Magma dynamics with the enthalpy method: Benchmark solutions and magmatic focusing at mid-ocean ridges

Journal of Petrology

Volumn 49, Issue 12, 2008, Pages 2099-2121

  Katz, Richard F ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Compaction; Mantle; PETSc; Simulation; Thermodynamics

Indexed keywords

BENCHMARKING; DEFORMATION MECHANISM; ENTHALPY; MAGMATISM; MANTLE CONVECTION; MANTLE PROCESS; MID-OCEAN RIDGE; OCEANIC LITHOSPHERE; ONE-DIMENSIONAL MODELING; PERMEABILITY; PETROGENESIS; TECTONIC SETTING; TWO PHASE FLOW; TWO-DIMENSIONAL MODELING; VISCOSITY; VOLCANISM;

EID: 59349099342     PISSN: 00223530     EISSN: 14602415     Source Type: Journal    
DOI: 10.1093/petrology/egn058     Document Type: Article

References (92)

1. Aharonov, E., Whitehead, J. A., Kelemen, P. B. & Spiegelman, M. (1995). Channeling instability of upwelling melt in the mantle. Journal of Geophysical Research - Solid Earth 100, 20433-20450.
2. Ahern, J. L. & Turcotte, D. L. (1979). Magma migration beneath an ocean ridge. Earth and Planetary Science Letters 45, 115-122.
3. Albers, M. (2000). A local mesh refinement multigrid method for 3-d convection problems with strongly variable viscosity. Journal of Computational Physics 160(1), 126-150, doi: 10.1006/ jcph.2000.6438.
4. Alexiades, V. & Solomon, A.D. (1993) Mathematical Modeling of Melting and Freezing Processes. New York: Hemisphere.
5. Asimow, P. D. & Stolper, E. M. (1999). Steady-state mantle - melt interactions in one dimension: I. Equilibrium transport and melt focusing. Journal of Petrology 40(3), 475-494.
6. Asimow, P. D., Hirschmann, M. M. & Stolper, E. M. (1997). An analysis of variations in isentropic melt productivity. Philosophical Transactions of the Royal Society of London, series A 355 1723), 255-281.
7. Balay, S. Buschelman, K. Gropp, W. D. Kaushik, D. Knepley, M. McInnes, L. C. Smith, B. F. and Zhang, H. (2001). PETSc Web page http://www.mcs.and.gov/petsc.
8. Balay, S. Buschelman, K. Gropp, W. D. Kaushik, D. Knepley, M. McInnes, L. C. Smith, B. F. & Zhang, H. (2004). PETSc users manual. Argonne National Laboratory,Technical Report ANL-95/11 - Revision 2.1.5.
9. Barcilon, V. & overa, O. (1989). olitary waves in magma dynamics. Journal of Fluid Mechanics 204, 121-133.
10. Batchelor, G. K. (1967). An Introduction to Fluid Mechanics. Cambridge: Cambridge University Press.
11. Bear, J. (1972). Dynamics of Fluids in Porous Media. Amsterdam: Elsevier.
12. Bercovici, D. & Ricard, Y. (2003). Energetics of a two-phase model of lithospheric damage, shear localization and plate-boundary formation. Geophysical Journal International 152, 581-596.
13. Bercovici, D., Ricard,Y. & Schubert, G. (2001). A two-phase model for compaction and damage 1. General theory. Journal of Geophysical Research - Solid Earth 106, 8887-8906.
14. Bouhifd, M. A., Besson, P., Courtial, P., Gerardin, C., Navrotsky, A. & Richet, P. (2007). Thermochemistry and melting properties of basalt. Contributions to Mineralogy and Petrology 153, 689-698, doi:10.1007/s00410-006-0170-8.
15. Bown, J. W. & White, R. S. (1994). Variation with spreading rate of oceanic crustal thickness and geochemistry. Earth and Planetary Science Letters 121, 435-449.
16. Buck, W. R. & Su, W. S. (1989). Focused mantle upwelling below midocean ridges due to feedback between viscosity and melting. Geophysical Research Letters 16(7), 641-644.
