calc_FadingCorr: Fading Correction after Huntley & Lamothe (2001)

In Luminescence: Comprehensive Luminescence Dating Data Analysis

Fading Correction after Huntley & Lamothe (2001)

Description

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

Usage

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

Arguments

age.faded	numeric vector (required): uncorrected age with error in ka (see example)
g_value	vector (required): g-value and error obtained from separate fading measurements (see example). Alternatively an RLum.Results object can be provided produced by the function analyse_FadingMeasurement, in this case tc is set automatically
tc	numeric (required): time in seconds between irradiation and the prompt measurement (cf. Huntley & Lamothe 2001). Argument will be ignored if g_value was an RLum.Results object
tc.g_value	numeric (with default): the time in seconds between irradiation and the prompt measurement used for estimating the g-value. If the g-value was normalised to, e.g., 2 days, this time in seconds (i.e., 172800) should be given here. 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 had 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. 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): enables or disables txtProgressBar
verbose	logical (with default): enables or disables terminal output

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 between irradiation and the prompt measurement, this is t_{c}, always a t_{c} value needs to 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 realised 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.

Value

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

Function version

0.4.3

How to cite

Kreutzer, S., 2024. calc_FadingCorr(): Fading Correction after Huntley & Lamothe (2001). Function version 0.4.3. 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., 2024. Luminescence: Comprehensive Luminescence Dating Data Analysis. R package version 0.9.24. https://CRAN.R-project.org/package=Luminescence

Note

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

Author(s)

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

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.

See Also

RLum.Results, analyse_FadingMeasurement, get_RLum, uniroot

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)

Luminescence documentation built on June 22, 2024, 9:54 a.m.