This function applies the approach described in Kars et al. (2008) or Guralnik et al. (2015),
which are both developed from the model of Huntley (2006) to calculate the expected sample
specific fraction of saturation of a feldspar and also to calculate fading
corrected age using this model. \(\rho\)' (rhop), the density of recombination
centres, is a crucial parameter of this model and must be determined
separately from a fading measurement. The function analyse_FadingMeasurement
can be used to calculate the sample specific \(\rho\)' value.
Kars et al. (2008) - Single saturating exponential
To apply the approach after Kars et al. (2008) use fit.method = "EXP".
Firstly, the unfaded D0 value is determined through applying equation 5 of
Kars et al. (2008) to the measured LxTx data as a function of irradiation
time, and fitting the data with a single saturating exponential of the form:
$$LxTx(t*) = A x \phi(t*) x (1 - exp(-(t* / D0)))$$
where
$$\phi(t*) = exp(-\rho' x ln(1.8 x s_tilde x t*)^3)$$
after King et al. (2016) where A is a pre-exponential factor,
t* (s) is the irradiation time, starting at the mid-point of
irradiation (Auclair et al. 2003) and s_tilde (3x10^15 s^-1) is the athermal
frequency factor after Huntley (2006).
Using fit parameters A and D0, the function then computes a natural dose
response curve using the environmental dose rate, D_dot (Gy/s) and equations
[1] and [2]. Computed LxTx values are then fitted using the
plot_GrowthCurve function and the laboratory measured LnTn can then
be interpolated onto this curve to determine the fading corrected
De value, from which the fading corrected age is calculated.
Guralnik et al. (2015) - General-order kinetics
To apply the approach after Guralnik et al. (2015) use fit.method = "GOK".
The approach of Guralnik et al. (2015) is very similar to that of
Kars et al. (2008), but instead of using a single saturating exponential
the model fits a general-order kinetics function of the form:
$$LxTx(t*) = A x \phi(t*) x (1-(1+(1/D0) x t* x c)^(-1/c))$$
where A, \(\phi\), t* and D0 are the same as above and c is a
dimensionless kinetic order modifier (cf. equation 10 in
Guralnik et al., 2015).
Level of saturation
The calc_Huntley2006 function also calculates the level of saturation (n/N)
and the field saturation (i.e. athermal steady state, (n/N)_SS) value for
the sample under investigation using the sample specific \(\rho\)',
unfaded D0 and D_dot values, following the approach of Kars et al. (2008).
Uncertainties
Uncertainties are reported at 1 sigma and are assumed to be normally
distributed and are estimated using Monte-Carlo re-sampling (n.MC = 1000)
of \(\rho\)' and LxTx during dose response curve fitting, and of \(\rho\)'
in the derivation of (n/N) and (n/N)_SS.
Age calculated from 2D0 of the simulated natural DRC
In addition to the age calculated from the equivalent dose derived from
Ln/Tn projected on the simulated natural dose response curve (DRC), this function
also calculates an age from twice the characteristic saturation dose (D0)
of the simulated natural DRC. This can be a useful information for
(over)saturated samples (i.e., no intersect of Ln/Tn on the natural DRC)
to obtain at least a "minimum age" estimate of the sample. In the console
output this value is denoted by "Age @2D0 (ka):".