A Bayesian approach to calibrating apatite fission track annealing models for laboratory and geological timescales

We present a new approach for modelling annealing of fission tracks in apatite, aiming to address various problems with existing models. We cast the model in a fully Bayesian context, which allows us explicitly to deal with data and parameter uncertainties and correlations, and also to deal with the predictive uncertainties. We focus on a well-known annealing algorithm [Laslett, G.M., Green, P.F., Duddy, I.R., Gleadow. A.J.W., 1987. Thermal annealing of fission tracks in apatite. 2. A quantitative-analysis. Chem. Geol., 65 (1), 1-13], and build a hierachical Bayesian model to incorporate both laboratory and geological timescale data as direct constraints. Relative to the original model calibration, we find a better (in terms of likelihood) model conditioned just on the reported laboratory data. We then include the uncertainty on the temperatures recorded during the laboratory annealing experiments. We again find a better model, but the predictive uncertainty when extrapolated to geological timescales is increased due to the uncertainty on the laboratory temperatures. Finally, we explictly include a data set [Vrolijk, P., Donelick, R.A., Quenq, J., Cloos. M., 1992. Testing models of fission track annealing in apatite in a simple thermal setting: site 800, leg 129. In: Larson, R., Lancelet, Y. (Eds.), Proceedings of the Ocean Drilling Program, Scientific Results, vol. 129, pp. 169-176] which provides low-temperature geological timescale constraints for the model calibration. When combined with the laboratory data, we find a model which satisfies both the low-temperature and high-temperature geological timescale benchmarks, although the fit to the original laboratory data is degraded. However, when extrapolated to geological timescales, this combined model significantly reduces the well-known rapid recent cooling artifact found in many published thermal models for geological samples.