Abstract
The present study deals with the torsion deformation of partially molten samples of pyroxene gabbro-norite, spinel lherzolite, basalt lava and dacite pumice at high temperatures (600–1200C) and over a range of frequencies (20 Hz –2.10−3 Hz). The anelastic and viscoelastic properties of partially molten samples of rocks have been studied using oscillatory force torsion apparatus. Measurements of the complex shear modulus (G*) and internal friction (Q−1) at small strains (~ 10−7) show that samples do not possess a relaxed shear viscosity at the highest temperatures of experiments, if the melt phase is less than 60 vol%. Frequency dependence of the internal friction indicates that the viscoelasticity of the melt phase starts to overwhelm other mechanisms of anelastic behaviour at the high temperature - low frequency range ωτ 1, where ωτ is the normalised frequency. Below the softening temperature of the melt phase, there is a general dependence of Q−1 ∝ ω−0.17±0.01, where ω is the angular velocity of forced oscillations. Above the softening temperature, Q−1 ∝ ω−α where the empirical exponent α > 0.35 and depends on the melt fraction and the shape of the crystals. At low temperatures and moderate melt fractions (10–20 vol%), there may be a band of frequencies and temperatures where internal friction has a weak frequency dependence or some poorly resolved peaks. The nature of these peaks can be associated with several shear stress relaxation processes such as grain boundary sliding, rotation of grains suspended in the viscous melt, and movement of melt between adjacent melt pockets. The relative contribution of these relaxation processes depends on the melt fraction, grain size and normalised frequency ωτ.
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References
Alidibirov, M., D.B. Dingwell, R.J. Stevenson, K.-U. Hess, S.L. Webb, and J. Zinke, Physical properties of the 1980 Mount St. Helens cryptodome magma, Bull. Volcanol., 59, 103–111, 1997.
Anderson, D.L., Theory of the Earth, pp. 279–302, Blackwell Scie. Publ., Boston, 1989.
Anderson, D.L., and J.W. Given, Absorption band Q model for the Earth, J. Geophys. Res., 87, 3993–3904, 1982.
Anderson, D.L., and J.B. Minster, The frequency dependence of Q in the Earth and implications for mantle rheology and Chandler wobble, Geophys. J. R. astr. Soc., 58, 431–440, 1979.
Arzi, A., Critical phenomena in the rheology of partially melted rocks, Tectonophysics, 44, 173–184, 1978.
Bagdassarov, N.S., Viscoelastic properties of mica based glass ceramic aggregate, Phys. Chem. Miner., 26, 513–520, 1999.
Bagdassarov, N.S., and D.B. Dingwell, Frequency dependent rheology of vesicular rhyolite. J. Geophys. Res., 98, 6477–6487, 1993.
Bagdassarov, N.S., D.B. Dingwell, and S.L. Webb, Effect of boron, phosphorus and fluorine on shear stress relaxation in haplogranite melts, Eur. J. Mineral., 5, 409–425, 1993.
Bagdassarov, N.S., D.B. Dingwell, and S.L. Webb, Viscoelasticity of crystal- and bubble-bearing rhyolite melts, Phys. Earth Planet. Inter., 83, 83–89, 1994.
Bagdassarov, N.S., and A.M. Dorfman, Viscoelastic behaviour of partially molten granites, Tectonophysics, 290, 27 – 45, 1998.
Berckhemer, H., F. Auer, and J. Drisler, High-temperature anelasticity and elasticity of mantle peridotite, Phys. Earth Planet. Inter., 20, 48–59, 1979.
Berckhemer, H., W. Kampfmann, and E. Aulbach, Anelasticity and elasticity of mantle rocks near partial melting, in: High-Pressure Researches in Geoscience, edited by E.W. Schreyer, pp. 113–132, Schwaizerbart’sche Verlagsbuchhandlung, Stuttgart, 1982a.
Berckhemer, H., W. Kampfmann, E. Aulbach, and H. Schmeling, Shear modulus and Q of forsterite and dunite near partial melting from forced-oscillation experiments, Phys. Earth Planet. Inter. 29, 30–41, 1982b.
Berryman, J.G., Long-wavelength propagation in composite elastic media. 1. Spherical inclusions. 2. Ellipsoidal inclusions, J. Acoust. Soc. Am., 68(6), 1809–1831, 1980.
