| Pb0corr {IsoplotR} | R Documentation |
Common Pb correction
Description
Applies a common-Pb correction to a U-Pb dataset using either the Stacey-Kramers mantle evolution model, isochron regression, or any nominal inital Pb isotope composition.
Usage
Pb0corr(x, option = 3, omit4c = NULL)
Arguments
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
|
Details
IsoplotR implements nine different methods to correct for
the presence of non-radiogenic (‘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 common-Pb correction:
\left[\frac{{}^{206|7}Pb}{{}^{204}Pb}\right]_r =
\left[\frac{{}^{206|7}Pb}{{}^{204}Pb}\right]_m -
\left[\frac{{}^{206|7}Pb}{{}^{204}Pb}\right]_\circ
where [{}^{206|7}Pb/^{204}Pb]_r marks the radiogenic
{}^{206}Pb or {}^{207}Pb component;
[{}^{206|7}Pb/^{204}Pb]_m is the measured ratio; and
[{}^{206|7}Pb/^{204}Pb]_\circ is the non-radiogenic component.
IsoplotR offers three different ways to determine
[{}^{206|7}Pb/^{204}Pb]_\circ. The first and easiest option
is to simply use a nominal value such as the
{}^{206|7}Pb/^{204}Pb-ratio of a cogenetic feldspar,
assuming that this is representative for the common-Pb composition
of the entire sample. A second method is to determine the
non-radiogenic isotope composition by fitting an isochron line
through multiple aliquots of the same sample, using the
3-dimensional 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
common-Pb composition from the two-stage 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}Pb-ratio 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}Pb-based
common lead correction can be used:
\frac{{}^{206|7}Pb_r}{{}^{208}Pb_\circ} =
\frac{{}^{206|7}Pb_m}{{}^{208}Pb_\circ} -
\left[\frac{{}^{206|7}Pb}{{}^{208}Pb}\right]_\circ
where {}^{208}Pb_\circ marks the non-radiogenic
{}^{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} Pb-based common lead correction can be used:
\left[\frac{{}^{207}Pb}{{}^{206}Pb}\right]_m = f
\left[\frac{{}^{207}Pb}{{}^{206}Pb}\right]_\circ + (1-f)
\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 U-Pb
measurements on the concordia line in Tera-Wasserburg 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 common-Pb problem, a second reason for U-Pb discordance
is radiogenic Pb-loss 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.
Value
Returns a list in which x.raw contains the original data and
x the common Pb-corrected compositions. All other items in
the list are inherited from the input data.
References
Ludwig, K.R., 1998. On the treatment of concordant uranium-lead ages. Geochimica et Cosmochimica Acta, 62(4), pp.665-676.
Stacey, J.T. and Kramers, 1., 1975. Approximation of terrestrial lead isotope evolution by a two-stage model. Earth and Planetary Science Letters, 26(2), pp.207-221.
Examples
attach(examples)
corrected <- Pb0corr(UPb,option=2)
concordia(corrected)
# produces identical results as:
dev.new()
concordia(UPb,common.Pb=2)