17. Butler, S. (2009) The effects of buoyancy on shear-induced melt bands in a compacting porous medium. Physics of the Earth & Planetary Interiors (Submitted).
18. Cagnioncle, A.-M., Parmentier, E.M. & Elkins-Tanton, L.T. (2007). Effect of solid flow above a subducting slab on water distribution and melting at convergent plate boundaries. Journal of Geophysical Research - Solid Earth 112, doi: 10.1029/2007JB004934.
19. Carbotte, S. M., Small, C. & Donnelly, K. (2004). The influence of ridge migration on the magmatic segmentation of mid-ocean ridges. Nature 429, 743-746.
20. Cheadle, M. J., Elliott, M. T. & McKenzie, D. (2004). Percolation threshold and permeability of crystallizing igneous rocks: The importance of textural equilibrium. Geology 32, 757-760.
21. Choblet, G. & Parmentier, E. M. (2001). Mantle upwelling and melting beneath slow spreading centers: Effects of variable rheology and melt productivity. Earth and Planetary Science Letters 184, 589-604.
22. Cooper, R. F. (1990). Differential stress-induced melt migration - an experimental approach. Journal of Geophysical Research - Solid Earth 95(B5), 6979-6992.
23. Cordery, M. J. & Morgan, J. P. (1992). Melting and mantle flow beneath a midocean spreading center. Earth and Planetary Science Letters 111(2-4), 493-516.
24. Cordery, M. J. & Morgan, J. P. (1993). Convection and melting at midocean ridges. Journal of Geophysical Research - Solid Earth 98(B11), 19477-19503.
25. Daines, M. J. & Kohlstedt, D. L. (1997). Influence of deformation on melt topology in peridotites. Journal of Geophysical Research-Solid Earth 102, 10257-10271.
26. Denbigh, K. G. (1981). The Principles of Chemical Equilibrium. 4th edn. Cambridge: Cambridge University Press.
27. Elliott, T. & Spiegelman, M. (2003). Melt migration in oceanic crustal production: A U-series perspective. In: Holland, H. D., Rudnick, R. L. & Turekian, K. K. (eds) The Crust, Treatise on Geochemistry, Vol. 3. Oxford: Elsevier-Pergamon, pp. 465-510.
28. Faul, U. H. (2001). Melt retention & segregation beneath mid-ocean ridges. Nature 410, 920-923.
29. Faul, U. H. (1997). Permeability of partially molten upper mantle rocks from experiments and percolation theory. Journal of Geophysical Research - Solid Earth 102, 10299-10311.
30. Faul, U. H., Toomey, D.R. & Waff, H.S. (1994). Intergranular basaltic melt is distributed in thin, elongated inclusions. Geophysical Research Letters 21, 29-32.
31. Forsyth, D.W., Scheirer, D. S., Webb, S. C., Dorman, L. M., Orcutt, J. A., Harding, A. J., Blackman, D. K., Morgan, J. P., Detrick, R. S., Shen, Y., Wolfe, C. J., Canales, J. P., Toomey, D. R., Sheehan, A. F., Solomon, S. C. & Wilcock, W. S. D. (1998). Imaging the deep seismic structure beneath a mid-ocean ridge: The MELT experiment. Science 280, 1215-1218.
32. Fowler, A. (1985). A mathematical model of magma transport in the asthenosphere. Geophysical and Astrophysical Fluid Dynamics 33 63-96.
33. Ghiorso, M. (1994). Algorithms for the estimation of phase stability in heterogeneous thermodynamic systems. Geochimica et Cosmochimica Acta 58(24), 5489-5501.
34. Ghiorso, M. S. & Sack, R. O. (1995). Chemical mass-transfer in magmatic processes. 4. a revised and internally consistent thermodynamic model for the interpolation & extrapolation of liquid - solid equilibria in magmatic systems at elevated temperature and pressure. Contributions to Mineralogy and Petrology 119, 197-212.
35. Ghods, A. & Arkani-Hamed, J. (2000). Melt migration beneath mid-ocean ridges. Geophysical Journal International 140, 687-697.
