Calculations of and effects on quantitative limits for multivariate analyses of geological materials with laser-induced breakdown spectroscopy

Abstract

Quantitative analysis methods in all applications require robust measurements of quantification limits (LOQ); the threshold at which predicted values can be trusted. Although established LOQ protocols exist for univariate techniques, based on classical peak area measurements that vary directly with concentration of analytes, there is limited work on how best to quantify measurement limits when analyzed using more modern multivariate analysis (MVA) methods. This is especially the case for the technique of laser-induced breakdown spectroscopy (LIBS), which in the last decade has emerged as a promising technique for elemental analyses in many LIBS applications, wherein MVA modelling techniques outperform univariate methods.Accordingly, this study provides the final step in a protocol for generating robust quantification models for LIBS, with carefully determined accuracies for geological applications within. Its goal is to provide a template for calculating LOQ based on multivariate LIBS regression models, and to understand how this value is affected by several external factors: instrumentation (Mount Holyoke College ChemLIBS vs. Los Alamos National Laboratory ChemCam flight model), outlier removal method (highest natural concentration vs. statistically-based method), and acquisition atmosphere (Mars vs. air vs. vacuum), for two methods of calculating instrument sensitivity from experimental data (taken from metal spectra vs. noise-free regions of rock spectra).Partial-least squares regression models are made for almost every combination of the aforementioned parameters for the major oxides MnO, Na2O, SiO2 and minor and trace elements Li, Ni, Pb, Rb, Sr, and Zn. ChemLIBS models use 2607 geochemical standards, while ChemCam and ChemLIBS comparison models use 205 standards common to both instrument's datasets.Because LOQs determine the minimum predicted concentration to have confidence in, these values have a direct impact on model testing errors. The effect of LOQ on model validation is also summarized by comparing test accuracies before and after LOQ application. This step is essential to fully understand appropriate quantification of rock geochemistries with LIBS.Results show that LOQ is influenced by the variety within the composition of training standards and penalizes regression vectors that over- or under-fit the calibration data. These characteristics make LOQ an essential metric for better understanding model quality ‘behind the scenes’, in addition to common measures like test accuracy and R2 correlation. Applying LOQ to MVA models is therefore especially important when quantifying elements within such complex standards as rocks.