This function calculates the cosmic dose rate taking into account the soft- and hard-component of the cosmic ray flux and allows corrections for geomagnetic latitude, altitude above sea-level and geomagnetic field changes.
Usage
calc_CosmicDoseRate(
depth,
density,
latitude,
longitude,
altitude,
corr.fieldChanges = FALSE,
est.age = NA,
half.depth = FALSE,
error = 10,
...
)Arguments
- depth
numeric (required): depth of overburden (m). For more than one absorber use
c(depth_1, depth_2, ..., depth_n)- density
numeric (required): average overburden density (g/cm^3). For more than one absorber use
c(density_1, density_2, ..., density_n)- latitude
numeric (required): latitude (decimal degree), N positive
- longitude
numeric (required): longitude (decimal degree), E positive
- altitude
numeric (required): altitude (m above sea-level)
- corr.fieldChanges
logical (with default): correct for geomagnetic field changes after Prescott & Hutton (1994). Apply only when justified by the data.
- est.age
numeric (with default): estimated age range (ka) for geomagnetic field change correction (0-80 ka allowed)
- half.depth
logical (with default): How to overcome with varying overburden thickness. If
TRUEonly half the depth is used for calculation. Apply only when justified, i.e. when a constant sedimentation rate can safely be assumed.- error
numeric (with default): general error (percentage) to be implemented on corrected cosmic dose rate estimate
- ...
further arguments (
verboseto disable/enable console output).
Value
Returns a terminal output. In addition an RLum.Results-object is returned containing the following element:
- summary
data.frame summary of all relevant calculation results.
- args
list used arguments
- call
call the function call
The output should be accessed using the function get_RLum
Details
This function calculates the total cosmic dose rate considering both the soft- and hard-component of the cosmic ray flux.
Internal calculation steps
(1) Calculate total depth of all absorber in hg/cm^2 (1 hg/cm^2 = 100 g/cm^2)
$$absorber = depth_1*density_1 + depth_2*density_2 + ... + depth_n*density_n$$
(2)
If half.depth = TRUE
$$absorber = absorber/2$$
(3) Calculate cosmic dose rate at sea-level and 55 deg. latitude
a) If absorber is > 167 g/cm^2 (only hard-component; Allkofer et al. 1975): apply equation given by Prescott & Hutton (1994) (c.f. Barbouti & Rastin 1983)
$$D0 = C/(((absorber+d)^\alpha+a)*(absober+H))*exp(-B*absorber)$$
b) If absorber is < 167 g/cm^2 (soft- and hard-component): derive D0 from Fig. 1 in Prescott & Hutton (1988).
(4) Calculate geomagnetic latitude (Prescott & Stephan 1982, Prescott & Hutton 1994)
$$\lambda = arcsin(0.203*cos(latitude)*cos(longitude-291)+0.979* sin(latitude))$$
(5) Apply correction for geomagnetic latitude and altitude above sea-level. Values for F, J and H were read from Fig. 3 shown in Prescott & Stephan (1982) and fitted with 3-degree polynomials for lambda < 35 degree and a linear fit for lambda > 35 degree.
$$Dc = D0*(F+J*exp((altitude/1000)/H))$$
(6) Optional: Apply correction for geomagnetic field changes in the last 0-80 ka (Prescott & Hutton 1994). Correction and altitude factors are given in Table 1 and Fig. 1 in Prescott & Hutton (1994). Values for altitude factor were fitted with a 2-degree polynomial. The altitude factor is operated on the decimal part of the correction factor.
$$Dc' = Dc*correctionFactor$$
Usage of depth and density
(1) If only one value for depth and density is provided, the cosmic dose
rate is calculated for exactly one sample and one absorber as overburden
(i.e. depth*density).
(2) In some cases it might be useful to calculate the cosmic dose rate for a
sample that is overlain by more than one absorber, e.g. in a profile with
soil layers of different thickness and a distinct difference in density.
This can be calculated by providing a matching number of values for
depth and density (e.g. depth = c(1, 2), density = c(1.7, 2.4))
(3) Another possibility is to calculate the cosmic dose rate for more than
one sample of the same profile. This is done by providing more than one
values for depth and only one for density. For example,
depth = c(1, 2, 3) and density = 1.7 will calculate the cosmic dose rate
for three samples in 1, 2 and 3 m depth in a sediment of density 1.7 g/cm^3.
