Description Usage Arguments Details Value References See Also Examples
Plots cogenetic ArAr, KCa, PbPb, RbSr, SmNd, ReOs, LuHf,
UThHe or ThU data as XY scatterplots, fits an isochron curve
through them using the york
function, and computes the
corresponding isochron age, including decay constant uncertainties.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75  isochron(x, ...)
## Default S3 method:
isochron(x, xlim = NA, ylim = NA, alpha = 0.05,
sigdig = 2, show.numbers = FALSE, levels = NA, clabel = "",
ellipse.col = c("#00FF0080", "#FF000080"), ci.col = "gray80",
line.col = "black", lwd = 1, plot = TRUE, title = TRUE,
model = 1, xlab = "x", ylab = "y", hide = NULL, omit = NULL,
omit.col = NA, ...)
## S3 method for class 'ArAr'
isochron(x, xlim = NA, ylim = NA, alpha = 0.05,
sigdig = 2, show.numbers = FALSE, levels = NA, clabel = "",
ellipse.col = c("#00FF0080", "#FF000080"), inverse = TRUE,
ci.col = "gray80", line.col = "black", lwd = 1, plot = TRUE,
exterr = TRUE, model = 1, hide = NULL, omit = NULL,
omit.col = NA, ...)
## S3 method for class 'KCa'
isochron(x, xlim = NA, ylim = NA, alpha = 0.05,
sigdig = 2, show.numbers = FALSE, levels = NA, clabel = "",
ellipse.col = c("#00FF0080", "#FF000080"), ci.col = "gray80",
line.col = "black", lwd = 1, plot = TRUE, exterr = TRUE,
model = 1, hide = NULL, omit = NULL, omit.col = NA, ...)
## S3 method for class 'PbPb'
isochron(x, xlim = NA, ylim = NA, alpha = 0.05,
sigdig = 2, show.numbers = FALSE, levels = NA, clabel = "",
ellipse.col = c("#00FF0080", "#FF000080"), inverse = TRUE,
ci.col = "gray80", line.col = "black", lwd = 1, plot = TRUE,
exterr = TRUE, model = 1, growth = FALSE, hide = NULL,
omit = NULL, omit.col = NA, ...)
## S3 method for class 'RbSr'
isochron(x, xlim = NA, ylim = NA, alpha = 0.05,
sigdig = 2, show.numbers = FALSE, levels = NA, clabel = "",
ellipse.col = c("#00FF0080", "#FF000080"), ci.col = "gray80",
line.col = "black", lwd = 1, plot = TRUE, exterr = TRUE,
model = 1, hide = NULL, omit = NULL, omit.col = NA, ...)
## S3 method for class 'ReOs'
isochron(x, xlim = NA, ylim = NA, alpha = 0.05,
sigdig = 2, show.numbers = FALSE, levels = NA, clabel = "",
ellipse.col = c("#00FF0080", "#FF000080"), ci.col = "gray80",
line.col = "black", lwd = 1, plot = TRUE, exterr = TRUE,
model = 1, hide = NULL, omit = NULL, omit.col = NA, ...)
## S3 method for class 'SmNd'
isochron(x, xlim = NA, ylim = NA, alpha = 0.05,
sigdig = 2, show.numbers = FALSE, levels = NA, clabel = "",
ellipse.col = c("#00FF0080", "#FF000080"), ci.col = "gray80",
line.col = "black", lwd = 1, plot = TRUE, exterr = TRUE,
model = 1, hide = NULL, omit = NULL, omit.col = NA, ...)
## S3 method for class 'LuHf'
isochron(x, xlim = NA, ylim = NA, alpha = 0.05,
sigdig = 2, show.numbers = FALSE, levels = NA, clabel = "",
ellipse.col = c("#00FF0080", "#FF000080"), ci.col = "gray80",
line.col = "black", lwd = 1, plot = TRUE, exterr = TRUE,
model = 1, hide = NULL, omit = NULL, omit.col = NA, ...)
