numOSL (version 1.0)

decomp: Decomposition decay curve in OSL dating

Description

Function decomp() decomposes the OSL decay curve (type "CW" or "LM") to a specified number of components.

Usage

decomp(Sigdata, ncomp = 3, typ = c("cw","lm"),
       control.args = list(), transf = FALSE, 
       LEDpower = 60, LEDwavelength = 470, plot = TRUE,
       xlog= TRUE, lwd = 3, samplename = NULL, outfile = NULL)

Arguments

Sigdata

data.frame(required): two columns, time (t1,t2,etc) and correspond signal values (s1,s2,etc) to be decomposed

ncomp

numeric(with default): the number of components to be decomposed, which must be an integer in the range [1,7]

typ

character(with default): type ("cw" or "lm") of the OSL decay curve, default typ="cw"

control.args

list(with default): further arguments used in differential evolution algorithm, see details

transf

logical(with default): whether transform estimated parameters or not, see details

LEDpower

numeric(with default): LED power (mW/cm2) used for intensity ramping during the measurement

LEDwavelength

numeric(with default): LED wavelength (nm) used for stimulation during the measurement

plot

logical(with default): whether plot the fitted results or not

xlog

logical(with default): tansform x-axis to log-scale for plotting or not

lwd

numeric(with default): the width of curves for plotting

samplename

character(optional): name of the sample

outfile

character(optional): if specified, decomposed signal values will be written to a file of name outfile in .csv format and saved to the current work directory

Value

• Return an invisible list containing following elements:
• Comp.Signal
  fitted values for observations and each component
• pars
  estimated parameters and associated standard errors
• value
  sum of square of residual errors
• errorflag
  error message generated during the calculation, if parameters' standard errors can be estimated, errorflag=0, else 1

Details

This function decomposes OSL decay curve to a specified number of components using a combination of differential evolution and Levenberg-Marquardt algorithm. Both OSL decay curve of type "CW" and "LM" can be decomposed. For OSL decay curve of type "CW", the fitting model (accroding to Bluszcz and Adamiec, 2006) is: I(t)=a1*exp(-b1*t)+a2*exp(-b2*t)+...+ak*exp(-bk*t) , k=1, 2, ..., 7, which is identical to: I(t)=a1*b1*exp(-b1*t)+a2*b2*exp(-b2*t)+...+ak*bk*exp(-bk*t) , k=1, 2, ..., 7 if "transf" is set to be TRUE. where I(t) is the luminescence intensity as a function of time(t), a is the number of trapped electrons, b is the detrapping rates. Initial parameters are estimated using the differential evolution method suggested by Bluszcz A and Adamiec G (2006), then Levenberg-Marquardt algorithm (minpack: original FORTRAN 77 version by Jorge More, Burton Garbow, Kenneth Hillstrom. FORTRAN 90 version by John Burkardt) will be performed to obtain a final optimization. In some radical cases, differential evolution will fail in parameter initializing, or Levenberg-Marquardt algorithm may fails, then a serise of simple attempts will be carryed out using Levenberg-Marquardt algorithm. Arguments (control.args) that employed to control the performance of differential evolution algorithm are: factor: used for control the number of parents (NP), np=factor*ncomp, default factor=20; f: weighting factor, ranging from 0 to 1.2, default f=0.5; cr: crossover constant, ranging from 0 to 1, default cr=0.9; maxiter: the maximum iterative number allowed, default maxiter=1e3; tol: a tolerance for stopping the iteration, if magnitude of all standard deviations of parameters within the whole population are smaller than tol, the iteration will be terminated. default tol=0.1 For OSL decay curve of type "LM", the fitting model (accroding to Bulur E, 2000) is: I(t)=a1*(t/P)*exp(-b1*t^2/(2*P))+a2*(t/P)*exp(-b2*t^2/(2*P))+...+ ak*(t/P)*exp(-bk*t^2/(2*P)) , k=1, 2, ..., 7, which is identical to: I(t)=a1*b1*(t/P)*exp(-b1*t^2/(2*P))+a2*b2*(t/P)*exp(-b2*t^2/(2*P))+...+ ak*bk*(t/P)*exp(-bk*t^2/(2*P)) , k=1, 2, ..., 7 if "transf" is set to be TRUE where I(t) is the luminescence intensity as a function of time(t), P is the total stimulation time, a is the number of trapped electrons, b is the detrapping rates. Initial detrapping rates are estimated using the detrapping values described after Jain et al. (2003). Possible combinations of detrapping rates for a given component are calculated using permutation and combinations. For example, if ncomp=3, then the possible number of combinations is C(3,7)=35. Then for each combination that contains three detrapping rates, the correspond number of trapped electrons can be coarsely obtained using Linear Algebra method outlined by Bluszcz A (1996). Then the Levenberg-Marquardt algorithm will be used to optimize the finial result.

References

Bluszcz, A., 1996. Exponential function fitting to TL growth data and similar applications. Geochronometria, 13, pp.135-141.

Bluszcz, A., Adamiec, G., 2006. Application of differential evolution to fitting OSL decay curves. Radiation Measurements, 41 (7-8), pp.886-891.

Bulur, E., 2000. A simple transformation for converting CW-OSL curves to LM-OSL curves. Radiation Measurements, 32, pp.141-145.

Differential evolution, http://en.wikipedia.org/wiki/Differential_evolution Jain, M., Murray, A.S., Boetter-Jensen, L., 2003. Characterisation of blue-light stimulated luminescence components in different quartz samples: implications for dose measurement. Radiation Measurements, 37 (4-5), pp.441-449.

Jorge, M., Burton, G., Kenneth, H., 1980. User Guide for MINPACK-1, Technical Report ANL-80-74, Argonne National Laboratory.

Further reading

Adamiec, G., 2005. OSL decay curves-relationship between single- and multiple-grain aliquots. Radiation Measurements, 39, pp.63-75.

Choi, J.H., Duller G.A.T., Wintle, A.G., 2006. Analysis of quartz LM-OSL curves. Ancient TL, 24, pp. 9-20.

Li, S.H., Li, B., 2006. Dose measurement using the fast component of LM-OSL signals from quartz. Radiation Measurements, 41, pp.534-541.

See Also

decompc; fastED

Examples

# loading signal data
 data(Signaldata)
 # decompose natural OSL signal of type "CW" to 3 components
 res<-decomp(Signaldata$cw[,c(1,2)],ncomp=3,typ="cw",samplename="GL1")
 res 
 # decompose the whole signal table (exclude the zero-redose decay curve)
 decomp(Signaldata$cw[,-12])$pars
 # decompose OSL signal of type "LM" to 4 components
 res<-decomp(Signaldata$lm,ncomp=4,typ="lm")
 print(res)