central: Calculate U-Th-He and fission track central ages and...

Description Usage Arguments Details Value References See Also Examples

View source: R/central.R

Description

Computes the geometric mean composition of a continuous mixture of fission track or U-Th-He data and returns the corresponding age and fitting parameters.

Usage

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central(x, ...)

## Default S3 method:
central(x, alpha = 0.05, ...)

## S3 method for class 'UThHe'
central(x, alpha = 0.05, model = 1, ...)

## S3 method for class 'fissiontracks'
central(x, mineral = NA, alpha = 0.05, ...)

Arguments

x

an object of class UThHe or fissiontracks, OR a 2-column matrix with (strictly positive) values and uncertainties

...

optional arguments

alpha

cutoff value for confidence intervals

model

choose one of the following statistical models:

1: weighted mean. This model assumes that the scatter between the data points is solely caused by the analytical uncertainty. If the 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 underestimated by a factor √{MSWD}.

2: unweighted mean. A second way to deal with over- or underdispersed datasets is to simply ignore the analytical uncertainties.

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

mineral

setting this parameter to either apatite or zircon changes the default efficiency factor, initial fission track length and density to preset values (only affects results if x$format=2)

Details

The central age assumes that the observed age distribution is the combination of two sources of scatter: analytical uncertainty and true geological dispersion.

  1. For fission track data, the analytical uncertainty is assumed to obey Poisson counting statistics and the geological dispersion is assumed to follow a lognormal distribution.

  2. For U-Th-He data, the U-Th-(Sm)-He compositions and uncertainties are assumed to follow a logistic normal distribution.

  3. For all other data types, both the analytical uncertainties and the true ages are assumed to follow lognormal distributions.

The difference between the central age and the weighted mean age is usually small unless the data are imprecise and/or strongly overdispersed.

Value

If x has class UThHe, returns a list containing the following items:

uvw

(if the input data table contains Sm) or uv (if it does not): the mean log[U/He], log[Th/He] (, and log[Sm/He]) composition.

covmat

the covariance matrix of uvw or uv.

mswd

the reduced Chi-square statistic of data concordance, i.e. mswd=SS/df, where SS is the sum of squares of the log[U/He]-log[Th/He] compositions.

model

the fitting model.

df

the degrees of freedom (2n-2) of the fit (only reported if model=1).

p.value

the p-value of a Chi-square test with df degrees of freedom (only reported if model=1.)

age

a three- or four-element vector with:

t: the central age.

s[t]: the standard error of t.

ci[t]: the width of a 100(1-α)\% confidence interval for t.

disp[t]: the studentised 100(1-α)\% confidence interval enhanced by a factor of √{mswd} (only reported if model=1).

w

the geological overdispersion term. If model=3, this is a three-element vector with the standard deviation of the (assumedly) Normal dispersion and the lower and upper half-widths of its 100(1-α)\% confidence interval. w=0 if codemodel<3.

OR, otherwise:

age

a three-element vector with:

t: the central age.

s[t]: the standard error of t.

ci[t]: the width of a 100(1-α)\% confidence interval for t.

disp

a three-element vector with the overdispersion (standard deviation) of the excess scatter, and the upper and lower half-widths of its 100(1-α)\% confidence interval.

mswd

the reduced Chi-square statistic of data concordance, i.e. mswd=X^2/df, where X^2 is a Chi-square statistic of the EDM data or ages

df

the degrees of freedom (n-2)

p.value

the p-value of a Chi-square test with df degrees of freedom

References

Galbraith, R.F. and Laslett, G.M., 1993. Statistical models for mixed fission track ages. Nuclear Tracks and Radiation Measurements, 21(4), pp.459-470.

Vermeesch, P., 2008. Three new ways to calculate average (U-Th)/He ages. Chemical Geology, 249(3), pp.339-347.

See Also

weightedmean, radialplot, helioplot

Examples

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