Calculate lead isotope age models

The functions calculate the age model and their respective mu and kappa values according to the publications they are named after (see References). pb_iso_age_model() provides a wrapper for them and allows to calculate all age models simultaneously.

Usage

pb_iso_age_model(
  df,
  ratio_206_204 = "206Pb/204Pb",
  ratio_207_204 = "207Pb/204Pb",
  ratio_208_204 = "208Pb/204Pb",
  model = c("SK75", "CR75", "AJ84", "all")
)

stacey_kramers_1975(
  df,
  ratio_206_204 = "206Pb/204Pb",
  ratio_207_204 = "207Pb/204Pb",
  ratio_208_204 = "208Pb/204Pb"
)

cumming_richards_1975(
  df,
  ratio_206_204 = "206Pb/204Pb",
  ratio_207_204 = "207Pb/204Pb",
  ratio_208_204 = NULL
)

albarede_juteau_1984(
  df,
  ratio_206_204 = "206Pb/204Pb",
  ratio_207_204 = "207Pb/204Pb",
  ratio_208_204 = "208Pb/204Pb"
)

Arguments

df

The data frame from which the age model parameters should be calculated.

ratio_206_204

Name of the column with the 206Pb/204Pb ratio as character string. Default is 206Pb/204Pb.

ratio_207_204

Name of the column with the 207Pb/204Pb ratio as character string. Default is 207Pb/204Pb.

ratio_208_204

Name of the column with the 208Pb/204Pb ratio as character string. Default is 208Pb/204Pb.

model

Character string with the abbreviation of the model to calculate:

SK75 for Stacey & Kramers (1975)
CR75 for Cumming & Richards (1975)
AJ84 for Albarède & Juteau (1984)
all for all models at once

Value

If df is an ASTR object, the output is an object of the same type including the ID column, the contextual columns, the lead isotope ratios used for calculation of the age model parameters, and the calculated age model parameters. In all other cases, the data frame provided as input with columns added for the calculated age model parameters.

The used age model is indicated in the column names of the output by the abbreviations for the models given above. They represent the initials of the author's last names and the publication year (e. g. SK75 for Stacey & Kramers 1975).

Details

See the references for the respective publications of the age models. The function for the age model of Albarède & Juteau (1984) is based on the MATLAB-script of F. Albarède (version 2020-11-06). The age model published in Albarède et al. (2012) should not be used according to F. Albarède and is therefore not implemented. Instead, he recommends to use the age model published in Albarède & Juteau (1984).

The ratio of 208Pb/204Pb is not necessary for cumming_richards_1975. The function takes it as argument only to be consistent with the input of the other age model functions. If provided, it will be ignored.

References

Albarède, F. and Juteau, M. (1984) Unscrambling the lead model ages. Geochimica et Cosmochimica Acta 48(1), pp. 207-212. https://dx.doi.org/10.1016/0016-7037(84)90364-8.

Albarède, F., Desaulty, A.-M. and Blichert-Toft, J. (2012) A geological perspective on the use of Pb isotopes in Archaeometry. Archaeometry 54, pp. 853–867. https://doi.org/10.1111/j.1475-4754.2011.00653.x.

Cumming, G.L. and Richards, J.R. (1975) Ore lead isotope ratios in a continuously changing earth. Earth and Planetary Science Letters 28(2), pp. 155–171. https://dx.doi.org/10.1016/0012-821X(75)90223-X.

Stacey, J.S. and Kramers, J.D. (1975) Approximation of terrestrial lead isotope evolution by a two-stage model. Earth and Planetary Science Letters 26(2), pp. 207–221. https://dx.doi.org/10.1016/0012-821X(75)90088-6.

Examples