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.
central(x, ...)# S3 method for default
central(x, alpha = 0.05, ...)
# S3 method for UThHe
central(x, alpha = 0.05, model = 1, ...)
# S3 method for fissiontracks
central(x, mineral = NA, alpha = 0.05, ...)
an object of class UThHe or fissiontracks,
OR a 2-column matrix with (strictly positive) values and
uncertainties
optional arguments
cutoff value for confidence intervals
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 \(\sqrt{MSWD}\).
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.
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)
If x has class UThHe, 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.)
the \(100(1-\alpha/2)\%\) percentile of the t-
distribution for df degrees of freedom (not reported if
model=2).
a three- or four-element vector with:
t: the central age.
s[t]: the standard error of t.
ci[t]: the \(100(1-\alpha)\%\) confidence interval for
t for the appropriate number of degrees of freedom.
disp[t]: the studentised \(100(1-\alpha)\%\) confidence
interval 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 the corresponding
\(100(1-\alpha)\%\) confidence interval. w=0 if
codemodel<3.
OR, otherwise:
t: the central age.
s[t]: the standard error of t.
ci[t]: the \(100(1-\alpha)\%\) confidence interval for
t for the appropriate number of degrees of freedom.
df
degrees of freedomThe 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 Poisson 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.
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.
# NOT RUN {
data(examples)
print(central(examples$UThHe)$age)
# }
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