Three-dimensional passive mantle flow beneath mid-ocean ridges: An analytical approach

Geophysical Journal International

Volumn 175, Issue 2, 2008, Pages 783-805

  Ligi, Marco ^a   Cuffaro, Marco ^a,b   Chierici, Francesco ^c   Calafato, Antonino ^d  

^a ISMAR CNR   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

^c INAF ISTITUTO DI RADIOASTRONOMIA   (Italy)

^d UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Fourier analysis; Magma genesis and partial melting; Mantle processes; Mid ocean ridge processes; Numerical approximations and analysis; Oceanic transform and fracture zone processes

Indexed keywords

FOURIER TRANSFORM; MANTLE PROCESS; MID-OCEAN RIDGE; NUMERICAL MODEL; PLATE BOUNDARY; PLATE MOTION; SEAFLOOR SPREADING;

EID: 54849430954     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2008.03931.x     Document Type: Article

References (61)

1. Archibald, R. & Gelb, A., 2002. A method to reduce the Gibbs ringing artefact in the MIR scans while keeping tissue boundary integrity, IEEE Trans. Med. Imag., 21, 305-319.
2. Bateman, H., 1953. Higher Transcendental Functions, McGraw-Hill, New York.
3. Bell, D.R. & Rossman, G.R., 1992. The distribution of hydroxyl in garnets from the subcontinental mantle of southern Africa, Contrib. Mineral. Petrol., 111, 161-178.
4. Bender, J.F., Langmuir, C.H. & Hanson, G.N., 1984. Petrogeneis of basalt glasses from the Tamayo Region, East Pacific Rise, J. Petrol., 25, 213-254.
5. Blackman, D.K. & Forsyth, D.W., 1991. Isostatic compensation of tectonic features of the Mid-Atlantic Ridge: 25-27°30′S, J. Geophys. Res., 96 (B7), 11741-11758.
6. Blackman, D.K. & Forsyth, D.W., 1992. The effects of plate thickening on three-dimensional, passive flow of the mantle beneath mid-ocean ridges, in Mantle Flow and Melt Generation at Mid-Ocean Ridges pp. 311-326, eds Phipps Morgan, J., Blackman, D.K. & Sinton, J.K. (Geophysical Monograph, 71, American Geophysical Union, Washington DC, 1992).
7. Bonatti, E., Ligi, M., Brunelli, D., Cipriani, A., Fabretti, P., Ferrante, V., Gasperini, L. & Ottolini, L., 2003. Mantle thermal pulses below the Mid-Atlantic Ridge and temporal variations in the formation of oceanic lithosphere, Nature, 423, 499-505.
8. Bosley, D.L., 1996. A technique for the numerical verification of asymptotic expansions, SIAM Review, 38 (1), 128-135.
9. Bown, J.W. & White, R.S., 1994. Variation with spreading rate of oceanic crustal thickness and geochemistry, Earth Planet. Sci. Lett., 121 (3-4), 435-449.
10. Braun, M.G., Hirth, G. & Parmentier, E.M., 2000. The effect of deep damp melting on mantle flow and melt generation beneath mid-ocean ridges. Earth Planet. Sci. Lett., 176, 339-356.
11. Buck, W.R. & Su, W. 1989. Focused mantle upwelling below mid-ocean ridges due to feedback between viscosity and melting, Geophys. Res. Lett., 16 (7), 641-644.
12. Buck, R., 1999. Mapping mantle melting, Science, 286, 692-693.
13. Carrier, G.F. & Pearson, C.E., 1991. Ordinary differential equations, Society for Industrial and Applied Mathematics, Philadelphia, 230 pp.
14. Chen, Y.J., 1992. Oceanic crustal thickness versus spreading rate, Geophys. Res. Lett., 19 (8), 753-756.
15. Choblet, G. & Parmentier, E.M., 2001. Mantle upwelling and melting beneath slow-spreading centers: Effects of variable rheology and melt productivity, Earth Planet. Sci. Lett., 184, 589-604.
16. Chopra, P.N. & Paterson, M.S., 1981. The experimental deformation of dunite, Tectonophysics, 78 (1-4), 453-473.
17. Cordery, M.J. & Morgan, J.P., 1992. Melting and mantle flow beneath a mid-ocean spreading center, Earth Planet. Sci. Lett., 111 (2-4), 493-516.
18. Cordery, M.J. & Morgan, J.P., 1993. Convection and melting at mid-ocean ridges, J. Geophys. Res., 98 (B11), 19477-19504.