Brawer, S., Relaxation in viscous liquids and glasses, pp. 131–142, Amer Cer Soc, Inc. Columbus, Ohio, 1985.
Carter, N.L., and S. Kirby, Transient creep and semi-brittle behavior of crystalline rocks, Pure Appl. Geophys, 116, 807–839, 1978.
Caputo, M., Linear models of dissipation whose Q is almost frequency independent — II,. Geophys J. R astr Soc., 13, 529–539, 1967.
Cooper, R.F., Differential stress-induced melt migration: an experimental approach, J. Geophys. Res., 95, 6979–6992, 1990.
Cooper, R.F., D.L. Kohlstedt, and K. Chyung, Solution-precipitation enhanced creep in solid-liquid aggregates which display a non-zero dihedral angle, Acta Metall., 37, 1759–1771, 1989.
Day, D.E., and G.E. Rindone, Internal friction of progressively crystallised glasses, J. Amer. Cer Soc., 44, 161–167, 1961.
Drury, M.R., and J.D. Fitz Gerald, Grain boundary melt films in an experimentally deformed olivine-pyroxene rocks: implications for melt distribution in upper mantle rocks, Geophys. Res. Lett., 23, 701–704, 1996.
Dryden J.R., D. Kucerovsky, D.S. Wilkinson, and D.F. Watt, Creep deformation due to a viscous grain boundary phase, Acta Metall., 37, 2007–2015, 1989.
Esquivel-Sirvent, R., D.H. Green, and S.S. Yun, Critical behavior in the fluid/solid transition of suspensions, Appl. Phys. Lett., 67, 3087 – 3089, 1995.
Fernandez, A.N., and B. Barbarin, Relative rheology of coeval mafic and felsic magmas: Nature resulting interaction process. Shape and mineral fabrics of mafic microgranular enclaves, in: Enclaves and granite petrology. Developments in Petrology 13, edited by J. Didier and B. Barbarin, pp. 263–276, Elsevier, Amsterdam — Oxford — New York —Tokyo, 1991.
Findley, W.N., J.S. Lai, and K. Onaran, Creep and relaxation of nonlinear viscoelstic materials, 368 pp., North-Holland Publishing Company, Amsterdam-NY-Oxford, 1976.
Getting, I.C., J. Paffeholz, and H.A. Spetzler, Measuring attenuation in geologic materials at seismic frequencies and amplitudes, in: The brittle-ductile transition in rocks, edited by A. Duba et al., pp. 239–243, AGU, Washington, 1990.
Gittus, J., Creep, viscoelasticity and creep fracture in solids, 725 pp., Applied Science Publishers, London, 1975.
Götze W., and L. Sjögren, Relaxation processes in supercooled liquids, Rep. Progr. Phys., 55, 241–376, 1992.
Green, D.H., and R.F. Cooper, Dilatational anelasticity in partial melts: viscosity, attenuation, and velocity dispersion, J. Geophys. Res., 98, 19,807–19,817, 1993
Green, D.H., R.F. Cooper, and S. Zhang, Attenuation spectra of olivine/basalt partial melts: transformation of Newtonian creep response, Geophys. Res. Lett., 17, 2097–2100, 1990.
Gribb, T.T., and R.F. Cooper, Low-frequency shear attenuation in polycrstalline olivine: Grain boundary diffusion and the physical significance of the Andrade model for viscoelastic rheology, J. Geophys. Res., 103, 27,267–27,279, 1998.
Gribb, T.T., S. Zhang, and R.F. Cooper, Melt migration and related attenuation in equilibrated partial melts, in: Magmatic systems, edited by M.P. Ryan, pp. 19–36, Acad. Press, San Diego, 1994.
Gueguen, Y., M. Darot, P. Mazot, and J. Woigard, Q−1 of forsterite single crystals. Phys. Earth Planet. Inter., 55, 254–258, 1989.
Gueguen, Y., J. Woirgard, and M. Darot, Attenuation mechanism and anelasticity in the upper mantle, in: Anelasticity in the Earth, Geodynamic series, vol 4, edited by F.D. Stacey, M.S. Paterson and A. Nicholas, pp. 86–94, AGU GSA, Boulder Colorado, 1981.