36. 2O on mantle wedge melting. Earth and Planetary Science Letters 249, 74-89, doi:10.1016/j.epsl.2006.06.043.
37. Hall, C. E. & Parmentier, E.M. (2000). Spontaneous melt localization in a deforming solid with viscosity variations due to water weakening. Geophysical Research Letters 27(1), 9-12.
38. Hewitt, I. J. & Fowler, A. C. (2008). Partial melting in an upwelling mantle column. Philosophical Transactions of the Royal Society of London, Series A doi:10.1098/rspa. 2008.0045.
39. Hirth, G. & Kohlstedt, D. (2003). Rheology of the upper mantle and the mantle wedge: A view from the experimentalists. In: Eiler, J. (ed.) The Subduction Factory. Geophysical Monograph, American Geophysical Union, pp. 83-105.
40. Holtzman, B. K. & Kohlstedt, D. L. (2007). Stress-driven melt segregation and strain partitioning in partially molten rocks: Effects of stress and strain. Journal of Petrology 48, 2379-2406, doi:10.1093/petrology/egm065.
41. Holtzman, B. K. Groebner, N. J. Zimmerman, M. E. Ginsberg, S. B. & Kohlstedt, D. L. (2003). Stress-driven melt segregation in partially molten rocks. Geochemistry, Geophysics, Geosystems 4, article number 8607.
42. Jull, M., Kelemen, P. B & Sims, K. (2002). Consequences of diffuse and channelled porous melt migration on uranium series disequilibria. Geochimica et Cosmochimica Acta 66, 4133-4148.
43. Karato, S. & Wu, P. (1993). Rheology of the upper mantle - a synthesis. Science 260, 771-778.
44. Katz, R. F. (2005). The deep roots of volcanoes: Models of magma dynamics with applications to subduction zones. PhD thesis, Columbia University, New york.
45. Katz, R. F. & Worster, M. G. (2008). Simulation of directional solidification, thermochemical convection, and chimney formation in Hele - Shaw cell. Journal of Computational Physics, doi:10.1016/ j.jcp.2008.06.039.
46. Katz, R. F., Spiegelman, M. & Carbotte, S. M. (2004). Ridge migration, asthenospheric flow and the origin of magmatic segmentation in the global mid-ocean ridge system. Geophysical Research Letters 31 L15605.
47. Katz, R. F., Spiegelman, M. & Holtzman, B. (2006). The dynamics of melt & shear localization in partially molten aggregates. Nature 442 676-679, doi:10.1038/nature05039.
48. Katz, R. F., Knepley,M. G., Smith, B., Spiegelman, M. & Coon, E.T. (2007). Numerical simulation of geodynamic processes with the Portable Extensible Toolkit for Scientific Computation. Physics of the Earth and Planetary Interiors 163, 52-68, doi:10.1016/ j.pepi.2007.04.016.
49. Kelemen, P., Parmentier, M., Rilling, J., Mehl, L. & Hacker, B. (2002). Thermal convection of the mantle wedge. Geochimica Cosmochimica Acta 66(15A), A389-A389.
50. Kelemen, P. B., Shimizu, N. & Salters, V. J. M. (1995). Extraction of mid-ocean-ridge basalt from the upwelling mantle by focused flow of melt in dunite channels. Nature 375(6534), 747-753.
51. Kelemen, P. B., Hirth, G., Shimizu, N., Spiegelman, M. & Dick, H. J. B. (1997). A review of melt migration processes in the adiabatically upwelling mantle beneath oceanic spreading ridges. Philosophical Transactions of the Royal Society of London, Series A 355 1723), 283-318.
52. Langmuir, C. H., Klein, E. & Plank, T. (1992). Petrological systematics of mid-oceanic ridge basalts: Constraints on melt generation beneath ocean ridges. In: Phipps Morgan, J., Blackman, D. K. & Sinton, J. M. (eds) Mantle Flow and Melt Generation at Midocean Ridges, Geophysical: Monograph, American Geophysical Union 71, pp. 183-280.