## S3 method for class 'ThU'
isochron(x, type = 2, xlim = NA, ylim = NA,
alpha = 0.05, sigdig = 2, show.numbers = FALSE, levels = NA,
clabel = "", ellipse.col = c("#00FF0080", "#FF000080"),
ci.col = "gray80", line.col = "black", lwd = 1, plot = TRUE,
exterr = TRUE, model = 1, hide = NULL, omit = NULL,
omit.col = NA, ...)
## S3 method for class 'UThHe'
isochron(x, xlim = NA, ylim = NA, alpha = 0.05,
sigdig = 2, show.numbers = FALSE, levels = NA, clabel = "",
ellipse.col = c("#00FF0080", "#FF000080"), ci.col = "gray80",
line.col = "black", lwd = 1, plot = TRUE, model = 1,
hide = NULL, omit = NULL, omit.col = "grey", ...)

x 
EITHER a matrix with the following five columns:
OR an object of class 
... 
optional arguments to be passed on to the generic plot
function if 
xlim 
2element vector with the xaxis limits 
ylim 
2element vector with the yaxis limits 
alpha 
confidence cutoff for the error ellipses and confidence intervals 
sigdig 
the number of significant digits of the numerical values reported in the title of the graphical output 
show.numbers 
logical flag ( 
levels 
a vector with additional values to be displayed as different background colours within the error ellipses. 
clabel 
label for the colour scale 
ellipse.col 
a vector of two background colours for the error
ellipses. If 
ci.col 
the fill colour for the confidence interval of the intercept and slope. 
line.col 
colour of the isochron line 
lwd 
line width 
plot 
if 
title 
add a title to the plot? 
model 
construct the isochron using either:

xlab 
text label for the horizontal plot axis 
ylab 
text label for the vertical plot axis 
hide 
vector with indices of aliquots that should be removed from the plot. 
omit 
vector with indices of aliquots that should be plotted but omitted from the isochron age calculation. 
omit.col 
colour that should be used for the omitted aliquots. 
inverse 
if if if if 
exterr 
propagate external sources of uncertainty (J, decay constant)? 
growth 
add StaceyKramers Pbevolution curve to the plot? 
type 
following the classification of Ludwig and Titterington (1994), one of either:

Given several aliquots from a single sample, isochrons allow the
nonradiogenic component of the daughter nuclide to be quantified
and separated from the radiogenic component. In its simplest form,
an isochron is obtained by setting out the amount of radiogenic
daughter against the amount of radioactive parent, both normalised
to a nonradiogenic isotope of the daughter element, and fitting a
straight line through these points by least squares regression
(Nicolaysen, 1961). The slope and intercept then yield the
radiogenic daughterparent ratio and the nonradiogenic daughter
composition, respectively. There are several ways to fit an
isochron. The easiest of these is ordinary least squares
regression, which weighs all data points equally. In the presence
of quantifiable analytical uncertainty, it is equally
straightforward to use the inverse of the yerrors as weights. It
is significantly more difficult to take into account uncertainties
in both the x and the yvariable (York, 1966). IsoplotR
does so for its UThHe isochron calculations. The York (1966)
method assumes that the analytical uncertainties of the x and
yvariables are independent from each other. This assumption is
rarely met in geochronology. York (1968) addresses this issue with
a bivariate error weighted linear least squares algorithm that
accounts for covariant errors in both variables. This algorithm was
further improved by York et al. (2004) to ensure consistency with
the maximum likelihood approach of Titterington and Halliday
(1979).
IsoplotR
uses the York et al. (2004) algorithm for its
ArAr, KCa, PbPb, RbSr, SmNd, ReOs and LuHf isochrons. The
maximum likelihood algorithm of Titterington and Halliday (1979)
was generalised from two to three dimensions by Ludwig and
Titterington (1994) for Useries disequilibrium dating. Also this
algorithm is implemented in IsoplotR
. The extent to which
the observed scatter in the data can be explained by the analytical
uncertainties can be assessed using the Mean Square of the Weighted
Deviates (MSWD, McIntyre et al., 1966), which is defined as:
MSWD = ([X  \hat{X}] Σ_{X}^{1} [X  \hat{X}]^T)/df
where X are the data, \hat{X} are the fitted values,
and Σ_X is the covariance matrix of X, and df
= k(n1) are the degrees of freedom, where k is the
dimensionality of the linear fit. MSWD values that are far smaller
or greater than 1 indicate under or overdispersed measurements,
respectively. Underdispersion can be attributed to overestimated
analytical uncertainties. IsoplotR
provides three
alternative strategies to deal with overdispersed data:
Attribute the overdispersion to an underestimation of the analytical uncertainties. In this case, the excess scatter can be accounted for by inflating those uncertainties by a factor √{MSWD}.
