doserate: Dose Rate Estimation

In gamma: Dose Rate Estimation from in-Situ Gamma-Ray Spectrometry Measurements

Dose Rate Estimation

Description

• dose_fit() builds a calibration curve for gamma dose rate estimation.

• dose_predict() predicts in situ gamma dose rate.

Usage

dose_fit(object, background, doses, ...)

dose_predict(object, spectrum, ...)

## S4 method for signature 'GammaSpectra,GammaSpectrumOrNumeric,matrix'
dose_fit(
  object,
  background,
  doses,
  range_Ni,
  range_NiEi,
  details = list(authors = "", date = Sys.time())
)

## S4 method for signature 'GammaSpectra,GammaSpectrumOrNumeric,data.frame'
dose_fit(
  object,
  background,
  doses,
  range_Ni,
  range_NiEi,
  details = list(authors = "", date = Sys.time())
)

## S4 method for signature 'CalibrationCurve,missing'
dose_predict(
  object,
  sigma = 1,
  epsilon = 0.015,
  water_content = NULL,
  use_MC = FALSE
)

## S4 method for signature 'CalibrationCurve,GammaSpectrum'
dose_predict(
  object,
  spectrum,
  sigma = 1,
  epsilon = 0.015,
  water_content = NULL,
  use_MC = FALSE
)

## S4 method for signature 'CalibrationCurve,GammaSpectra'
dose_predict(
  object,
  spectrum,
  sigma = 1,
  epsilon = 0.015,
  water_content = NULL,
  use_MC = FALSE
)

Arguments

object	A GammaSpectra or CalibrationCurve object.
background	A GammaSpectrum object or a length-two numeric vector giving the background noise integration value and error, respectively. If no background subtraction is wanted, you can set background = c(0,0,)
doses	A matrix or data.frame object with gamma dose values and uncertainties. The row names must match the names of the spectrum.
...	Currently not used.
spectrum	An optional GammaSpectrum or GammaSpectra object in which to look for variables with which to predict. If omitted, the fitted values are used.
range_Ni, range_NiEi	A length-two numeric vector giving the energy range to integrate within (in keV).
details	A list of length-one vector specifying additional informations about the instrument for which the curve is built.
sigma	A numeric value giving the confidence level of which the error from the slope is considered in the final uncertainty calculation
epsilon	A numeric value giving an extra relative error term, introduced by the calibration of the energy scale of the spectrum, e.g., 0.015 for an additional 1.5% error
water_content	numeric or matrix gravimetric field water content to correct the gamma-dose rate to using the correction factor by Aitken (1985) to obtain the dry gamma-dose rate. Example: c(0.05,0.0001) for water content of 5% +/- 0.01 %. The default is NULL (nothing is corrected). The correction only works on the final dose rate. For more information see details.
use_MC	A logical parameter, enabling/disabling Monte Carlo simulations for estimating the dose rate uncertainty

Details

To estimate the gamma dose rate, one of the calibration curves distributed with this package can be used. These built-in curves are in use in several luminescence dating laboratories and can be used to replicate published results. As these curves are instrument specific, the user may have to build its own curve.

The construction of a calibration curve requires a set of reference spectra for which the gamma dose rate is known and a background noise measurement. First, each reference spectrum is integrated over a given interval, then normalized to active time and corrected for background noise. The dose rate is finally modelled by the integrated signal value used as a linear predictor (York et al., 2004).

Value

• dose_fit() returns a CalibrationCurve object.

• dose_predict() returns a data.frame with the following columns:

  name

  (character) the name of the spectra.

  signal_Ni

  (numeric) the integrated signal value (according to the value of threshold; see signal_integrate()) for energy = FALSE

  signal_err_Ni

  (numeric) the integrated signal error value (according to the value of threshold; see signal_integrate()) for energy = FALSE.

  dose_Ni

  (numeric) the predicted gamma dose rate for energy = FALSE.

  dose_err_Ni

  (numeric) the predicted gamma dose rate error for energy = FALSE.

  signal_Ni

  (numeric) the integrated signal value (according to the value of threshold; see signal_integrate()).

  signal_err_NiEi

  (numeric) the integrated signal error value (according to the value of threshold; see signal_integrate()) for energy = TRUE.

  dose_NiEi

  (numeric) the predicted gamma dose rate for energy = TRUE.

