iDaD

Summary

The iDAD software is based on a new mathematical theory 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.

Marginal probability density functions for bone age with no noise added to synthetic ²³⁴U/²³⁸U, ²³⁰Th/²³⁸U activity ratios. The green bar indicates the true bone age of 70 ka, the dashed line the best ﬁt solution found from minimizing the least squares misﬁt term φ(κ, t) in (32). The two red bars are the 95% credible intervals about the best ﬁt solution. The PDFs are scaled to the same maximum height and have the same age scale. The tighter constraint in the noiseless case is apparent with a perfect recovery and a smaller spread to the PDF.

Download

The GUI software is a java front end to a piece of Fortran source code that has been compiled to run on several platforms, including Windows XP and Windows 7, Mac OSX, and Linux Ubuntu. These files are very large (up to 300 MB). A stand alone version of the fortran source code is also provided. Both the compiled and fortran versions are available from the download page along with installation instructions. You will need to register with iEarth prior to download. Enquires should be directed to the author.

References

Sambridge, M., Grün, R., and Eggins, S., 2012. U-series dating of bone in an open system: The diffusion-adsorption-decay model, Quaternary Geochronology, 9, 42-53, doi:10.1016/j.quageo.2012.02.010.