lambda.tetrad.fit {GCDkit}R Documentation

Shape components for REE patterns (Anenburg & Williams 2022)

Description

Fits orthogonal polynomial functions (shape components λ) to REE patterns normalised to average chondritic composition of O'Neill et al. (2016). Optionally, the tetrad effect can be quantified using the tetrad coefficients (τ).

Usage

lambda.tetrad.fit(k, method = "REE.chondrite..O.Neill.2016", params = "standard", 
    norml = TRUE, uncert = 2, cean = FALSE, euan = TRUE, gdan = FALSE, 
    fitl4 = TRUE, fitt1 = FALSE, fitt2 = FALSE, fitt3 = FALSE, fitt4 = FALSE, plot = TRUE) 

Arguments

k

Numeric vector of 14 elements, from La to Lu. Missing values permitted, but must be included as either zeroes or NAs.

method

GCDkit search string for the chondrite REE composition; currently unused. The method is designed to work only with the O'Neill et al. (2016) CI values.

params

Set this to "legacy" only if full compatibility with O'Neill original spreadsheet supplementary to the 2016 is required (which should rarely if ever be the case). For all other cases, leave this as the default "standard".

norml

logical; Normalise the ppm values? Only use FALSE if the input is REE ratios such as from partitioning studies. Do not normalise manually to a scheme other than O'Neill et al. (2016). If data to plot are present as ppm, then use these and keep norml as the default TRUE.

uncert

numeric; Assumed uncertainty on REE data (%). This setting will not change any of the fitting parameters. Instead, it will affect the reduced χ^2 uncertainty estimate, useful for assessing uncertainties over a large database. See citations below for more details.

cean

logical; Is there a Ce anomaly present? If yes, excludes Ce from the fitting. FALSE by default. Could be set to TRUE just in case, but note that it might reduce the fit quality because Ce is close to the far end of patterns.

euan

logical; Is there a Eu anomaly present? If yes, excludes Eu from the fitting. TRUE by default. Being in the middle of the pattern, leaving it TRUE even when a Eu anomaly is not present will hardly affect the fit.

gdan

logical; Is there a Gd anomaly present? If yes, excludes Gd from the fitting. Note that Gd anomalies are redox insensitive and always emerge from anthropogenic contamination. If a Gd anomaly is observed in natural samples, it is likely to be a tetrad effect and not a Gd anomaly.

fitl4

logical; Should λ_4 be fitted? This should typically be left to the default TRUE, but can be set to FALSE for noisy data where λ_4 has a large magnitude, but with large errors (i.e., low significance).

fitt1, fitt2, fitt3, fitt4

logical; Should tetrads (τ_1 to τ_4) be fitted? Although they can be set separately, it is best to have all as either TRUE or FALSE. Should only be used if tetrads are known to exist or suspected, because their inclusion (TRUE) will break orthogonality of lambda coefficients. See citations below for more information.

plot

logical; should be the normalized REE pattern plotted?

Details

The shape components are characterised by shape coefficients (λ). They represent: the average pattern height, or overall REE concentrations (λ_0); the linear pattern slope (λ_1); quadratic curvature (λ_2); cubic curvature or sinusoidality (λ_3); and an optional higher-order "W"-shape (λ_4, typically turned on by default).

Optionally, the tetrad effect can be quantified using the tetrad coefficients (τ). This method is superior to other tetrad-fitting techniques in that it can accurately fit all four tetrads, regardless of overall pattern curvature (captured in lambda coefficients). It also works in cases when Ce and Eu anomalies are present.

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

tetrad2.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

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

REEpatternsExplorer

tetradAnenburg

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")
    lambda.tetrad.fit(WR["Po-1", REE], cean = FALSE, euan = TRUE)
    
    z <- c(84.6,32.1,11.6,51.7,10.9,2.99,16.1,2.6,18.2,4.4,
        14.8,2.18,14.5,2.27)
    names(z) <- REE
    
    # Assuming Eu anomaly only
    lambda.tetrad.fit(z, cean = FALSE, euan = TRUE, gdan = FALSE, 
        fitl4 = TRUE,fitt1 = FALSE, fitt2 = FALSE, fitt3 = FALSE, 
        fitt4 = FALSE) 
    
    # But the pattern features Ce anomaly and tetrad effect too
    lambda.tetrad.fit(z, cean = TRUE, euan = TRUE, gdan = FALSE, 
        fitl4 = TRUE, fitt1 = TRUE, fitt2 = TRUE, fitt3 = TRUE, 
        fitt4 = TRUE) 

[Package GCDkit version 6.3.0 Index]