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Estimating ferric iron content in clinopyroxene using machine learning models

  • Wei-hua Huang , Yang Lyu , Ming-hao Du , Can He , Shang-de Gao , Ren-jun Xu , Qun-ke Xia and J ZhangZhou
Published/Copyright: September 29, 2022
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American Mineralogist
From the journal American Mineralogist Volume 107 Issue 10

Abstract

Clinopyroxene ferric iron content is an important consideration for garnet-clinopyroxene geothermometry and estimations of water storage in the Earth’s interior but remains difficult and expensive to measure. Here, we develop seven classic algorithms and machine learning methods to estimate Fe3+/ΣFe in clinopyroxene using major element data from electron microprobe analyses. The models were first trained using a large data set of clinopyroxene Fe3+/ΣFe values determined by Mössbauer spectroscopy and spanning a wide compositional range, with major uncertainties ranging from 0.25 to 0.3 and root-mean-square errors on the test data set ranging from 0.071 to 0.089. After dividing the entire data set into three compositional sub-data sets, the machine learning models were trained and compared for each sub-data set. Our results suggest that ensemble learning algorithms (random forest and Extra-Trees) perform better than principal component analysis-based elastic net polynomial, artificial neural network, artificial neural network ensemble, decision trees, and linear regressions. Using a sub-data set excluding clinopyroxene in spinel peridotite and omphacite in eclogite, the new models achieved uncertainties of 0.15 to 0.2 and root-mean-square errors on the test data set ranging from 0.051 to 0.078, decreasing prediction errors by 30–40%. By incorporating compositional data on coexisting spinel, new models for clinopyroxene in spinel peridotite show improved performance, indicating the interaction between spinel and clinopyroxene in spinel peridotite. Feature importance analysis shows Na+, Ca2+, and Mg2+ to be the most important for predicting Fe3+ content, supporting the coupled substitution between Ca2+-M2+ and Na+-M3+ in natural clinopyroxenes. The application of our models to garnet-clinopyroxene geothermometry greatly improves temperature estimates, achieving uncertainties of ±50 °C, compared with uncertainties of ±250 °C using previous models assuming all Fe as Fe2+ or calculating Fe3+ by charge conservation. Differences in the ferric iron contents, as calculated using the machine learning models, of clinopyroxenes that did or did not experience hydrogen difusion during their crystallization from basaltic magma support a redox-driven mechanism for hydrogen diffusion in clinopyroxene.

Keywords: Clinopyroxene; Fe3+/ΣFe; machine learning; geothermometer; redox

Acknowledgments and Funding

The authors thank Y.H. Zhang, X.M. Zhou, Z.W. Huang, H.H. Wang, S.H. Wei, Z.X. Zhang, W.K. Wang, W.Y. Zhang, W.J. Zhou, W.Q. Liu, X. Chen, L.H. Chen, R.Z. Wang, L.Y. Jin, G.L. Li, Y.D. Lu, L.Z. Zhao, and Y.F. Xu for their assistance in compiling the data and applying the Python codes. We are thankful to Hongluo Zhang and Avishek Rudra for discussions. We are grateful to Robert Dennen for polishing the language of the paper. We highly appreciate insightful reviews by Laura Rzehak and Fang Huang. Finally, the authors acknowledge support from the Key Laboratory of Big Data and Deep Earth Resources of Zhejiang Province and the Fundamental Research Funds for the Central Universities (grant no. K20210168).

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Received: 2021-06-21
Accepted: 2021-09-23
Published Online: 2022-09-29
Published in Print: 2022-10-26

© 2022 Mineralogical Society of America

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  7. Estimating ferric iron content in clinopyroxene using machine learning models
  8. Pyradoketosite, a new, unexpected, polymorph of Ag3SbS3 from the Monte Arsiccio mine (Apuan Alps, Tuscany, Italy)
  9. Pyrite geochemistry and its implications on Au-Cu skarn metallogeny: An example from the Jiguanzui deposit, Eastern China
  10. Synthesis of ferrian and ferro-saponites: Implications for the structure of (Fe,Mg)-smectites formed under reduced conditions
  11. Natural cubic perovskite, Ca(Ti,Si,Cr)O3–δ, a versatile potential host for rock-forming and less-common elements up to Earth’s mantle pressure
  12. Nazarovite, Ni12P5, a new terrestrial and meteoritic mineral structurally related to nickelphosphide, Ni3P
  13. Zinconigerite-2N1S ZnSn2Al12O22(OH)2 and zinconigerite-6N6S Zn3Sn2Al16O30(OH)2, two new minerals of the nolanite-spinel polysomatic series from the Xianghualing skarn, Hunan Province, China
  14. Tracing structural relicts of the ikaite-to-calcite transformation in cryogenic cave glendonite
  15. Oxygen-fugacity evolution of magmatic Ni-Cu sulfide deposits in East Kunlun: Insights from Cr-spinel composition
  16. New Mineral Names
https://doi.org/10.2138/am-2022-8189
Keywords for this article
Clinopyroxene; Fe3+/ΣFe; machine learning; geothermometer; redox

Articles in the same Issue

  1. Experimentally derived F, Cl, and Br fluid/melt partitioning of intermediate to silicic melts in shallow magmatic systems
  2. Spectroscopic study on the local structure of sulfate ( S O 4 2 − ) incorporated in scorodite (FeAsO4·2H2O) lattice: Implications for understanding the Fe(III)-As(V)- S O 4 2 − -bearing minerals formation
  3. Oxidation of arcs and mantle wedges by reduction of manganese in pelagic sediments during seafloor subduction
  4. Raman scattering and Cr3+ luminescence study on the structural behavior of δ-AlOOH at high pressures
  5. Jadeite and related species in shocked meteorites: Limitations on inference of shock conditions
  6. Pressure-induced C23–C37 transition and compression behavior of orthorhombic Fe2S to Earth’s core pressures and high temperatures
  7. Estimating ferric iron content in clinopyroxene using machine learning models
  8. Pyradoketosite, a new, unexpected, polymorph of Ag3SbS3 from the Monte Arsiccio mine (Apuan Alps, Tuscany, Italy)
  9. Pyrite geochemistry and its implications on Au-Cu skarn metallogeny: An example from the Jiguanzui deposit, Eastern China
  10. Synthesis of ferrian and ferro-saponites: Implications for the structure of (Fe,Mg)-smectites formed under reduced conditions
  11. Natural cubic perovskite, Ca(Ti,Si,Cr)O3–δ, a versatile potential host for rock-forming and less-common elements up to Earth’s mantle pressure
  12. Nazarovite, Ni12P5, a new terrestrial and meteoritic mineral structurally related to nickelphosphide, Ni3P
  13. Zinconigerite-2N1S ZnSn2Al12O22(OH)2 and zinconigerite-6N6S Zn3Sn2Al16O30(OH)2, two new minerals of the nolanite-spinel polysomatic series from the Xianghualing skarn, Hunan Province, China
  14. Tracing structural relicts of the ikaite-to-calcite transformation in cryogenic cave glendonite
  15. Oxygen-fugacity evolution of magmatic Ni-Cu sulfide deposits in East Kunlun: Insights from Cr-spinel composition
  16. New Mineral Names
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