U-series dating of bone in an open system: The diffusion-adsorption-decay model

A new theory is described for the uptake of U in an open system applied to the dating of archaeological bones. Analytical solutions are obtained for the rate of radioactive decay of 238U, 234U and 230Th as a function of position for the case where both 238U and 234U diffuse across a bone, and where external supply of 234U is not in equilibrium with 238U. The new theory constitutes a forward model for predicting 238U, 234U and 230Th activity profiles across a bone given an age and diffusion coefficient. The forward model can be used in an inversion process whereby observations of activity profiles of 238U, 234U and 230Th as a function of position are used to infer the bone age of a sample together with robust measures of uncertainty. Differences from previous studies are that no closed system assumptions are required and no apparent age calculations necessary, while diffusion of 234U across the bone is accounted for in the inversion process. The procedure also does not require U-concentration profiles for the calculation of model parameters. The measurement of U-concentration profiles are, however, useful for the assessment of the reliability of the calculated results. Because of the assumption of constant 234U/238U ratios at the boundaries of the bone, DAD age results are generally older than closed system U-series results derived from the same isotopic data. Allowance is made for both correlated and uncorrelated errors in activity measurements as well as theoretical error caused by inhomogeneities in the sample. The implementation of the new approach (which we term the DAD model for Diffusion–Adsorption–Decay) is straightforward and efficient enough to allow estimation of age and its uncertainty on a desktop computer. Software for performing age estimation with the new model is available from the corresponding author.

► New mathematical solutions for coupled U-series diffusion/decay in open system applied to bones.
► New method to estimate burial age of bone from U-series activity profiles using this model.
► Comprehensive treatment of error propagation into burial age.
► Application to three bones using data from MC-ICPMS.
► Computer program available as open source.