Compositional Data Analysis in Geochemical Systems

Compositional data analysis (CoDA) provides a coherent framework for treating geochemical measurements that represent parts of a whole, such as oxide or elemental abundances in rocks, soils or waters. Traditional statistical methods can mislead when applied directly to proportions or concentrations that sum to a constant, since increases in one component necessarily imply decreases in others. CoDA overcomes this by transforming compositions into logratio coordinates, enabling valid application of multivariate methods while preserving essential properties such as scale invariance and subcompositional coherence. In geochemistry, CoDA facilitates robust classification of lithologies, detection of geochemical anomalies, spatial prediction of element distributions and the quantification of mixing processes. Recent advances integrate CoDA with geostatistical simulation and machine learning to create predictive maps of earth materials, to quantify uncertainty in spatial models and to unravel thermodynamic and kinetic controls on element distributions. By treating relative information explicitly, CoDA enhances global efforts in mineral exploration, environmental monitoring and water-quality assessment, supporting decisions from resource management to pollution control.

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Compositional Data Analysis in Geochemical Systems publication trend

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Technical terms

Composition: A vector of non-negative parts representing proportions or concentrations that sum to a constant total.

Simplex: The sample space of all possible compositions, characterised by its own Aitchison geometry rather than Euclidean space.

Logratio transformation: A family of functions (including centred, additive and isometric logratios) that map compositions into real coordinate space by taking logarithms of ratios among parts.

Isometric logratio (ilr) coordinates: Orthonormal logratio coordinates derived from sequential binary partitions, preserving distances and enabling standard statistical analyses.

References

1. Type of probability distribution reflects how close mixing dynamics in river chemistry are to thermodynamic equilibrium. The Science of The Total Environment (2024).
2. Surficial and Deep Earth Material Prediction from Geochemical Compositions. Natural Resources Research (2018).
3. Classical and Robust Regression Analysis with Compositional Data. Mathematical Geosciences (2020).
4. The Mathematics of Compositional Analysis. Austrian Journal of Statistics (2016).