
@article{Aitchison1984,
  title = {The Statistical Analysis of Geochemical Compositions},
  author = {Aitchison, John},
  year = {1984},
  volume = {16},
  pages = {531--564},
  doi = {10.1007/BF01029316},
  journal = {Journal of the International Association for Mathematical Geology},
  keywords = {compositional data},
  number = {6}
}

@article{Blundy2003,
  ids = {Blundy2003a},
  title = {Partitioning of Trace Elements between Crystals and Melts},
  author = {Blundy, Jon and Wood, Bernard},
  year = {2003},
  month = may,
  volume = {210},
  pages = {383--397},
  issn = {0012-821X},
  doi = {10.1016/S0012-821X(03)00129-8},
  abstract = {Advances in analytical geochemistry have made it possible to determine precisely the concentration of many trace elements and their isotopes in rocks. These data provide the cornerstone for geochemical models of the Earth and terrestrial planets. However, our understanding of how trace elements behave has not kept pace with the analytical advances. As a result, geochemists are often hampered in their interpretation of geochemical data by an incomplete knowledge of trace element partitioning under the conditions of interest. Through advances in trace element microbeam analysis it is now possible to determine partition coefficients experimentally under important conditions, such as during melting of the crust and mantle. This large body of experimental data can be used to investigate the fundamental controls on element partitioning. Simple continuum theories of elastic strain and point charges in crystal lattices, that account, respectively, for mismatch in ionic radius and ionic charge between the substituent trace ion and the lattice site on which it is accommodated, provide a very useful theoretical framework. This approach can be used as the basis for quantitative models of trace element partitioning, in terms of pressure, temperature, redox state and composition, and as a means of predicting partition coefficients for elements not routinely analysed. Experimental studies of partitioning are supported by atomistic computer simulations at zero K. Developments in computational techniques that enable direct simulation of high temperature and pressure mineral-melt partitioning will revolutionise the field in the near future. Use of novel, spectroscopic techniques to probe the structural environment of trace elements in crystals and glasses will provide valuable new data for computational and theoretical models. Extension of high temperature partitioning theory to ambient conditions is an essential step in understanding current climate change proxies, and tackling a host of environmental problems.},
  journal = {Earth and Planetary Science Letters},
  keywords = {ionic radius,lattice strain,rare earth elements,trace elements},
  number = {3}
}

@book{Deer2013,
  title = {An Introduction to the Rock-Forming Minerals},
  author = {Deer, W.A. and Howie, R.A. and Zussman, J.},
  year = {2013},
  edition = {3},
  publisher = {{Mineralogical Society of Great Britain and Ireland}},
  address = {{Twickenham, UK}},
  isbn = {978-0-903056-27-4}
}

@incollection{Hofmann2014,
  title = {3.3 - {{Sampling Mantle Heterogeneity}} through {{Oceanic Basalts}}: {{Isotopes}} and {{Trace Elements}}},
  shorttitle = {3.3 - {{Sampling Mantle Heterogeneity}} through {{Oceanic Basalts}}},
  booktitle = {Treatise on {{Geochemistry}} ({{Second Edition}})},
  author = {Hofmann, A. W.},
  editor = {Holland, Heinrich D. and Turekian, Karl K.},
  year = {2014},
  month = jan,
  pages = {67--101},
  publisher = {{Elsevier}},
  address = {{Oxford}},
  doi = {10.1016/B978-0-08-095975-7.00203-5},
  abstract = {This chapter is in part an update of a previous, more abbreviated review (Hofmann, 1997). It covers the subject in greater depth, and it reflects some significant changes in the author's views since the writing of the earlier paper. In particular, the spatial range of equilibrium attained during partial melting may be much smaller than previously thought, because of new experimental diffusion data and new results from natural settings. Also, the question of `layered' versus `whole-mantle' convection, including the depth of subduction and of the origin of plumes, has to be reassessed in light of the recent breakthroughs achieved by seismic mantle tomography. As the spatial resolution of seismic tomography and the pressure range, accuracy, and precision of experimental data on melting relations, phase transformations, and kinetics continue to improve, the interaction between these disciplines and geochemistry sensu stricto will continue to improve our understanding of what is actually going on in the mantle. The established views of the mantle being engaged in simple two- or single-layer convection are becoming obsolete. In many ways, we are just at the beginning of this new phase of mantle geology, geophysics, and geochemistry.},
  isbn = {978-0-08-098300-4},
  keywords = {Basalts’ lead paradox,Crust-Mantle differentiation,Local equilibrium,Major elements,Mantle geochemistry,Regional equilibrium,Trace elements}
}