Note
Despite its universal use the equation to calculate the cosmic dose rate provided by Prescott & Hutton (1994) is falsely stated to be valid from the surface to 10^4 hg/cm^2 of standard rock. The original expression by Barbouti & Rastin (1983) only considers the muon flux (i.e. hard-component) and is by their own definition only valid for depths between 10-10^4 hg/cm^2.
Thus, for near-surface samples (i.e. for depths < 167 g/cm^2) the equation of Prescott & Hutton (1994) underestimates the total cosmic dose rate, as it neglects the influence of the soft-component of the cosmic ray flux. For samples at zero depth and at sea-level the underestimation can be as large as ~0.1 Gy/ka. In a previous article, Prescott & Hutton (1988) give another approximation of Barbouti & Rastin's equation in the form of
$$D = 0.21*exp(-0.070*absorber+0.0005*absorber^2)$$
which is valid for depths between 150-5000 g/cm^2. For shallower depths (< 150 g/cm^2) they provided a graph (Fig. 1) from which the dose rate can be read.
As a result, this function employs the equation of Prescott & Hutton (1994) only for depths > 167 g/cm^2, i.e. only for the hard-component of the cosmic ray flux. Cosmic dose rate values for depths < 167 g/cm^2 were obtained from the "AGE" program (Gruen 2009) and fitted with a 6-degree polynomial curve (and hence reproduces the graph shown in Prescott & Hutton 1988). However, these values assume an average overburden density of 2 g/cm^3.
It is currently not possible to obtain more precise cosmic dose rate values for near-surface samples as there is no equation known to the author of this function at the time of writing.
How to cite
Burow, C., 2024. calc_CosmicDoseRate(): Calculate the cosmic dose rate. Function version 0.5.2. 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
Allkofer, O.C., Carstensen, K., Dau, W.D., Jokisch, H., 1975. Letter to the editor. The absolute cosmic ray flux at sea level. Journal of Physics G: Nuclear and Particle Physics 1, L51-L52.
Barbouti, A.I., Rastin, B.C., 1983. A study of the absolute intensity of muons at sea level and under various thicknesses of absorber. Journal of Physics G: Nuclear and Particle Physics 9, 1577-1595.
Crookes, J.N., Rastin, B.C., 1972. An investigation of the absolute intensity of muons at sea-level. Nuclear Physics B 39, 493-508.
Gruen, R., 2009. The "AGE" program for the calculation of luminescence age estimates. Ancient TL 27, 45-46.
Prescott, J.R., Hutton, J.T., 1988. Cosmic ray and gamma ray dosimetry for TL and ESR. Nuclear Tracks and Radiation Measurements 14, 223-227.
Prescott, J.R., Hutton, J.T., 1994. Cosmic ray contributions to dose rates for luminescence and ESR dating: large depths and long-term time variations. Radiation Measurements 23, 497-500.
Prescott, J.R., Stephan, L.G., 1982. The contribution of cosmic radiation to the environmental dose for thermoluminescence dating. Latitude, altitude and depth dependences. PACT 6, 17-25.
Examples
##(1) calculate cosmic dose rate (one absorber)
calc_CosmicDoseRate(depth = 2.78, density = 1.7,
latitude = 38.06451, longitude = 1.49646,
altitude = 364, error = 10)
#>
#>
#> [calc_CosmicDoseRate]
#>
#> ---------------------------------------------------------
#> depth (m) : 2.78
#> density (g cm^-3) : 1.7
#> latitude (N deg.) : 38.06451
#> longitude (E deg.) : 1.49646
#> altitude (m) : 364
#> ---------------------------------------------------------
#> total absorber (g cm^-2) : 472.6
#>
#> cosmic dose rate (Gy ka^-1) : 0.1518
#> [@sea-level & 55 deg. N G.lat]
#>
#> geomagnetic latitude (deg.) : 41.1
#>
#> cosmic dose rate (Gy ka^-1) : 0.161 +- 0.0161
#> [corrected]
