Calculation of 230ThU isochrons, ages, and errors

If analytical errors are responsible for the scatter of points on a ²³⁰Th-²³⁴U-²³⁸U isochron diagram, the isochron should be fitted by a technique that1. weights the points according to their analytical errors and error correlations, and

• 2. either takes into account the presence of some of the same data in two coupled XY isochrons or (equivalently) uses a single, three-dimensional XYZ isochron.

A method based on maximum-likelihood estimation is presented that fulfills these requirements, and the relevant equations for errors in age and initial 234U238U">²³⁴U²³⁸U are given. Equations for estimating the necessary isotope-ratio errors and error-correlations for both alpha-spectrometric and mass-spectrometric data are also developed.