@article{Hunter2007,
  title = {Matplotlib: {{A 2D Graphics Environment}}},
  shorttitle = {Matplotlib},
  author = {Hunter, John D.},
  year = {2007},
  volume = {9},
  pages = {90--95},
  issn = {1521-9615},
  doi = {10.1109/MCSE.2007.55},
  journal = {Computing in Science \& Engineering},
  number = {3}
}

@article{LeBas1992,
  title = {The Construction of the {{Total Alkali}}-{{Silica}} Chemical Classification of Volcanic Rocks},
  author = {Le Bas, M. J. and Le Maitre, R. W. and Woolley, A. R.},
  year = {1992},
  month = mar,
  volume = {46},
  pages = {1--22},
  issn = {0930-0708, 1438-1168},
  doi = {10.1007/BF01160698},
  abstract = {SummaryThis paper describes the reasoning that lies behind the construction of the field boundaries in the Total Alkali-Silica diagram (TAS) for the chemical classification of volcanic rocks. It shows that by utilizing nomenclature in common use by petrologists in combination with a large computer database of geochemical analytical information derived from the published literature, it was possible to construct a Total Alkali-Silica diagram for volcanic rocks of only 15 fields, which has straight-line boundaries and necessitates the definition of only 11 points to construct the diagram. One of the principal constraints on the positioning of the boundaries between the various named fields was to minimize the degree of overlap between adjacent fields.},
  journal = {Mineralogy and Petrology},
  language = {en},
  number = {1}
}

@article{Lehnert2000,
  title = {A Global Geochemical Database Structure for Rocks},
  author = {Lehnert, K. and Su, Y. and Langmuir, C.H. and Sarbas, B. and Nohl, U.},
  year = {2000},
  month = may,
  volume = {1},
  issn = {1525-2027},
  doi = {10.1029/1999GC000026},
  abstract = {This technical brief describes a geochemical and petrological database structure based on the relational model that has broad applicability to chemical analyses of geological materials. Notable features of the database structure are its comprehensiveness and flexibility. The structure consists of 34 interrelated tables, which can accommodate any type of analytical values for all different materials of rock samples (volcanic glasses, minerals, inclusions, etc.) and for samples from any tectonic setting. A broad spectrum of supplementary information (metadata) is included that describes the quality of the analytical data and sample characteristics, such as petrography, geographical location, and sampling process, and that can be used to evaluate, filter, and sort the chemical data. All data in the database are linked to their original reference. The database structure can be implemented in any relational database management system (RDBMS). It is currently applied in two different rock database projects (RidgePetDB and GEOROC).},
  journal = {Geochemistry, Geophysics, Geosystems},
  keywords = {data management,database,geochemistry,petrology},
  number = {5}
}

@article{Li2009,
  title = {Sulfur {{Contents}} at {{Sulfide}}-{{Liquid}} or {{Anhydrite Saturation}} in {{Silicate Melts}}: {{Empirical Equations}} and {{Example Applications}}},
  shorttitle = {Sulfur {{Contents}} at {{Sulfide}}-{{Liquid}} or {{Anhydrite Saturation}} in {{Silicate Melts}}},
  author = {Li, Chusi and Ripley, Edward M.},
  year = {2009},
  month = may,
  volume = {104},
  pages = {405--412},
  issn = {0361-0128},
  doi = {10.2113/gsecongeo.104.3.405},
  journal = {Economic Geology},
  language = {en},
  number = {3}
}

@inproceedings{McKinney2010,
  title = {Data Structures for Statistical Computing in Python},
  booktitle = {Proceedings of the 9th Python in Science Conference},
  author = {McKinney, Wes},
  editor = {{van der Walt}, St{\'e}fan and Millman, Jarrod},
  year = {2010},
  pages = {51--56}
}

