# diseq: Set up U-series disequilibrium correction for U-Pb... In pvermees/IsoplotR: Statistical Toolbox for Radiometric 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

 ```1 2 3``` ```diseq(U48 = list(x = 1, sx = 0, option = 0), ThU = list(x = 1, sx = 0, option = 0), RaU = list(x = 1, sx = 0, option = 0), PaU = list(x = 1, sx = 0, option = 0)) ```

## Arguments

 `U48` a list containing three items (`x`, `sx` 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. `ThU` a list containing three items (`x`, `sx` 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. `RaU` a list containing three items (`x`, `sx` 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. `PaU` a list containing three items (`x`, `sx` 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.

## Details

There are three ways to correct for the initial disequilibrium between the activity of {}^{238}U, {}^{234}Th, {}^{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

n0

the initial atomic abundances of all the parent and daughter isotopes (used by `mclean`)

`mclean`, `concordia`, `ludwig`
 ```1 2 3 4 5``` ```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,show.age=1) ```