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Isoplotr: a Free and Open Toolbox for Geochronology

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Isoplotr: a Free and Open Toolbox for Geochronology Geoscience Frontiers 9 (2018) 1479e1493 HOSTED BY Contents lists available at ScienceDirect China University of Geosciences (Beijing) Geoscience Frontiers journal homepage: www.elsevier.com/locate/gsf Research Paper IsoplotR: A free and open toolbox for geochronology Pieter Vermeesch Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT, UK article info abstract Article history: This paper reviews the basic principles of radiometric geochronology as implemented in a new software Received 14 November 2017 package called IsoplotR, which was designed to be free, flexible and future-proof. IsoplotR is free Received in revised form because it is written in non-proprietary languages (R, Javascript and HTML) and is released under the 27 March 2018 GPL license. The program is flexible because its graphical user interface (GUI) is separated from the Accepted 2 April 2018 command line functionality, and because its code is completely open for inspection and modification. To Available online 11 April 2018 Handling Editor: M. Santosh increase future-proofness, the software is built on free and platform-independent foundations that adhere to international standards, have existed for several decades, and continue to grow in popularity. IsoplotR 40 39 Keywords: currently includes functions for U-Pb, Pb-Pb, Ar/ Ar, Rb-Sr, Sm-Nd, Lu-Hf, Re-Os, U-Th-He, fi Geochronology ssion track and U-series disequilibrium dating. It implements isochron regression in two and three Software dimensions, visualises multi-aliquot datasets as cumulative age distributions, kernel density estimates Statistics and radial plots, and calculates weighted mean ages using a modified Chauvenet outlier detection cri- terion that accounts for the analytical uncertainties in heteroscedastic datasets. Overdispersion of geochronological data with respect to these analytical uncertainties can be attributed to either a pro- portional underestimation of the analytical uncertainties, or to an additive geological scatter term. IsoplotR keeps track of error correlations of the isotopic ratio measurements within aliquots of the same samples. It uses a statistical framework that will allow it to handle error correlations between aliquots in the future. Other ongoing developments include the implementation of alternative user in- terfaces and the integration of IsoplotR with other data reduction software. Ó 2018, China University of Geosciences (Beijing) and Peking University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/). 1. Introduction a Microsoft Excel add-in called Isoplot has served this pur- pose extremely well. Geology is, in essence, a historical science in which timing is of Developed by Kenneth R. Ludwig over a period of two decades, the utmost importance. Geochronology underpins the study of Isoplot is a user-friendly toolbox that allows geologists to Earth history and puts fundamental constraints on the rate of calculate and visualise geochronological data within a familiar biological evolution (Chen and Benton, 2012; Gradstein et al., 2012). spreadsheet environment (Ludwig, 1988, 1999, 2003a, 2012). Few Technological advances in mass spectrometry, such as the wide- computer programs have been as widely used in the Earth Sciences spread availability of multi-collector instruments, are ever as Isoplot. Written in Visual Basic for Applications (VBA), Iso- increasing the precision of the isotopic data that form the basis of plot takes isotopic data as input and produces publication-ready the chronostratigraphic timescale. A plethora of mathematical- figures as output. Unfortunately, recent versions of Excel are statistical techniques are available to extract chronological con- incompatible with Isoplot, whose creator has retired and no straints from these isotopic measurements. Examples of this longer maintains the code. These software issues are a major include isochrons, concordia diagrams, age spectra and frequency problem for the field of radiometric geochronology, to the point distributions. Implementing these methods in a rigorous and self- where some laboratories keep an old Windows XP computer with consistent manner requires appropriate software. For many years, Excel 2003 around for the sole purpose of running Isoplot. This paper introduces a new computer code called IsoplotR as a free, open and more future-proof alternative for Isoplot. The principal aim of this paper is to provide a general overview of the E-mail address: [email protected]. design philosophy and basic operating principles behind the soft- Peer-review under responsibility of China University of Geosciences (Beijing). ware, rather than a detailed manual of all its components. Section 2 https://doi.org/10.1016/j.gsf.2018.04.001 1674-9871/Ó 2018, China University of Geosciences (Beijing) and Peking University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC- ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 1480 P. Vermeesch / Geoscience Frontiers 9 (2018) 