@article{ONeill2016,
  title = {The {{Smoothness}} and {{Shapes}} of {{Chondrite}}-Normalized {{Rare Earth Element Patterns}} in {{Basalts}}},
  author = {O'Neill, Hugh St C.},
  year = {2016},
  month = aug,
  volume = {57},
  pages = {1463--1508},
  issn = {0022-3530},
  doi = {10.1093/petrology/egw047},
  abstract = {The customary practice for displaying REE abundances is to normalize them to chondritic abundances and then to plot these normalized abundances in order of atomic number, Z , although the 3 + ionic radius, rREE , is proposed here as a preferable independent variable. In basalts, the resulting CI-normalized REE patterns usually appear smooth (excepting Eu), such that they may be fitted to polynomials in rREE with three to five terms, depending on analytical precision. The polynomials can be rearranged into an orthogonal form:  ln([REE]/[REE] CI )={$\lambda$} 0 +{$\lambda$} 1f1orth +{$\lambda$} 2f2orth +\ldots{}  where f1orth , f2orth , etc. are themselves polynomials of rREE , chosen such that the coefficients {$\lambda$} 0 , {$\lambda$} 1 , {$\lambda$} 2 , etc. are not correlated with each other. The terms have a simple, intuitive meaning: {$\lambda$} 0 is the average of the logarithms of the CI-normalized REE abundances; the term in f1orth describes the linear slope of the pattern; that in f2orth describes the quadratic curvature, etc. For most basalts, fits using only three terms ({$\lambda$} 0 , {$\lambda$} 1 , and {$\lambda$} 2 ) capture REE patterns to better than {$\pm$}5\%. The {$\lambda$} n , called the `shape coefficients', can be used to compare the shapes of CI-normalized REE patterns quantitatively, allowing large numbers of data to be assessed, revealing trends not evident from studies of single localities. Especially instructive are {$\lambda$} 2 vs {$\lambda$} 1 diagrams. The usefulness of this approach is demonstrated using the REE patterns of common types of basalts from (mainly) oceanic settings: ocean floor basalts (OFB), ocean island basalts (OIB), and some convergent margin basalts. It is shown that the global population of OFB is characterized by a narrow dispersion of {$\lambda$} 0 at a given MgO content, but with large variations of {$\lambda$} 1 and {$\lambda$} 2 . Convergent margin basalts have much greater variation of {$\lambda$} 0 at a given [MgO], but most plot in the same area of the {$\lambda$} 2 vs {$\lambda$} 1 diagram. OIB are well separated from the OFB global array on this diagram, with Hawaiian shield basalts occupying a unique area. Because REE mineral/melt partition coefficients are also smooth functions of rREE , many mass-balance equations for petrogenetic processes that relate observed concentrations to initial concentrations, [REE] o , such as batch or fractional melting, or crystallization, may be fitted to the same orthogonal polynomials:  ln([REE]/[REE] o )={$\psi$} 0 +{$\psi$} 1f1orth +{$\psi$} 2f2orth +\ldots{} .  The orthogonality ensures that all {$\lambda$} n and {$\psi$} n terms of the same order n sum independently of the terms of the other orders, such that {$\lambda$} n = {$\lambda$}n0 + {$\psi$} n , where {$\lambda$}n0 is the shape coefficient of the source or parent magma. On {$\lambda$} 2 vs {$\lambda$} 1 diagrams, this approach can be used to relate the shapes of patterns in parental basalts to the shapes of the patterns of their sources, or differentiated basalts to their parental melts, by means of `petrogenetic process vectors' consisting of the {$\psi$} 1 and {$\psi$} 2 terms, which plot as vectors on the {$\lambda$} 2 vs {$\lambda$} 1 diagrams. For example, the difference between OIB and the global array of OFB can be shown to be due to garnet in the sources of OIB. The global array of OFB requires a remarkably constant degree of partial melting ( F ) of a source with constant {$\lambda$} 0 to produce their parental magmas, or a compensating correlation between F and source {$\lambda$} 0 . Assuming a constant source, with previously suggested depleted mantle compositions, F is {$\sim$}19\%, with the standard deviation of the population being only 2\%. Hawaiian shield tholeiites may be products of 1\textendash{}2\% melting at substantially higher pressures, perhaps straddling the garnet-to-spinel transition, of a source with REE patterns near the median of the REE patterns of OFB sources. Other OIB are the result of lower degrees of melting, usually of more light REE-enriched sources.},
  journal = {Journal of Petrology},
  language = {en},
  number = {8}
}

