# detzrcr user guide

#### Magnus Kristoffersen

#### 2020-07-23

## Installing and running the package

The latest version of R must be installed and Rstudio is recommended. The released version of the package can be installed from CRAN

    install.packages("detzrcr")

or the development version can be installed from github (requires `devtools`)

    # install.packages("devtools")
    devtools::install_github(magnuskristoffersen/detzrcr)

Launch the user interface with

    library("detzrcr")
    run_detzrcr()

## Required input format

The data must be input in a csv-file which is uploaded to the `Data input` tab (Fig. 1) in the shiny interface.

Fig. 1: Data input tab

This file has certain requirements

- Each row contains one analysis
- Contains columns with headers sample and age
- Discordancy and uncertainty of the age data, if included, in columns with headers disc and uncert, respectively
- Discordancy is percentage discordance where 0 signifies concordance, a negative value normal and a positive value reverse discordance
- Uncertainty is the \(1\sigma\) absolute uncertainty of the age
- Hf data as measured \(^{176}\)Hf/\(^{177}\)Hf and measured \(^{176}\)Lu/\(^{177}\)Hf in columns hfhf and luhf, respectively or as initial \(\epsilon\)Hf in column ehf_i
- Data in Hf columns can be left empty
- It is recommended to include an identifier for the analysis, there is no required name for this column but it can be point, analysis etc.

Example input format
sample | point | disc | age | uncert | hfhf | luhf
--- | --- | --- | --- | --- | --- | ---
SA13_114 | SA13_114-06 | -42.6 | 282 | 5 | NA | NA
SA13_114 | SA13_114-65 | -20.1 | 2077 | 49 | NA | NA
SA13_114 | SA13_114-01 | -15.5 | 1620 | 16 | NA | NA
SA13_114 | SA13_114-28 | -13.1 | 548 | 9 | NA | NA
SA13_114 | SA13_114-60 | -12.1 | 824 | 8 | NA | NA

## Features

- Plot age data as KDEs and PDPs
- Plot age and Hf model age as ECDFs
  - Add confidence bands
- Plot age and Hf model age in upper quantile vs. lower quantile space
  - Add confidence limits
  - Add Gaussian mixture model
- Plot Hf data as initial \(\epsilon\)Hf vs. age or initial \(^{176}\)Hf/\(^{177}\)Hf vs. age
  - Add sample contours
- Export publication quality figures (as pdf)
- Calculate similarity measures
  - Satkoski likeness (Satkoski et al. 2013)
  - 1-O (Andersen et al. 2016a)
- Export similarity and Hf tables as csv files

## Usage

`detzrcr` has been designed to be easy to use with no prior knowledge of `R` required. We therefore chose to build the package as a `shiny` based user interface where the user can simply upload a data file and output publication quality figures (using `ggplot2`) and tables.

Data is uploaded in the `Data input` tab (Fig. ). From this tab a concordance filter can be applied to the data (defaults to \(\pm\) 10%). The different featuresof the R-package can then be used by selecting the appropriate panel tab in the user interface. By selecting the `Density distribution` tab the user can plot the U-Pb age data as KDEs (user selectable fixed bandwidth) or PDPs (local variable bandwidth based on the absolute \(1\sigma\) uncertainty). Which samples to plot and in what order can be selected from the `Select sample` menu (Fig. fig2). This feature is also available for all other plot and table options.

Fig. 2: Density distribution tab

ECDFs of U-Pb age data as well as Hf model age data can be plotted from the `ECDF` tab, 95% confidence bands calculated using the Dvoretzky-Kiefer-Wolfowitz (DKW) inequality (Dvoretzky et al. 1956) can be added. In the `UQ vs. LQ` tab U-Pb age data and Hf model age data is plotted in UQ vs. LQ space where (95% DWK) confidence limits and a gaussian mixture model can be added (Fig. 3).

Fig. 3: UQ vs. LQ with mixture model

Hf data can be plotted from the `Lu-Hf` tab as initial \(\epsilon\)Hf vs. age or initial \(^{176}\)Hf/\(^{177}\)Hf vs. age, where sample contours can be added. The implemented similarity measures are found in the `Likeness` and `1-O` tabs where the likeness (Satkoski et al. 2013) and 1-O (Andersen et al. 2016a) parameters are calculated and displayed. Likeness can be calculated in both 1 dimension (U-Pb age only) and 2 dimensions (U-Pb age and initial \(\epsilon\)Hf). 1-O can be calculated for U-Pb age and Hf model age. In each of these panels the two options can be combined into one table with U-Pb data in the upper triangle and Hf data in the lower triangle (Fig. 4). All tables can be saved to csv-files.