#> ---------------------------------------------------------
#>
##(2a) calculate cosmic dose rate (two absorber)
calc_CosmicDoseRate(depth = c(5.0, 2.78), density = c(2.65, 1.7),
latitude = 38.06451, longitude = 1.49646,
altitude = 364, error = 10)
#>
#>
#> [calc_CosmicDoseRate]
#>
#> ---------------------------------------------------------
#> depth (m) : 5
#> depth (m) : 2.78
#> density (g cm^-3) : 2.65
#> density (g cm^-3) : 1.7
#> latitude (N deg.) : 38.06451
#> longitude (E deg.) : 1.49646
#> altitude (m) : 364
#> ---------------------------------------------------------
#> total absorber (g cm^-2) : 1797.6
#>
#> cosmic dose rate (Gy ka^-1) : 0.0705
#> [@sea-level & 55 deg. N G.lat]
#>
#> geomagnetic latitude (deg.) : 41.1
#>
#> cosmic dose rate (Gy ka^-1) : 0.0747 +- 0.0075
#> [corrected]
#> ---------------------------------------------------------
#>
##(2b) calculate cosmic dose rate (two absorber) and
##correct for geomagnetic field changes
calc_CosmicDoseRate(depth = c(5.0, 2.78), density = c(2.65, 1.7),
latitude = 12.04332, longitude = 4.43243,
altitude = 364, corr.fieldChanges = TRUE,
est.age = 67, error = 15)
#> [1] "corr.fac 1.04562628608 diff.one 0.02 alt.fac 1.281314304"
#>
#>
#> [calc_CosmicDoseRate]
#>
#> ---------------------------------------------------------
#> depth (m) : 5
#> depth (m) : 2.78
#> density (g cm^-3) : 2.65
#> density (g cm^-3) : 1.7
#> latitude (N deg.) : 12.04332
#> longitude (E deg.) : 4.43243
#> altitude (m) : 364
#> ---------------------------------------------------------
#> total absorber (g cm^-2) : 1797.6
#>
#> cosmic dose rate (Gy ka^-1) : 0.0705
#> [@sea-level & 55 deg. N G.lat]
#>
#> geomagnetic latitude (deg.) : 15.1
#>
#> cosmic dose rate (Gy ka^-1) : 0.072 +- 0.0108
#> [corrected]
#> ---------------------------------------------------------
#>
##(3) calculate cosmic dose rate and export results to .csv file
#calculate cosmic dose rate and save to variable
results<- calc_CosmicDoseRate(depth = 2.78, density = 1.7,
latitude = 38.06451, longitude = 1.49646,
altitude = 364, error = 10)
#>
#>
#> [calc_CosmicDoseRate]
#>
#> ---------------------------------------------------------
#> depth (m) : 2.78
#> density (g cm^-3) : 1.7
#> latitude (N deg.) : 38.06451
#> longitude (E deg.) : 1.49646
#> altitude (m) : 364
#> ---------------------------------------------------------
#> total absorber (g cm^-2) : 472.6
#>
#> cosmic dose rate (Gy ka^-1) : 0.1518
#> [@sea-level & 55 deg. N G.lat]
#>
#> geomagnetic latitude (deg.) : 41.1
#>
#> cosmic dose rate (Gy ka^-1) : 0.161 +- 0.0161
#> [corrected]
#> ---------------------------------------------------------
#>
# the results can be accessed by
get_RLum(results, "summary")
#> depth density latitude longitude altitude total_absorber.gcm2 d0
#> 1 2.78 1.7 38.06451 1.49646 364 472.6 0.1518269
#> geom_lat dc
#> 1 41.0685 0.161002
#export results to .csv file - uncomment for usage
#write.csv(results, file = "c:/users/public/results.csv")
##(4) calculate cosmic dose rate for 6 samples from the same profile
## and save to .csv file
#calculate cosmic dose rate and save to variable
results<- calc_CosmicDoseRate(depth = c(0.1, 0.5 , 2.1, 2.7, 4.2, 6.3),
density = 1.7, latitude = 38.06451,
longitude = 1.49646, altitude = 364,
error = 10)
#>
#>
#> [calc_CosmicDoseRate]
#>
#> Calculating cosmic dose rate for 6 samples.
#>
#> depth (m) d0 (Gy/ka) dc (Gy/ka) dc_error (Gy/ka)
#> 1 0.1 0.2599 0.2756 0.0276
#> 2 0.5 0.1999 0.2120 0.0212
#> 3 2.1 0.1640 0.1739 0.0174
#> 4 2.7 0.1532 0.1625 0.0162
#> 5 4.2 0.1299 0.1377 0.0138
#> 6 6.3 0.1045 0.1109 0.0111
#export results to .csv file - uncomment for usage
#write.csv(results, file = "c:/users/public/results_profile.csv")