Broken ²⁰⁶Pb/²³⁸U carbonate chronometers and ²⁰⁷Pb/²³⁵U fixes

Abstract. Carbonate U–Pb dating has become a key tool for Quaternary palaeoclimatology and palaeoanthropology beyond the ∼800 ka 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 deficit) in radiogenic ²⁰⁶Pb compared to secular equilibrium. 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. We advocate the use of the ²⁰⁷Pb/²³⁵U isochron method as a more accurate and precise alternative to ²⁰⁶Pb/²³⁸U geochronology for >2 Ma carbonates that are suspected to have experienced significant levels of initial ²³⁴U/²³⁸U disequilibrium.