diseq: Set up U-series disequilibrium correction for U-Pb...

In IsoplotR: Statistical Toolbox for Radiometric Geochronology

Set up U-series disequilibrium correction for U-Pb geochronology

Description

The U-Pb method conventionally assumes initial secular equilibrium of all the intermediate daughters of the {}^{238}U-{}^{206}Pb and {}^{235}U-{}^{207}Pb decay chains. Violation of this assumption may produce inaccurate results. diseq sets up initial disequilibrium parameters that are subsequently passed on to the read.data function for incorporation in other functions.

Usage

diseq(
  U48 = list(x = 1, sx = 0, option = 0, m = 0, M = 20, x0 = 1, sd = 10),
  ThU = list(x = 1, sx = 0, option = 0, m = 0, M = 20, x0 = 1, sd = 10),
  RaU = list(x = 1, sx = 0, option = 0, m = 0, M = 20, x0 = 1, sd = 10),
  PaU = list(x = 1, sx = 0, option = 0, m = 0, M = 20, x0 = 1, sd = 10),
  buffer = 1e-05
)

Arguments

U48	a list containing seven items (x, sx, m, M, x0, sd and option) specifying the {}^{234}U/{}^{238}U disequilibrium. If option=0, then x and sx are ignored and no disequilibrium correction is applied. If option=1, then x contains the initial {}^{234}U/{}^{238}U ratio and sx its standard error. If option=2, then x contains the measured {}^{234}U/{}^{238}U ratio and sx its standard error. m, M specify the minimum and maximum search limits of the initial {}^{234}U/{}^{238}U activity ratio. x0 and sd specify the mean and standard deviation of the prior distribution for the the initial {}^{234}U/{}^{238}U activity ratio.
ThU	a list containing seven items (x, sx, m, M, x0, sd and option) specifying the {}^{230}Th/{}^{238}U disequilibrium. If option=0, then x and sx are ignored and no disequilibrium correction is applied. If option=1, then x contains the initial {}^{230}Th/{}^{238}U ratio and sx its standard error. If option=2, then x contains the measured {}^{230}Th/{}^{238}U ratio and sx its standard error. If option=3, then x contains the measured Th/U ratio of the magma (assumed or determined from the whole rock or volcanic glass) and sx its standard error. This only applies for Th-bearing U-Pb data formats 7 and 8. m, M, x0 and sd are analogous to the eponymous settings for ThU.
RaU	a list containing seven items (x, sx, m, M, x0, sd and option) specifying the {}^{226}Ra/{}^{238}U disequilibrium. If option=0, then x and sx are ignored and no disequilibrium correction is applied. If option=1, then x contains the initial {}^{226}Ra/{}^{238}U ratio and sx its standard error. m, M, x0 and sd are analogous to the eponymous settings for ThU.
PaU	a list containing seven items (x, sx, m, M, x0, sd and option) specifying the {}^{231}Pa/{}^{235}U disequilibrium. If option=0, then x and sx are ignored and no disequilibrium correction is applied. If option=1, then x contains the initial {}^{231}Pa/{}^{235}U ratio and sx its standard error. m, M, x0 and sd are analogous to the eponymous settings for ThU.
buffer	small amount of padding to avoid singularities in the prior distribution, which uses a logistic transformation: y = \ln\left(\frac{x-m+buffer}{M+buffer-x}\right)

Details

There are three ways to correct for the initial disequilibrium between the activity of {}^{238}U, {}^{234}U, {}^{230}Th, and {}^{226}Ra; or between {}^{235}U and {}^{231}Pa:

1. Specify the assumed initial activity ratios and calculate how much excess {}^{206}Pb and {}^{207}Pb these would have produced.

2. Measure the current activity ratios to infer the initial ratios. This approach only works for young samples.

3. The initial {}^{230}Th/{}^{238}U activity ratio can also be estimated by providing the Th/U-ratio of the magma.

Value

a list with the following items:

U48, ThU, RaU, PaU

the same as the corresponding input arguments

equilibrium

a boolean flag indicating whether option=TRUE and/or x=1 for all activity ratios

Q

the eigenvectors of the disequilibrium matrix exponential

Qinv

the inverse of Q

L

a named vector of all the relevant decay constants

See Also

mclean, concordia, ludwig

Examples

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))
fn <- system.file("diseq.csv",package="IsoplotR")
UPb <- read.data(fn,method='U-Pb',format=2,d=d)
concordia(UPb,type=2,xlim=c(0,700),ylim=c(0.05,0.5))

IsoplotR documentation built on Oct. 19, 2024, 5:07 p.m.