concordia  R Documentation 
Plots UPb data on Wetherill, TeraWasserburg or UThPb 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 Chisquared pvalues. 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 TeraWasserburg), 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,
hide = NULL,
omit = NULL,
omit.fill = NA,
omit.stroke = "grey",
...
)
x 
an object of class 
tlim 
age limits of the concordia line 
type 
one of

show.numbers 
logical flag ( 
levels 
a vector with 
clabel 
label for the colour legend (only used if

ellipse.fill 
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: multiple colours: a colour palette: a reversed palette: For empty ellipses, set 
ellipse.stroke 
the stroke colour for the error
ellipses. Follows the same formatting guidelines as

concordia.col 
colour of the concordia line 
exterr 
show decay constant uncertainties? 
show.age 
one of either:

oerr 
indicates whether the analytical uncertainties of the output are reported in the plot title as:

sigdig 
number of significant digits for the concordia/discordia age 
common.Pb 
common lead projection:

ticks 
either a scalar indicating the desired number of age ticks to be placed along the concordia line, OR a vector of tick ages. 
anchor 
control parameters to fix the intercept age or common Pb composition of the isochron fit. This can be a scalar or a vector. If If If If 
hide 
vector with indices of aliquots that should be removed from the concordia diagram 
omit 
vector with indices of aliquots that should be plotted but omitted from concordia or discordia age calculation 
omit.fill 
fill colour that should be used for the omitted aliquots. 
omit.stroke 
stroke colour that should be used for the omitted aliquots. 
... 
optional arguments passed on to 
The concordia diagram is a graphical means of assessing the
internal consistency of UPb data. It sets out the measured
^{206}
Pb/^{238}
U and
^{207}
Pb/^{235}
Uratios against each other (‘Wetherill’
diagram); or, equivalently, the ^{207}
Pb/^{206}
Pb and
^{206}
Pb/^{238}
Uratios (‘TeraWasserburg’
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(1alpha
)% 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 nonradiogenic
(‘common’) lead or to constrain the timing of prior lead loss.
If show.age=1
, returns a list with the following items:
a named vector with the (weighted mean) UPb composition
the covariance matrix of the (weighted mean) UPb composition
a vector with three items (equivalence
,
concordance
and combined
) containing the MSWD (Mean
of the Squared Weighted Deviates, a.k.a the reduced Chisquared
statistic) of isotopic equivalence, age concordance and combined
goodness of fit, respectively.
a vector with three items (equivalence
,
concordance
and combined
) containing the pvalue of
the Chisquare test for isotopic equivalence, age concordance and
combined goodness of fit, respectively.
a threeelement vector with the number of degrees of
freedom used for the mswd
calculation.
a twoor threeelement 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.age1
).
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)
pvalue of a Chisquare test for age homogeneity
(only reported if type=3
).
mean square of the weighted deviates – a
goodnessoffit measure. mswd > 1
indicates overdispersion
w.r.t the analytical uncertainties (not reported if
show.age=3
).
the number of aliquots in the dataset
Ludwig, K.R., 1998. On the treatment of concordant uraniumlead ages. Geochimica et Cosmochimica Acta, 62(4), pp.665676.
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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