evolution: Th-U evolution diagram

Description

Plots Th-U data on a $^{234}$U/$^{238}$U-$^{230}$Th/$^{238}$U evolution diagram, a $^{234}$U/$^{238}$U-age diagram, or (if $^{234}$U/$^{238}$U is assumed to be in secular equilibrium), a $^{230}$Th/$^{232}$Th-$^{238}$U/$^{232}$Th diagram; calculates isochron ages.

Usage

evolution(
  x,
  xlim = NULL,
  ylim = NULL,
  tticks = NULL,
  aticks = NULL,
  oerr = 3,
  transform = FALSE,
  Th0i = 0,
  show.numbers = FALSE,
  levels = NA,
  clabel = "",
  ellipse.fill = c("#00FF0080", "#FF000080"),
  ellipse.stroke = "black",
  line.col = "darksalmon",
  isochron = FALSE,
  model = 1,
  exterr = FALSE,
  sigdig = 2,
  hide = NULL,
  omit = NULL,
  omit.fill = NA,
  omit.stroke = "grey",
  ...
)

Arguments

x

an object of class ThU

xlim

x-axis limits

ylim

y-axis limits

tticks

time intervals of the evolution grid

aticks

initial activity ratio ticks of the evolution grid

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').

transform

if TRUE, plots $^{234}$U/$^{238}$U vs. Th-U age.

Th0i

initial $^{230}$Th correction.

0: no correction

1: if x$format is 1 or 2, project the data along an isochron fit. If x$format is 3 or 4, infer the initial $^{230}$Th/$^{238}$U activity ratio from the isochron.

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, anchor the isochrons to the equiline, based on 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).

show.numbers

label the error ellipses with the grain numbers?

levels

a vector with additional values to be displayed as different background colours within the error ellipses.

clabel

label of the colour legend.

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

line.col

colour of the age grid

isochron

fit an isochron to the data?

model

if isochron=TRUE, choose one of three regression models:

1: maximum likelihood regression, using either the modified error weighted least squares algorithm of York et al. (2004) for 2-dimensional data, or the Maximum Likelihood formulation of Ludwig and Titterington (1994) for 3-dimensional data. These algorithms take into account the analytical uncertainties and error correlations, under the assumption that the scatter between the data points is solely caused by the analytical uncertainty. If this 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 underestipmated by a factor $\sqrt{MSWD}$.

2: total least squares regression: a second way to deal with over- or underdispersed datasets is to simply ignore the analytical uncertainties.

3: maximum likelihood regression with overdispersion: instead of attributing any overdispersion (MSWD > 1) to underestimated analytical uncertainties (model 1), one can also attribute it to the presence of geological uncertainty, which manifests itself as an added (co)variance term.

exterr

propagate the decay constant uncertainty in the isochron age?

sigdig

number of significant digits for the isochron age

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 isochron 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

Similar to the concordia diagram (for U-Pb data) and the helioplot diagram (for U-Th-He data), the evolution diagram simultaneously displays the isotopic composition and age of U-series data. For carbonate data (Th-U formats 1 and 2), the Th-U evolution diagram consists of a scatter plot that sets out the $^{234}$U/$^{238}$U-activity ratios against the $^{230}$Th/$^{238}$U-activity ratios as error ellipses, and displays the initial $^{234}$U/$^{238}$U-activity ratios and ages as a set of intersecting lines. Alternatively, the $^{234}$U/$^{238}$U-ratios can also be set out against the $^{230}$Th-$^{234}$U-$^{238}$U-ages. In both types of evolution diagrams, IsoplotR provides the option to project the raw measurements along the best fitting isochron line and thereby remove the detrital $^{230}$Th-component. This procedure allows a visual assessment of the degree of homogeneity within a dataset, as is quantified by the MSWD.

Neither the U-series evolution diagram, nor the $^{234}$U/$^{238}$U vs. age plot is applicable to igneous datasets (Th-U formats 3 and 4), in which $^{234}$U and $^{238}$U are in secular equilibrium. For such datasets, IsoplotR produces an Osmond-style regression plot that is decorated with a fanning set of isochron lines.

References

Ludwig, K.R. and Titterington, D.M., 1994. Calculation of $^{230}$Th/U isochrons, ages, and errors. Geochimica et Cosmochimica Acta, 58(22), pp.5031-5042.

Ludwig, K.R., 2003. Mathematical-statistical treatment of data and errors for $^{230}$Th/U geochronology. Reviews in Mineralogy and Geochemistry, 52(1), pp.631-656.

Examples

Run this code

attach(examples)
evolution(ThU)

dev.new()
evolution(ThU,transform=TRUE,isochron=TRUE,model=1)