Advertisement

Partial Melting and Melt Segregation in a Convecting Mantle

  • Harro Schmeling
Chapter
Part of the Petrology and Structural Geology book series (PESG, volume 11)

Abstract

Various causes for mantle melting (decompression, heating or release of water) combined with current estimates of upper mantle temperatures and the state of stress in the lithosphere suggest that in many regions the asthenosphere might be partially molten, but melts may not always be able to rise to the surface. The governing equations describing melting, melt segregation, compaction and depletion in a deforming medium are discussed with emphasis on the physical processes involved. To combine these processes with a convecting upper mantle flow, a “Compaction Boussinesq Approximation” (CBA) is introduced and tested with known solutions. Driving forces include thermal, melt, depletion and enrichment buoyancy. The bulk viscosity and its dependence on porosity has a significant effect on the melt flow even for distances large compared to the compaction length. 1D and 2D solitary porosity waves are discussed with particular emphasis on a variable bulk viscosity, compaction, and dilatation of the matrix. Melting, segregation and solidification processes are studied in a self-consistent model of a variable viscosity plume head arriving at the base of the lithosphere. It is shown that melt buoyancy dominates segregation velocities. However, a variable bulk viscosity may still have some influence on the segregation velocities, while dynamic pressures may be neglected. In the absence of a mantle plume a partially molten undepleted asthenosphere may develop melting instabilities, driven by thermal, melt and depletion buoyancy. This instability propagates laterally with velocities of the order of several cm/a and has a length scale of about 2 times the thickness of the partially molten asthenosphere. Volcanism associated with this propagating instability might have a similar appearance as hot spot tracks suggesting that this instability might be an alternative mechanism to the plume hypothesis at least for some volcanic chains.

