Evaluation of Matrix Effects in SIMS Using Gaussian Process Regression: The Case of Olivine Mg Isotope Microanalysis

Matrix effects by secondary ion mass spectrometry (SIMS) are empirically corrected by calibration using matrix-matched reference materials. However, conventional parametric regression cannot estimate the prediction uncertainty to account for the difference in compositions of new data and reference materials. Applying Gaussian process regression (GPR), a nonparametric probabilistic method, enables the correction for matrix effect while providing quantitative prediction uncertainty.

We developed GPR models for estimating instrumental mass fractionation (IMF). Magnesium isotope dataset of 17 olivine reference materials was used as training data, and the developed model was applied to another data set of extraterrestrial olivines.

The GPR model using FeO/MgO, CaO/MgO, Cr₂O₃/MgO, and MnO/MgO achieved the higher prediction accuracy of IMF (R² = 0.98) than a previous study. We found that minor elements in olivine, such as Ca, Cr, and Mn, independently affected the matrix effect. We also demonstrated the effectiveness of this method for extraterrestrial materials.

We concluded that GPR is a powerful approach for correcting the SIMS matrix effect, especially when minor elements impact the matrix effect. This approach can be applied to other trace element and isotope analyses of solid-solution minerals.