (17 September), 1086-1094.
Dalrymple, G.B. 1991. The Age of the Earth. Stanford University Press,
Stanford, CA.
Dupre, B., Lambret, B., & Allegre, A.J. 1982. Isotopic variations within a
single oceanic island: The Terceira case. Nature 299 (14 October), 620-622.
Faure, G. 1986. Principles of Isotope Geology. 2nd Edition. John Wiley & Sons,
New York
Field, D. & Raheim, A. 1979. A geologically meaningless Rb-Sr total rock
isochron. Nature 282 (29 November), 497-499.
Leeman, W.P. 1974. Late Cenozoic alkali-rich basalt from the Western Grand
Canyon Area, Utah and Arizona: isotopic composition of strontium. Geological
Society of America Bulletin 85 (November), 1691-1696.
Levsky, L.K. 1975. Comments on paper by J. Matsuda ' A virtual Rb-Sr isochron
for an open system.' Geochemical Journal 9, 181-182
Matsuda, J. 1974. A virtual Rb-Sr isochron for an open system. Geochemical
Journal 8, 153-155.
Shaffer, N.R. & Faure, G. 1976. Regional variations of 87Sr/86Sr ratios
and mineral compositions of sediment from the Ross Sea, Antarctica.
Geological Society of America Bulletin 87 (October), 1491-1500.
- Steve.
-- Steven H. Schimmrich Callsign KB9LCG s-schim@uiuc.edu Department of Geology, University of Illinois at Urbana-Champaign 245 Natural History Building, Urbana, IL 61801 (217) 244-1246 http://www.uiuc.edu/ph/www/s-schim Deus noster refugium