Derivation of isotope ratios, errors, and error correlations for U-Pb geochronology using ²⁰⁵Pb-²³⁵U-(²³³U)-spiked isotope dilution thermal ionization mass spectrometric data

A comprehensive treatment of the derivation of U-Pb isotope ratios and their corresponding uncertainties from isotope dilution thermal ionization mass spectrometric measurements is presented. Standard parametric statistical methods of error propagation are utilized to convolve uncertainties associated with instrumental mass fractionation, tracer subtraction, blank Pb and U subtraction, and initial common Pb correction. Derivations include errors and error correlations for total sample U/Pb and Pb isotope ratios (including radiogenic and initial common Pb) for two- and three-dimensional isochron calculations, radiogenic U/Pb and Pb isotope ratios for concordia and radiogenic model age calculations, and the propagation of model age errors from radiogenic isotope ratios.