Compositional Calibration

An emerging field in the statistics of (geo)chemical data is compositional data analysis. In this field the ratio of concentrations between elements is seen as the essential information, while the absolute concentration is considered irrelevant. E.g. for physical age determination the ratio of concentration of various nuclides is very important, while the absolute concentrations change subject to dilution and depletion processes. In many applications chemical data is rescaled to 100%, or transformed with a log ratio transformation. In both cases the information about the absolute concentration is lost.

The aim of the contribution is to initiate a discussion on how the compositional approach might modify the tasks and methods of metrology. Asking a sligthly different question might lead to different answers. We will consider the calibration of an LA-ICP-MS (laser ablation inductive coupled plasma mass spectrometer), which measures multiple, but not all elements (quasi) simultaneously.

If log ratios are considered the relevant quantity, we should be able to measure them unbiasedly and provide a precision assessment of their measurement. We show that both aspects are problematic, when the log ratio is applied to measurements independently calibrated with respect to absolute standards. The same individual absolute errors can correspond to very different relative errors due to inherent correlation between the counts.

A supplementary concept for a traceable calibration of relative concentrations is introduced and discussed. In the example we use a method based on multivariate Poisson regression for a compositional calibration of LA-ICP-MS measurements. A compositionally calibrated measurement does not carry absolute information, but only relative information about a subset of elements. The concept of a compositional error compatible with the variance concepts in compositional data analysis is introduced. This error can not be computed from classical absolute calibration information of single elements and provides essential information for compositional methods.

In the case of the LA-ICP-MS the absolute amount of material turned into plasma is strongly matrix dependent, while the counting ratios for different elements are much less so. In such cases a relative calibration can guarantee better compositional precision and allows the useage of much loosely matrix-matched standards in a well-defined range of matrix compositions.