53. Maclennan, J. (2009) Concurrent mixing and cooling of melts under Iceland. Journal of Petrology (submitted).
54. Maclennan, J., Jull, M., McKenzie, D., Slater, L. & Gronvold, K. (2002). The link between volcanism and deglaciation in Iceland. Geochemistry, Geophysics, Geosystems 3, 1062, doi:10.1029/2001GC000282.
55. Magde, L. S. & Sparks, D. W. (1997). Three-dimensional mantle upwelling, melt generation, and melt migration beneath segment slow spreading ridges. Journal of Geophysical Research - Solid Earth 102, 20571-20583.
56. McKenzie, D. (1984). The generation and compaction of partially molten rock. Journal of Petrology 25(3), 713-765.
57. 238U disequilibrium and the melting processes beneath ridge axes. Earth and Planetary Science Letters 72, (2-3): 149-157, doi:10.1016/0012821X(85)90001-9.
58. Phipps Morgan, J. (1987). Melt migration beneath mid-ocean spreading centers. Geophysical Research Letters 14(12), 1238-1241.
59. 2O freezing: A simulation of young sea ice. Journal of Geophysical Research - Oceans 109, doi:10.1029/2001JC001109.
60. Rabinowicz, M. & Ceuleneer, G. (2005). The effect of sloped isotherms on melt migration in the shallow mantle: A physical and numerical model based on observations in the Oman ophiolite. Earth and Planetary Science Letters 229, 231-246.
61. Rabinowicz, M. & Vigneresse, J. L. (2004). Melt segregation under compaction and shear channeling: Application to granitic magma segregation in a continental crust. Journal of Geophysical Research - Solid Earth 109, B04407, doi:10.1029/2002JB002372.
62. Rabinowicz, M., Nicolas, A. & Vigneresse, J. L. (1984). A rolling-mill effect in the asthenosphere beneath oceanic spreading centers. Earth and Planetary Science Letters 67, 97-108.
63. Ramberg, H. (1971). Temperature changes associated with adiabatic decompression in geological processes. Nature 234, 539-540.
64. Ribe, N. M. (1985a). The generation and composition of partial melts in the Earth's mantle. Earth and Planetary Science Letters 73, 361-376.
65. Ribe, N. M. (1985b). The deformation and compaction of partial molten zones. Geophysical Journal of the Royal Astronomical Society 83 487-501.
66. Richardson, C.N. (1998). Melt flow in a variable viscosity matrix. Geophysical Research Letters 25(7), 1099-1102.
67. Saal, A. E. & van Orman, J. A. (2004). The Ra-226 enrichment in oceanic basalts: Evidence for melt-cumulate diffusive interaction processes within the oceanic lithosphere. Geochemistry, Geophysics, Geosystems 5, Q02008, doi:10.1029/2003GC.
68. Schmelling, H. (2000). Partial melting & melt segregation in a convecting mantle. In: Bagdassarov, N., Laporte, D. & Thompson, A. B. (eds) Physics and Chemistry of Partially Molten Rocks. Dordrecht: Kluwer Academic Publisher, pp. 141-178.
69. Schubert, G., Turcotte, D. L. & Olsen, P. (2001). Mantle Convection in the Earth and Planets. Cambridge: Cambridge University Press.
70. Scott, D. R. & Stevenson, D. J. (1986). Magma ascent by porous flow. Journal of Geophysical Research - Solid Earth 91, 9283-9296.
71. Scott, D. R. & Stevenson, D. J. (1989). A self-consistent model of melting, magma migration and buoyancy-driven circulation beneath mid-ocean ridges. Journal of Geophysical Research - Solid Earth 94, 2973-2988.
72. Simpson, G. (2008). The Mathematics of magma migration. PhD thesis, Columbia University, New York.
73. Sims, K. W. W., Goldstein, S. J., Blichert-Toft, J., Perfit, M. R., Kelemen, P., Fornari, D. J., Michael, P., Murrell, M. T., Hart, S. R., DePaolo, D. J., Layne, G., Ball, L., Jull, M. & Bender, J. (2002). Chemical and isotopic constraints on the generation and transport of magma beneath the East Pacific Rise. Geochimica et Cosmochimica Acta 66, 3481-3504.
