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Tetrahedral Plots of the Phase Relations for Basalts

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Abstract

The phase relations of quaternary systems are generally represented by projections onto ternary compositional planes. Such projections often obscure relationships that would only be evident in a three-dimensional tetrahedral plot. The tetrahedral plot requires that compositions of the minerals and melts be transformed into Cartesian coordinates. It is shown here how this transformation is carried out. The application is demonstrated by tetrahedral plots of experimental melt compositions of partially molten lherzolite. Furthermore, the plot can be used to evaluate whether or not a particular basaltic composition represents a primary melt. The methods are applicable to any four-component system.

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References

  • Bender, J. F., Hodges, F. N., and Bence, A. E., 1978, Petrogenesis of basalt from the project FAMOUS area: Experimental study from 0 to 15 kilobars: Earth Planet. Sci. Lett., v. 41, p. 277–302.

    Article  Google Scholar 

  • Eggins, S. M., 1992, Petrogenesis of Hawaiian tholeiites: 1. Phase equilibria constraints: Contrib. Mineral. Petrol., v. 110, p. 387–397.

    Google Scholar 

  • Elthon, D., and Scarfe, C. M., 1984, High pressure phase equilibria of a high magnesia basalt and the genesis of primary oceanic basalts: Am. Mineral., v. 69, p. 1–15.

    Google Scholar 

  • Frey, F. A., and Rhodes, J. M., 1993, Intershield geochemical differences among Hawaiian volcanoes: Implications for source compositions, melting processes and magma ascent paths: Philos. Trans R. Soc. Lond. Ser. A, v. 342, p. 121–136.

    Google Scholar 

  • Fujii, T., and Bougault, H., 1983, Melting reactions of magnesian abyssal tholeiite and the origin of MORBs: Earth Planet. Sci. Lett., v. 62, p. 283–295.

    Article  Google Scholar 

  • Fujii, T., and Scarfe, C. M., 1985, Composition of liquids coexisting with spinel lherzolite at 10 kbar and the genesis of MORBs: Contrib. Mineral. Petrol., v. 90, p. 18–28.

    Article  Google Scholar 

  • Garcia, M. O., Hulsebosch, T. P., and Rhodes, J. M., 1995, Olivine-rich submarine basalts from the sourthwest rift zone of Mauna Loa volcano: Implications for magmatic processes and geochemical evolution: Geophys. Monogr., v. 92, p. 219–239.

    Google Scholar 

  • Ghiorso, M. S., and Sack, R. O., 1995, Chemical mass-transfer in magmatic processes: IV. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid–solid equilibria in magmatic systems at elevated temperatures and pressures: Contrib. Mineral. Petrol., v. 119, p. 197–212.

    Google Scholar 

  • Hirose, K., and Kushiro, I., 1993, Partial melting of dry peridotites at high pressures: Determination of compositions of melts segregated from peridotite using aggregates of diamond: Earth Planet. Lett., v. 114, p. 477–480.

    Google Scholar 

  • Ito, K., and Kennedy, G. C., 1974, The composition of liquids formed by partial melting of eclogites at high temperatures and pressures: J. Geol., v. 82, p. 383–392.

    Google Scholar 

  • Kushiro, I., 1996, Partial melting of a fertile mantle peridotite at high pressures: An experimental study using aggregates of diamond: Geophys. Monogr., v. 95, p. 109–122.

    Google Scholar 

  • Longhi, J., 2002, Some phase equilibrium systematics of lherzolite melting: I: Geochem. Geophys. Geosyst., v. 3, no. 3, p. 1–18.

    Google Scholar 

  • Maaløe, S., 1979, Compositional range of primary tholeiitic magmas evaluated from major element trends: Lithos, v. 12, p. 59–72.

    Article  Google Scholar 

  • Maaløe, S., 1985, Principles of igneous petrology: Springer-Verlag, Berlin, 371 p.

    Google Scholar 

  • Maaløe, S., and Aoki, K., 1977, The major element composition of the upper mantle estimated from the composition of lherzolites: Contrib. Mineral. Petrol., v. 63, p. 161–173.

