concordia {IsoplotR} | R Documentation |
Concordia diagram
Description
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.
Usage
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",
...
)
Arguments
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 |
Details
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.
Value
If show.age=1
, returns a list with the following items:
- x
a named vector with the (weighted mean) U-Pb composition
- cov
the covariance matrix of the (weighted mean) U-Pb composition
- mswd
a vector with three items (
equivalence
,concordance
andcombined
) 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.- p.value
a vector with three items (
equivalence
,concordance
andcombined
) containing the p-value of the Chi-square test for isotopic equivalence, age concordance and combined goodness of fit, respectively.- df
a three-element vector with the number of degrees of freedom used for the
mswd
calculation.- age
a two-or three-element vector with:
t
: the concordia_age (in Ma)
s[t]
: the standard error oft
disp[t]
: the standard error oft
augmented by\sqrt{mswd}
to account for any overdispersion.
If show.age=2
, 3
or 4
, returns a list with the
following items:
- model
the fitting model (
=show.age-1
).- par
a vector with the upper and lower intercept ages (if
type=1
) or the lower intercept age and common Pb intercept(s) (iftype=2
). Ifshow.age=4
, includes an overdispersion term as well.- cov
the covariance matrix of the elements in
par
.- logpar
the logarithm of
par
- logcov
the logarithm of
cov
- err
a matrix with on or two rows:
s
: the standard errors of the parameter estimatesdisp
: the standard errors of the parameter estimates augmented by\sqrt{mswd}
to account for overdispersed datasets (only reported ifshow.age=2
).- df
the degrees of freedom of the concordia fit (concordance + equivalence)
- p.value
p-value of a Chi-square test for age homogeneity (only reported if
type=3
).- mswd
mean square of the weighted deviates – a goodness-of-fit measure.
mswd > 1
indicates overdispersion w.r.t the analytical uncertainties (not reported ifshow.age=3
).- n
the number of aliquots in the dataset
References
Ludwig, K.R., 1998. On the treatment of concordant uranium-lead ages. Geochimica et Cosmochimica Acta, 62(4), pp.665-676.
Examples
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))