Quantifying the Tetrad Effect, Shape Components, and Ce–Eu–Gd Anomalies in Rare Earth Element Patterns

Plots of chondrite-normalised rare earth element (REE) patterns often appear as smooth curves. These curves can be decomposed into orthogonal polynomial functions (shape components), each of which captures a feature of the total pattern. The coefficients of these components (known as the lambda coefficients— λ λ ) can be derived using least-squares fitting, allowing quantitative description of REE patterns and dimension reduction of parameters required for this. The tetrad effect is similarly quantified using least-squares fitting of shape components to data, resulting in the tetrad coefficients ( τ τ ). Our method allows fitting of all four tetrad coefficients together with tetrad-independent λ λ curvature. We describe the mathematical derivation of the method and two tools to apply the method: the online interactive application BLambdaR, and the Python package pyrolite. We show several case studies that explore aspects of the method, its treatment of redox-anomalous REE, and possible pitfalls and considerations in its use.