mclean: Predict disequilibrium concordia compositions

Description

Returns the predicted ${}^{206}$Pb/${}^{238}$U and ${}^{207}$Pb/${}^{235}$U ratios for any given time with or without initial U-series disequilibrium.

Usage

mclean(tt = 0, d = diseq(), exterr = FALSE, i = 1)

Arguments

the age of the sample

an object of class diseq

exterr

propagate the uncertainties associated with decay constants and the ${}^{238}$U/${}^{235}$U-ratio.

aliquot to be used, if d$ThU$option=3.

Value

a list containing the predicted ${}^{206}$Pb/${}^{238}$U, ${}^{207}$Pb/${}^{235}$U and ${}^{207}$Pb/${}^{206}$Pb ratios at time tt; the derivatives of the ${}^{206}$Pb/${}^{238}$U, ${}^{207}$Pb/${}^{235}$U and ${}^{207}$Pb/${}^{206}$Pb ratios with respect to time; and the derivatives of the ${}^{206}$Pb/${}^{238}$U, ${}^{207}$Pb/${}^{235}$U and ${}^{207}$Pb/${}^{206}$Pb ratios with respect to the intermediate decay constants and ${}^{238}$U/${}^{235}$U-ratio.

Details

U decays to Pb in 14 (for ${}^{238}$U) or 11/12 (for ${}^{235}$U) steps. Conventional U-Pb geochronology assumes that secular equilibrium between all the short lived intermediate daughters was established at the time of isotopic closure. Under this assumption, the relative abundances of those intermediate daughters can be neglected and the age equation reduces to a simple function of the measured Pb/U ratios. In reality, however, the assumption of initial secular equilibrium is rarely met. Accounting for disequilibrium requires a more complex set of age equations, which are based on a coupled system of differetial equations. The solution to this system of equations is given by a matrix exponential. IsoplotR solves this matrix exponential for any given time, using either the assumed initial activity ratios, or (for young samples) the measured activity ratios of the longest lived intermediate daughters. Based on a Matlab script by Noah McLean.

Examples

Run this code

# NOT RUN {
d <- diseq(U48=list(x=0,option=1),ThU=list(x=2,option=1),
           RaU=list(x=2,option=1),PaU=list(x=2,option=1))
mclean(tt=2,d=d)
# }