Tolosana-Delgado R., van den Boogaart K.G., Fišerová E., Hron K., Dunkl I. (2016) Joint Compositional Calibration: An Example for U–Pb Geochronology. In: Martín-Fernández J., Thió-Henestrosa S. (eds) Compositional Data Analysis. CoDaWork 2015. Springer Proceedings in Mathematics & Statistics, vol 187. Springer, Cham
This contribution explores several issues arising in the measurement of a (geo)chemical composition with Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS), specially in the case that the quantities of interest are linear functions of (log)-ratios. These quantities are scale invariant, but in general cannot be estimated without taking into account possible additive noise effects of the instrumentation, incompatible with a purely compositional approach. The proposed ways to a solution heavily build upon the multi-Poisson distribution, highlighting the counting nature of the readings delivered by these instruments. The model can be fitted using a generalized linear model formalism, and it allows for a joint calibration of all components at once. Relevance of these considerations is shown with some simulation studies and in a real case of multi-isotopic geochronological analyses. Results suggest that the most critical aspect of this analytical technique is the assumption that the amount of ablated mass per second between samples of unknown and known compositions is similar (matrix matching): if this cannot be ensured, absolute estimations of the abundance of each of these isotopes fails, while their (log)ratios are perfectly estimable. This opens the door to using the model for a joint calibration by loosening the condition of matrix matching and using several standards of different composition.
Poisson regressionGLMCount compositionMulti-element calibrationConcordia plot apologies for the delay