Abstract
We use the technique of direct minimization of the Gibbs free energy of the 8-component (K2O-Na2O-Fe2O3-FeO-CaO-MgO-Al2O3-SiO2) multiphase system in order to determine the equilibrium mineral assemblages of rocks of different bulk chemical compositions equilibrated at various P-T conditions. The calculated modal compositions of rocks and experimental data on elastic moduli of single crystals are then used to calculate densities and isotropic elastic wave velocities of rocks together with their pressure and temperature derivatives. Sufficient accuracy of the calculations is confirmed by comparison with experimental data on the gabbro-eclogite transformation and precise ultrasonic measurements of elastic wave velocities in a number of magmatic and metamorphic rocks.
We present calculated phase diagrams with isolines of density, elastic wave velocities, and their pressure and temperature derivatives for several anhydrous magmatic rocks, from granite to lherzolite. Density and elastic properties of rocks are controlled by their chemical compositions, especially the SiO2 content, and by P-T of equilibration, and they increase with pressure due to mineral reactions changing mineral assemblages from plagioclase-bearing and garnet-free to garnetbearing and plagioclase-free. TheV p -density correlation is high, and shows two clear trends: one for iron-poor ultramafic rocks and another for all the other rocks considered. Mineral reactions, which occur at high pressures, changeV p and density of anhydrous magmatic rocks following the well-known Birch (or a similar) law.
Felsic, intermediate and mafic rocks can be well distinguished in theV p -V p /V s - diagram, although their values ofV p can be close to one another. TheV p -V p /V s -density diagrams together with calculated phase diagrams can serve as efficient instruments for petrologic interpretation of seismic velocities.
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References
Aleinikov, A.L., N.I. Nemzorov and N.I. Khalevin: 1986,Multiwave seismics for studying deep structure of ore regions, Nauka, Moscow (in Russian).
Alexandrov, K.S. and T.V. Ryzhova: 1961a, ‘The elastic properties of rock-forming minerals. I: Pyroxenes and amphiboles’,Bull. Acad. Sci. USSR Geophys. Ser. 9, 871.
Alexandrov, K.S. and T.V. Ryzhova: 1961b, ‘The elastic properties of rock-forming minerals. II: Layered silicates’,Bull. Acad. Sci. USSR Geophys. Ser. 9, 1165.
Alexandrov, K.S., T.V. Ryzhova and B.P. Belikov: 1964, ‘The elastic properties of pyroxenes’,Sov. Phys. Crystallogr. 8, 589–591.
Babeyko, A. Yu., S.V. Sobolev, E.D. Sinelnikov, Yu.P. Smirnov and N.A. Derevschikova: 1994, ‘Calculation of elastic properties in lower part of the Kola borehole from bulk chemical compositions of core samples’,Surveys Geophys. (This volume).
Bass, J.D. and D.J. Weidner: 1984, ‘Elasticity of single-crystal orthoferrosilite’,J. Geophys. Res. B89, 4359–4371.
Belikov, B.P., K.S. Alexandrov and T.V. Ryzhova: 1970,Elastic properties of rock-forming minerals and rocks, Nauka, Moscow, 176p (in Russian).
Berman, R.G.: 1988, ‘Internally consistent thermodynamic data for minerals in the system Na2O-K2O-CaO-MgO-FeO-Fe2O3-Al2O3-SiO2-TiO2-H2O-CO2’,J. Petrol. 29, 445–522.
Berman, R.G.: 1990, ‘Mixing properties of Ca-Mg-Fe-Mn garnets’,Am. Mineral. 75, 328–344.
Bertrand, G.L., W.E. Acree and T.E. Burchfield: 1983, ‘Thermochemical excess properties of multicomponent systems: representation and estimation from binary mixing data’,J. Solut. Chem. 12, 327–346.
Birch, F.: 1961, ‘The velocity of compressional waves in rocks to 10 kbar. Part 2’,J. Geophys. Res. 66, 2199–2224.
Birch, F.: 1966, ‘Compressibility; elastic constants’, in S.P. Clark, Jr. (ed.),Handbook of physical constants, Geol. Soc. Am. Mem.97, pp. 97–174.
Burke, M.M. and D.M. Fountain: 1990, ‘Seismic properties of rocks from an exposure of extended continental crust - new laboratory measurements from the Ivrea Zone’,Tectonophysics 182, 119–146.
De Capitani, C. and T.H. Brown: 1987, ‘The computation of chemical equilibrium in complex systems containing non-ideal solutions’,Geochim. Cosmochim. Acta 51, 2639–2652.