Ignore the analytical uncertainties and perform an ordinary least squares regression.
Attribute the overdispersion to the presence of 'geological scatter'. In this case, the excess scatter can be accounted for by adding an overdispersion term that lowers the MSWD to unity.
If x
has class PbPb
, ArAr
, KCa
,
RbSr
, SmNd
, ReOs
or LuHf
, or
UThHe
, returns a list with the following items:
the intercept of the straight line fit and its standard error.
the slope of the fit and its standard error.
the covariance of the slope and intercept
the degrees of freedom of the linear fit (df=n2)
a fourelement list containing:
y
: the atmospheric ^{40}Ar/^{36}Ar or initial
^{40}Ca/^{44}Ca, ^{207}Pb/^{204}Pb,
^{187}Os/^{188}Os, ^{87}Sr/^{87}Rb,
^{143}Nd/^{144}Nd or ^{176}Hf/^{177}Hf
ratio.
s[y]
: the propagated uncertainty of y
ci[y]
: the studentised 100(1α)\% confidence
interval for y
.
disp[y]
: the studentised 100(1α)\% confidence
interval for y
enhanced by √{mswd} (only
applicable if model=1
).
a fourelement list containing:
t
: the ^{207}Pb/^{206}Pb,
^{40}Ar/^{39}Ar, ^{40}K/^{40}Ca,
^{187}Os/^{187}Re, ^{87}Sr/^{87}Rb,
^{143}Nd/^{144}Nd or ^{176}Hf/^{177}Hf age.
s[t]
: the propagated uncertainty of t
ci[t]
: the studentised 100(1α)\% confidence
interval for t
.
disp[t]
: the studentised 100(1α)\% confidence
interval for t
enhanced by √{mswd} (only
applicable if model=1
).
the mean square of the residuals (a.k.a 'reduced
Chisquare') statistic (omitted if model=2
).
the pvalue of a Chisquare test for linearity
(omitted if model=2
)
the overdispersion term, i.e. a threeelement vector with
the standard deviation of the (assumedly) Normally distributed
geological scatter that underlies the measurements, and the lower
and upper halfwidths of its 100(1α)\% confidence
interval (only returned if model=3
).
OR, if x
has class ThU
:
if x$type=1
or x$type=3
: the best fitting
^{230}Th/^{232}Th intercept,
^{230}Th/^{238}U slope, ^{234}U/^{232}Th
intercept and ^{234}U/^{238}U slope, OR, if
x$type=2
or x$type=4
: the best fitting
^{234}U/^{238}U intercept,
^{230}Th/^{232}Th slope, ^{234}U/^{238}U
intercept and ^{234}U/^{232}Th slope.
the covariance matrix of par
.
the degrees of freedom for the linear fit, i.e. (3n3) if
x$format=1
or x$format=2
, and (2n2) if
x$format=3
or x$format=4
if type=1
: the ^{230}Th/^{232}Th
intercept; if type=2
: the ^{230}Th/^{238}U
intercept; if type=3
: the ^{234}Th/^{232}Th
intercept; if type=4
: the ^{234}Th/^{238}U
intercept and its propagated uncertainty.
if type=1
: the ^{230}Th/^{238}U slope;
if type=2
: the ^{230}Th/^{232}Th slope; if
type=3
: the ^{234}U/^{238}U slope; if
type=4
: the ^{234}U/^{232}Th slope and its
propagated uncertainty.
the covariance between a
and b
.
the mean square of the residuals (a.k.a 'reduced Chisquare') statistic.
the pvalue of a Chisquare test for linearity.
