cad: Plot continuous data as cumulative age distributions

Description

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

Usage

cad(x, ...)
# S3 method for default
cad(
  x,
  pch = NA,
  verticals = TRUE,
  xlab = "age [Ma]",
  col = "black",
  hide = NULL,
  ...
)
# S3 method for other
cad(
  x,
  pch = NA,
  verticals = TRUE,
  xlab = "age [Ma]",
  col = "black",
  hide = NULL,
  ...
)
# S3 method for detritals
cad(
  x,
  pch = NA,
  verticals = TRUE,
  xlab = "age [Ma]",
  col = "rainbow",
  hide = NULL,
  ...
)
# S3 method for UPb
cad(
  x,
  pch = NA,
  verticals = TRUE,
  xlab = "age [Ma]",
  col = "black",
  type = 4,
  cutoff.76 = 1100,
  cutoff.disc = discfilter(),
  common.Pb = 0,
  hide = NULL,
  ...
)
# S3 method for PbPb
cad(
  x,
  pch = NA,
  verticals = TRUE,
  xlab = "age [Ma]",
  col = "black",
  common.Pb = 1,
  hide = NULL,
  ...
)
# S3 method for ArAr
cad(
  x,
  pch = NA,
  verticals = TRUE,
  xlab = "age [Ma]",
  col = "black",
  i2i = FALSE,
  hide = NULL,
  ...
)
# S3 method for KCa
cad(
  x,
  pch = NA,
  verticals = TRUE,
  xlab = "age [Ma]",
  col = "black",
  i2i = FALSE,
  hide = NULL,
  ...
)
# S3 method for ThPb
cad(
  x,
  pch = NA,
  verticals = TRUE,
  xlab = "age [Ma]",
  col = "black",
  i2i = TRUE,
  hide = NULL,
  ...
)
# S3 method for ThU
cad(
  x,
  pch = NA,
  verticals = TRUE,
  xlab = "age [ka]",
  col = "black",
  Th0i = 0,
  hide = NULL,
  ...
)
# S3 method for ThPb
cad(
  x,
  pch = NA,
  verticals = TRUE,
  xlab = "age [Ma]",
  col = "black",
  i2i = TRUE,
  hide = NULL,
  ...
)
# S3 method for ReOs
cad(
  x,
  pch = NA,
  verticals = TRUE,
  xlab = "age [Ma]",
  col = "black",
  i2i = TRUE,
  hide = NULL,
  ...
)
# S3 method for SmNd
cad(
  x,
  pch = NA,
  verticals = TRUE,
  xlab = "age [Ma]",
  col = "black",
  i2i = TRUE,
  hide = NULL,
  ...
)
# S3 method for RbSr
cad(
  x,
  pch = NA,
  verticals = TRUE,
  xlab = "age [Ma]",
  col = "black",
  i2i = TRUE,
  hide = NULL,
  ...
)
# S3 method for LuHf
cad(
  x,
  pch = NA,
  verticals = TRUE,
  xlab = "age [Ma]",
  col = "black",
  i2i = TRUE,
  hide = NULL,
  ...
)
# S3 method for UThHe
cad(
  x,
  pch = NA,
  verticals = TRUE,
  xlab = "age [Ma]",
  col = "black",
  hide = NULL,
  ...
)
# S3 method for 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, ThPb, 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

col

if x has class detritals, the name of one of R's built-in colour palettes (e.g., 'heat.colors', 'terrain.colors', 'topo.colors', 'cm.colors'), OR a vector with the names or codes of two colours to use as the start and end of a colour ramp (e.g. col=c('yellow','blue')).

For all other data formats, the name or code for a colour to give to a single sample dataset

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), the concordia_age (type=5), or the $^{208}$Pb/$^{232}$Th age (type=6).

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

discordance cutoff filter. This is an object of class discfilter.

common.Pb

common lead correction:

0: none

1: use the Pb-composition stored in

settings('iratio','Pb207Pb206') (if x has class UPb and x$format<4);

settings('iratio','Pb206Pb204') and settings('iratio','Pb207Pb204') (if x has class PbPb or x has class UPb and 3<x$format<7); or

settings('iratio','Pb206Pb208') and settings('iratio','Pb207Pb208') (if x has class UPb and x$format=7 or 8).

2: use the isochron intercept as the initial Pb-composition

3: use the Stacey-Kramers two-stage model to infer the initial Pb-composition (only applicable if x has class UPb)

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, $^{176}$Hf/$^{177}$Hf or $^{204}$Pb/$^{208}$Pb ratio from an isochron fit. Setting i2i to FALSE uses the default values stored in settings('iratio',...).

Th0i

initial $^{230}$Th correction.

0: no correction

1: project the data along an isochron fit

2: if x$format is 1 or 2, correct the data using the measured present day $^{230}$Th/$^{238}$U, $^{232}$Th/$^{238}$U and $^{234}$U/$^{238}$U activity ratios in the detritus. If x$format is 3 or 4, correct the data using the measured $^{238}$U/$^{232}$Th activity ratio of the whole rock, as stored in x by the read.data() function.

3: correct the data using an assumed initial $^{230}$Th/$^{232}$Th-ratio for the detritus (only relevant if x$format is 1 or 2).

Details

Empirical cumulative distribution functions or cumulative age distributions 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 CAD is a step function that sets out the rank order of the dates against their numerical value:

$CAD(t) = \sum_i 1(t<t_i)/n$

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).

Examples

Run this code

attach(examples)
cad(DZ,verticals=FALSE,pch=20)