@article{Palme2014,
  title = {Cosmochemical {{Estimates}} of {{Mantle Composition}}},
  author = {Palme, H. and O'Neill, H. St. C.},
  editor = {Holland, Heinrich D. and Turekian, Karl K.},
  year = {2014},
  volume = {3},
  pages = {1--39},
  doi = {10.1016/B978-0-08-095975-7.00201-1},
  abstract = {The composition of the primitive mantle derived here shows that Earth was assembled from material that shows many of the same chemical fractionation processes as chondritic meteorites. These processes occurred at the initial stage of the solar system formation, under conditions thought to be present in the solar nebula. But the stable isotope record excludes chondritic meteorites as the `building blocks' of Earth. Meteorites formed in local environments separated from that part of the inner solar system where much of the material forming the terrestrial planets was sourced.},
  journal = {Treatise on Geochemistry (Second Edition)},
  keywords = {Chondritic meteorites,Collisional erosion,Depletion of volatile elements,Earth's bulk composition,Earth's primitive mantle,Late veneer,Stable isotopes in Earth and meteorites}
}

@article{Pearce2008,
  title = {Geochemical Fingerprinting of Oceanic Basalts with Applications to Ophiolite Classification and the Search for {{Archean}} Oceanic Crust},
  author = {Pearce, Julian A.},
  year = {2008},
  volume = {100},
  pages = {14--48},
  issn = {0024-4937},
  doi = {10.1016/j.lithos.2007.06.016},
  journal = {Lithos},
  number = {1}
}

@article{Pearson1897,
  title = {Mathematical Contributions to the Theory of Evolution.\textemdash{{On}} a Form of Spurious Correlation Which May Arise When Indices Are Used in the Measurement of Organs},
  author = {Pearson, Karl},
  year = {1897},
  month = jan,
  volume = {60},
  pages = {489--498},
  doi = {10.1098/rspl.1896.0076},
  abstract = {(1) If the ratio of two absolute measurements on the same or different organs be taken it is convenient to term this ratio an index. If u = f1(x, y) and v = f2(x, y) be two functions of the three variables x, y, z, and these variables be selected at random so that there exists no correlation between x, y, y, z, or z, x, there will still be found to exist correlation between u and v. Thus a real danger arises when a statistical biologist attribntes the correlation between two functions like u and v to organic relationship. The particular case that is likely to occur is when u and v are indices with the same denominator for the correlation of indices seems at first sight a very plausible measure of organic correlation.},
  journal = {Proceedings of the Royal Society of London},
  number = {359-367}
}

@article{Pedregosa2011,
  title = {Scikit-Learn: {{Machine Learning}} in {{Python}}},
  shorttitle = {Scikit-Learn},
  author = {Pedregosa, Fabian and Varoquaux, Ga{\"e}l and Gramfort, Alexandre and Michel, Vincent and Thirion, Bertrand and Grisel, Olivier and Blondel, Mathieu and Prettenhofer, Peter and Weiss, Ron and Dubourg, Vincent and Vanderplas, Jake and Passos, Alexandre and Cournapeau, David and Brucher, Matthieu and Perrot, Matthieu and Duchesnay, {\'E}douard},
  year = {2011},
  month = oct,
  volume = {12},
  pages = {2825-2830},
  issn = {1533-7928},
  abstract = {Scikit-learn is a Python module integrating a wide range of state-of-the-art machine learning algorithms for medium-scale supervised and unsupervised problems. This package focuses on bringing machine learning to non-specialists using a general-purpose high-level language.  Emphasis is put on ease of use, performance, documentation, and API consistency.  It has minimal dependencies and is distributed under the simplified BSD license, encouraging its use in both academic and commercial settings.  Source code, binaries, and documentation can be downloaded from http://scikit-learn.sourceforge.net.},
  journal = {Journal of Machine Learning Research}
}

