Prediction of Geochemical Composition from XRF Core Scanner Data: A New Multivariate Approach Including Automatic Selection of Calibration Samples and Quantification of Uncertainties

Abstract

A multivariate log-ratio calibration (MLC) model for XRF-core-scanning devices is presented, based on a combination of basic XRF-spectrometry theory and principles of compositional data analysis. The performance of the MLC model is evaluated in comparison with other empirical calibration procedures for XRF core scanner data using two data sets acquired with two different XRF core scanners. The quality of calibration models is assessed by calculating the uncertainties associated with predicted concentrations using cross-validation techniques. Results show that (1) the commonly used direct linear calibration (DLC) methods, which are based on the questionable assumption of a unique linear relation between intensities and concentrations and do not acknowledge the compositional nature of the calibration problem, give poor results; (2) the univariate log-ratio calibration (ULC) model, which is consistent with the compositional nature of the calibration problem but does not fully incorporate absorption and enhancement effects on intensities, and permits estimation of "relative" concentrations only, is markedly better, and (3) the MLC algorithm introduced in this contribution, which incorporates measurement uncertainties, accommodates absorption and enhancement effects on intensities, and exploits the covariance between and among intensities and concentrations, is the best by far. The predictive power of the MLC model may be further increased by employing automatic sample selection based on the multivariate geometry of intensity measurements in log-ratio space. The precision attained by MLC in conjunction with automatic sample selection is comparable to that attained by conventional XRF analysis of heterogenous materials under laboratory conditions. A solution to the long-standing problem of XRF core scanner calibration implies that high-resolution records of sediment composition with associated uncertainties can now be routinely established, which should increase the range of quantitative applications of XRF-core-scanning devices and strengthen inferences based on analysis of geochemical proxies.

Holocene paleohydrological reconstruction of Lake Strzeszyńskie (western Poland) and its implications for the central European climatic transition zone

“…The obtained element intensities are non-linear functions of element concentrations predominantly due to matrix absorption and enhancement effects (Weltje and Tjallingii 2008). Therefore high-resolution XRF scanning records are presented as log-ratios of element intensities as these are a linear functions of log-ratios of concentrations and allow the application of meaningful multivariate statics (Weltje et al 2015). Compositional changes are explored using biplots of the log-transformed XRF data that visualize the loadings (variables) and scores (data points) of the principal component analyses (PCA).…”

“…The vector length of the variables indicates the strength of the variables but is also sensitive to elements with low count rates and high noise levels. To avoid misinterpretations introduced by analytical noise, the vector lengths were scaled by the precision of the elements using the replicate measurements (Weltje et al 2015).…”

Compositional data analysis of Holocene sediments from the West Bengal Sundarbans, India: Geochemical proxies for grain-size variability in a delta environment

“…As a result, calibration requires an alternative approach 162 within the scope of CoDa in the form of the Log-Ratio Calibration Equation (LRCE): a 163 univariate log-ratio calibration (ULC) approach that combines conventional calibration 164 approaches in ratio form (Weltje et al, 2015). 165…”

“…It is only through CoDa however that such a 683 trend can be illustrated in the first place as ratios by themselves possess the undesirable 684 property of asymmetry, meaning that conclusions based on evaluation of the ratio of twoM A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT (Weltje, 2012;Weltje et al, 2015). Taking this approach further, the Rb and K log-687 transformed data shown in Fig.…”

“…The key advantages of XRFM A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT element intensities are obtained directly at the surface of a split sediment core (allowing 139 for the extraction of near-continuous records of element intensities), and the spatial 140 resolution of ED-XRF core-scanning is much higher than conventional discrete sampling 141 destructive methods (Weltje and Tjallingii, 2008). However, one of the main drawbacks 142 of the approach has been the conversion of element intensities measured by ED-XRF 143 core-scanners to element concentrations (Weltje and Tjallingii, 2008 specimen homogeneity is very poorly constrained due to the inhomogeneity of samples 149 and the irregular surface of a split-core (Weltje and Tjallingii, 2008;Weltje et al, 2015). 150…”