  dose_err_NiEi

  (numeric) the predicted gamma dose rate error for energy = TRUE.

  dose_final

  (numeric) the predicted final gamma dose rate as the mean of dose_Ni and dose_NiEi

  dose_err_final

  (numeric) the predicted final gamma dose rate error as SE(\dot{D}_{\gamma}) = \sqrt{(\frac{SE(\dot{D}_{\gamma\mathrm{Ni}})}{\dot{D}_{\gamma\mathrm{Ni}}})^2 + (\frac{SE(\dot{D}_{\gamma\mathrm{NiEi}})}{\dot{D}_{\gamma\mathrm{NiEi}}})^2}

Uncertainty calculation of the gamma-dose rate

The analytical uncertainties of the final gamma-dose rate (SE(\dot{D}_{\gamma})) are calculated as follows:

\sigma_{\dot{D_\gamma}} = \sqrt((\frac{m_{\delta}s}{m})^2 + (\frac{s_{\delta}}{s})^2 + \epsilon^2)

with m and m_{\delta} being the slope of the fit an its uncertainty, \sigma the error scaler for the slope uncertainty, s and s_{\delta} the integrated signal and its uncertainty, and \epsilon an additional relative uncertainty term that can be set by the user using the argument epsilon.

If the parameter use_MC is set to TRUE, the a Monte Carlo sampling approach is chosen to approximate the uncertainties on the dose rate:

\sigma_{\dot{D_\gamma}} := \sqrt((\frac{SD(\mathcal{N}(\mu_{slope}, \sigma_{slope}) \times \mathcal{N}(\mu_{signal}, \sigma_{signal}) + \mathcal{N}(\mu_{intercept}, \sigma_{intercept})) * \rho}{\dot{D_\gamma}})^2 + \epsilon^2) * \dot{D_\gamma}

\ rho is the parameter sigma provided with the function call, SD equals the the call to sd(), i.e. the calculation of the standard deviation. To achieve a good Gaussian normal approximation with sample 1+e06 times (the values is fixed).

Water content correction

If gamma-dose rates are measured in the field, they are measured at "as-is" conditions. In dating studies, however, using the dry dose rate is often more desirable to model the long-term effect of different assumptions for the water content. If the parameter water_content, either as numeric vector or as matrix with the number of rows equal to the number of processed spectra, if different values are desired, the final gamma-dose rate is corrected for the water content provided. Final uncertainties are obtained using the square root of the summed squared relative uncertainties of the dose rate and the water content.

A word of caution: When estimating the water content in the laboratory, the water analytical uncertainty is usually minimal, and it does not make sense to correct with a relative water content of, e.g., c(0.02,0.02) (2% +/- 2%) because this massively inflates the final dose rate error.

Note

See vignette(doserate) for a reproducible example.

Author(s)

N. Frerebeau

References

Aitken, M.J. (1985). Thermoluminescence dating. London: Academic Press.

Mercier, N. & Falguères, C. (2007). Field Gamma Dose-Rate Measurement with a NaI(Tl) Detector: Re-Evaluation of the "Threshold" Technique. Ancient TL, 25(1), p. 1-4.

York, D., Evensen, N. M., Martínez, M. L. & De Basabe Delgado, J. (2004). Unified Equations for the Slope, Intercept, and Standard Errors of the Best Straight Line. American Journal of Physics, 72(3), p. 367-75. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1119/1.1632486")}.

See Also

signal_integrate()

Examples

## Import CNF files
## Spectra
spc_dir <- system.file("extdata/BDX_LaBr_1/calibration", package = "gamma")
spc <- read(spc_dir)

## Background
bkg_dir <- system.file("extdata/BDX_LaBr_1/background", package = "gamma")
bkg <- read(bkg_dir)

## Get dose rate values
data("clermont")
(doses <- clermont[, c("gamma_dose", "gamma_error")])

## Build the calibration curve
calib_curve <- dose_fit(spc, bkg, doses,
                        range_Ni = c(300, 2800),
                        range_NiEi = c(165, 2800))

## Plot the curve
plot(calib_curve, threshold = "Ni")

## Estimate gamma dose rates
dose_predict(calib_curve, spc)

gamma documentation built on Sept. 24, 2024, 1:07 a.m.