Carbonate ²⁰⁶Pb /²³⁸U problems and potential ²⁰⁷Pb /²³⁵U fixes

Carbonate U–Pb dating has become a key tool for Quaternary palaeoclimatology and palaeoanthropology beyond the age limit of Th–U disequilibrium dating. U–Pb geochronology is based on the paired radioactive decay of ²³⁸U to ²⁰⁶Pb and of ²³⁵U to ²⁰⁷Pb. Current carbonate U–Pb data processing algorithms rely mostly on the ²⁰⁶Pb /²³⁸U clock and attach little weight to the ²⁰⁷Pb /²³⁵U data. A key weakness of this approach is the need to correct the ²⁰⁶Pb /²³⁸U data for initial ²³⁴U /²³⁸U disequilibrium, which may cause an excess or (occasionally) a deficit in radiogenic ²⁰⁶Pb compared to secular equilibrium. Uncorrected initial disequilibrium may bias ²⁰⁶Pb /²³⁸U dates by up to 4 Myr. We introduce a new disequilibrium correction algorithm, using matrix exponentials. This algorithm can be used to undo the effects of U-series disequilibrium using either an assumed initial composition or a measured set of modern ²³⁴U /²³⁸U (and optionally ²³⁰Th/²³⁸U) activity ratios. Using a deterministic Bayesian inversion algorithm, we show that disequilibrium corrections work well for relatively young samples but become unreliable beyond 1.5 Ma and impossible beyond 2 Ma. Using theoretical models and real world examples from Siberia, South Africa, and Israel, we show that the uncertainty of the disequilibrium correction of such old samples exceeds the correction itself. Previous “Monte Carlo” error propagation methods underestimate these uncertainties by up to an order of magnitude. For carbonates older than 2 Ma that likely experienced significant initial ²³⁴U /²³⁸U disequilibrium, we recommend using the ²⁰⁷Pb /²³⁵U isochron method instead of ²⁰⁶Pb /²³⁸U geochronology. ²⁰⁷Pb /²³⁵U isochrons require only a small and simple correction for initial ²³¹Pa depletion. This makes ²⁰⁷Pb /²³⁵U dating more accurate than ²⁰⁶Pb /²³⁸U geochronology. However, the ²⁰⁷Pb /²³⁵U method is no panacea. Its precision is limited by the lower abundance of ²⁰⁷Pb compared to ²⁰⁶Pb. In some samples, this loss of precision results in a failure to outperform the Bayesian credible intervals of the disequilibrium-corrected ²⁰⁶Pb /²³⁸U dates. Such samples remain undatable, unless prior information is available to constrain the initial ²³⁴U /²³⁸U activity ratios.