Skip to main content
SpringerLink
Log in

Optimization of the garnet-biotite geothermometer: Part II. Calibration equations and accuracy of the estimation

  • Published:
Geology of Ore Deposits Aims and scope Submit manuscript

Abstract

Calibrations of the garnet-biotite geothermometer are considered with allowance for the effect of the nonideality of the coexisting garnet and biotite upon K D . The calibrations based on the model of an asymmetric subregular Prp-Alm-Grs-Sps solid solution with W Grt i−j (after Ganguly et al. (1996) and Holdaway (2000) and taking into account the experimental data published by Perchuk et al. (1983)) are the most accurate. The same may be said about the equations additionally taking into consideration the model of the symmetric regular Phl-Ann-Ms-(Ti-Bt) solution with W Bt i−j after Holdaway et al., (1997), Kaneko and Miano (2004), and the data published by Ferry and Spear (1978) and Perchuk et al. (1983). These equations well reproduce the temperature at which the Prp + Ann = Alm + Phl equilibrium is reached in experiments, and they are the least sensitive to the variation of the Ca and Mn contents in garnet and AlVI and Ti in biotite. The uncertainty of the temperature interval is 30–46°C (2σ).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aivazyan, S.A., Enyukov, I.S., and Meshalkin, L.D., Prikladnaya Statistika: Issledovanie Zavisimostei (Applied Statistics: Dependence Analysis), Moscow: Finansy Statistika, 1985.

    Google Scholar 

  • Aranovich, L.Y., Lavrent’eva, I.V., and Kosyakova, N.A., Calibration of the Biotite-Garnet and Biotite-Orthopyroxene Geothermometers Corrected for the Variable Al Level in Biotite, Geoch. Int., 1988a, vol. 25, pp. 50–59.

    Google Scholar 

  • Aranovich, L.Ya., Lavrent’eva, I.V., and Kosyakova, N.A., Biotite-Garnet and Biotite-Orthopyroxene Geothermometers: Calibration with Allowance for Variable Al content in Biotite, Geokhimiya, 1988b, vol. 26. no. 5, pp. 668–676.

    Google Scholar 

  • Belsley, D.A., Kuh, E., and Welsch, R.E., Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, Hoboken, Wiley, 2004.

    Google Scholar 

  • Berman, R.G., Mixing Properties of Ca-Mg-Fe-Mn Garnets, Am. Mineral., 1990, vol. 75, pp. 328–344.

    Google Scholar 

  • Bushmin, S.A. and Glebovitsky, V.A., Scheme of Mineral Facies of Metamorphic Rocks, Zap. Ross. Mineral. O-va, 2008, vol. 137, no. 2, pp. 1–14 [Geol. Ore Deposits (Engl. Transl.), 2008, vol. 50, spec. issue no. 8 (Zapiski Russian Mineral. Soc.), pp. 659–669].

    Google Scholar 

  • Draper, N.R. and Smith, H., Applied Regression Analysis, New York: Wiley, 1981.

    Google Scholar 

  • Ferry, J.M. and Spear, F.S., Experimental Calibration of the Partitioning of Fe and Mg between Biotite and Garnet, Contrib. Mineral. Petrol., 1978, vol. 66, pp. 113–117.

    Article  Google Scholar 

  • Ganguly, J., Cheng, W., and Tirone, M., Thermodynamics of Alumosilicate Garnets: Experimental Determination in Pyroxene-Almandine Diffusion Couples, Contrib. Mineral. Petrol., 1998, vol. 131, pp. 171–180.

    Article  Google Scholar 

  • Gessmann, C.K., Spiering, B., and Raith, M., Experimental Study of the Fe-Mg Exchange between Garnet and Biotite: Constraints on the Mixing Behavior and Analysis of the Cation-Exchange Mechanisms, Am. Mineral., 1997, vol. 82, pp. 1225–1240.

    Google Scholar 

  • Gulbin, Yu.L., Optimization of Garnet-Biotite Geothermometer. I. Temperature Trends Zap. Ross. Mineral. O-va, 2010, vol. 139, no. 5, pp. 1–17 [Geol. Ore Deposits (Engl. Transl.), 2011, vol. 53, spec. issue no. 7 (Zapiski Russian Mineral. Soc.), pp.

    Google Scholar 

  • Hodges, K.V. and Spear, F.S., Geothermometry, Geobarometry and the Al2SiO5 Triple Point at Mt. Moosilauke, New Hampshire, Am. Mineral., 1982, vol. 67, pp. 1118–1134.

