isochron: Calculate and plot isochrons

Description

Plots cogenetic Ar-Ar, Pb-Pb, Rb-Sr, Sm-Nd, Re-Os, Lu-Hf, U-Th-He or Th-U data as X-Y scatterplots, fits an isochron curve through them using the york function, and computes the corresponding isochron age, including decay constant uncertainties.

Usage

isochron(x, ...)
# S3 method for default
isochron(x, xlim = NA, ylim = NA, alpha = 0.05,
  sigdig = 2, show.numbers = FALSE, levels = NA,
  ellipse.col = c("#00FF0080", "#FF000080"), line.col = "red", lwd = 2,
  title = TRUE, model = 1, ...)
# S3 method for ArAr
isochron(x, xlim = NA, ylim = NA, alpha = 0.05,
  sigdig = 2, show.numbers = FALSE, levels = NA,
  ellipse.col = c("#00FF0080", "#FF000080"), inverse = TRUE,
  line.col = "red", lwd = 2, plot = TRUE, exterr = TRUE, model = 1,
  ...)
# S3 method for PbPb
isochron(x, xlim = NA, ylim = NA, alpha = 0.05,
  sigdig = 2, show.numbers = FALSE, levels = NA,
  ellipse.col = c("#00FF0080", "#FF000080"), inverse = TRUE,
  line.col = "red", lwd = 2, plot = TRUE, exterr = TRUE, model = 1,
  ...)
# S3 method for RbSr
isochron(x, xlim = NA, ylim = NA, alpha = 0.05,
  sigdig = 2, show.numbers = FALSE, levels = NA,
  ellipse.col = c("#00FF0080", "#FF000080"), line.col = "red", lwd = 2,
  plot = TRUE, exterr = TRUE, model = 1, ...)
# S3 method for ReOs
isochron(x, xlim = NA, ylim = NA, alpha = 0.05,
  sigdig = 2, show.numbers = FALSE, levels = NA,
  ellipse.col = c("#00FF0080", "#FF000080"), line.col = "red", lwd = 2,
  plot = TRUE, exterr = TRUE, model = 1, ...)
# S3 method for SmNd
isochron(x, xlim = NA, ylim = NA, alpha = 0.05,
  sigdig = 2, show.numbers = FALSE, levels = NA,
  ellipse.col = c("#00FF0080", "#FF000080"), line.col = "red", lwd = 2,
  plot = TRUE, exterr = TRUE, model = 1, ...)
# S3 method for LuHf
isochron(x, xlim = NA, ylim = NA, alpha = 0.05,
  sigdig = 2, show.numbers = FALSE, levels = NA,
  ellipse.col = c("#00FF0080", "#FF000080"), line.col = "red", lwd = 2,
  plot = TRUE, exterr = TRUE, model = 1, ...)
# S3 method for ThU
isochron(x, type = 2, xlim = NA, ylim = NA, alpha = 0.05,
  sigdig = 2, show.numbers = FALSE, levels = NA,
  ellipse.col = c("#00FF0080", "#FF000080"), line.col = "red", lwd = 2,
  plot = TRUE, exterr = TRUE, model = 1, ...)
# S3 method for UThHe
isochron(x, xlim = NA, ylim = NA, alpha = 0.05,
  sigdig = 2, show.numbers = FALSE, line.col = "red", lwd = 2,
  plot = TRUE, model = 1, ...)

Arguments

EITHER a matrix with the following five columns:

X: the x-variable
sX: the standard error of X
Y: the y-variable
sY: the standard error of Y
rXY: the correlation coefficient of X and Y

an object of class ArAr, PbPb, ReOs, RbSr, SmNd, LuHf, UThHe or ThU.

...

optional arguments to be passed on to the generic plot function if model=2

xlim

2-element vector with the plot limits of the x-axis

ylim

2-element vector with the plot limits of the y-axis

alpha

confidence cutoff for the error ellipses and confidence intervals

sigdig

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

show.numbers

logical flag (TRUE to show grain numbers)

levels

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

ellipse.col

a vector of two background colours for the error ellipses. If levels=NA, then only the first colour will be used. If levels is a vector of numbers, then ellipse.col is used to construct a colour ramp.

line.col

colour of the isochron line

lwd

line width

title

add a title to the plot?

model

construct the isochron using either:

Error weighted least squares regression
Ordinary least squares regression

inverse

if TRUE and x has class ArAr, plots $^{36}$Ar/$^{40}$Ar vs. $^{39}$Ar/$^{40}$Ar.

if TRUE and x has class PbPb, plots $^{207}$Pb/$^{206}$Pb vs. $^{204}$Pb/$^{206}$Pb.

plot

if FALSE, suppresses the graphical output

exterr

propagate external sources of uncertainty (J, decay constant)?

type

following the classification of Ludwig and Titterington (1994), one of either:

