helioplot: Visualise U-Th-He data on a logratio plot or ternary diagram

In IsoplotR: Statistical Toolbox for Radiometric Geochronology

Visualise U-Th-He data on a logratio plot or ternary diagram

Description

Plot U-Th(-Sm)-He data on a (log[He/Th] vs. log[U/He]) logratio plot or U-Th-He ternary diagram

Usage

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",
  ...
)

Arguments

x	an object of class UThHe
logratio	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.
model	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.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: 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').
contour.col	two-element 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: 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
ellipse.stroke	the stroke colour for the error ellipses. Follows the same formatting guidelines as ellipse.fill
sigdig	number of significant digits for the barycentric age
xlim	optional limits of the x-axis (log[U/He]) of the logratio plot. If xlim=NA, the axis limits are determined automatically.
ylim	optional limits of the y-axis (log[Th/He]) of the logratio plot. If ylim=NA, the axis limits are determined automatically.
fact	three-element vector with scaling factors of the ternary diagram if fact=NA, these will be determined automatically
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 plot function

Details

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.

References

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.

See Also

radialplot

Examples

attach(examples)
helioplot(UThHe)
dev.new()
helioplot(UThHe,logratio=FALSE)

IsoplotR documentation built on Oct. 19, 2024, 5:07 p.m.