lambda.tetrad.fit {GCDkit} | R Documentation |
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).
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)
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 " |
norml |
logical; Normalise the ppm values? Only use |
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. |
euan |
logical; Is there a Eu anomaly present? If yes, excludes Eu from the fitting. |
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 |
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 |
plot |
logical; should be the normalized REE pattern plotted? |
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.
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 " |
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 |
Unused values (e.g., when tetrads are not fitted) will return NA
.
tetrad2.r
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.
Michael Anenburg, Michael.Anenburg@anu.edu.au
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
For online calculations and plotting, visit ALambdaR and BLambdaR...
Also see pyrolite package for Python with REE shape coefficients capabilities (λ and τ).
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)