`Rosholt type-II' isochron, setting out $^{230}$Th/$^{232}$Th vs. $^{238}$U/$^{232}$Th
`Osmond type-II' isochron, setting out $^{230}$Th/$^{238}$U vs. $^{232}$Th/$^{238}$U
`Rosholt type-II' isochron, setting out $^{234}$U/$^{232}$Th vs. $^{238}$U/$^{232}$Th
`Osmond type-II' isochron, setting out $^{234}$U/$^{238}$U vs. $^{232}$Th/$^{238}$U

Value

if x has class PbPb, ArAr, RbSr, SmNd, ReOs or LuHf, or UThHe, returns a list with the following items:

a

the intercept of the straight line fit and its standard error.

b

the slope of the fit and its standard error.

cov.ab

the covariance of the slope and intercept

df

the degrees of freedom of the linear fit ($df=n-2$)

y0

a four-element list containing:

y: the atmospheric $^{40}$Ar/$^{36}$Ar or initial $^{207}$Pb/$^{204}$Pb, $^{187}$Os/$^{188}$Os, $^{87}$Sr/$^{86}$Sr, $^{143}$Nd/$^{144}$Nd or $^{176}$Hf/$^{177}$Hf ratio.

s[y]: the propagated uncertainty of y

ci[y]: the $100(1-\alpha/2)\%$ confidence interval for y given the appropriate degrees of freedom.

disp[y]: the $100(1-\alpha/2)\%$ confidence interval for y enhanced by $\sqrt{mswd}$ (only applicable if model=1).

age

a four-element list containing:

t: the $^{207}$Pb/$^{206}$Pb, $^{40}$Ar/$^{39}$Ar, $^{187}$Os/$^{187}$Re, $^{87}$Sr/$^{86}$Sr, $^{143}$Nd/$^{144}$Nd or $^{176}$Hf/$^{177}$Hf age.

s[t]: the propagated uncertainty of t

ci[t]: the $100(1-\alpha/2)\%$ confidence interval for t given the appropriate degrees of freedom.

disp[t]: the $100(1-\alpha/2)\%$ confidence interval for t enhanced by $\sqrt{mswd}$ (only applicable if model=1).

tfact

the $100(1-\alpha/2)\%$ percentile of a t-distribution with df degrees of freedom.

additionally, if model=1:

mswd: the mean square of the residuals (a.k.a `reduced Chi-square') statistic (omitted if model=2).
p.value: the p-value of a Chi-square test for linearity

OR, if x has class ThU:

par

if type=1 or type=3: the best fitting $^{230}$Th/$^{232}$Th intercept, $^{230}$Th/$^{238}$U slope, $^{234}$U/$^{232}$Th intercept and $^{234}$U/$^{238}$U slope, OR, if type=2 or type=4: the best fitting $^{234}$U/$^{238}$U intercept, $^{230}$Th/$^{232}$Th slope, $^{234}$U/$^{238}$U intercept and $^{234}$U/$^{232}$Th slope.

cov

the covariance matrix of par.

df

the degrees of freedom for the linear fit, i.e. $(3n-3)$ if x$format=1 or x$format=2, and $(2n-2)$ if x$format=3 or x$format=4

a

if type=1: the $^{230}$Th/$^{232}$Th intercept; if type=2: the $^{230}$Th/$^{238}$U intercept; if type=3: the $^{234}$Th/$^{232}$Th intercept; if type=4: the $^{234}$Th/$^{238}$U intercept and its propagated uncertainty.

b

if type=1: the $^{230}$Th/$^{238}$U slope; if type=2: the $^{230}$Th/$^{232}$Th slope; if type=3: the $^{234}$U/$^{238}$U slope; if type=4: the $^{234}$U/$^{232}$Th slope and its propagated uncertainty.

cov.ab

the covariance between a and b.

mswd

the mean square of the residuals (a.k.a `reduced Chi-square') statistic.

p.value

the p-value of a Chi-square test for linearity.

y0

a four-element vector containing:

y: the initial $^{234}$U/$^{238}$U-ratio

s[y]: the propagated uncertainty of y

ci[y]: the $100(1-\alpha/2)\%$ confidence interval for y

disp[y]: the $100(1-\alpha/2)\%$ confidence interval for y enhanced by $\sqrt{mswd}$.

age

a four-element vector containing:

t: the initial $^{234}$U/$^{238}$U-ratio

s[t]: the propagated uncertainty of t

ci[t]: the $100(1-\alpha/2)\%$ confidence interval for t

disp[t]: the $100(1-\alpha/2)\%$ confidence interval for t enhanced by $\sqrt{mswd}$.

d

a matrix with the following columns: the X-variable for the isochron plot, the analytical uncertainty of X, the Y-variable for the isochron plot, the analytical uncertainty of Y, and the correlation coefficient between X and Y.

xlab

the x-label of the isochron plot

ylab

the y-label of the isochron plot

References

Nicolaysen, L.O., 1961. Graphic interpretation of discordant age measurements on metamorphic rocks. Annals of the New York Academy of Sciences, 91(1), pp.198-206.

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.

Examples

Run this code

# NOT RUN {
data(examples)
isochron(examples$ArAr)

# }

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