Pb0corr  R Documentation 
Applies a commonPb correction to a UPb dataset using either the StaceyKramers mantle evolution model, isochron regression, or any nominal inital Pb isotope composition.
Pb0corr(x, option = 3, omit4c = NULL)
x 
an object of class 
option 
one of either

omit4c 
vector with indices of aliquots that should be
omitted from the isochron regression (only used if

IsoplotR
implements nine different methods to correct for
the presence of nonradiogenic (‘common’) lead. This includes three
strategies tailored to datasets that include ^{204}
Pb
measurements, three strategies tailored to datasets that include
^{208}
Pb measurements, and a further three strategies for
datasets that only include ^{206}
Pb and
^{207}
Pb.
^{204}
Pb is the only one of lead's four stable isotopes that
does not have a naturally occurring radioactive parent. This makes
it very useful for commonPb correction:
\left[\frac{{}^{2067}Pb}{{}^{204}Pb}\right]_r =
\left[\frac{{}^{2067}Pb}{{}^{204}Pb}\right]_m 
\left[\frac{{}^{2067}Pb}{{}^{204}Pb}\right]_\circ
where [{}^{2067}Pb/^{204}Pb]_r
marks the radiogenic
{}^{206}
Pb or {}^{207}
Pb component;
[{}^{2067}Pb/^{204}Pb]_m
is the measured ratio; and
[{}^{2067}Pb/^{204}Pb]_\circ
is the nonradiogenic component.
IsoplotR
offers three different ways to determine
[{}^{2067}Pb/^{204}Pb]_\circ
. The first and easiest option
is to simply use a nominal value such as the
{}^{2067}
Pb/^{204}
Pbratio of a cogenetic feldspar,
assuming that this is representative for the commonPb composition
of the entire sample. A second method is to determine the
nonradiogenic isotope composition by fitting an isochron line
through multiple aliquots of the same sample, using the
3dimensional regression algorithm of Ludwig (1998).
Unfortunately, neither of these two methods is applicable to
detrital samples, which generally lack identifiable cogenetic
minerals and aliquots. For such samples, IsoplotR
infers the
commonPb composition from the twostage crustal evolution model of
Stacey and Kramers (1975). The second stage of this model is
described by:
\left[\frac{{}^{206}Pb}{{}^{204}Pb}\right]_\circ =
\left[\frac{{}^{206}Pb}{{}^{204}Pb}\right]_{3.7Ga} +
\left[\frac{{}^{238}U}{{}^{204}Pb}\right]_{sk}
\left(e^{\lambda_{238}3.7Ga}e^{\lambda_{238}t}\right)
where \left[{}^{206}Pb/{}^{204}Pb\right]_{3.7Ga} = 11.152
and
\left[{}^{238}U/{}^{204}Pb\right]_{sk} = 9.74
. These
Equations can be solved for t
and
\left[{}^{206}Pb/{}^{204}Pb\right]_\circ
using the method of
maximum likelihood. The {}^{207}
Pb/{}^{204}
Pbratio is
corrected in exactly the same way, using
\left[{}^{207}Pb/{}^{204}Pb\right]_{3.7Ga} = 12.998
.
In the absence of ^{204}
Pb measurements, a ^{208}
Pbbased
common lead correction can be used:
\frac{{}^{2067}Pb_r}{{}^{208}Pb_\circ} =
\frac{{}^{2067}Pb_m}{{}^{208}Pb_\circ} 
\left[\frac{{}^{2067}Pb}{{}^{208}Pb}\right]_\circ
where {}^{208}Pb_\circ
marks the nonradiogenic
{}^{208}Pb
component, which is obtained by removing the
radiogenic component for any given age.
If neither {}^{204}
Pb nor {}^{208}
Pb were measured,
then a ^{207}
Pbbased common lead correction can be used:
\left[\frac{{}^{207}Pb}{{}^{206}Pb}\right]_m = f
\left[\frac{{}^{207}Pb}{{}^{206}Pb}\right]_\circ + (1f)
\left[\frac{{}^{207}Pb}{{}^{204}Pb}\right]_r
where f
is the fraction of common lead, and
[{}^{207}Pb/{}^{206}Pb]_r
is obtained by projecting the UPb
measurements on the concordia line in TeraWasserburg space. Like
before, the initial lead composition
[{}^{207}Pb/{}^{206}Pb]_\circ
can be obtained in three
possible ways: by analysing a cogenetic mineral, by isochron
regression through multiple aliquots, or from the Stacey and
Kramers (1975) model.
Besides the commonPb problem, a second reason for UPb discordance
is radiogenic Pbloss during igneous and metamorphic activity.
This moves the data away from the concordia line along a linear
array, forming an isochron or ‘discordia’ line. IsoplotR
fits this line using the Ludwig (1998) algorithm. If the data are
plotted on a Wetherill concordia diagram, the program will not only
report the usual lower intercept with the concordia line, but the
upper intercept as well. Both values are geologically meaningful as
they constrain both the initial igneous age as well as the timing
of the partial resetting event.
Returns a list in which x.raw
contains the original data and
x
the common Pbcorrected compositions. All other items in
the list are inherited from the input data.
Ludwig, K.R., 1998. On the treatment of concordant uraniumlead ages. Geochimica et Cosmochimica Acta, 62(4), pp.665676.
Stacey, J.T. and Kramers, 1., 1975. Approximation of terrestrial lead isotope evolution by a twostage model. Earth and Planetary Science Letters, 26(2), pp.207221.
attach(examples)
corrected < Pb0corr(UPb,option=2)
concordia(corrected)
# produces identical results as:
dev.new()
concordia(UPb,common.Pb=2)
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