An algorithm for U-Pb geochronology by secondary ion mass spectrometry

Secondary ion mass spectrometry (SIMS) is a widely used technique for in situ U-Pb geochronology of accessory minerals. Existing algorithms for SIMS data reduction and error propagation make a number of simplifying assumptions that degrade the precision and accuracy of the resulting U-Pb dates. This paper uses an entirely new approach to SIMS data processing that introduces the following improvements over previous algorithms. First, it treats SIMS measurements as compositional data using log-ratio statistics. This means that, unlike existing algorithms, (a) its isotopic ratio estimates are guaranteed to be strictly positive numbers, (b) identical results are obtained regardless of whether data are processed as normal ratios (e.g. 206Pb / 238U) or reciprocal ratios (e.g. 238U / 206Pb), and (c) its uncertainty estimates account for the positive skewness of measured isotopic ratio distributions. Second, the new algorithm accounts for the Poisson noise that characterises secondary electron multiplier (SEM) detectors. By fitting the SEM signals using the method of maximum likelihood, it naturally handles low-intensity ion beams, in which zero-count signals are common. Third, the new algorithm casts the data reduction process in a matrix format and thereby captures all sources of systematic uncertainty. These include significant inter-spot error correlations that arise from the Pb / U-UO(2) / U calibration curve. The new algorithm has been implemented in a new software package called simplex. The simplex package was written in R and can be used either online, offline, or from the command line. The programme can handle SIMS data from both Cameca and SHRIMP instruments.