calc_FadingCorr() R function from [Luminescence]

Fading Correction after Huntley & Lamothe (2001)

Apply a fading correction according to Huntley & Lamothe (2001) for a given $g$ -value and a given $t_{c}$


calc_FadingCorr(
  age.faded,
  g_value,
  tc,
  tc.g_value = tc,
  n.MC = 10000,
  seed = NULL,
  interval = c(0.01, 500),
  txtProgressBar = TRUE,
  verbose = TRUE
)

Arguments

age.faded: numeric vector (required ): vector of length 2 containing the uncorrected age and the error in ka (see example).
g_value: vector or RLum.Results (required ): either a vector of length 2 containing the g-value and error obtained from separate fading measurements (see example), or an RLum.Results

object produced by analyse_FadingMeasurement . If the latter, the tc

argument is set automatically.
tc: numeric (required ): time in seconds between irradiation and the prompt measurement (cf. Huntley & Lamothe 2001). The argument is ignored when g_value is an RLum.Results object.
tc.g_value: numeric (with default): time in seconds between irradiation and the prompt measurement used in the estimation of the g-value. If the g-value was normalised, the normalisation time (in seconds) should be given, e.g., for a g-value normalised to 2 days, the value 172800 should be used. If nothing is provided the time is set to tc, which is usual case for g-values obtained using the SAR method and $g$ -values that have been not normalised to 2 days.
n.MC: integer (with default): number of Monte Carlo simulation runs for error estimation. If n.MC = 'auto' is used the function tries to find a 'stable' error for the age. See details for further information. Note: This may take a while!
seed: integer (optional): sets the seed for the random number generator in R using set.seed
interval: numeric (with default): a vector containing the end-points (age interval) of the interval to be searched for the root in 'ka'. This argument is passed to the function stats::uniroot used for solving the equation.
txtProgressBar: logical (with default): enable/disable the progress bar.
verbose: logical (with default): enable/disable output to the terminal.

Returns

Returns an S4 object of type RLum.Results .

Slot: @data


Object	Type	Comment
`age.corr`	data.frame	Corrected age
`age.corr.MC`	numeric	MC simulation results with all possible ages from that simulation

Slot: @info


Object	Type	Comment
`info`	character	the original function call

Details

This function solves the equation used for correcting the fading affected age including the error for a given $g$ -value according to Huntley & Lamothe (2001):

\frac{A_{f}}{A} = 1 - \kappa * \Big[ln(\frac{A}{t_c}) - 1\Big]

with $\kappa$ defined as

\kappa = \frac{\frac{\mathrm{g\_value}}{ln(10)}}{100}

$A$ and $A_{f}$ are given in ka. $t_c$ is given in s, however, it is internally recalculated to ka.

As the $g$ -value slightly depends on the time $t_{c}$ between irradiation and the prompt measurement, a value for tc must always be provided. If the $g$ -value was normalised to a distinct time or evaluated with a different tc value (e.g., external irradiation), also the $t_{c}$ value for the $g$ -value needs to be provided (argument tc.g_value

and then the $g$ -value is recalculated to $t_{c}$ of the measurement used for estimating the age applying the following equation:

\kappa_{tc} = \kappa_{tc.g} / (1 - \kappa_{tc.g} * ln(tc/tc.g))

where

\kappa_{tc.g} = g / 100 / ln(10)

The error of the fading-corrected age is determined using a Monte Carlo simulation approach. Solving of the equation is performed using uniroot . Large values for n.MC will significantly increase the computation time.

‘n.MC = 'auto'’

The error estimation based on a stochastic process, i.e. for a small number of MC runs the calculated error varies considerably every time the function is called, even with the same input values. The argument option n.MC = 'auto' tries to find a stable value for the standard error, i.e. the standard deviation of values calculated during the MC runs (age.corr.MC), within a given precision (2 digits) by increasing the number of MC runs stepwise and calculating the corresponding error.

If the determined error does not differ from the 9 values calculated previously within a precision of (here) 3 digits the calculation is stopped as it is assumed that the error is stable. Please note that (a) the duration depends on the input values as well as on the provided computation resources and it may take a while, (b) the length (size) of the output vector age.corr.MC, where all the single values produced during the MC runs are stored, equals the number of MC runs (here termed observations).

To avoid an endless loop the calculation is stopped if the number of observations exceeds 10^7. This limitation can be overwritten by setting the number of MC runs manually, e.g. n.MC = 10000001. Note: For this case the function is not checking whether the calculated error is stable.

‘seed’

This option allows to recreate previously calculated results by setting the seed for the R random number generator (see set.seed for details). This option should not be mixed up with the option ‘n.MC = 'auto'’ . The results may appear similar, but they are not comparable!

FAQ

Q : Which $t_{c}$ value is expected?

A : $t_{c}$ is the time in seconds between irradiation and the prompt measurement applied during your $D_{e}$ measurement. However, this $t_{c}$ might differ from the $t_{c}$ used for estimating the $g$ -value. In the case of an SAR measurement $t_{c}$ should be similar, however, if it differs, you have to provide this $t_{c}$ value (the one used for estimating the $g$ -value) using the argument tc.g_value.

Q : The function could not find a solution, what should I do?

A : This usually happens for model parameters exceeding the boundaries of the fading correction model (e.g., very high $g$ -value). Please check whether another fading correction model might be more appropriate.

Note

Special thanks to Sébastien Huot for his support and clarification via e-mail.

Function version

0.4.4

Examples


##run the examples given in the appendix of Huntley and Lamothe, 2001

##(1) faded age: 100 a
results <- calc_FadingCorr(
   age.faded = c(0.1,0),
   g_value = c(5.0, 1.0),
   tc = 2592000,
   tc.g_value = 172800,
   n.MC = 100)

##(2) faded age: 1 ka
results <- calc_FadingCorr(
   age.faded = c(1,0),
   g_value = c(5.0, 1.0),
   tc = 2592000,
   tc.g_value = 172800,
   n.MC = 100)

##(3) faded age: 10.0 ka
results <- calc_FadingCorr(
   age.faded = c(10,0),
   g_value = c(5.0, 1.0),
   tc = 2592000,
   tc.g_value = 172800,
   n.MC = 100)

##access the last output
get_RLum(results)

How to cite

Kreutzer, S., 2025. calc_FadingCorr(): Fading Correction after Huntley & Lamothe (2001). Function version 0.4.4. In: Kreutzer, S., Burow, C., Dietze, M., Fuchs, M.C., Schmidt, C., Fischer, M., Friedrich, J., Mercier, N., Philippe, A., Riedesel, S., Autzen, M., Mittelstrass, D., Gray, H.J., Galharret, J., Colombo, M., Steinbuch, L., Boer, A.d., 2025. Luminescence: Comprehensive Luminescence Dating Data Analysis. R package version 1.0.1. https://r-lum.github.io/Luminescence/

References

Huntley, D.J., Lamothe, M., 2001. Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating. Canadian Journal of Earth Sciences, 38, 1093-1106.

Author(s)

Sebastian Kreutzer, Institute of Geography, Heidelberg University (Germany) , RLum Developer Team

Luminescence package Read PDF manual

Maintainer: Sebastian Kreutzer
License: GPL-3
Last published: 2025-03-07

Useful links

calc_FadingCorr function