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Abstract We provide a new algorithm for mass‐balance calculations in petrology and geochemistry based on the log‐ratio approach championed initially by John Aitchison (e.g., Aitchison, 1982,https://doi.org/10.1111/j.2517-6161.1982.tb01195.x; Aitchison, 1984,https://doi.org/10.1007/bf01029316) along with the underlying principles, mathematical frameworks, and data requirements. Log‐ratio Inversion of Mixed End‐members (LIME) is written in MATLAB and calculates phase proportions in an experiment or rock given a bulk composition, the composition of each phase, and the associated compositional uncertainties. An important advantage of LIME is that performing the mass‐balance calculation in inverse log‐ratio space constrains phase proportions to be between 0 and 100 wt.%. Further, the resulting LIME phase proportions provide realistic estimates of uncertainty regardless of data distribution. These two characteristics of LIME improve upon standard multiple linear regression techniques, which may yield negative values for phase proportions if non‐constrained or report oversimplified symmetric errors. Primary applications of LIME include estimating phase abundances, calculating melting and metamorphic reaction stoichiometries, and checking for open system behavior in phase equilibria experiments. The technique presented here covers whole‐rock analysis, mineralogy, and phase abundance, but could be extended to isotopic tracers, trace element modeling, and regolith component un‐mixing. We highlight the importance of uncertainty estimations for phase abundances to the fields of petrology and geochemistry by comparing our results from LIME to previously published mass‐balance calculations. Furthermore, we present case studies that demonstrate the role of mass‐balance calculations in determining magma crystallinity and defining melting reactions.
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WISTFUL: Whole‐Rock Interpretative Seismic Toolbox for Ultramafic Lithologies
Abstract To quantitatively convert upper mantle seismic wave speeds measured into temperature, density, composition, and corresponding and uncertainty, we introduce theWhole‐rockInterpretativeSeismicToolboxForUltramaficLithologies (WISTFUL). WISTFUL is underpinned by a database of 4,485 ultramafic whole‐rock compositions, their calculated mineral modes, elastic moduli, and seismic wave speeds over a range of pressure (P) and temperature (T) (P = 0.5–6 GPa,T = 200–1,600°C) using the Gibbs free energy minimization routine Perple_X. These data are interpreted with a toolbox of MATLAB® functions, scripts, and three general user interfaces:WISTFUL_relations, which plots relationships between calculated parameters and/or composition;WISTFUL_geotherms, which calculates seismic wave speeds along geotherms; andWISTFUL_inversion, which inverts seismic wave speeds for best‐fit temperature, composition, and density. To evaluate our methodology and quantify the forward calculation error, we estimate two dominant sources of uncertainty: (a) the predicted mineral modes and compositions, and (b) the elastic properties and mixing equations. To constrain the first source of uncertainty, we compiled 122 well‐studied ultramafic xenoliths with known whole‐rock compositions, mineral modes, and estimatedP‐Tconditions. We compared the observed mineral modes with modes predicted using five different thermodynamic solid solution models. The Holland et al. (2018,https://doi.org/10.1093/petrology/egy048) solution models best reproduce phase assemblages (∼12 vol. % phase root‐mean‐square error [RMSE]) and estimated wave speeds. To assess the second source of uncertainty, we compared wave speed measurements of 40 ultramafic rocks with calculated wave speeds, finding excellent agreement (VpRMSE = 0.11 km/s). WISTFUL easily analyzes seismic datasets, integrates into modeling, and acts as an educational tool.
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- Award ID(s):
- 1844340
- PAR ID:
- 10372952
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Geochemistry, Geophysics, Geosystems
- Volume:
- 23
- Issue:
- 8
- ISSN:
- 1525-2027
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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