1479e1493 discusses the software architecture, which uses a modular design The code base for the GUI and the core data processing algo- with future-proofness and extendability in mind. Section 3 pre- rithms are surgically separated. The command-line functionality is sents three fundamental types of input format that are used by grouped in a lightweight package called IsoplotR that may be IsoplotR to capture the covariance structure of isotopic ratio data. installed from the ‘Comprehensive R Archive Network’ (CRAN) by We will see that this covariance structure plays a fundamental role typing install.packages(‘IsoplotR’) at the command in all of IsoplotR’s methods. prompt. Once installed, the package can be loaded into memory by Section 4 reviews the important subject of linear regression, typing library(IsoplotR). The IsoplotR package has minimal which underpins the construction of isochrons. IsoplotR dependencies and should work on a basic R installation. In contrast, currently implements three different types of (error weighted) the GUI is written in HTML and Javascript and interacts with linear regression algorithms that account for error correlations be- IsoplotR via an interface package (Chang et al., 2017). It is pro- tween variables and between aliquots in two or three dimensions. vided in a second R package called IsoplotRgui that is available Section 5 explains how these three methods represent different from GitHub (see the IsoplotR website for details). Iso- approaches of dealing with overdispersion. Section 6 introduces a plotRgui is separate from but depends on IsoplotR. weighted mean plot to visualise multiple age estimates and pro- The clean separation between the two programs allows Iso- poses a heuristic method to detect outliers. Section 7 presents three plotR to remain light and easy to install. This is important for any approaches to construct uncertainty bounds for isochron ages, future R packages that may wish to incorporate IsoplotR func- weighted means and so forth. It introduces a profile log-likelihood tions. A second reason for keeping the code base of the GUI and method for the calculation of asymmetric confidence intervals. command line functionality separated is that other user interfaces Section 8 discusses three further methods to visualise multi- are planned, for example within Excel (Section 17). Incorporating aliquot collections of ages. Cumulative age distributions (CADs) all these additional functions into a single package would add un- and kernel density estimates (KDEs) show the frequency distribu- necessary bulk and redundancy. IsoplotR and IsoplotRgui are tion of the age measurements but do not explicitly take into ac- free and open software. The computer code for both programs is count the analytical uncertainties. The radial plot is introduced as a made available under the GPL license, which permits re-use and more appropriate data visualisation tool for ‘heteroscedastic’ data modification provided that any derived code is released under the (i.e. data with unequal measurements uncertainties). The radial same conditions (Free Software Foundation, 2007). plot provides a good vehicle to assess the dispersion of multi- aliquot datasets. Overdispersed datasets require further process- 3. Input formats ing using continuous or discrete mixture models that are discussed in Section 9. In an abstract sense, IsoplotR is a set of functions F that take Sections 10e15 provide specific details about the Rb-Sr, Sm-Nd, some isotopic data A as input and generate some numerical and/or Lu-Hf, Re-Os, 40Ar/39Ar, U-Pb, Pb-Pb, U-Th-He, fission track and U- graphical output B: series dating methods. Section 16 introduces a selection of statis- tical methods to help interpret collections of multiple geochrono- B ¼ FðAÞ (1) logical datasets that are useful in detrital geochronology. Finally, 40 36 39 36 Section 17 sets out a roadmap for future developments to improve For example, A could be some Ar/ Ar- and Ar/ Ar-mea- 40 39 the accuracy and precision of geochronological data, and to provide surements and B could be the Ar/ Ar-age. Or A could be some 87 86 87 86 closer integration of IsoplotR with earlier steps of the data pro- Sr/ Sr- and Rb/ Sr-measurements and B a vector with the cessing chain. slope and intercept of an isochron fit to these data. A may also include decay constants, stable isotope ratios and other parameters that are associated with analytical uncertainty. 2. Software architecture Regardless of the application, the error propagation of B is as important as estimation of B itself (Ludwig, 2003a). Without There are three ways to use IsoplotR: online, offline and from analytical uncertainties, it is impossible to ascertain whether the the command line. difference between two geochronological dates is real, or simply an The online version can be accessed at http://isoplotr.london- artifact of analytical imprecision. IsoplotR propagates the geochron.com (see Supplementary Information), and is conve- analytical uncertainty of B using one of two methods. If F is a nient in several ways. First, it requires no software installation.
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