Algorithms for estimating uncertainties in initial radiogenic isotope ratios and model ages

Initial radiogenic daughter-product isotope ratios such as 143Nd/144Nd, 176Hf/177Hf, 87Sr/86Sr, and 187Os/188Os, their geochemical reservoir normalized equivalents (ε and γ values), and model ages are frequently used for geochemical inference. These calculated quantities are a function of not only the present day parent–daughter ratios and radiogenic isotope ratios, but also the compositions of the geochemical reservoirs, decay rates, and independent geochronological constraints. Here, equations to determine the combined standard uncertainties in these calculated quantities that include uncertainties in all input quantities, are derived. The values and uncertainties of these model values are reviewed, and it is found that in many cases the uncertainties associated with input quantities such as decay rates and reservoir compositions are similar to, or exceed analytical uncertainties. Fortunately, most of these uncertainties are highly correlated between samples (i.e., are systematic) and can often be neglected when the objective is to determine the difference between isotope ratios (or other associated quantities). A program designed to easily implement these equations is appended.