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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Recent work has linked the statistical form of compositional distributions in river chemistry to underlying thermodynamic disequilibrium. Analyses of dissolved ions in a major catchment demonstrated that lognormal distributions typify near-equilibrium solutes such as calcium and bicarbonate, whereas power-law distributions emerge for species far from saturation, providing a novel diagnostic of mixing dynamics and dissipation in fluvial systems.

In spatial mapping of regolith and deep earth materials, compositional geostatistics combined with machine-learning algorithms has proven effective for classification of surficial deposits and crustal blocks. By applying isometric logratio transformations prior to random-forest modelling and geostatistical simulation, researchers have generated probability maps of geological classes, thereby improving the discovery of superficial peat deposits and major crustal provinces.

Advances in regression modelling have introduced classical and robust frameworks that respect the simplex geometry of compositional covariates and responses. Balance-coordinate representations allow the interpretation of regression coefficients in terms of geochemical contrasts, enable hypothesis testing for subcompositional independence and improve resilience to outliers in mapping datasets from regional geochemical surveys.

Compositional Data Analysis in Geochemical Systems publication trend

The graph below shows the total number of articles in compositional data analysis in geochemical systems across all publications each year (not limited to Nature Index journals).

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).