Key words

Asthenosphere compaction segregation convective melting modeling 

References

  1. Agee, C. B., and D. Walker, Olivine flotation in mantle melt, Earth Planet. Sci. Lett., 114, 315–324, 1993.CrossRefGoogle Scholar
  2. Akaogi, M., E. Ito, and A. Navrotsky, Olivine-modified spinel-spinel transitions in the system Mg2SiO4−Fe2SiO4: Calorimetric measurements, thermochemical calculation, and geophysical application, J. Geophys. Res., 94, 15,671–15,685, 1989.CrossRefGoogle Scholar
  3. Akaogi, M., H. Kojitani, K. Matsuzaka, T. Suzuki, and E. Ito, Postspinel transformations in the system Mg2SiO4−Fe2SiO4: Element partitioning, calorimetry, and thermodynamic calculation., in; Properties of Earth and Planetary Materials at High Pressure and Temperature, Geophys. Monogr. 101, pp. 373–384, AGU, Washington, 1998.CrossRefGoogle Scholar
  4. Bai, Q., and D. L. Kohlstedt, Substantial hydrogen solubility in olivine and implications for water storage in the mantle, Nature, 357, 672–674, 1992.CrossRefGoogle Scholar
  5. Barcilon, V., and F. M. Richter, Nonlinear waves in compacting media, J. Fluid Mech., 164, 429–448, 1986.CrossRefGoogle Scholar
  6. Barcilon, V., and O. M. Lovera, Solitary waves in magma dynamics, J. Fluid Mech., 204, 121–133, 1989.CrossRefGoogle Scholar
  7. Barnouin-Jha, K., E. M. Parmentier, and D. W. Sparks, Buoyant mantle upwelling and crustal production at oceanic spreading centers: On-axis segmentation and off-axis melting, J. Geophys. Res., 102, 11,979–11,989, 1997.CrossRefGoogle Scholar
  8. Bell, D. R., and G. R. Rossman, Water in the earth’s mantle: the role of nominally anhydrous minerals, Science, 255, 1391–1397, 1992.CrossRefGoogle Scholar
  9. Bittner, D., and H. Schmeling, Numerical modelling of melting processes and induced diapirism in the lower crust, Geophys. J. Int., 123, 59–70, 1995.CrossRefGoogle Scholar
  10. Ceuleneer, G., M. Monnereau, M. Rabinowicz, and C. Rosemberg, Thermal and petrological consequences of melt migration within mantle plumes, Phil. Trans. R. Soc. Lond. A, 342, 53–64, 1993.CrossRefGoogle Scholar
  11. Connolly, J. A. D., and Y. Y. Podladchikov, Compaction-driven fluid flow in viscoelastic rock, Geodinamica Acta (Paris), 11, 55–84, 1998.CrossRefGoogle Scholar
  12. Cordery, M. J., and J. Phipps Morgan, Convection and melting at mid-ocean ridges, J. Geophys. Res., 98, 19,477–19,503, 1993.CrossRefGoogle Scholar
  13. Farnetani, D. G., and M. A. Richards, Thermal entrainment and melting in mantle plumes. Earth Planet. Sci. Lett., 136, 251–267, 1995.CrossRefGoogle Scholar
  14. Faul, U. H., Permeability of partially molten upper mantle rocks from experiments and percolation theory, J. Geophys. Res., 102, 10,299–10,311, 1997.CrossRefGoogle Scholar
  15. Faul, U. H., D. R. Toomey, and H. S. Waff, Intergranular basaltic melt is distributed in thin, elongated inclusions, Geophys. Res. Lett., 21, 29–32, 1994.CrossRefGoogle Scholar
  16. Herzberg, C. T., Magma density at high pressure Part 2: A test of the olivine flotation hypothesis, in: Magmatic Processes: Physicochemical Processes, edited by B. O. Mysen, pp. 47–58, Geochemical Society, Special Publication No. 1, 1987.Google Scholar
  17. Herzberg, C, and J. Zhang, Melting experiments on anhydrous peridotite KLB-1: Compositions of magmas in the upper mantle and transition zone, J. Geophys. Res., 101, 8271–8295, 1996.CrossRefGoogle Scholar
  18. Hirschmann, M. M., M. S. Ghiorso, L. E. Wasylenki, P. D. Asimov, and E. M. Stolper, Calculation of peridotite partial melting from thermodynamic models of minerals and melts. I. Review of methods and comparison with experiments, J. Petrol., 39, 1091–1115, 1998.CrossRefGoogle Scholar
  19. Hirth, G., and D. L. Kohlstedt, Water in the oceanic upper mantle: implications for rheology, melt extraction and the evolution of the lithosphere, Earth Planet. Set Lett., 144, 93–108, 1996.CrossRefGoogle Scholar
  20. Inoue, T., and H. Sawamoto, High pressure melting of pyrolite under hydrous condition and its geophysical implications, in: High-pressure research: Application to Earth and Planetary Sciences, edited by Y. Syono and M. H. Manghnani, pp. 323–331, Terra Scientific Publ. Comp., Tokyo/AGU, Washington D.C., 1992.CrossRefGoogle Scholar
  21. Irifune, T., and A. E. Ringwood, Phase transformations in subducted oceanic crust and buoyancy relationships at depths of 600–800 km in the mantle, Earth Planet. Sci. Lett., 117, 101–110, 1993.CrossRefGoogle Scholar
