Statistics for LA-ICP-MS based fission track dating

Abstract

Despite the conceptual elegance and simplicity of the External Detector Method (EDM) for fission track dating, an increasing number of laboratories are switching to LA-ICP-MS as a means of measuring the uranium content of apatite, zircon and sphene. LA-ICP-MS based fission track (LAFT) dating offers shorter turnaround times, removes the need to handle radioactive materials and hydrofluoric acid, and facilitates double-dating with the U-Pb method. This paper aims to bring the statistical treatment of LAFT data on an equal footing with the EDM by formulating four different analytical protocols, depending on the accuracy and reproducibility of the uranium measurements. Under the ‘absolute’ dating approach, the spontaneous track densities and uranium concentrations are directly plugged into the fundamental fission track age equation, assuming that both of these measured quantities have been determined accurately, and that the fission decay constant and equivalent isotopic track length are known. The ‘zeta calibration’ approach avoids making these assumptions by normalisation to a reference material of known age. Uranium zoning has a detrimental effect on the accuracy of LAFT ages. This effect can be removed by counting only those fission tracks located within the laser ablation pit. Alternatively, the uranium heterogeneity may be quantified by fitting multiple ablation spots in some or all the analysed grains, using a (lognormal) distributional assumption for the uranium concentration. LAFT dating is arguably less well suited than the EDM to young and U-poor samples that lack sufficient spontaneous fission tracks to reveal visual evidence for uranium zoning. Such samples occasionally contain no fission tracks at all, resulting in infinite analytical uncertainties. This paper introduces a pragmatic solution to this problem, in which the uranium measurement are converted to ‘virtual’ induced fission track counts to produce strictly positive ages with finite standard errors. With the age equation and zero-track strategy in place, LAFT ages can be subjected to more sophisticated statistical analysis. Using a logarithmic transformation, these ages can be visualised on radial plots and deconvolved into finite and continuous mixtures. The methods introduced in this paper have been implemented in a software package called IsoplotR that is available free of charge at http://isoplotr.london-geochron.com.