CALCULATION OF (230)TH/U ISOCHRONS, AGES, AND ERRORS

If analytical errors are responsible for the scatter of points on a Th-230-U-234-U-238 isochron diagram, the isochron should be fitted by a technique that (1) 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 U-234/U-238 are given. Equations for estimating the necessary isotope-ratio errors and error-correlations for both alpha-spectrometric and mass-spectrometric data are also developed.