    Google Scholar 

  • Hoerl, A.E. and Kennard, R.W., Ridge Regression: Biased Estimation for Nonorthogonal Problems, Technometrics, 1970, vol. 12, pp. 55–67.

    Article  Google Scholar 

  • Hoisch, T.D., Equilibria within the Mineral Assemblage Quartz + Muscovite + Biotite + Garnet + Plagioclase and Implications for the Mixing Properties of Octahedrally-Coordinated Cations in Muscovite and Biotite, Contrib. Miner. Pertrol., 1991, vol. 108, pp. 43–54.

    Article  Google Scholar 

  • Holdaway, M.J., Application of New Experimental and Garnet Margules Data to the Garnet-Biotite Geothermometer, Am. Mineral., 2000, vol. 85, pp. 881–892.

    Google Scholar 

  • Huang, M.-H., Buick, I.S., and Hou, L.W., Tectonometamorphic Evolution of the Eastern Tibet Plateau: Evidence from the Central Songpan Garzé Orogenic Belt, J. Petrol., 2003, vol. 44, pp. 255–278.

    Article  Google Scholar 

  • Ikeda, T., Pressure-Temperature Conditions of the Ryoke Metamorphic Rocks in Yanai District, SW Japan, Contrib. Miner. Pertrol., 2004, vol. 146, pp. 577–589.

    Article  Google Scholar 

  • Kaneko, Y. and Miyano, T., Recalibration of Mutually Consistent Garnet-Biotite and Garnet-Cordierite Geothermometers, Lithos, 2004, vol. 73, pp. 255–269.

    Article  Google Scholar 

  • Kleemann, U. and Reinhardt, J., Garnet-Biotite Thermometry Revisited: The Effect of AlVI and Ti in Biotite, Eur. J. Mineral., 1994, vol. 6, pp. 925–941.

    Google Scholar 

  • McMullin, D.W.A., Berman, R.G., and Greenwood, H.J., Calibration of the SGAM Thermobarometer for Pelitic Rocks Using Data from Phase-Equilibrium Experiments and Natural Assemblages, Can. Mineral., 1991, vol. 29, pp. 889–908.

    Google Scholar 

  • Nikitina, L.P., Refinement of Garnet-Biotite Geothermometer: Development of Mutually Coordinated Geological Thermometers and Barometers, Zap. Vseross. Mineral. Ob-va, 1991, vol. 120, no. 1, pp. 18–31.

    Google Scholar 

  • Nikitina, L.P. and Ivanov, M.V., Geologicheskaya geotermobarometriya na osnove reaktsii mineraloobrazovaniya s uchastiem faz peremennogo sostsava (Geological Geothermo), St. Petersburg: Nedra, 1992.

    Google Scholar 

  • Perchuk, L.L. and Lavrent’eva, I.V. Experimental Investigation of Exchange Equilibria in the System Condierite-Garnet-Biotite, in Kinetics and Equilibrium in Mineral Reactions, Adv. Phys. Res., 1983, vol. 3, pp. 199–239.

    Article  Google Scholar 

  • Perchuk, L.L., Lavrent’eva, I.V., Aranovich, L.Ya., et al., Biotit-granat-kordieritovye ravnovesiya i evolyutsiya metamorfizma (Biotite-Garnet-Cordierite Equilibria and Metamorphic Evolution), Moscow: Nauka, 1983.

    Google Scholar 

  • Powell, R., Holland, T., and Worley, B., Calculating Phase Diagram Involving Solid Solution via Non-Linear Equations Example Using THERMOCALC, J. Metamorph. Geol., 1998, vol. 16, pp. 577–588.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg State Mining University, 21-ay Liniya 2, St. Petersburg, 199106, Russia

    Yu. L. Gulbin

Authors
  1. Yu. L. Gulbin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. L. Gulbin.

Additional information

Original Russian Text © Yu.l. Gulbin, 2010, published in Zapiski RMO (Proceedings of the Russian Mineralogical Society), 2010, No. 6, pp. 22–38.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gulbin, Y.L. Optimization of the garnet-biotite geothermometer: Part II. Calibration equations and accuracy of the estimation. Geol. Ore Deposits 53, 543–557 (2011). https://doi.org/10.1134/S1075701511070099

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1075701511070099

Keywords

Search

Navigation