the 100(1α/2)\% percentile of a
tdistribution with df
degrees of freedom.
a fourelement vector containing:
y
: the initial ^{234}U/^{238}Uratio
s[y]
: the propagated uncertainty of y
ci[y]
: the studentised 100(1α)\% confidence
interval for y
.
disp[y]
: the studentised 100(1α)\% confidence
interval for y
enhanced by √{mswd}.
a three (or four) element vector containing:
t
: the initial ^{234}U/^{238}Uratio
s[t]
: the propagated uncertainty of t
ci[t]
: the studentised 100(1α)\% confidence
interval for t
disp[t]
: the studentised 100(1α)\% confidence
interval for t
enhanced by √{mswd} (only reported
if model=1
).
the overdispersion term, i.e. a threeelement vector with
the standard deviation of the (assumedly) Normally distributed
geological scatter that underlies the measurements, and the lower
and upper halfwidth of its 100(1α)\% confidence
interval (only returned if model=3
).
a matrix with the following columns: the Xvariable for the isochron plot, the analytical uncertainty of X, the Yvariable for the isochron plot, the analytical uncertainty of Y, and the correlation coefficient between X and Y.
the xlabel of the isochron plot
the ylabel of the isochron plot
Ludwig, K.R. and Titterington, D.M., 1994. Calculation of ^{230}Th/U isochrons, ages, and errors. Geochimica et Cosmochimica Acta, 58(22), pp.50315042.
Nicolaysen, L.O., 1961. Graphic interpretation of discordant age measurements on metamorphic rocks. Annals of the New York Academy of Sciences, 91(1), pp.198206.
Titterington, D.M. and Halliday, A.N., 1979. On the fitting of parallel isochrons and the method of maximum likelihood. Chemical Geology, 26(3), pp.183195.
York, D., 1966. Leastsquares fitting of a straight line. Canadian Journal of Physics, 44(5), pp.10791086.
York, D., 1968. Least squares fitting of a straight line with correlated errors. Earth and Planetary Science Letters, 5, pp.320324.
York, D., Evensen, N.M., Martinez, M.L. and De Basebe Delgado, J., 2004. Unified equations for the slope, intercept, and standard errors of the best straight line. American Journal of Physics, 72(3), pp.367375.
1 2 3 4 5 6 7 
$a
[1] 3.309029e03 7.819574e06
$b
[1] 1.507141e02 4.949318e05
$cov.ab
[1] 3.804838e10
$mswd
[1] 5.695801
$p.value
[1] 6.230807e08
$model
[1] 1
$y0
[1] 302.2034502 0.7141377
$age
[1] 61.6010915 0.3233058
attr(,"class")
[1] "isochron"
$par
a b A B
1.1258923 0.1526918 0.7465559 0.1887426
$cov
a b A B
a 0.0002616864 0.0002868350 0.0003300569 0.0003634355
b 0.0002868350 0.0004043853 0.0004166950 0.0004588357
A 0.0003300569 0.0004166950 0.0005253042 0.0005279771
B 0.0003634355 0.0004588357 0.0005279771 0.0006290208
$mswd
1.433654
$p.value
[1] 0.1765025
$model
[1] 1
$a
a
1.12589233 0.01617673
$b
b
0.15269176 0.02010933
$cov.ab
[1] 0.000286835
$y0
48_0 s[48_0]
1.17424494 0.02351751
$age
t s[t]
115.176486 3.558932
$xlab
expression(paste(""^"232", "Th/"^"238", "U"))
$ylab
expression(paste(""^"234", "U/"^"238", "U"))
$d
X sX Y sY rXY
[1,] 0.1677 0.00467883 1.1050 0.01392300 0.2367
[2,] 0.2820 0.00640140 1.0813 0.01254308 0.2645
[3,] 0.3699 0.00761994 1.0385 0.01131965 0.2701
[4,] 0.4473 0.00872235 1.0512 0.01103760 0.2744
[5,] 0.5065 0.00947155 1.0490 0.01038510 0.2712
[6,] 0.5520 0.00999120 1.0390 0.00987050 0.2667
attr(,"class")
[1] "isochron"
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