Hanson, D.R., and H.A. Spetzler, Transient creep in natural and synthetic, iron-bearing olivine single crystals: mechanical results and dislocation microstructures, Tectonophysics, 235, 293–315, 1994.
Hill, R., A self-consistent mechanics of composite materials,. J. Mech. Phys. Solids, 13, 213–222, 1965.
Isaak, D.G., High-temperature anelsticity of iron-bearing olivines. J. Geophys. Res., 97, 1871–1885, 1992.
Ivins, E.R., and C.G. Sammis, On lateral viscosity contrast in the mantle and the rheology of low-frequency geodynamics, J. Geophys. Res., 123, 305 – 322, 1995.
Ivins, E.R., and C.G. Sammis, Transient creep of composite lower crust. 1. Constitutive theory, J. Geophys. Res., 101, 27, 981– 28,004, 1996.
Jackson, I., Progress in the experimental study of seismic wave attenuation, Annu.. Rev. Earth Planet. Sci., 21, 375–406, 1993.
Jackson, I., and M.S. Paterson, Shear modulus and internal friction of calcite rocks at seismic frequencies: pressure, frequency and grain size dependence, Phys. Earth Planet. Inter., 45, 349–367, 1987.
Jackson, I., M.S. Paterson, and J.D. Fitz Gerald, Seismic wave dispersion and attenuation in Aheim dunite: an experimental study, Geophys. J. Int., 108, 517–534, 1992.
Jackson, I., M. Paterson, H. Niesler, and R.M. Waterford, Rock anelasticity measurements at high pressure, low strain amplitude and seismic frequency, Geophys. Res. Lett., 11, 1235–1238, 1984.
Jäckle, J., Models of glass transition, Rep. Prog. Phys., 49, 171–231, 1986.
Ji, S., and P. Zhao, Strength of two-phase rocks: a model based on fiber-loading theory, J. Struct. Geology, 16, 253–262, 1994.
Johnson, D.H., and M.N. Toksöz, Thermal cracking and amplitude dependent attenuation, J. Geophys. Res., 85, 937–942, 1980.
Kampfmann, W., Laborexperimente zum elastischen und anelastischen Verhalten hochtemperierter magmatischer Gesteine im Frequenzbereich seismischer Wellen. Berichte des Instituts für Meteorologie und Geophysik, 137 pp., J. W. Goethe Universität Frankfurt, Frankfurt/Main, 1984.
Kampfmann, W., and H. Berckhemer, High temperature experiments on the elastic and anelastic behaviour of magmatic rocks, Phys. Earth Planet. Inter., 40, 223–247, 1985.
Karato, S., and H.A. Spetzler, Defect microdynamics in minerals and solid-state mechanisms of seismic wave attenuation and velocity dispersion in the mantle, Rev. Geophys., 28, 399–421, 1990.
Kê, T.-S., A grain boundary model and the mechanism of viscous intercrystalline slip, J. Appl. Phys., 20, 274–280, 1949.
Kohlstedt, D.L., and M.E., Zimmermann, Rheology of partially molten mantle rocks, Ann. Rev. Planet. Scie., 24, 41– 62, 1996.
Körnig, M., and G. Müller, Rheological models and interpretation of postglacial uplift, Geophys. J. Int., 98, 243–253, 1989.
Landau, L.D., and E.M., Lifshitz, Fluid Mechanics. Course of Theoretical Physics, vol. 6, Hydrodynamics, 730 pp., 2-d ed., Pergamon Press, New York, 1987.
Leak, G.M., Grain boundary damping I: Pure Iron, Proc. Phys. Soc., 78, 1520–1528, 1961.
Mavko, G.M., Velocity and attenuation in partially molten rocks, J. Geophys. Res., 85, 5173–5189, 1980.
Mavko, G.M., and A., Nur, Melt squirt in the astenosphere. J. Geophys. Res., 80, 1444–1448, 1975.
Means, W.D., and M.W. Jessel, Accommodation migration of grain boundaries, Tectonophysics, 127, 67 – 86, 1986.
Mosher, D.R., and R. Raj, Use of the Internal friction technique to measure rates of grain boundary sliding, Acta Metall., 22, 1469–1474, 1974.
Müller, G., Generalised Maxwell bodies and estimates of mantle viscosity, Geophys. J. R. astr. Soc., 87, 1113–1141, 1986.
