Pb0corr: Common Pb correction

In IsoplotR: Statistical Toolbox for Radiometric Geochronology

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 UPb
option	one of either 1: nominal common Pb isotope composition 2: isochron regression 3: Stacey-Kramers correction
omit4c	vector with indices of aliquots that should be omitted from the isochron regression (only used if option=2)

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)

IsoplotR documentation built on Nov. 10, 2023, 9:08 a.m.