diseq {IsoplotR}R Documentation

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{}^{238}U-206{}^{206}Pb and 235{}^{235}U-207{}^{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{}^{234}U/238{}^{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{}^{234}U/238{}^{238}U ratio and sx its standard error.

If option=2, then x contains the measured 234{}^{234}U/238{}^{238}U ratio and sx its standard error.

m, M specify the minimum and maximum search limits of the initial 234{}^{234}U/238{}^{238}U activity ratio.

x0 and sd specify the mean and standard deviation of the prior distribution for the the initial 234{}^{234}U/238{}^{238}U activity ratio.

ThU

a list containing seven items (x, sx, m, M, x0, sd and option) specifying the 230{}^{230}Th/238{}^{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{}^{230}Th/238{}^{238}U ratio and sx its standard error.

If option=2, then x contains the measured 230{}^{230}Th/238{}^{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{}^{226}Ra/238{}^{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{}^{226}Ra/238{}^{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{}^{231}Pa/235{}^{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{}^{231}Pa/235{}^{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(xm+bufferM+bufferx)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{}^{238}U, 234{}^{234}U, 230{}^{230}Th, and 226{}^{226}Ra; or between 235{}^{235}U and 231{}^{231}Pa:

  1. Specify the assumed initial activity ratios and calculate how much excess 206{}^{206}Pb and 207{}^{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{}^{230}Th/238{}^{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))

[Package IsoplotR version 6.2 Index]