cad: Plot continuous data as cumulative age distributions

In IsoplotR: Statistical Toolbox for Radiometric Geochronology

Description

Plot a dataset as a Cumulative Age Distribution (CAD), also known as a ‘empirical cumulative distribution function’.

Usage

cad(x, ...)

## Default S3 method:
cad(x, pch = NA, verticals = TRUE,
  xlab = "age [Ma]", colmap = "heat.colors", col = "black",
  hide = NULL, ...)

## S3 method for class 'detritals'
cad(x, pch = NA, verticals = TRUE,
  xlab = "age [Ma]", colmap = "heat.colors", hide = NULL, ...)

## S3 method for class 'UPb'
cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]",
  col = "black", type = 4, cutoff.76 = 1100, cutoff.disc = c(-15,
  5), common.Pb = 0, hide = NULL, ...)

## S3 method for class 'PbPb'
cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]",
  col = "black", common.Pb = 1, hide = NULL, ...)

## S3 method for class 'ArAr'
cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]",
  col = "black", i2i = FALSE, hide = NULL, ...)

## S3 method for class 'KCa'
cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]",
  col = "black", i2i = FALSE, hide = NULL, ...)

## S3 method for class 'ThU'
cad(x, pch = NA, verticals = TRUE, xlab = "age [ka]",
  col = "black", i2i = FALSE, detritus = 0, Th02 = c(0, 0),
  Th02U48 = c(0, 0, 1e+06, 0, 0, 0, 0, 0, 0), hide = NULL, ...)

## S3 method for class 'ReOs'
cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]",
  col = "black", i2i = TRUE, hide = NULL, ...)

## S3 method for class 'SmNd'
cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]",
  col = "black", i2i = TRUE, hide = NULL, ...)

## S3 method for class 'RbSr'
cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]",
  col = "black", i2i = TRUE, hide = NULL, ...)

## S3 method for class 'LuHf'
cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]",
  col = "black", i2i = TRUE, hide = NULL, ...)

## S3 method for class 'UThHe'
cad(x, pch = NA, verticals = TRUE, xlab = "age [Ma]",
  col = "black", hide = NULL, ...)

## S3 method for class 'fissiontracks'
cad(x, pch = NA, verticals = TRUE,
  xlab = "age [Ma]", col = "black", hide = NULL, ...)

Arguments

x	a numerical vector OR an object of class UPb, PbPb, ArAr, KCa, UThHe, fissiontracks, ReOs, RbSr, SmNd, LuHf, ThU or detritals
...	optional arguments to the generic plot function
pch	plot character to mark the beginning of each CAD step
verticals	logical flag indicating if the horizontal lines of the CAD should be connected by vertical lines
xlab	x-axis label
colmap	an optional string with the name of one of R's built-in colour palettes (e.g., heat.colors, terrain.colors, topo.colors, cm.colors), which are to be used for plotting data of class detritals.
col	colour to give to single sample datasets (not applicable if x has class detritals)
hide	vector with indices of aliquots that should be removed from the plot.
type	scalar indicating whether to plot the ^{207}Pb/^{235}U age (type=1), the ^{206}Pb/^{238}U age (type=2), the ^{207}Pb/^{206}Pb age (type=3), the ^{207}Pb/^{206}Pb-^{206}Pb/^{238}U age (type=4), or the (Wetherill) concordia age (type=5)
cutoff.76	the age (in Ma) below which the ^{206}Pb/^{238}U-age and above which the ^{207}Pb/^{206}Pb-age is used. This parameter is only used if type=4.
cutoff.disc	two element vector with the maximum and minimum percentage discordance allowed between the ^{207}Pb/^{235}U and ^{206}Pb/^{238}U age (if ^{206}Pb/^{238}U < cutoff.76) or between the ^{206}Pb/^{238}U and ^{207}Pb/^{206}Pb age (if ^{206}Pb/^{238}U > cutoff.76). Set cutoff.disc=NA if you do not want to use this filter.
common.Pb	apply a common lead correction using one of three methods: 1: use the isochron intercept as the initial Pb-composition 2: use the Stacey-Kramer two-stage model to infer the initial Pb-composition 3: use the Pb-composition stored in settings('iratio','Pb206Pb204') and settings('iratio','Pb207Pb204')
i2i	‘isochron to intercept’: calculates the initial (aka ‘inherited’, ‘excess’, or ‘common’) ^{40}Ar/^{36}Ar, ^{40}Ca/^{44}Ca, ^{207}Pb/^{204}Pb, ^{87}Sr/^{86}Sr, ^{143}Nd/^{144}Nd, ^{187}Os/^{188}Os, ^{230}Th/^{232}Th or ^{176}Hf/^{177}Hf ratio from an isochron fit. Setting i2i to FALSE uses the default values stored in settings('iratio',...) or zero (for the Pb-Pb method). When applied to data of class ThU, setting i2i to TRUE applies a detrital Th-correction.
detritus	detrital ^{230}Th correction (only applicable when x$format == 1 or 2. 0: no correction 1: project the data along an isochron fit 2: correct the data using an assumed initial ^{230}Th/^{232}Th-ratio for the detritus. 3: correct the data using the measured present day ^{230}Th/^{238}U, ^{232}Th/^{238}U and ^{234}U/^{238}U-ratios in the detritus.
Th02	2-element vector with the assumed initial ^{230}Th/^{232}Th-ratio of the detritus and its standard error. Only used if detritus==2
Th02U48	9-element vector with the measured composition of the detritus, containing X=0/8, sX, Y=2/8, sY, Z=4/8, sZ, rXY, rXZ, rYZ. Only used if isochron==FALSE and detritus==3

Details

Empirical cumulative distribution functions or cumulative age distributions CADs are the most straightforward way to visualise the probability distribution of multiple dates. Suppose that we have a set of n dates t_i. The the CAD is a step function that sets out the rank order of the dates against their numerical value:

CAD(t) = ∑_i 1(t<t_i)/n

where 1(\ast) = 1 if \ast is true and 1(\ast) = 0 if \ast is false. CADs have two desirable properties (Vermeesch, 2007). First, they do not require any pre-treatment or smoothing of the data. This is not the case for histograms or kernel density estimates. Second, it is easy to superimpose several CADs on the same plot. This facilitates the intercomparison of multiple samples. The interpretation of CADs is straightforward but not very intuitive. The prominence of individual age components is proportional to the steepness of the CAD. This is different from probability density estimates such as histograms, in which such components stand out as peaks.

References

Vermeesch, P., 2007. Quantitative geomorphology of the White Mountains (California) using detrital apatite fission track thermochronology. Journal of Geophysical Research: Earth Surface, 112(F3).

See Also

kde, radialplot

Examples

data(examples)
cad(examples$DZ,verticals=FALSE,pch=20)

IsoplotR documentation built on Dec. 9, 2018, 1:04 a.m.