tetradAnenburg {GCDkit}R Documentation

Shape components for REE patterns (Anenburg & Williams 2022)

Description

Fits orthogonal polynomial functions (shape components λ) to REE patterns normalized to average chondritic composition of O'Neill et al. (2016). The tetrad effect is quantified using the tetrad coefficients (τ).

Usage

tetradAnenburg(x,...)

Arguments

x

numeric; a matrix with REE data

...

further parameters of the function

Details

tetradAnenburg is merely a wrapper for the function lambda.tetrad.fit with arguments fitt1, fitt2, fitt3, fitt4 set to TRUE that does all the work.

Value

Returns a numeric vector with the following columns:

adj.r2

Adjusted r-squared.

red.chi.sq

Reduced χ^2. The magnitude of this parameter depends on the "uncert" setting. This parameter is occasionally referred to as MSWD (mean squared weighted deviation).

lambda0, lambda1, lambda2, lambda3, lambda4

Lambda shape coefficients (λ_0, λ_1, λ_2, λ_3, λ_4).

tau1, tau2, tau3, tau4

Tetrad coefficients (τ_1, τ_2, τ_3, τ_4).

lambda0.se, lambda1.se, lambda2.se, lambda3.se, lambda4.se

Standard errors for lambda coefficients.

tau1.se, tau2.se, tau3.se, tau4.se

Standard errors for tau coefficients.

lambda0.pval, lambda1.pval, lambda2.pval, lambda3.pval, lambda4.pval

p-values for lambda coefficients.

tau1.pval, tau2.pval, tau3.pval, tau4.pval

p-values for tau coefficients. Typically, all four tetrads should have the same sign (positive or negative), and about the same magnitude. Only occasionally, τ_1 is of a larger magnitude than τ_2 to τ_4.

La_MFR, Ce_MFR, Pr_MFR, Nd_MFR...

Measured-to-fit-ratios for all REE. This takes the ratio of individual normalised REE and compares them to hypothetical REE contents derived from the polynomial fit. These values should be as close to 1 as possible. If Ce or Eu are far from unity, it may indicate a Ce or Eu anomaly, and the cean or euan arguments should be set to TRUE to remove them from the fitting procedure, and improve the fit for all other elements. In this case, Ce_MFR and Eu_MFR are the anomaly magnitudes (often referred to as Ce/Ce* and Eu/Eu*). If any other elements are consistently far from 1, this could indicate (1) presence of tetrad effect, (2) noisy data, (3) oxide interferences of LREE on the HREE.

Unused values (e.g., when tetrads are not fitted) will return NA.

Plugin

tetrad.r

Note

When reporting results, also state which fitting settings were used as they will often change the coefficient values. Please cite Anenburg & Williams (2022) when using this in your work.

Author(s)

Michael Anenburg, Michael.Anenburg@anu.edu.au

wrapper function for GCDkit: Vojtěch Janoušek, vojtech.janousek@geology.cz

References

Anenburg M (2020) Rare earth mineral diversity controlled by REE pattern shapes. Min Mag 85:629-639 doi: 10.1180/mgm.2020.70

Anenburg M, Williams MJ (2022) Quantifying the tetrad effect, shape components, and Ce-Eu-Gd anomalies in Rare Earth Element patterns. Math Geosci 54:47-70 doi: 10.1007/s11004-021-09959-5

O'Neill HS (2016) The smoothness and shapes of chondrite-normalised rare earth element patterns in basalts. J Petrol 57:1463-1508. doi: 10.1093/petrology/egw047

See Also

lambdaTetradFit

REEpatternsExplorer

For online calculations and plotting, visit ALambdaR and BLambdaR...

spider

tetrad

Also see pyrolite package for Python with REE shape coefficients capabilities (λ and τ).

Examples

    sampleDataset("sazava")
    tetradAnenburg(WR[,REE], cean = FALSE, euan = TRUE) 

[Package GCDkit version 6.3.0 Index]