Abstract
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—lambda ) 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 (tau ). Our method allows fitting of all four tetrad coefficients together with tetrad-independent lambda 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.
Highlights
Rare earth element (REE) patterns are plots of measured REE abundances in a sample, in which the concentration of each element is divided by its corresponding concentration in a reference material, a process termed normalisation (Coryell et al 1963)
The magnitude of the tetrad effect can only be calculated if all four elements are measured and do not present anomalies. This eliminates tetrad 2, as it includes Pm, which does not occur naturally, and Eu, which is commonly anomalous because of its two oxidation states (Eu2+ and Eu3+). This can lead to elimination of tetrad 1, as Ce is occasionally anomalous because of its two oxidation states, Ce3+ and Ce4+, with the latter being common in low-temperature environments; this is especially problematic because the tetrad effect is most likely to occur in surface environments and highly evolved magmatic systems (Bau 1997) up to the low hundreds of degrees Celsius
5.3 λ4 and Ce Anomalies in the Troodos Ophiolite In our final case study, we examine REE patterns from oceanic plagiogranites collected from the Troodos ophiolite in Cyprus by Anenburg et al (2015)
Summary
Rare earth element (REE) patterns are plots of measured REE abundances in a sample, in which the concentration of each element is divided by its corresponding concentration in a reference material, a process termed normalisation (Coryell et al 1963). Additional measures, such as Dy/Dy* (the deviation of Dy from a straight line connecting La and Yb) that attempts to quantify pattern concavity, are only reliable for simple patterns (Davidson et al 2013). A quick glance at the pattern reveals it to be an artefact of its curvature, in which Dy is located precisely at the La–Yb interpolating line, by chance In cases of such complexity, descriptions of REE pattern are often supplemented by qualitative terms such as “sinusoidal”, “U-shaped”, or “spoon-shaped”. Using normalised element ratios to describe an overall sloping REE pattern which is simultaneously spoon-shaped and sinusoidal becomes a futile endeavour In such cases a simple visual inspection of the pattern is more informative, as “a picture is worth a thousand words”. We explicate the method of using λ shape components and coefficients to describe REE patterns, and expand it to include τ coefficients that describe the tetrad effect—subtle variation in REE behaviours that affects individual groups of four consecutive elements
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