helioplot  R Documentation 
Plot UTh(Sm)He data on a (log[He/Th] vs. log[U/He]) logratio plot or UThHe 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",
...
)
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.barycentre 
show the mean composition as a white ellipse? 
show.numbers 
show the grain numbers inside the error ellipses? 
oerr 
indicates whether the analytical uncertainties of the output are reported in the plot title as:

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.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

sigdig 
number of significant digits for the barycentric 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 barycentric 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 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 â€˜helioplotâ€™ (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 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 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 \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
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.
radialplot
attach(examples)
helioplot(UThHe)
dev.new()
helioplot(UThHe,logratio=FALSE)
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