Chapter

Compositional Data Analysis

Volume 187 of the series Springer Proceedings in Mathematics & Statistics pp 181-209

Date:

Joint Compositional Calibration: An Example for U–Pb Geochronology

  • R. Tolosana-DelgadoAffiliated withHelmholtz Zentrum Dresden-Rossendorf, Helmholtz Institute Freiberg for Resource Technology Email author 
  • , K. G. van den BoogaartAffiliated withHelmholtz Zentrum Dresden-Rossendorf, Helmholtz Institute Freiberg for Resource Technology
  • , E. FišerováAffiliated withDepartment of Mathematical Analysis and Applications of Mathematics, Palacky University
  • , K. HronAffiliated withDepartment of Mathematical Analysis and Applications of Mathematics, Palacky University
  • , I. DunklAffiliated withDepartment of Sedimentology and Environmental Geology, Georg August University

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Abstract

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.

Keywords

Poisson regression GLM Count composition Multi-element calibration Concordia plot apologies for the delay