19. Evans, R.L. et al., 1999. Asymmetric electrical structure in the mantle beneath the east pacific rise at 17°S, S cience, 286, 752-756.
20. Forsyth, D.W. et al., 1998. Imaging the deep seismic structure beneath a mid-ocean ridge: The MELT experiment, Science, 280, 1215-1218.
21. Gelb, A., 2001. A hybrid approach to spectral reconstruction of piecewise smooth functions, J. Sci. Comput., 15, 293-322.
22. Gelb, A., 2004. Parameter optimization and reduction of roundoff error for the Gegenbauer reconstruction method, J. Sci. Comput., 20, 433-459.
23. Gottlieb, D., Hussaini, M.Y. & Orszag, S., 1984. Theory and applications of spectral methods, in Spectral Methods for Partial Differential Equations, p. 276, eds Voigt, R.G., Gottlieb, D. & Hussaini, M.Y., SIAM, Philadelfia.
24. Gottlieb, D. & Shu, C.W., 1995. On the Gibbs phenomenon IV: recovering exponential accuracy in a sub-interval from a Gegenbauer partial sum of a picewise analytic functions, Math. Comput., 64, 1081-1095.
25. Gottlieb, D. & Shu, C.W., 1997. On the Gibbs phenomenon and its resolution, SIAM Rev., 39, 644-668.
26. Gottlieb, D., Shu, C.W., Solomonoff, A. & Vandeven, H., 1992. On the gibbs phenomenon I: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function, J. Comput. Appl. Math, 43, 81-92.
27. Hellebrand, E., Snow, J.E., Hoppe, P. & Hofmann, A.W., 2002. Garnet-field melting and late-stage refertilization in "residual"abyssal peridotites from the central Indian ridge. J. Petrol., 43, 2305-2338.
28. Hirth, G. & Kohlstedt, D.L., 1996. Water in the oceanic upper mantle: Implications for rheology, melt extraction and the evolution of the lithosphere, Earth Planet. Sci. Lett., 144 (1-2), 93-108.
29. Jha, K., Parmentier, E.M. & Morgan, J.P., 1994. The role of mantle-depletion and melt-retention buoyancy in spreading-center segmentation, Earth Planet. Sci. Lett., 125 (1-4), 221-234.
30. Karato, S., 1986. Does partial melting reduce the creep strength of the upper mantle?, Nature, 319, 309-310.
31. Karato, S. & Wu, P., 1993. Rheology of the upper mantle -a synthesis, Science, 260, 771-778.
32. Katz, R.F., Spiegelman, M. & Langmuir, C.H., 2003. A new parameterization of hydrous mantle melting. Geochem. Geophys. Geosyst., 4, 1073.
33. 4, Contrib. Mineral. Petrol., 123, 345-357.
34. Kuo, B.-Y. & Forsyth, D.W., 1988. Gravity anomalies of the ridge-transform system in the South Atlantic between 31 and 34.5°S: upwelling centers and variations in crustal thickness, Mar. Geophys. Res., 10, 205-232.
35. Ligi, M., Bonatti, E., Cipriani, A. & Ottolini, L., 2005. Water-rich basalts at mid-ocean-ridge cold spots, Nature, 434, 66-69.
36. Lin, J., Purdy, G.M., Schouten, H., Sempere, J.-C. & Zervas, C., 1990. Evidence from gravity data for focused magmatic accretion along the Mid-Atlantic Ridge, Nature, 344, 627-632.
37. Lundstrom, C.C., Gill, J., Williams, Q. & Perfit, M.R., 1995. Mantle melting and basalt extraction by equilibrium porous flow, Science, 270, 1958-1961.
38. Lundstrom, C.C., Williams, Q. & Gill, J., 1998. Investigating solid mantle upwelling rates beneath mid-ocean ridges using U-series disequilibria, 1: A global approach, Earth Planet. Sci. Lett., 157 (3-4), 151-165.
39. Macdonald, K.C., 1982. Mid-ocean ridges: Fine scale tectonics, volcanic and hydrothermal processes within the plate boundary zone, Ann. Rev. Earth Planet. Sci., 10, 155-190.
40. Macdonald, K.C., Fox, P.J., Perram, L.J., Eisen, M.F., Haymon, R.M., Miller, S.P., Carbotte, S.M., Cormier, M.-H. & Shor, A.N., 1988. A new view of the mid-ocean ridge from the behavior of ridge-axis discontinuities, Nature, 335, 217-225.