Christensen, N.I.: 1965, ‘ Compressional wave velocities in metamorphic rocks to 10 kilobars’,J. Geophys. Res. 70, 6147–6164.
Christensen, N.I.: 1982, ‘ Seismic velocities’, in R.S. Carmichael (ed.),Handbook of physical properties of rocks, Vol.II, CRC Press, pp. 1–228.
Dobretsov, N.L., V.V. Reverdatto, V.S. Sobolev, N.V. Sobolev and V.V. Hlestov: 1970,Metamorphic facies, Nedra, Moscow (in Russian).
Fey, Y., S.K. Saxena and G. Eriksson: 1986, ‘Some binary and ternary silicate solution models’,Contr. Miner. Petrol. 94, 221–229.
Fountain, D.M.: 1976, ‘The Ivrea-Verbano and Strona-Ceneri zones, northern Italy: a cross-section of the continental crust - new evidence from seismic velocities of rock samples’,Tectonophysics 33, 145–165.
Fountain, D.M. and N.I. Christensen: 1989, ‘Composition of the continental crust and upper mantle; a review’, in: L.C. Pakiser and W.D. Mooney (eds.),Geophysical Framework of the Continental United States, Geol. Soc. Am. Mem. 172, pp. 711–742.
Fountain, D.M., M.H. Salisbury and J. Percival: 1990, ‘Seismic structure of the continental crust based on rock velocity measurements from the Kapuskasing uplift’,J. Geophys. Res. B95, 1160–1186.
Galdin, N.E.: 1977,Physical properties of metamorphic and igneous rocks at high pressure and temperature, Nedra, Moscow, 127p (in Russian).
Gasparik, T.: 1984, ‘Experimental study of subsolidus phase relations and mixing properties of pyroxene in the system CaO-Al2O3-SiO2’,Geochim. Cosmochim. Acta 48, 2537–2546.
Gasparik, T.: 1985a, ‘Experimentally determined compositions of diopside-jadeite pyroxene in equilibrium with albite and quartz at 1200–1300 °C and 15–34 kbar’,Geochim. Cosmochim. Acta 49, 865–870.
Gasparik, T.: 1985b, ‘Experimental study of subsolidus phase relations and mixing properties of pyroxene and plagioclase in the system Na2O-CaO-Al2O3-SiO2’,Contr. Miner. Petrol. 89, 346–357.
Green, D.H. and R.C. Liebermann: 1976, ‘Phase equilibria and elastic properties of a pyrolite model for the oceanic upper mantle’,Tectonophysics 32, 61–92.
Green, D.H. and A.E. Ringwood: 1967, ‘An experimental investigation of the gabbro to eclogite transformation and its petrological applications’,Geochim. Cosmochim. Acta 31, 767–833.
Green, D.H. and A.E. Ringwood: 1972, ‘A comparison of recent experimental data on the gabbrogarnet granulite-eclogite transition’,J. Geology 80, 277–288.
Green, T.H.: 1967, ‘An experimental investigation of sub-solidus assemblages formed at high pressure in high-alumina basalt, kyanite eclogite and grosspydite compositions’,Contr. Miner. Petrol. 16, 84–114.
Green, T.H.: 1970, ‘High pressure experimental studies on the mineralogical constitution of the lower crust’,Phys. Earth Pl. Inter. 3, 441–451.
Goldsmith, J.R.: 1980, ‘The melting and breakdown reactions of anorthite at high pressures and temperatures’,Am. Miner. 65, 272–284.
Hansen, B.: 1981, ‘The transition from pyroxene granulite facies to garnet clinopyroxene granulite facies. Experiments in the system CaO-MgO-Al2O3-SiO2’,Contr. Miner. Petrol. 76, 234–242.
Haselton, H.T., G.L. Hovis, B.S. Hemingway and R.A. Robie: 1983, ‘Calorimetric investigation of the excess entropy of mixing in analbite-sanidine solid solutions: lack of evidence for Na,K short-range order and implications for two-feldspar thermometry’,Am. Miner. 68, 398–413.
Hashin, Z. and S. Shtrikman: 1963, ‘A variational approach to the elastic behavior of multiphase materials’,J. Mech. Phys. Solids 11, 127–140.
Helffrich, G.R., S. Stein and B.J. Wood: 1989, ‘Subduction zone thermal structure and mineralogy and their relationship to seismic wave reflections and conversions at the slab/mantle interface’,J. Geophys. Res. B94, 753–63.
