Description Usage Arguments Details References See Also Examples
Plot UTh(Sm)He data on a (log[He/Th] vs. log[U/He]) logratio plot or UThHe ternary diagram
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x 
an object of class 
logratio 
Boolean flag indicating whether the data should be shown on bivariate log[He/Th] vs. log[U/He] diagram, or a UThHe ternary diagram. 
model 
choose one of the following statistical models:

show.central.comp 
show the geometric mean composition as a white ellipse? 
show.numbers 
show the grain numbers inside the error ellipses? 
alpha 
probability cutoff for the error ellipses and confidence intervals 
contour.col 
twoelement vector with the fill colours to be assigned to the minimum and maximum age contour 
levels 
a vector with additional values to be displayed as different background colours within the error ellipses. 
clabel 
label of the colour scale 
ellipse.col 
a vector of two background colours for the error
ellipses. If 
sigdig 
number of significant digits for the central age 
xlim 
optional limits of the xaxis (log[U/He]) of the
logratio plot. If 
ylim 
optional limits of the yaxis (log[Th/He]) of the
logratio plot. If 
fact 
threeelement vector with scaling factors of the
ternary diagram if 
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 central age calculation. 
omit.col 
colour that should be used for the omitted aliquots. 
... 
optional arguments to the generic 
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 UThHe 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 threedimensional 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 UThHe(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 UTh(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
UTh(Sm)He dating, the central age is defined as the age
that corresponds to the arithmetic mean composition in logratio
space, which is equivalent to the geometric mean in compositional
dataspace (Vermeesch, 2008). IsoplotR
's helioplot
function performs this calculation using the same algorithm that is
used to obtain the weighted mean UPb 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
√{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 UTh(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 UPb concordia
diagram and the
Useries 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 (UTh)/He ages. Chemical Geology, 249(3), pp.339347.
Vermeesch, P., 2010. HelioPlot, and the treatment of overdispersed (UThSm)/He data. Chemical Geology, 271(3), pp.108111.
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