agespectrum: Plot a (40Ar/39Ar) release spectrum

Description

Produces a plot of boxes whose widths correspond to the cumulative amount of \(^{39}\)Ar (or any other variable), and whose heights express the analytical uncertainties. Only propagates the analytical uncertainty associated with decay constants and J-factors after computing the plateau composition.

Usage

agespectrum(x, ...)
# S3 method for default
agespectrum(
  x,
  oerr = 3,
  plateau = TRUE,
  random.effects = FALSE,
  levels = NA,
  clabel = "",
  plateau.col = c("#00FF0080", "#FF000080"),
  non.plateau.col = "#00FFFF80",
  sigdig = 2,
  line.col = "red",
  lwd = 2,
  xlab = "cumulative fraction",
  ylab = "X",
  hide = NULL,
  omit = NULL,
  ...
)
# S3 method for other
agespectrum(
  x,
  oerr = 3,
  plateau = TRUE,
  random.effects = FALSE,
  levels = NA,
  clabel = "",
  plateau.col = c("#00FF0080", "#FF000080"),
  non.plateau.col = "#00FFFF80",
  sigdig = 2,
  line.col = "red",
  lwd = 2,
  xlab = "cumulative fraction",
  ylab = "X",
  hide = NULL,
  omit = NULL,
  ...
)
# S3 method for ArAr
agespectrum(
  x,
  oerr = 3,
  plateau = TRUE,
  random.effects = FALSE,
  levels = NA,
  clabel = "",
  plateau.col = c("#00FF0080", "#FF000080"),
  non.plateau.col = "#00FFFF80",
  sigdig = 2,
  exterr = FALSE,
  line.col = "red",
  lwd = 2,
  i2i = FALSE,
  hide = NULL,
  omit = NULL,
  ...
)

Value

If plateau=TRUE, returns a list containing the output of the

weightedmean function, plus the following items:

fract

the fraction of \(^{39}\)Ar contained in the plateau

indices of the steps that are retained for the plateau age calculation

Arguments

x

a three-column matrix whose first column gives the amount of \(^{39}\)Ar in each aliquot, and whose second and third columns give the age and its uncertainty.

an object of class ArAr

...

optional parameters to the generic plot function

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').

plateau

logical flag indicating whether a plateau age should be calculated. If plateau=TRUE, the function computes the weighted mean of the largest succession of steps that pass the Chi-square test for age homogeneity. If TRUE, it returns a list with plateau parameters.

random.effects

if TRUE, computes the weighted mean using a random effects model with two parameters: the mean and the dispersion. This is akin to a `model-3' isochron regression.

if FALSE, attributes any excess dispersion to an underestimation of the analytical uncertainties. This akin to a `model-1' isochron regression.

levels

a vector with additional values to be displayed as different background colours of the plot symbols.

clabel

label of the colour legend

plateau.col

Fill colours of the rectangles used to mark the steps belonging to the age plateau. This can either be a single colour or multiple colours to form a colour ramp (to be used if levels!=NA):

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 boxes, set plateau.col=NA

non.plateau.col

if plateau=TRUE, the steps that do NOT belong to the plateau are given a different colour.

sigdig

the number of significant digits of the numerical values reported in the title of the graphical output.

line.col

colour of the average age line

lwd

width of the average age line

xlab

x-axis label

ylab

y-axis label

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 age plateau calculation

exterr

propagate the external (decay constant and calibration factor) uncertainties?

i2i

`isochron to intercept': calculates the initial (aka `inherited', `excess', or `common') \(^{40}\)Ar/\(^{36}\)Ar ratio from an isochron fit. Setting i2i to FALSE uses the default values stored in settings('iratio',...)

Details

IsoplotR defines the `plateau age' as the weighted mean age (using a random effects model with two sources of dispersion) of the longest sequence (in terms of cumulative \(^{39}\)Ar content) of consecutive heating steps that pass the modified Chauvenet criterion (see weightedmean). Note that this definition is different (and simpler) than the one used by Isoplot (Ludwig, 2003). However, it is important to mention that all definitions of an age plateau are heuristic by nature and should not be used for quantitative inference. It is possible (and likely) that the plateau steps exhibit significant overdispersion. This overdispersion can be manually reduced by removing individual heating steps with the optional omit argument.

Examples

Run this code

attach(examples)
par(mfrow=c(2,1))
agespectrum(ArAr)
# removing the first 6 steps yields the longest plateau
# that passes the chi-square test for homogeneity
agespectrum(ArAr,omit=1:6)