@article{Smith2005,
  title = {Adiabat\_1ph: {{A}} New Public Front-End to the {{MELTS}}, {{pMELTS}}, and {{pHMELTS}} Models},
  shorttitle = {Adiabat\_1ph},
  author = {Smith, Paula M. and Asimow, Paul D.},
  year = {2005},
  volume = {6},
  issn = {1525-2027},
  doi = {10.1029/2004GC000816},
  abstract = {The program adiabat\_1ph is a simple text-menu driver for subroutine versions of the algorithms MELTS, pMELTS, and pHMELTS [Asimow et al., 2004; Ghiorso et al., 2002; Ghiorso and Sack, 1995]. It may be used to calculate equilibrium assemblages along a thermodynamic path set by the user and can simultaneously calculate trace element distributions. The MELTS family of algorithms is suitable for multicomponent systems, which may be anhydrous, water-undersaturated, or water-saturated, with the options of buffering oxygen fugacity and/or water activity. A wide variety of calculations can be performed either subsolidus or with liquid(s) present; melting and crystallization may be batch, fractional, or continuous. The software is suitable for Linux, MacOS X, and Windows, and many aspects of program execution are controlled by environment variables. Perl scripts are also provided that may be used to invoke adiabat\_1ph with some command line options and to produce output that may be easily imported into spreadsheet programs, such as Microsoft Excel. Benefits include a batch mode, which allows almost complete automation of the calculation process when suitable input files are written. This technical brief describes version 1.04, which is provided as ancillary material. Binaries, scripts, documentation, and example files for this and future releases may be downloaded at http://www.gps.caltech.edu/{$\sim$}asimow/adiabat. On a networked computer, adiabat\_1ph automatically checks whether a newer version is available.},
  copyright = {Copyright 2005 by the American Geophysical Union.},
  journal = {Geochemistry, Geophysics, Geosystems},
  keywords = {geochemical software,mantle melting,MELTS,pHMELTS,pMELTS,trace elements},
  language = {en},
  number = {2}
}

@article{Sun1989,
  title = {Chemical and Isotopic Systematics of Oceanic Basalts: Implications for Mantle Composition and Processes},
  shorttitle = {Chemical and Isotopic Systematics of Oceanic Basalts},
  author = {Sun, S.-s and McDonough, W. F.},
  year = {1989},
  month = jan,
  volume = {42},
  pages = {313--345},
  issn = {0305-8719, 2041-4927},
  doi = {10.1144/GSL.SP.1989.042.01.19},
  abstract = {Skip to Next Section
Trace-element data for mid-ocean ridge basalts (MORBs) and ocean island basalts (OIB) are used to formulate chemical systematics for oceanic basalts. The data suggest that the order of trace-element incompatibility in oceanic basalts is Cs {$\approx$} Rb {$\approx$} ({$\approx$} Tl) {$\approx$} Ba({$\approx$} W) {$>$} Th {$>$} U {$\approx$} Nb = Ta {$\approx$} K {$>$} La {$>$} Ce {$\approx$} Pb {$>$} Pr ({$\approx$} Mo) {$\approx$} Sr {$>$} P {$\approx$} Nd ({$>$} F) {$>$} Zr = Hf {$\approx$} Sm {$>$} Eu {$\approx$} Sn ({$\approx$} Sb) {$\approx$} Ti {$>$} Dy {$\approx$} (Li) {$>$} Ho = Y {$>$} Yb. This rule works in general and suggests that the overall fractionation processes operating during magma generation and evolution are relatively simple, involving no significant change in the environment of formation for MORBs and OIBs.
In detail, minor differences in element ratios correlate with the isotopic characteristics of different types of OIB components (HIMU, EM, MORB). These systematics are interpreted in terms of partial-melting conditions, variations in residual mineralogy, involvement of subducted sediment, recycling of oceanic lithosphere and processes within the low velocity zone. Niobium data indicate that the mantle sources of MORB and OIB are not exact complementary reservoirs to the continental crust. Subduction of oceanic crust or separation of refractory eclogite material from the former oceanic crust into the lower mantle appears to be required. The negative europium anomalies observed in some EM-type OIBs and the systematics of their key element ratios suggest the addition of a small amount ({$\leqslant$}1\% or less) of subducted sediment to their mantle sources. However, a general lack of a crustal signature in OIBs indicates that sediment recycling has not been an important process in the convecting mantle, at least not in more recent times ({$\leqslant$}2 Ga). Upward migration of silica-undersaturated melts from the low velocity zone can generate an enriched reservoir in the continental and oceanic lithospheric mantle. We propose that the HIMU type (eg St Helena) OIB component can be generated in this way. This enriched mantle can be re-introduced into the convective mantle by thermal erosion of the continental lithosphere and by the recycling of the enriched oceanic lithosphere back into the mantle.},
  copyright = {\textcopyright{} 1989 The Geological Society},
  journal = {Geological Society, London, Special Publications},
  language = {en},
  number = {1}
}

@article{Wickham2014,
  title = {Tidy {{Data}}},
  author = {Wickham, Hadley},
  year = {2014},
  month = sep,
  volume = {59},
  pages = {1--23},
  issn = {1548-7660},
  doi = {10.18637/jss.v059.i10},
  copyright = {Copyright (c) 2013 Hadley  Wickham},
  journal = {Journal of Statistical Software},
  language = {en},
  number = {1}
}