41. Mackwell, S.J., Kohlstedt, D.L. & Paterson, M.S., 1985. The role of water in the deformation of olivine single-christals, J. Geophys. Res., 90 (NB13), 1319-1333.
42. Magde, L.S. & Sparks, D.W., 1997. Three-dimensional mantle upwelling, melt generation, and melt migration beneath segment slow spreading ridges, J. Geophys. Res., 102 (B9), 20571-20584.
43. Magde, L.S., Sparks, D.W. & Detrick, R.S., 1997. The relationship between buoyant mantle flow, melt migration, and gravity bull's eyes at the Mid-Atlantic Ridge between 33°N and 35°N, Earth Planet. Sci. Lett., 148 (1-2), 59-67.
44. McKenzie, D. & O'Nions, R.K., 1991. Partial Melt distributions from inversion of rare earth elements concentrations. J. Petrol., 32, 1021-1091.
45. Morgan, J.P., 1987. Melt migration beneath mid-ocean spreading centers, Geophys. Res. Lett., 14 (12), 1238-1241.
46. Morgan, J.P. & Forsyth, D.W., 1988. Three-dimensional flow and temperature perturbations due to a transform offset: Effects on oceanic crustal and upper mantle structure, J. Geophys. Res., 93 (B4), 2955-2966.
47. Morgan, J.P., Morgan, W.J. & Price, E., 1995. Hotspot melting generates both hotspot volcanism and a hotspot snell, J. Geophys. Res., 100, 8045-8062.
48. Morgan, J.P., 1997. The generation of a compositional lithosphere by mid-ocean ridge melting and its effect on subsequent off-axis hotspot upwelling and melting, Earth Planet. Sci. Lett., 146 (1-2), 213-232.
49. Reddy, J.N., 1982. Penalty-finite-element analysis of 3-D Navier-Stokes equations, Comp. Meth. Appl. Mech. Engng., 35, 87-106.
50. Reid, I. & Jackson, H.R., 1981. Oceanic spreading rate and crustal thickness, Mar. Geophys. Res., 5, 165-172.
51. Reynolds, J.P. & Langmuir, C.H., 1997. Petrological systematics of the Mid-Atlantic Ridge south of Kane: Implications for ocean crust formation, J. Geophys. Res., 102, 14915-14946.
52. Schouten, H. & Klitgord, K.D., 1982. The memory of the accreting plate boundary and the continuity of fracture zones, Earth Planet. Sci. Lett., 59 (2), 255-266.
53. Scott, D.R. & Stevenson, D.J., 1989. A self-consistent model of melting, magma migration and buoyancy-driven circulation beneath mid-ocean ridges. J. Geophys. Res., 94, 2973-2988.
54. Shen, Y. & Forsyth, D.W., 1992. The effects of temperature- and pressure-dependent viscosity on three-dimensional passive flow of the mantle beneath a ridge-transform system, J. Geophys. Res., 97 (B13), 19717-19728.
55. Sotin, C.J. & Parmentier, E.M., 1989. Dynamical consequences of compositional and thermal density stratification beneath spreading centers. Geophys. Res. Lett., 16, 835-838.
56. Sparks, D.W. & Parmentier, E.M., 1991. Melt extraction from the mantle beneath spreading centers, Earth Planet. Sci. Lett., 105 (4), 368-377.
57. Sparks, D.W., Parmentier, E.M. & Morgan, J.P., 1993. Three-dimensional mantle convection beneath a segmented spreading center: Implications for along-axis variations in crustal thickness and gravity, J. Geophys. Res., 98 (B12), 21977-21996.
58. Spiegelman, M. & McKenzie, D., 1987. Simple 2-D models for melt extraction at mid-ocean ridges and island arcs, Earth Planet. Sci. Lett., 83 (1-4), 137-152.
59. Turcotte, D.L. & Morgan, J.P., 1992. The physics of magma migration and mantle flow beneath a Mid-Ocean Ridge, in Mantle Flow and Melt Generation at Mid-Ocean Ridges, eds Phipps Morgan, J., Blackman, D.K. & Sinton, J.K., pp. 155-182. (Geophysical Monograph, 71, American Geophysical Union, Washington DC, 1992).
60. Turcotte, D.L. & Schubert, G., 1982. Geodynamics Applications of Continuum Physics to Geological Problems, p. 450, John Wiley and Sons, New York.
61. White, R.S., McKenzie, D. & O'Nions, R.K., 1992. Oceanic crustal thickness from seismic measurements and rare earth element inversions, J. Geophys. Res., 97 (B13), 19683-19715.