  22. Ito, G., J. Lin, and C.W. Gable, Dynamics of mantle flow and melting at a ridge-centered hotspot: Iceland and the Mid-Atlantic ridge. Earth Planet. Sci. Lett., 144, 53–74, 1996.CrossRefGoogle Scholar
  23. Iwamori, H., D. McKenzie, and E. Takahashi, Melt generation by isentropic mantle upwelling, Earth Planet. Sci. Lett., 134, 253–266, 1995.CrossRefGoogle Scholar
  24. Jha, K., E. M. Parmentier, and J. Phipps Morgan, The role of mantle-depletion and melt-retention buoyancy in spreading-center segmentation, Earth Planet. Sci. Lett., 125, 221–234, 1994.CrossRefGoogle Scholar
  25. Jordan, T. H., Mineralogies, densities and seismic velocities of garnet lherzolites and their geophysical implications, in: The Mantle Sample: Inclusions in Kimberlites and other Volcanics, edited by F.R. Boyd and O. A. Meyer, pp. 1–14, AGU, Washington, 1979.CrossRefGoogle Scholar
  26. Katsura, T., and E. Ito, The system Mg2SiO4−Fe2SiO4 at high pressures and temperatures: Precise determinations of stabilities of olivine, modified spinel, and spinel, J. Geophys. Res., 94, 15,663–15,670, 1989.CrossRefGoogle Scholar
  27. Khodakovskii, G., M. Rabinowicz, G. Ceuleneer, and V. P. Trubitsyn, Melt percolation in a partially molten mantle mush: effect of a variable viscosity, Earth Planet. Sci. Lett., 134, 267–281, 1995.CrossRefGoogle Scholar
  28. Kohlstedt, D. L., H. Keppler, and D. C. Rubie, Solubility of water in the α, β and γ phases of (Mg, Fe)2SiO4, Contrib. Mineral. Petrol., 123, 345–357, 1996.CrossRefGoogle Scholar
  29. Langmuir, C. H., E. M. Klein, and T. Plank, Petrological systematics of mid-ocean ridge basalts: Constraints on melt generation beneath ocean ridges, in: Mantle Flow and Melt Generation at Mid-Ocean Ridges, edited by J. Phipps Morgan, D. K. Blackman and J. M. Sinton, pp. 183–280, Geophysical Monograph 71, American Geophysical Union, 1992.CrossRefGoogle Scholar
  30. Manglik, A., and U. R. Christensen, Effect of mantle depletion buoyancy on plume flow and melting beneath a stationary plate, J. Geophys. Res., 102, 5019–5028, 1997.CrossRefGoogle Scholar
  31. McKenzie, D., The generation and compaction of partially molten rock, J. Petr., 25, 713–765, 1984.Google Scholar
  32. McKenzie, D., The extraction of magma from the crust and mantle, Earth Planet. Sci. Lett., 74, 81–91, 1985.CrossRefGoogle Scholar
  33. McKenzie, D. P., The compaction of igneous and sedimentary rocks, J. Geol. Soc, London, 144, 299–307, 1987.CrossRefGoogle Scholar
  34. McKenzie, D., and M. J. Bickle, The volume and composition of melt generated by extension of the lithosphere, J. Petr., 29, 625–679, 1988.Google Scholar
  35. Mibe, K, T. Fujii, and A. Yasuda, Connectivity of aqueous fluid in the earth’s upper mantle, Geophys. Res. Lett., 25, 1233–1236, 1998.CrossRefGoogle Scholar
  36. O’Connell, R. J., and B. Budiansky, Viscoelastic properties of fluid-saturated cracked solids, J. Geophys. Res., 82, 5719–5735, 1977.CrossRefGoogle Scholar
  37. Ohtani, E., A. Suzuki, and T. Kato,: Flotation of olivine and diamond in mantle melt at high pressure: Implications for fractionation in the deep mantle and ultradeep origin of diamond, in: Properties of Earth and Planetary Materials at high pressure and temperature. Geophys. Monograph 101, edited by M. Manghnani and T. Yagi, pp. 227–239, American Geophysical Union, Washington, 1998.CrossRefGoogle Scholar
  38. Olson, P., Mechanics of flood basalt magmatism, in: Magmatic Systems, edited by M. P. Ryan, pp. 1–18, Academic Press, 1994.CrossRefGoogle Scholar
  39. Parmentier, E. M. and J. Phipps Morgan, Spreading rate dependence of three-dimensional structure in oceanic spreading centres, Nature, 348, 325–328, 1990.CrossRefGoogle Scholar
  40. Phipps Morgan, J., Melt migration beneath mid-ocean spreading centers, Geophys. Res. Lett., 14, 1238–1241, 1987.CrossRefGoogle Scholar
  41. Ribe, N. M., The deformation and compaction of partial molten zones, Geophys. J. R. astr. Soc., 83, 487–501, 1985a.CrossRefGoogle Scholar
  42. Ribe, N. M., The generation and composition of partial melts in the earth’s mantle, Earth Planet. Sci. Lett., 73, 361–376, 1985b.CrossRefGoogle Scholar
  43. Ribe, N. M., Theory of melt segregation—A review, J. Volcan. Geotherm. Res., 33, 241–253, 1987.CrossRefGoogle Scholar
  44. Ribe, N. M., and M. D. Smooke, A stagnation point flow model for melt extraction from a mantle plume, J. Geophys. Res., 92, 6437–6443, 1987.CrossRefGoogle Scholar
  45. Ribe, N. M., U. R. Christensen, and J. Theißing, The dynamics of plume—ridge interaction, 1: Ridge-centered plumes, Earth Planet. Sci. Lett., 134, 155–168, 1995.CrossRefGoogle Scholar