74. Sparks, D. W. & Parmentier, E. M. (1991). Melt extraction from the mantle beneath spreading centers. Earth and Planetary Science Letters 105(4), 368-377.
75. Spiegelman, M. (2003). Linear analysis of melt band formation by simple shear. Geochemistry, Geophysics, Geosystems 4, doi:10.1029/ 2002GC000499.
76. Spiegelman, M. (1993a). Flow in deformable porous-media. part 1 Simple analysis. Journal of Fluid Mechanics 247, 17-38.
77. Spiegelman, M. (1993b). Flow in deformable porous media. part 2. Numerical analysis - The relationship between shock waves and solitary waves. Journal of Fluid Mechanics 247, 39-63.
78. Spiegelman, M. (1993c). Physics of melt extraction: Theory, implications, and applications. Philosophical Transactions of the Royal Society of London, Series A 342, 23-41.
79. Spiegelman, M. (1996). Geochemical consequences of melt transport in 2-d: The sensitivity of trace elements to mantle dynamics. Earth and Planetary Science Letters 139, 115-132.
80. Spiegelman, M. & Elliott, T. (1993). Consequences of melt transport for uranium series disequilibrium in young lavas. Earth and Planetary Science Letters 118, 1-20.
81. Spiegelman, M. & Kelemen, P. B. (2003). Extreme chemical variability as a consequence of channelized melt transport. Geochemistry, Geophysics, Geosystems 4, doi:10.1029/2002GC000336.
82. Spiegelman, M. & McKenzie, D. (1987). Simple 2-D models for melt extraction at mid-ocean ridges and island arcs. Earth and Planetary Science Letters 83, 137-152.
83. Spiegelman, M., Kelemen, P. B. & Aharonov, E. (2001). Causes and consequences of flow organization during melt transport: The reaction infiltration instability in compactible media. Journal of Geophysical Research - Solid Earth 106(B2), 2061-2077.
84. Stevenson, D. J. (1989). Spontaneous small-scale melt segregation in partial melts undergoing deformation. Geophysical Research Letters 16, 1067-1070.
85. Stevenson, D. J. & Scott, D. R. (1991). Mechanics of fluid-rock systems. Annual Reviews of Fluid Mechanics 23, 305-339.
86. Stracke, A., Zindler, A., Salters, J. M., McKenzie, D. & Grönvold, K. (2003). The dynamics of melting beneath Theistareykir, northern Iceland. Geochemistry, Geophysics, Geosystems 4(10), doi:10.1029/2002GC000347.
87. Stracke, A., Bourdon, B. & McKenzie, D. (2006). Melt extraction in the Earth's mantle: Constraints from U-Th-Pa-Ra studies in oceanic basalts. Earth and Planetary Science Letters 244, 97-112, doi:10.1016/j.epsl.2006.01.057.
88. Tackley, P. J. (2000). Mantle convection and plate tectonics: Toward an integrated physical and chemical theory. Science 288, 2002-2007.
89. Šrámek, O., Ricard, Y. & Bercovici, D. (2007). Simultaneous melting and compaction in deformable two-phase media. Geophysical Journal International 168, 964-982, doi:10.1111/j.1365-246X.2006.03269.x.
90. Wark, D. A. & Watson, E. B. (1998). Grain-scale permeabilities of texturally equilibrated, monomineralic rocks. Earth and Planetary Science Letters 164, 591-605.
91. Wark, D. A., Williams, C. A., Watson, E. B. & Price, J. D. (2003). Reassessment of pore shapes in microstructurally equilibrated rocks, with implications for permeability of the upper mantle. Journal of Geophysical Research - Solid Earth 108, doi:10.1029/ 2001JB001575.
92. Zhu, W. L. & Hirth, G. (2003). A network model for permeability in partially molten rocks. Earth and Planetary Science Letters 212 407-416.