    Article  Google Scholar 

  • Maaløe, S., and Jakobsson, S. P., 1980, The PT phase relations of a primary oceanite from the Reykjanes peninsula, Iceland: Lithos, v. 13, p. 237–246.

    Article  Google Scholar 

  • Maaløe, S., and Petersen, S., 1976, Phase relations governing the derivation of alkaline basaltic magms from primary magmas at high pressures: Lithos, v. 9, p. 243–252.

    Article  Google Scholar 

  • O’Hara, M., 1968, The bearing of phase equilibria studies in synthetic and natural systems on the origin and evolution of basic and ultrabasic rocks: Earth Sci. Rev., v. 4, p. 69–133.

    Google Scholar 

  • Presnall, D. C., Dixon, J. R., O’Donnel, T. H., Brenner, N. L., Schrock, R. L., and Dycus, D. W., 1978, Liquidus phase relations on the join diopside–forsterite–anorthite from 1 atm to 20 kbar: Their bearing on the generation and crystallization of basaltic magma: Contrib. Mineral. Petrol., v. 66, p. 203–220.

    Article  Google Scholar 

  • Rhodes, J. M., 1995, The 1852 and 1868 Mauna Loa picritic eruptions: Clues to parental magma compositions and magmatic plumbing systems: Geophys. Monogr., v. 92, p. 241–262.

    Google Scholar 

  • Ribe, N. M., and Christenen, U. R., 1999, The dynamical origin of Hawaiian volcanism: Earth Planet. Sci. Lett., v. 171, p. 517–531.

    Article  Google Scholar 

  • Robinson, J. A. C., Wood, B. J., and Blundy, J. D., 1998, The begining of melting of fertile and depleted peridotite at 1.5 GPa: Earth Planet. Sci. Lett., v. 155, p. 97–111.

    Article  Google Scholar 

  • Roeder, P. L., and Emslie, R. F., 1970, Olivine-liquid equilibrium: Contrib. Mineral. Petrol., v. 29, p. 275–289.

    Article  Google Scholar 

  • Sen, G., 1988, Petrogenesis of sinel lherzolite and pyroxenite suite xenoliths from the Koolau shield, Oahu, Hawaii: Implications for petrology and of the post-eruptive lithosphere beneath Hawaii: Contrib. Mineral. Petrol., v. 100, p. 61–91.

    Article  Google Scholar 

  • Schwab, B. E., and Johnston, A. D., 2001, Melting systematics of modally variable, compositionally intermediate peridotites and the effects of mineral fertility: J. Petrol., v. 42, p. 1789–1811.

    Article  Google Scholar 

  • Ulmer, P., 1989, The dependence of the Fe2+–MgO cation-partitioning between olivine and basaltic liquid on pressure, temperature and composition: Contrib. Mineral. Petrol., v. 101, p. 261–273.

    Article  Google Scholar 

  • Walter, M. J., 1998, Melting of garnet peridotite and the origin of komatiite and depleted lithosphere: J. Petrol., v. 39, p. 29–60.

    Article  Google Scholar 

  • Watson, S., and McKenzie, D., 1991, Melt generation by plumes: A study of Hawaiian volcanism: J. Petrol., v. 32, p. 501–537.

    Google Scholar 

  • Yoder, H. S., 1976, Generation of basaltic magma: National Academy of Science, Washington, DCs, 264 p.

    Google Scholar 

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Authors and Affiliations

  1. Department of Earth Sciences, Allegaten 41, 5007, Bergen, Norway

    Sven Maaløe

  2. Department of Geology, Appalachian State University, Boone, North Carolina

    Richard N. Abbott Jr.

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  1. Sven Maaløe
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  2. Richard N. Abbott Jr.
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Correspondence to Sven Maaløe.

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Maaløe, S., Abbott, R.N. Tetrahedral Plots of the Phase Relations for Basalts. Math Geol 37, 869–893 (2005). https://doi.org/10.1007/s11004-005-9212-5

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  • DOI: https://doi.org/10.1007/s11004-005-9212-5

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