Holbrook W.S, D. Gajewsk, A. Drammer and C. Prodehl: 1988, ‘Interpretation of wide-angle compressional and shear wave data in Southwest Germany: Poisson's ratio and petrological implications’,J. Geophys. Res. B93, 12081–12106.
Holland, T.J.B.: 1980, ‘The reaction albite = jadeite + quartz determined experimentally in the range 600–1200 °C’,Am. Miner. 65, 129–134.
Holland, T.J.B. and R. Powell: 1990, ‘An enlarged and updated internally consistent thermodynamic dataset with uncertainties and correlations: the system K2O-Na2O-CaO-MgO-MnO-FeO-Fe2O3-Al2O3-TiO2-SiO2-C-H2-O2’,J. Met. Geol. 8, 89–124.
Hughes, S., J.H. Luetgert and N.I. Christensen: 1993, ‘Reconciling deep seismic refraction and reflection data from the Grenvillian-Appalachian boundary in western New England’,Tectonophysics 225, 255–270.
Ito, K. and G.C. Kennedy: 1971, ‘An experimental study of the basalt-garnet granulite-eclogite transition’, in J.G. Heacock (ed.)The structure and physical properties of the Earths crust, Geophys. Monogr.14, pp. 303–314.
Jenkins, D.M. and R.C. Newton: 1979, ‘Experimental determination of the spinel peridotite to garnet peridotite inversion at 900 °C and 1000 °C in the system CaO-MgO-Al2O3-SiO2, and at 900 °C with natural garnet and olivine’,Contr. Miner. Petrol. 68, 407–419.
Jordan, T.H.: 1979, ‘Mineralogies, densities and seismic velocities of garnet lherzolites and their geophysical implications’, in: F.R. Boyd and H.O.A. Meyer (eds.)The mantle sample: inclusions in kimberlites and other volcanics, Proc. 2nd Int. Kimberlite Conf., Vol. 2, AGU, pp. 1–14.
Kandelin, J. and D.J. Weidner: 1988a, ‘Elastic properties of jadeite’,Phys. Earth Pl. Inter. 50, 251–260.
Kandelin, J. and D.J. Weidner: 1988b, ‘Elastic properties of hedenbergite’,J. Geophys. Res. B93, 1063–1072.
Kern, H.: 1982, ‘Elastic wave velocities and constants of elasticity of rocks at evaluated pressures and temperatures’, in G. Angenheister (ed.),Physical properties of rocks, Landolt-Bornstein, group V, Vol. 1, Subvol. b, Springer Verlag, Berlin, pp. 99–140.
Kern, H. and V. Schenk: 1985, ‘Elastic wave velocities in rocks from a lower crustal section in southern Calabria (Italy)’,Phys. Earth Pl. Inter. 40, 147–160.
Kern, H. and V. Schenk: 1988, ‘A model of velocity structure beneath Calabria, southern Italy, based on laboratory data’,Earth Pl. Sci. Lett. 87, 325–337.
Kerrick, D.M. and L.S. Darken: 1975, ‘Statistical thermodynamic models for ideal oxide and silicate solid solutions, with application to plagioclase’,Geochim. Cosmochim. Acta 39, 1431–1442.
Krylov, S.V., A.V. Bryksin and E.N. Ten: 1990, ‘Elastic properties of silica minerals and crystalline rocks in isotropic model’,Geol. and Geophys. 12, 90–97 (in Russian).
Kushiro, I. and H.C. Yoder, Jr.: 1966, ‘Anorthite-forsterite and anorthite-enstatite reactions and their bearing on the basalt-eclogite transformation’,J. Petrol. 7, 337–362.
Leitner, B.J., D.J. Weidner and R.C. Liebermann: 1980, ‘Elasticity of single crystal pyrope and implications for garnet solid solution series’,Phys. Earth Pl. Inter. 22, 111–121.
Le Maitre, R.W.: 1976, ‘The chemical variability of some common igneous rocks’,J. Petrol. 17, 589–637.
Lindsley, D.H.: 1981, ‘The formation of pigeonite on the join hedenbergite-ferrosilite at 11.5 and 15 kbar: experiments and a solution model’,Am. Miner. 66, 1175–1182.
Lindsley, D.H., J.E. Grover and P.M. Davidson: 1981, ‘The thermodynamics of the Mg2Si2O6CaMgSi2O6 join: a review and an improved model’, in: R.C. Newton, A. Navrotsky and B.J. Wood (eds.),Thermodynamics of minerals and melts, Adv. Phys. Geochem. 1, Springer Verlag, pp. 149–175.