Nowick, A.S., and B.S. Berry, Anelastic relaxation in crystalline solids, 678 pp., Academic Press, New York – London, 1972.
O’Connel, R.J., and B. Budiansky, Viscoelastic properties of fluid-saturated cracked solids, J. Geophys. Res., 82, 5719–5735, 1977.
Pinkerton, H., R.A. Herd, R.M. Kent, and L. Wilson, Field measurements of the rheological properties of basaltic lavas, Lunar and Planetary Science, XXVI, 1127–1128, 1995.
Pinkerton, H., and R. Stevenson, Methods determining the rheological properties of magmas at subsolidus temperatures, J. Volcan. Getherm. Res., 53, 47–66, 1992.
Pharr, G.M., and M.F. Ashby, On creep enhanced by a liquid phase, Acta Metall., 31, 129–138, 1983.
Plass, L., Wärmeubergang und Druckverlust bei Feststoff-Flüssig-Suspesionen feiner Teilchen im gesamten pumpfähigen Konzentrazionsbereich, Ph. D. thesis, Universität Erlangen-Nurnberg, 1972.
Pusey, P.N., and W. van Megen, Phase behaviour of concentrated suspensions of nearly hard colloidal spheres, Nature, 320, 340–342, 1986.
Raj, R., Transient behaviour of diffusion induced creep and creep rupture, Metall Trans., A, 6, 1499–1509, 1975.
Raj, R., Creep in polycrystalline aggregates by matter transport through a liquid phase, J. Geophys. Res., 87, 4731–4739, 1982.
Raj, R., and M.F. Ashby, On grain boundary sliding and diffusional creep, Metal. Trans., 2, 1113–1127, 1971.
Rutherford, M.J., H. Sigurdsson, S. Carey, and A. Davis, The May 18, 1980 eruption of Mount St. Helens 1. melt composition and experimental phase equilibria, J. Geophys. Res., 90, 2929–2947, 1985.
Rutter, E. H., and D.H. Neumann, Experimental deformation of partially molten Westerly granite under fluid-absent conditions, with implications for the extraction of granitic magmas, J. Geophys. Res., 100, 15 697–15 715, 1995.
Ryerson, F.J., H.C. Weed, and A.J. Piwinskii, Rheology of subliquidus magmas. 1. Picritic compositions, J. Volcanol. Geotherm. Res., 93, 3421–3436, 1988.
Sato, H., S. Sacks, T. Murase, G. Muncill, and H. Fukuyama, Qp — melting temperature relation in peridotite at high pressure and temperature: attenuation mechanism and implications for the mechanical properties of the upper mantle, J. Geophys. Res., 94, 10,647–10,661, 1989.
Smith, B.K., and F.O. Carpenter, Transient creep in orthosilicates, Phys. Earth. Planet. Inter., 49, 314–324, 1987.
Tonn, R., Comparison of seven methods for the computation of Q, Phys. Earth Planet. Inter., 55, 259–268, 1989.
Turnbaugh, J.E., and F.H. Norton, Low-frequency grain-boundary relaxation in alumina, J. Amer. Cer. Soc., 51, 344–348, 1968.
Ungarish, M., Hydrodynamics of suspensions, Springer-Verlag, Berlin — Heidelberg, 1993.
Versteeg, V.A., and D.L. Kohlstedt, Internal friction in lithium aluminosilicate glass-ceramics, J. Am. Ceram. Soc., 77, 1169–1177, 1994.
Walpole, L.J., On the overall elastic moduli of composite materials, J. Mech. Phys. Solids., 17, 235–251, 1969.
Weiner, A.T., M.H. Manghnani, and R. Raj, Internal friction in tholeiitic basalt, J. Geophys. Res., 92, 11,635–11,643, 1987.
Wu, T.T., The effect of the inclusion shape on the elastic moduli of a two-phase material, Int. J. Solid Structure, 2, 1–8, 1966.
Zener, C, Elasticity and anelasticity of metals, 163 pp., University of Chicago Press, Chicago, 1948.
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Bagdassarov, N.S. (2000). Anelastic and Viscoelastic Behaviour of Partially Molten Rocks and Lavas. In: Bagdassarov, N., Laporte, D., Thompson, A.B. (eds) Physics and Chemistry of Partially Molten Rocks. Petrology and Structural Geology, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4016-4_2
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