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

Abstract. 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.