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
tcis set automatically- tc
numeric (required): time in seconds between irradiation and the prompt measurement (cf. Huntley & Lamothe 2001). Argument will be ignored if
g_valuewas 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
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 |
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.
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., Colombo, M., 2024. Luminescence: Comprehensive Luminescence Dating Data Analysis. R package version 0.9.26. 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
Sebastian Kreutzer, Institute of Geography, Heidelberg University (Germany) , RLum Developer Team
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)
#>
#>
#> [calc_FadingCorr()]
#>
#> >> Fading correction according to Huntley & Lamothe (2001)
#> >> g-value re-calculated for the given tc
#>
#> .. used g-value: 5.312 ± 1.012 %/decade
#> .. used tc: 8.214e-05 ka
#> .. used kappa: 0.0231 ± 0.0044
#> ----------------------------------------------
#> seed: NA
#> n.MC: 100
#> observations: 100
#> ----------------------------------------------
#> Age (faded): 0.1 ka ± 0 ka
#> Age (corr.): 0.1169 ka ± 0.0042 ka
#> ----------------------------------------------
##(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)
#>
#>
#> [calc_FadingCorr()]
#>
#> >> Fading correction according to Huntley & Lamothe (2001)
#> >> g-value re-calculated for the given tc
#>
#> .. used g-value: 5.312 ± 1.012 %/decade
#> .. used tc: 8.214e-05 ka
#> .. used kappa: 0.0231 ± 0.0044
#> ----------------------------------------------
#> seed: NA
#> n.MC: 100
#> observations: 100
#> ----------------------------------------------
#> Age (faded): 1 ka ± 0 ka
#> Age (corr.): 1.2486 ka ± 0.0653 ka
#> ----------------------------------------------
##(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)
#>
#>
#> [calc_FadingCorr()]
#>
#> >> Fading correction according to Huntley & Lamothe (2001)
#> >> g-value re-calculated for the given tc
#>
#> .. used g-value: 5.312 ± 1.012 %/decade
#> .. used tc: 8.214e-05 ka
#> .. used kappa: 0.0231 ± 0.0044
#> ----------------------------------------------
#> seed: NA
#> n.MC: 100
#> observations: 100
#> ----------------------------------------------
#> Age (faded): 10 ka ± 0 ka
#> Age (corr.): 13.402 ka ± 0.8076 ka
#> ----------------------------------------------
##access the last output
get_RLum(results)
#> AGE AGE.ERROR AGE_FADED AGE_FADED.ERROR G_VALUE G_VALUE.ERROR KAPPA
#> 1 13.402 0.8076 10 0 5.312393 1.011901 0.02307143
#> KAPPA.ERROR TC TC.G_VALUE n.MC OBSERVATIONS SEED
#> 1 0.00439463 8.213721e-05 5.475814e-06 100 100 NA