concordia: Concordia diagram

Description Usage Arguments Details Value References Examples

View source: R/concordia.R

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

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concordia(x = NULL, tlim = NULL, alpha = 0.05, type = 1,
  show.numbers = FALSE, levels = NA, clabel = "",
  ellipse.col = c("#00FF0080", "#FF000080"),
  concordia.col = "darksalmon", exterr = FALSE, show.age = 0,
  sigdig = 2, common.Pb = 0, ticks = 5, anchor = list(FALSE, NA),
  hide = NULL, omit = NULL, omit.col = NA, ...)

Arguments

x

an object of class UPb

tlim

age limits of the concordia line

alpha

probability cutoff for the error ellipses and confidence intervals

type

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)

show.numbers

logical flag (TRUE to show grain numbers)

levels

a vector with length(x) values to be displayed as different background colours within the error ellipses.

clabel

label for the colour legend (only used if levels is not NA).

ellipse.col

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.col=NA

concordia.col

colour of the concordia line

exterr

show decay constant uncertainties?

show.age

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 √{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.

sigdig

number of significant digits for the concordia/discordia age

common.Pb

common lead correction:

0:none

1: use the Pb-composition stored in

settings('iratio','Pb206Pb204') (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=7 or 8).

2: use the isochron intercept as the initial Pb-composition

3: use the Stacey-Kramers two-stage model to infer the initial Pb-composition.

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 discordia fit. This is a two-element list.

The first element is a boolean flag indicating whether the discordia line should be anchored. If this is FALSE, then the second item is ignored and both the common Pb composition and age are estimated.

If the first element is TRUE and the second element is NA, then the common Pb composition is fixed at the values stored in settings('iratio',...).

If the first element is TRUE and the second element is a number, then the discordia line is forced to intersect the concordia line at an age equal to that number.

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.col

colour that should be used for the omitted aliquots.

...

optional arguments to the generic plot function

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 formats 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 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.

p.value

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.

df

a three-element vector with the number of degrees of freedom used for the mswd calculation.

age

a 4-element vector with:
t: the concordia age (in Ma)
s[t]: the estimated uncertainty of t
ci[t]: the studentised 100(1-α)\% confidence interval of t for the appropriate degrees of freedom
disp[t]: the studentised 100(1-α)\% confidence interval for t augmented by √{mswd} to account for overdispersed datasets.

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) (if type=2). If show.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 the following rows:

s: the estimated standard deviation for x

ci: the studentised 100(1-α)\% confidence interval of x for the appropriate degrees of freedom

disp[t]: the studentised 100(1-α)\% confidence interval for x augmented by √{mswd} to account for overdispersed datasets (only reported if show.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 if show.age=3).

fact

the (1-α/2)-percentile of a t-distribution with df degrees of freedom.

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

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data(examples)
concordia(examples$UPb,show.age=2)

dev.new()
concordia(examples$UPb,type=1,xlim=c(24.9,25.4),
          ylim=c(0.0508,0.0518),ticks=249:254,exterr=TRUE)

dev.new()
concordia(examples$UPb,type=2,show.age=2,anchor=list(TRUE,0))

pvermees/IsoplotR documentation built on Jan. 8, 2020, 7:03 p.m.