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.
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
)a list with the following items:
the same as the corresponding input arguments
a boolean flag indicating whether
option=TRUE and/or x=1 for all activity ratios
the eigenvectors of the disequilibrium matrix exponential
the inverse of Q
a named vector of all the relevant decay constants
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.
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.
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.
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.
small amount of padding to avoid singularities in the prior distribution, which uses a logistic transformation: \(y = \ln\left(\frac{x-m+buffer}{M+buffer-x}\right)\)
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:
Specify the assumed initial activity ratios and calculate how much excess \({}^{206}\)Pb and \({}^{207}\)Pb these would have produced.
Measure the current activity ratios to infer the initial ratios. This approach only works for young samples.
The initial \({}^{230}\)Th/\({}^{238}\)U activity ratio can also be estimated by providing the Th/U-ratio of the magma.
mclean, concordia,
ludwig
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))
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