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,
To quantitatively convert upper mantle seismic wave speeds measured into temperature, density, composition, and corresponding and uncertainty, we introduce the
- 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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Abstract 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. -
Abstract Elevated seismic noise for moderate‐size earthquakes recorded at teleseismic distances has limited our ability to see their complexity. We develop a machine‐learning‐based algorithm to separate noise and earthquake signals that overlap in frequency. The multi‐task encoder‐decoder model is built around a kernel pre‐trained on local (e.g., short distances) earthquake data (Yin et al., 2022,
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