Plot U-Th(-Sm)-He data on a (log[He/Th] vs. log[U/He]) logratio plot or U-Th-He ternary diagram
helioplot(
x,
logratio = TRUE,
model = 1,
show.barycentre = TRUE,
show.numbers = FALSE,
oerr = 3,
contour.col = c("white", "red"),
levels = NA,
clabel = "",
ellipse.fill = c("#00FF0080", "#0000FF80"),
ellipse.stroke = "black",
sigdig = 2,
xlim = NA,
ylim = NA,
fact = NA,
hide = NULL,
omit = NULL,
omit.fill = NA,
omit.stroke = "grey",
...
)an object of class UThHe
Boolean flag indicating whether the data should be shown on bivariate log[He/Th] vs. log[U/He] diagram, or a U-Th-He ternary diagram.
choose one of the following statistical models:
1: weighted mean. This model assumes that the scatter between
the data points is solely caused by the analytical uncertainty. If
the assumption is correct, then the MSWD value should be
approximately equal to one. There are three strategies to deal with
the case where MSWD>1. The first of these is to assume that the
analytical uncertainties have been underestimated by a factor
\(\sqrt{MSWD}\).
2: unweighted mean. A second way to deal with over- or
underdispersed datasets is to simply ignore the analytical
uncertainties.
3: weighted mean with overdispersion: instead of attributing
any overdispersion (MSWD > 1) to underestimated analytical
uncertainties (model 1), it can also be attributed to the presence
of geological uncertainty, which manifests itself as an added
(co)variance term.
show the mean composition as a white ellipse?
show the grain numbers inside the error ellipses?
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').
two-element vector with the fill colours to be assigned to the minimum and maximum age contour
a vector with additional values to be displayed as different background colours within the error ellipses.
label of the colour scale
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
number of significant digits for the barycentric age
optional limits of the x-axis (log[U/He]) of the
logratio plot. If xlim=NA, the axis limits are
determined automatically.
optional limits of the y-axis (log[Th/He]) of the
logratio plot. If ylim=NA, the axis limits are
determined automatically.
three-element vector with scaling factors of the
ternary diagram if fact=NA, these will be determined
automatically
vector with indices of aliquots that should be removed from the plot.
vector with indices of aliquots that should be plotted but omitted from the barycentric age calculation.
fill colour that should be used for the omitted aliquots.
stroke colour that should be used for the omitted aliquots.
optional arguments to the generic plot function
U, Th, Sm and He are compositional data. This means that it is not so much the absolute concentrations of these elements that bear the chronological information, but rather their relative proportions. The space of all possible U-Th-He compositions fits within the constraints of a ternary diagram or `helioplot' (Vermeesch, 2008, 2010). If Sm is included as well, then this expands to a three-dimensional tetrahaedral space (Vermeesch, 2008). Data that fit within these constrained spaces must be subjected to a logratio transformation prior to statistical analysis (Aitchison, 1986). In the case of the U-Th-He-(Sm)-He system, this is achieved by first defining two (or three) new variables:
\(u \equiv \ln[U/He]\) \(v \equiv \ln[Th/He]\) \((, w \equiv \ln[Sm/He] )\)
and then performing the desired statistical analysis (averaging, uncertainty propagation, ...) on the transformed data. Upon completion of the mathematical operations, the results can then be mapped back to U-Th-(Sm)-He space using an inverse logratio transformation:
\([He] = 1/[e^{u}+e^{v}+(e^{w})+1]\),
\([U] = e^{u}/[e^{u}+e^{v}+(e^{w})+1]\)
\([Th] = e^{v}/[e^{u}+e^{v}+(e^{w})+1]\),
\(([Sm] = e^{w}/[e^{u}+e^{v}+(e^{w})+1])\)
where \([He] + [U] + [Th] (+ [Sm]) = 1\). In the context of
U-Th-(Sm)-He dating, the barycentric age (which is
equivalent to the 'central age' of Vermeesch, 2008) is defined as
the date that corresponds to the compositional mean, which is
equivalent to the arithmetic mean composition in logratio space.
IsoplotR's helioplot function performs this
calculation using the same algorithm that is used to obtain the
weighted mean U-Pb composition for the concordia age
calculation. Overdispersion is treated similarly as in a regression
context (see isochron). Thus, there are options to
augment the uncertainties with a factor \(\sqrt{MSWD}\) (model
1); to ignore the analytical uncertainties altogether (model 2); or
to add a constant overdispersion term to the analytical
uncertainties (model 3). The helioplot function visualises
U-Th-(Sm)-He data on either a ternary diagram or a bivariate
\(\ln[Th/U]\) vs. \(\ln[U/He]\) contour plot. These diagrams
provide a convenient way to simultaneously display the isotopic
composition of samples as well as their chronological meaning. In
this respect, they fulfil the same purpose as the U-Pb
concordia diagram and the U-series
evolution plot.
Aitchison, J., 1986, The statistical analysis of compositional data: London, Chapman and Hall, 416 p.
Vermeesch, P., 2008. Three new ways to calculate average (U-Th)/He ages. Chemical Geology, 249(3), pp.339-347.
Vermeesch, P., 2010. HelioPlot, and the treatment of overdispersed (U-Th-Sm)/He data. Chemical Geology, 271(3), pp.108-111.
radialplot
attach(examples)
helioplot(UThHe)
dev.new()
helioplot(UThHe,logratio=FALSE)
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