Computes the logratio mean composition of a continuous mixture of fission track or U-Th-He data and returns the corresponding age and fitting parameters. Only propagates the systematic uncertainty associated with decay constants and calibration factors after computing the weighted mean isotopic composition. Does not propagate the uncertainty of any initial daughter correction, because this is neither a purely random or purely systematic uncertainty.
central(x, ...)# S3 method for default
central(x, ...)
# S3 method for UThHe
central(x, compositional = FALSE, model = 1, ...)
# S3 method for fissiontracks
central(x, exterr = FALSE, ...)
If x has class UThHe and compositional
is TRUE, returns a list containing the following items:
(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.
the covariance matrix of uvw or uv.
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.
the fitting model.
the degrees of freedom (\(2n-2\)) of the fit (only
reported if model=1).
the p-value of a Chi-square test with df
degrees of freedom (only reported if model=1.)
a two- or three-element vector with:
t: the 'barycentric' age, i.e. the age corresponding to uvw.
s[t]: the standard error of t.
disp[t]: the standard error of t enhanced by a
factor of \(\sqrt{mswd}\) (only reported if model=1).
the geological overdispersion term. If model=3,
this is a two-element vector with the standard deviation of the
(assumedly) Normal dispersion and its standard error. w=0 if
model<3.
OR, otherwise:
a two-element vector with the central age and its standard error.
a two-element vector with the overdispersion (standard deviation) of the excess scatter, and its standard error.
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
the degrees of freedom (\(n-2\))
the p-value of a Chi-square test with df
degrees of freedom
an object of class UThHe or fissiontracks,
OR a 2-column matrix with (strictly positive) values and
uncertainties
optional arguments
logical. If TRUE, calculates the
'barycentric' U-Th-He, age, i.e. the age corresponding to the
weighted mean logratio composition.
only relevant if compositional is
TRUE. If the scatter between the data points is solely
caused by the analytical uncertainty, then the MSWD value
should be approximately equal to one. There are three
strategies to deal with the case where MSWD>1.choose one of the
following statistical models:
1: assume that the analytical uncertainties have been
underestimated by a factor \(\sqrt{MSWD}\).
2: ignore the analytical
uncertainties.
3: attribute any excess dispersion to the presence of
geological uncertainty, which manifests itself as an added
(co)variance term.
include the zeta or decay constant uncertainty into the error propagation for the central age?
The central age assumes that the observed age distribution is the combination of two sources of scatter: analytical uncertainty and true geological dispersion.
For fission track data, the analytical uncertainty is assumed to obey Binomial counting statistics and the geological dispersion is assumed to follow a lognormal distribution.
For U-Th-He data, the U-Th-(Sm)-He compositions and uncertainties are assumed to follow a logistic normal distribution.
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.
The uncertainty budget of the central age does not include the
uncertainty of the initial daughter correction (if any), for the
same reasons as discussed under the weightedmean
function.
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.
weightedmean, radialplot,
helioplot
attach(examples)
print(central(UThHe)$age)
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