  46. Richardson, C. N., Melt flow in a variable viscosity matrix, Geophys. Res. Lett., 25, 1099–1102, 1998.CrossRefGoogle Scholar
  47. Richter, F. M. and D. McKenzie, Dynamical models for melt segregation from a deformable matrix, J. Geology, 92,129–140, 1984.CrossRefGoogle Scholar
  48. Schilling, J.-G., Fluxes and excess temperatures of mantle plumes inferred from their interaction with migrating mid-ocean ridges, Nature, 352, 397–403, 1991.CrossRefGoogle Scholar
  49. Schmeling, H., Numerical models on the influence of partial melt on elastic, anelastic, and electric properties of rocks. Part I: elasticity and anelasticity, Phys. Earth Planet. Int., 41, 34–57, 1985.CrossRefGoogle Scholar
  50. Schmeling, H., 1989 Compressible convection with constant and variable viscosity: the effect on slab formation, geoid, and topography, J. Geophys. Res., 94, 12,463–12,481, 1989.CrossRefGoogle Scholar
  51. Schmeling, H., and G. Y. Bussod, Variable viscosity convection and partial melting in the continental asthenosphere, J. Geophys. Res., 101, 5411–5423, 1996.CrossRefGoogle Scholar
  52. Schmeling, H. and G. Marquart, The influence of second-scale convection on the thickness of the continental lithosphere and crust, Tectonophysics, 189, 281–306, 1991.CrossRefGoogle Scholar
  53. Scott, D. R., and D. J. Stevenson, Magma solitons, Geophys. Res. Lett., 11, 1161–1164, 1984.CrossRefGoogle Scholar
  54. Scott, D. R. and D. J. Stevenson, Magma ascent by porous flow, J. Geophys. Res., 91, 9283–9296, 1986.CrossRefGoogle Scholar
  55. Shen, Y. and D. W. Forsyth, Geochemical constraints on the initial and final depths of melting beneath mid-ocean ridges, J. Geophys. Res., 100, 2211–2237, 1995.CrossRefGoogle Scholar
  56. Sleep, N. H., Tapping of melt by veins and dikes, J. Geophys. Res., 93, 10,255–10,272, 1988.Google Scholar
  57. Smith, D.G. (ed), The Cambridge Encyclopedia of Earth Sciences, 496 pp., Cambridge University Press, Cambridge, 1981.Google Scholar
  58. Sparks, D. W., and E. M. Parmentier, Melt extraction from the mantle beneath spreading centers, Earth Planet. Sci. Lett., 105, 368–377, 1991.CrossRefGoogle Scholar
  59. Spiegelman, M., Flow in deformable porous media. Part I. Simple analysis, J. Fluid Mech., 247, 17–38, 1993a.CrossRefGoogle Scholar
  60. Spiegelman, M., Flow in deformable porous media. Part II. Numerical analysis — the relationship between shock waves and solitary waves, J. Fluid Mech., 247, 39–63, 1993b.CrossRefGoogle Scholar
  61. Stolper, E., D. Walker, B.H. Hager, and J.F. Hays, Melt segregation from partially molten source regions: the importance of melt density and source region size, J. Geophys. Res., 86, 6261–6271, 1981.CrossRefGoogle Scholar
  62. Tackley, P.J., and D. J. Stevenson, A mechanism for spontaneous self-perpetuating volcanism on the terrestrial planets, in: Flow and Creep in the Solar System: Observations, Modeling and Theory, edited by D. B. Stone and S. K. Runcorn, pp. 307–321, Kluwer, Dordrecht, 1993.Google Scholar
  63. Takahashi, E., Melting of a dry peridotite KLB-1 up to 14 GPa: Implications on the origin of peridotitic upper mantle, J. Geophys. Res., 91, 9367–9382, 1986.CrossRefGoogle Scholar
  64. Thompson, A. B., Water in the earth’s upper mantle, Nature, 358, 295–302, 1992.CrossRefGoogle Scholar
  65. Turcotte, D.L., and J. Phipps Morgan, The Physics of magma migration and mantle flow beneath a mid-ocean ridge. Geophys. Monograph 71, pp. 155–182, American Geophysical Union, Washington D.C., 1992.CrossRefGoogle Scholar
  66. van Keken, P., Evolution of starting mantle plumes: a comparison between numerical and laboratory models, Earth Planet. Sci. Lett., 148, 1–11, 1997.CrossRefGoogle Scholar
  67. White, R. S., D. McKenzie, and R. K. O’Nions, Oceanic crustal thickness from seismic measurements and rare earth element inversions, J. Geophys. Res., 97, 19,683–19,715, 1992.Google Scholar
  68. White, R.S. and D. McKenzie, Mantle plumes and flood basalts, J. Geophys. Res., 100, 17,543–17,585, 1995.Google Scholar
  69. Wiggins, C. and M. Spiegelman, Magma migration and magmatic solitary waves in 3-D, Geophys. Res. Lett., 22, 1289–1292, 1995.CrossRefGoogle Scholar
  70. Zoback, M. L., First- and second-order patterns of stress in the lithosphere: The World Stress Map project, J. Geophys. Res., 97, 11,703–11,728, 1992.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Harro Schmeling
    • 1
  1. 1.Department of Geology and Geophysics, SOESTUniversity of Hawaii at ManoaHonoluluUSA

Personalised recommendations