ananke (version 0.1.0)

pb_age: Geological Model Age from Lead Isotope Analysis

Description

Compute geological model age (T) and U/Pb (mu) and Th/U (kappa) ratios from lead isotopic measurements.

Usage

pb_age(x, y, z, ...)
# S4 method for numeric,numeric,numeric
pb_age(
  x,
  y,
  z,
  t0 = 3.8,
  x_star = 18.75,
  y_star = 15.63,
  z_star = 38.86,
  mu = 9.66,
  kappa = 3.9,
  th232 = 0.049475,
  u238 = 0.155125,
  u235 = 0.98485,
  u238_235 = 137.79,
  tolerance = sqrt(.Machine$double.eps),
  stop = 100
)
# S4 method for list,missing,missing
pb_age(
  x,
  t0 = 3.8,
  x_star = 18.75,
  y_star = 15.63,
  z_star = 38.86,
  mu = 9.66,
  kappa = 3.9,
  th232 = 0.049475,
  u238 = 0.155125,
  u235 = 0.98485,
  u238_235 = 137.79,
  tolerance = sqrt(.Machine$double.eps),
  stop = 100
)

Value

A four columns data.frame:

age

Geological model age (in Ma).

mu

238U/204Pb ratio.

kappa

232Th/238U ratio.

residual

Newton loop residual.

Arguments

x

A numeric vector of 206Pb/204Pb ratios. If y and z are missing, must be a list (or a data.frame) with numeric components (columns) x, y and z.

y

A numeric vector of 207Pb/204Pb ratios. If missing, an attempt is made to interpret x in a suitable way.

z

A numeric vector of 208Pb/204Pb ratios. If missing, an attempt is made to interpret x in a suitable way.

...

Currently not used.

t0

A numeric value giving the time of the second stage of the reference model.

x_star

A numeric value giving the 206Pb/204Pb ratio at \(t = 0\).

y_star

A numeric value giving the 207Pb/204Pb ratio at \(t = 0\).

z_star

A numeric value giving the 208Pb/204Pb ratio at \(t = 0\).

mu

A numeric value giving the 238U/204Pb ratio of the reference model.

kappa

A numeric value giving the 232Th/238U ratio of the reference model.

th232

A numeric value giving the decay constants of 232Th.

u238

A numeric value giving the decay constants of 238U.

u235

A numeric value giving the decay constants of 235U.

u238_235

A numeric value giving the actual 238U/235U ratio.

tolerance

A numeric value specifying the tolerance (stopping criteria for the Newton–Raphson method).

stop

An integer giving the stopping rule (i.e. maximum number of iterations) to avoid infinite loop.

Author

N. Frerebeau, F. Albarede (original Matlab code)

References

Albarède, F., Desaulty, A.-M. & Blichert-Toft, J. (2012). A Geological Perspective on the Use of Pb Isotopes in Archaeometry. Archaeometry, 54: 853-867. tools:::Rd_expr_doi("10.1111/j.1475-4754.2011.00653.x").

Albarède, F. & Juteau, M. (1984). Unscrambling the Lead Model Ages. Geochimica et Cosmochimica Acta, 48(1): 207-12. tools:::Rd_expr_doi("10.1016/0016-7037(84)90364-8").

Allègre, C. (2005). Géologie isotopique. Belin sup. Paris: Belin.

Examples

Pb <- data.frame(
  x = c(18.23247, 18.22936, 18.23102), # Pb206/Pb204
  y = c(15.65199, 15.65216, 15.65097), # Pb207/Pb204
  z = c(38.5167, 38.51516, 38.51601)   # Pb208/Pb204
)

## Default reference values from Albarede & Juteau (1984)
pb_age(
  Pb,
  t0 = 3.8,
  x_star = 18.75, y_star = 15.63, z_star = 38.86,
  mu = 9.66, kappa = 3.90, th232 = 0.049475,
  u238 = 0.155125, u235 = 0.98485, u238_235 = 137.79
)

## Reference values from Albarede et al. (2012)
pb_age(
  Pb,
  t0 = 4.43,
  x_star = 18.75, y_star = 15.63, z_star = 38.83,
  mu = 9.66, kappa = 3.90, th232 = 0.049475,
  u238 = 0.155125, u235 = 0.98485, u238_235 = 137.79
)