Plots U-Pb data on Wetherill and Tera-Wasserburg concordia diagrams, calculate concordia ages and compositions, evaluates the equivalence of multiple (\(^{206}\)Pb/\(^{238}\)U-\(^{207}\)Pb/\(^{235}\)U or \(^{207}\)Pb/\(^{206}\)Pb-\(^{206}\)Pb/\(^{238}\)U) compositions, computes the weighted mean isotopic composition and the corresponding concordia age using the method of maximum likelihood, computes the MSWD of equivalence and concordance and their respective Chi-squared p-values. Performs linear regression and computes the upper and lower intercept ages (for Wetherill) or the lower intercept age and the \(^{207}\)Pb/\(^{206}\)Pb intercept (for Tera-Wasserburg), taking into account error correlations and decay constant uncertainties.
concordia(x, tlim = NULL, alpha = 0.05, wetherill = TRUE,
show.numbers = FALSE, levels = NA, clabel = clabel,
ellipse.col = c("#00FF0080", "#FF000080"), concordia.col = "darksalmon",
exterr = FALSE, show.age = 0, sigdig = 2, common.Pb = 0,
ticks = NULL, ...)an object of class UPb
age limits of the concordia line
probability cutoff for the error ellipses and confidence intervals
logical flag (FALSE for Tera-Wasserburg)
logical flag (TRUE to show grain
numbers)
a vector with length(x) values to be displayed
as different background colours within the error ellipses.
label for the colour legend (only used if
levels is not NA.
a vector of two background colours for the error
ellipses. If levels=NA, then only the first colour is
used. If levels is a vector of numbers, then
ellipse.col is used to construct a colour ramp.
colour of the concordia line
show decay constant uncertainty?
one of either:
0: plot the data without calculating an age
1: fit a concordia composition and age
2: fit a discordia line through the data using the maximum
likelihood algorithm of Ludwig (1998), which assumes that the
scatter of the data is solely due to the analytical
uncertainties. In this case, IsoplotR will either calculate
an upper and lower intercept age (for Wetherill concordia), or a
lower intercept age and common
(\(^{207}\)Pb/\(^{206}\)Pb)-ratio intercept (for
Tera-Wasserburg). If mswd>0, then the analytical
uncertainties are augmented by a factor \(\sqrt{mswd}\).
3: fit a discordia line ignoring the analytical uncertainties
4: fit a discordia line using a modified maximum likelihood
algorithm that includes accounts for any overdispersion by adding a
geological (co)variance term.
number of significant digits for the concordia/discordia age
apply a common lead correction using one of three methods:
1: use the Stacey-Kramer two-stage model to infer the initial
Pb-composition
2: use the isochron intercept as the initial Pb-composition
3: use the Pb-composition stored in
settings('iratio','Pb206Pb204') and
settings('iratio','Pb207Pb204')
an optional vector of age ticks to be added to the
concordia line to override IsoplotR's default spacing,
which is based on R's pretty function.
optional arguments to the generic plot function
if show.age=1, returns a list with the following items:
a named vector with the (weighted mean) U-Pb composition
the covariance matrix of the (weighted mean) U-Pb composition
a vector with three items (equivalence,
concordance and combined) containing the MSWD (Mean
of the Squared Weighted Deviates, a.k.a the reduced Chi-squared
statistic) of isotopic equivalence, age concordance and combined
goodness of fit, respectively.
a vector with three items (equivalence,
concordance and combined) containing the p-value of
the Chi-square test for isotopic equivalence, age concordance and
combined goodness of fit, respectively.
a three-element vector with the number of degrees of
freedom used for the mswd calculation. These values are
useful when expanding the analytical uncertainties if
mswd>1.
a 4-element vector with:
t: the concordia age (in Ma)
s[t]: the estimated uncertainty of t
ci[t]: the studentised \(100(1-\alpha)\%\) confidence
interval of t for the appropriate degrees of freedom
disp[t]: the studentised \(100(1-\alpha)\%\) confidence
interval for t augmented by \(\sqrt{mswd}\) to account for
overdispersed datasets.
if show.age=2, 3 or 4, returns a list with the
following items:
the fitting model (=show.age-1).
a two element vector with the upper and lower intercept
ages (if wetherill=TRUE) or the lower intercept age and
\(^{207}\)Pb/\(^{206}\)Pb intercept (if
wetherill=FALSE).
the covariance matrix of the elements in x.
a [2 x 2] or [3 x 2] matrix with the
following rows:
s: the estimated standard deviation for x
ci: the studentised \(100(1-\alpha)\%\) confidence
interval of x for the appropriate degrees of freedom
disp[t]: the studentised \(100(1-\alpha)\%\) confidence
interval for x augmented by \(\sqrt{mswd}\) to account for
overdispersed datasets (only reported if show.age=2).
the degrees of freedom of the concordia fit (concordance + equivalence)
p-value of a Chi-square test for age homogeneity
(only reported if type=3).
mean square of the weighted deviates -- a
goodness-of-fit measure. mswd > 1 indicates overdispersion
w.r.t the analytical uncertainties (not reported if
show.age=3).
two-element vector with the standard deviation of the
(assumedly) Normal overdispersion term and the corresponding
\(100(1-\alpha)\%\) confidence interval (only important if
show.age=4).
The concordia diagram is a graphical means of assessing the
internal consistency of U-Pb data. It sets out the measured
\(^{206}\)Pb/\(^{238}\)U- and
\(^{207}\)Pb/\(^{235}\)U-ratios against each other (`Wetherill'
diagram) or, equivalently, the \(^{207}\)Pb/\(^{206}\)Pb- and
\(^{206}\)Pb/\(^{238}\)U-ratios (`Tera-Wasserburg'
diagram). The space of concordant isotopic compositions is marked
by a curve, the `concordia line'. Isotopic ratio measurements are
shown as 100(1-alpha)% confidence ellipses. Concordant
samples plot near to, or overlap with, the concordia line. They
represent the pinnacle of geochronological robustness. Samples that
plot away from the concordia line but are aligned along a linear
trend form an isochron (or `discordia' line) that can be used
to infer the composition of the non-radiogenic
(`common') lead or to constrain the timing of prior lead loss.
Ludwig, K.R., 1998. On the treatment of concordant uranium-lead ages. Geochimica et Cosmochimica Acta, 62(4), pp.665-676.
# NOT RUN {
data(examples)
concordia(examples$UPb,show.age=2)
dev.new()
concordia(examples$UPb,wetherill=FALSE,
xlim=c(24.9,25.4),ylim=c(0.0508,0.0518),
ticks=249:254,exterr=TRUE)#' data(examples)
# }
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