Maaloe, S. and K.I. Aoki: 1977, ‘The major element composition of the upper mantle estimated from the composition of lherzolites’,Contr. Miner. Petrol. 63, 161–173.
Manghnani, M.H., R. Ramananantoandro and S.P. Clark, Jr.: 1974, ‘Compressional and shear wave velocities in granulite facies rocks and eclogites to 10 kbar’,J. Geophys. Res. 70, 5427–5446.
McDonough, W.F. and F.A. Frey: 1989, ‘Rare Earth elements in upper mantle rocks’,Rev. Mineral. 21, 99–146.
Newton, R.C., T.V. Charlu and O.J. Kleppa: 1980, ‘Thermochemistry of the high structural state plagioclases’,Geochim. Cosmochim. Acta 44, 933–941.
O'Neill, H.St.C.: 1981, ‘The transition between spinel lherzolite and garnet lherzolite and its use as a geobarometer’,Contr. Miner. Petrol. 77, 185–194.
Perkins III, D., and R.C. Newton: 1980, ‘The composition of coexisting pyroxenes and garnet in the system CaO-MgO-Al2O3-SiO2 at 900–1100 °C and high pressures’,Contr. Miner. Petrol. 75, 291–300.
Ringwood, A.E. and D.H. Green: 1966, ‘An experimental investigation of the gabbro-eclogite transformations and some geophysical implications’,Tectonophysics 3, 383–427.
Saxena, S.K. and N. Chatterjee: 1986, ‘Thermochemical data on mineral phases: the system CaO-MgO-Al2O3-SiO2’,J. Petrol. 27, 827–842.
Saxena, S.K. and G. Eriksson: 1983, ‘Theoretical computation of mineral assemblages in pyrolite and lherzolite’,J. Petrol. 24, 538–555.
Saxena, S.K., J. Sykes and G. Eriksson: 1986, ‘Phase equilibria in the pyroxene quadrilateral’,J. Petrol. 27, 843–852.
Schenk, V.: 1984, ‘Petrology of felsic granulites, metapelites, metabasics, ultramafics, and metacarbonates from southern Calabria (Italy): prograde metamorphism, uplift and cooling of a former lower crust’,J. Petrol. 25, 255–298.
Sobolev, S.V. and A.Yu. Babeyko: 1989, ‘Phase transformations in the lower continental crust and its seismic structure’, in R.S. Mereu, S. Mueller and D.M. Fountain (eds.),Properties and processes of Earth's lower crust, Geophys. Monogr. 51, AGU, pp. 311–320.
Sobolev S. V., A.Yu. Babeyko: 1992, A new tool for petrological interpretation of seismic data.Science and Technology in Russia. No. 0, December 1992, p. 14 (in Russian and in English).
Solov'ev, S.P.: 1970,Chemism of the igneous rocks and some problems of petrochemistry, Nauka, Leningrad (in Russian).
Sumino, Y. and O.L. Anderson: 1984, ‘Elastic constants of minerals’, in R.S. Carmichael (ed.),Handbook of physical properties of rocks, Vol.III, CRC Press, pp. 39–138.
Vaughan, M.I. and S. Guggengheim: 1986, ‘Elasticity of muscovite and its relationship to crystal structure’,J. Geophys. Res. B91, 4657–4664.
Volarovitch M.P. (ed.): 1988,Physical properties of minerals and rocks at high thermodynamic parameters. Nedra, Moscow, 226p (in Russian).
Watt, P.J., G.F. Davis and R.J. O'Connell: 1976, ‘The elastic properties of composite materials’,Rev. Geophys. Space Phys. 14, 541–563.
Wood, B.J.: 1987, ‘Thermodynamics of multicomponent systems containing several solid solutions’,Rev. Mineral. 17, 71–95.
Wood, B.J. and J.R. Holloway: 1984, ‘A thermodynamic model for subsolidus equilibria in the system CaO-MgO-Al2O3-SiO2’,Geochim. Cosmochim. Acta 48, 159–176.
Wood, B.J. and O.J. Kleppa: 1981, ‘Thermochemistry of forsterite-fayalite olivine solutions’,Geochim. Cosmochim. Acta 45, 529–534.
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Sobolev, S.V., Babeyko, A.Y. Modeling of mineralogical composition, density and elastic wave velocities in anhydrous magmatic rocks. Surv Geophys 15, 515–544 (1994). https://doi.org/10.1007/BF00690173
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DOI: https://doi.org/10.1007/BF00690173