Fig. 4: 1-O table

The 1-O table can also be displayed graphically (Fig. 5) where red indicates \(1-O \geq 0.05\), white \(0 < 1-O < 0.05\) and green \(1-O = 0\).

Fig. 5: 1-O table as figure

Constants used in Hf calculations can be changed in the `Constants` tab. Default values are as follows

- \(\lambda ^{176}Lu = 1.867 \times 10^{-11} a^{-1}\) (Söderlund et al. 2004)
- CHUR values: \(^{176}\)Lu/\(^{177}\)Hf\(=0.0336\), \(^{176}\)Hf/\(^{177}\)Hf\(=0.282785\) (Bouvier et al. 2008)
- Depleted mantle values: \(^{176}\)Lu/\(^{177}\)Hf\(=0.0388\), \(^{176}\)Hf/\(^{177}\)Hf\(=0.28325\) (from Griffin et al. (2004) modified to the aformentioned decay constant and CHUR values)
- \(^{176}\)Lu/\(^{177}\)Hf value used in two step depleted model age \(=0.015\)

## Reimink intercepts

The method of Reimink et al. (2016) to find the most likely time of lead loss in suites of discordant detrital zircon is added to the package. To use this feature the input data must include \(^{207}Pb/^{235}U\), \(1\sigma\) absolute error of \(^{207}Pb/^{235}U\), \(^{206}Pb/^{238}U\), \(1\sigma\) absolute error of \(^{206}Pb/^{238}U\), and error correlation with the column names r75, sigma75, r68, sigma68 and rho, respectively.

### Data source

All data shown herein are taken form Andersen et al. (2016b).

### References

Andersen, T., Elburg, M., Cawthorn-Blazeby, A., 2016a. U–Pb and Lu–Hf zircon data in young sediments reflect sedimentary recycling in eastern South Africa. J. Geol. Soc. London. 173, 337–351. https://dx.doi.org/10.1144/jgs2015-006

Andersen, T., Kristoffersen, M., Elburg, M.A., 2016b. How far can we trust provenance and crustal evolution information from detrital zircons? A south African case study. Gondwana Research 34, 129–148. https://doi.org/10.1016/j.gr.2016.03.003

Bouvier, A., Vervoort, J.D., Patchett, P.J., 2008. The Lu-Hf and Sm-Nd isotopic composition of CHUR: Constraints from unequilibrated chondrites and implications for the bulk composition of terrestrial planets. Earth Planet. Sci. Lett. 273, 48–57. https://dx.doi.org/10.1016/j.epsl.2008.06.010

Dvoretzky, A., Kiefer, J., Wolfowitz, J., 1956. Asymptotic Minimax Character of the Sample Distribution Function and of the Classical Multinomial Estimator. Ann. Math. Stat. 27, 642–669. https://dx.doi.org/10.1214/aoms/1177728174

Griffin, W.L., Belousova, E.A., Shee, S.R., Pearson, N.J., O’Reilly, S.Y., 2004. Archean crustal evolution in the northern Yilgam Craton: U-Pb and Hf-isotope evidence from detrital zircons. Precambrian Res. 131, 231–282.

Reimink, J. R., Davies, J. H. F. L., Waldron, J. W. F., & Rojas, X. (2016). Dealing with discordance: a novel approach for analysing U-Pb detrital zircon datasets. Journal of the Geological Society, 2015-114. https://doi.org/10.1144/jgs2015-114

Satkoski, A.M., Wilkinson, B.H., Hietpas, J., Samson, S.D., 2013. Likeness among detrital zircon populations — An approach to the comparison of age frequency data in time and space. GSA Bull. 125, 1783–1799. https://dx.doi.org/10.1130/B30888.1

Söderlund, U., Patchett, P.J., Vervoort, J.D., Isachsen, C.E., 2004. The 176Lu decay constant determined by Lu-Hf and U-Pb isotope systematics of Precambrian mafic intrusions. Earth Planet. Sci. Lett. 219, 311–324. https://dx.doi.org/10.1016/S0012-821X(04)00012-3