Plots U-Pb data on Wetherill, Tera-Wasserburg or U-Th-Pb concordia diagrams, calculates concordia_ages and compositions, evaluates the equivalence of multiple (\(^{206}\)Pb/\(^{238}\)U-\(^{207}\)Pb/\(^{235}\)U, \(^{207}\)Pb/\(^{206}\)Pb-\(^{206}\)Pb/\(^{238}\)U, or \(^{208}\)Th/\(^{232}\)Th-\(^{206}\)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 = NULL,
tlim = NULL,
type = 1,
show.numbers = FALSE,
levels = NA,
clabel = "",
ellipse.fill = c("#00FF0080", "#FF000080"),
ellipse.stroke = "black",
concordia.col = "darksalmon",
exterr = FALSE,
show.age = 0,
oerr = 3,
sigdig = 2,
common.Pb = 0,
ticks = 5,
anchor = 0,
cutoff.disc = discfilter(),
hide = NULL,
omit = NULL,
omit.fill = NA,
omit.stroke = "grey",
...
)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.
a two-or three-element vector with:
t: the concordia_age (in Ma)
s[t]: the standard error of t
disp[t]: the standard error of t augmented by
\(\sqrt{mswd}\) to account for any overdispersion.
If show.age=2, 3 or 4, returns a list with the
following items:
the fitting model (=show.age-1).
a vector with the upper and lower intercept ages (if
type=1) or the lower intercept age and common Pb
intercept(s) (if type=2). If show.age=4, includes an
overdispersion term as well.
the covariance matrix of the elements in par.
the logarithm of par
the logarithm of cov
a matrix with on or two rows:
s: the standard errors of the parameter estimates
disp: the standard errors of the parameter estimates
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).
the number of aliquots in the dataset
an object of class UPb
age limits of the concordia line
one of
1: Wetherill -- \({}^{206}\)Pb/\({}^{238}\)U
vs. \({}^{207}\)Pb/\({}^{235}\)U
2: Tera-Wasserburg -- \({}^{207}\)Pb/\({}^{206}\)Pb
vs. \({}^{238}\)U/\({}^{206}\)Pb
3: U-Th-Pb concordia -- \({}^{208}\)Pb/\({}^{232}\)Th
vs. \({}^{206}\)Pb/\({}^{238}\)U (only available if
x$format=7 or 8)
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).
Fill colour for the error ellipses. This can either be a single colour or multiple colours to form a colour ramp. Examples:
a single colour: rgb(0,1,0,0.5), '#FF000080',
'white', etc.;
multiple colours: c(rbg(1,0,0,0.5),
rgb(0,1,0,0.5)), c('#FF000080','#00FF0080'),
c('blue','red'), c('blue','yellow','red'), etc.;
a colour palette: rainbow(n=100),
topo.colors(n=100,alpha=0.5), etc.; or
a reversed palette: rev(topo.colors(n=100,alpha=0.5)),
etc.
For empty ellipses, set ellipse.fill=NA
the stroke colour for the error
ellipses. Follows the same formatting guidelines as
ellipse.fill
colour of the concordia line
show decay constant uncertainties?
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.
indicates whether the analytical uncertainties of the output are reported in the plot title as:
1: 1\(\sigma\) absolute uncertainties.
2: 2\(\sigma\) absolute uncertainties.
3: absolute (1-\(\alpha\))% confidence intervals, where
\(\alpha\) equales the value that is stored in
settings('alpha').
4: 1\(\sigma\) relative uncertainties (\(\%\)).
5: 2\(\sigma\) relative uncertainties (\(\%\)).
6: relative (1-\(\alpha\))% confidence intervals, where
\(\alpha\) equales the value that is stored in
settings('alpha').
number of significant digits for the concordia/discordia age
common lead projection:
0:none
1: use the Pb-composition stored in
settings('iratio','Pb207Pb206') (if x$format<4);
settings('iratio','Pb206Pb204') and
settings('iratio','Pb207Pb204') (if 3<x$format<7); or
settings('iratio','Pb208Pb206') and
settings('iratio','Pb208Pb207') (if x$format>6).
2: use the isochron intercept as the initial
Pb-composition. If show.age>1, the data are projected along
the isochron line, but the isochron itself is based on the
uncorrected data.
3: use the Stacey-Kramers two-stage model to infer the initial
Pb-composition.
either a scalar indicating the desired number of age ticks to be placed along the concordia line, OR a vector of tick ages.
control parameters to fix the intercept age or common Pb composition of the isochron fit. This can be a scalar or a vector.
If anchor[1]=0: do not anchor the isochron.
If anchor[1]=1: fix the common Pb composition at the values
stored in settings('iratio',...).
If anchor[1]=2: force the isochron line to intersect the
concordia line at an age equal to anchor[2].
If anchor[1]=3: anchor the non-radiogenic component to the
Stacey-Kramers mantle evolution model.
discordance cutoff filter. This is an object of
class discfilter.
vector with indices of aliquots that should be removed from the concordia diagram
vector with indices of aliquots that should be plotted but omitted from concordia or discordia age calculation
fill colour that should be used for the omitted aliquots.
stroke colour that should be used for the omitted aliquots.
optional arguments passed on to scatterplot
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). Alternatively, for data format 7 and 8, it is also
possible to plot \(^{208}\)Pb/\(^{232}\)Th against the
\(^{206}\)Pb/\(^{238}\)U. 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.
attach(examples)
concordia(UPb,show.age=2)
dev.new()
concordia(UPb,type=2,xlim=c(24.9,25.4),
ylim=c(0.0508,0.0518),ticks=249:254,exterr=TRUE)
dev.new()
concordia(UPb,show.age=2,anchor=c(2,260))
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