Optimization of SIMS-based stable isotope measurements with regression diagnostics

Stable isotope measurements with secondary ion mass spectrometry (SIMS) have become an increasingly popular tool for Earth scientists to investigate natural phenomena such as biomineralization and sediment diagenesis, or to track the fate of labelled tracers in stable isotope probing experiments. The random nature of secondary ions emitted from a sample is described by Poisson statistics, which can be used to predict the precision of SIMS measurements under ideal circumstances (e.g., the predicted standard error can be deduced from the total counts of secondary ions). However, besides this fundamental source of imprecision, real SIMS measurements are additionally affected by other factors such as sample heterogeneity, instrument instability, the development and geometry of the sputter pit, and sample charging. Although some of these biases can be avoided by proper instrument tuning and sample documentation (e.g. T/SEM to characterise the textural properties of a rock sample) prior to SIMS measurement, factors such as instrument instability or sample heterogeneity can never be fully eliminated. Here we propose a data treatment procedure capable of identifying the underlying cause of the loss of precision due to instrument instability and sample heterogeneity. The reduced chi-squared statistic, which compares the predicted precision with the precision derived from descriptive statistics, is traditionally used to flag problematic measurements but without pinpointing the cause of precision-loss. We constructed a more sensitive method by the application of regression diagnostics, which calculates the influence of outliers on the regression model, and thus allows for augmentation of the raw count data. Simulations show that the recalculated descriptive and predictive statistics deviate from the original precision along trajectories specific to sample heterogeneity and instrument instability. Thus the proposed diagnostic procedure increases information yield of SIMS isotope measurements.