Direct U–Pb dating of carbonates from micron-scale femtosecond laser ablation inductively coupled plasma mass spectrometry images using robust regression

Uranium–lead (U–Pb) dating of carbonates by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) spot analysis is an increasingly used method in the field of geosciences, as it brings very strong constraints over the geological history of basins, faults or reservoirs. Most ages currently published are based on the measurement of U and Pb ratios on spot ablations, using nanosecond lasers coupled to sector field or multi-collector ICP-MS. Here, we test a new strategy for the U–Pb dating of carbonates from 2D isotopic ratio maps, based on the use of a robust regression approach in the data reduction workflow. The isotopic maps, with a minimum area of 0.65 mm2 (∼ 1000 pixels of 13×25 µm resolution), are obtained using a 257 nm femtosecond laser ablation system at a high repetition rate (500 Hz) coupled to a high-resolution ICP-MS. The maps commonly show significant variations in isotope ratios at the pixel scale, allowing the plotting of pixel U–Pb ratios in concordia or isochron diagrams and the calculation of U–Pb ages. Due to the absence of individual ratio uncertainties, the ages are calculated using MM-robust linear regression rather than the more commonly used York-type regression. The goodness of fit to the data is assessed by the calculation of the residual standard error (RSE) of the regression and by the calculation of a mean square of weight deviates (MSWD) on discretised data. Several examples are provided that compare the ages calculated by robust regression with those obtained by other techniques (e.g. isotope dilution, LA-ICP-MS spot analyses and the pixel-pooling approach). For most samples, characterised by high U concentrations (> 1 ppm), robust regression allows for the calculation of ages and uncertainties similar to those obtained with the other approaches. However, for samples with lower U concentrations (< 0.5 ppm), the ages obtained are up to 10 % too young due to pixels with high U ∕ Pb acting as leverage points for the regression. We conclude that the U–Pb ages calculated by the regression method tested here, although statistically robust, should be critically analysed before validation, especially for samples with low U concentrations.