Direct observations of the viscosity of Earth's outer core and extrapolation of measurements of the viscosity of liquid iron

D.E. Smylie^a, V.V. Brazhkin^b, A. Palmer^c
^aDepartment of Earth and Space Science and Engineering, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada
^bInstitute for High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse 14, Troitsk, Moscow, 108840, Russian Federation
^cSander Geophysics Ltd., 260 Hunt Club Road, Ottawa, Ontario, K2P 1K2, Canada

Estimates vary widely as to the viscosity of Earth’s outer fluid core. Directly observed viscosity is usually orders of magnitude higher than the values extrapolated from high-pressure high-temperature laboratory experiments, which are close to those for liquid iron at atmospheric pressure. It turned out that this discrepancy can be removed by extrapolating via the widely known Arrhenius activation model modified by lifting the commonly used assumption of pressure-independent activation volume (which is possible due to the discovery that at high pressures the activation volume increases strongly with pressure, resulting in 10² Pa s at the top of the fluid core, and in 10¹¹ Pa s at its bottom). There are of course many uncertainties affecting this extrapolation process. This paper reviews two viscosity determination methods, one for the top and the other for the bottom of the outer core, the former of which relies on the decay of free core nutations and yields 2371 ± 1530 Pa s, while the other relies on the reduction in the rotational splitting of the two equatorial translational modes of the solid inner core oscillations and yields an average of 1.247 ± 0.035 × 10¹¹ Pa s. Encouraged by the good performance of the Arrhenius extrapolation, a differential form of the Arrhenius activation model is used to interpolate along the melting temperature curve and to find the viscosity profile across the entire outer core. The viscosity variation is found to be nearly log-linear between the measured boundary values.

PACS: 66.20.−d, 91.35.−x, 93.85.−q (all)
DOI: 10.3367/UFNe.0179.200901d.0091
URL: https://ufn.ru/en/articles/2009/1/d/
Web of Science

000266708800004
Scopus

2-s2.0-67849111476
ADS NASA

2009PhyU...52...79S
Citation: Smylie D E, Brazhkin V V, Palmer A "Direct observations of the viscosity of Earth's outer core and extrapolation of measurements of the viscosity of liquid iron" Phys. Usp. 52 79–92 (2009)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Смайли Д Е, Бражкин В В, Палмер А «Прямые наблюдения вязкости внешнего ядра Земли и экстраполяция измерений вязкости жидкого железа» УФН 179 91–105 (2009); DOI: 10.3367/UFNr.0179.200901d.0091

References (60) ↓ Cited by (22) Similar articles (9)

Lumb L I, Aldridge K D J. Geomag. Geoelectr. 43 93 (1991)
Anderson D L Theory Of The Earth (Boston: Blackwell Sci. Publ., 1989)
Davis R G, Whaler K A Phys. Earth Planet. Inter. 103 181 (1997)
de Wijs G A et al. Nature 392 805 (1998)
Alfè D, Kresse G, Gillan M J Phys. Rev. B 61 132 (2000)
Desgrandes C, Delhommelle J Phys. Rev. B 76 172102 (2007)
Vočadlo L et al. Faraday Discuss. 106 205 (1997)
Rutter M D et al. Geophys. Res. Lett. 29 1217 (2002)
Dobson D P et al. Am. Mineralogist 85 1838 (2000)
Urakawa S et al. Am. Mineralogist 86 578 (2001)
Terasaki H et al. Geophys. Res. Lett. 33 L22307 (2006)
Rutter M D et al. Phys. Rev. B 66 060102 (2002)
Dobson D P Phys. Earth Planet. Inter. 139 271 (2002)
Secco R A "Viscosity of the outer core" In Mineral Physics & Crystallography: A Handbook Of Physical Constans (AGU Reference Shelf, Vol. 2, Ed. T J Ahrens) (Washington, DC: American Geophysical Union, 1995) p. 218
Brazhkin V V Pis’ma ZhETF 68 469 (1998); Brazhkin V V JETP Lett. 68 502 (1998)
Brazhkin V V, Lyapin A G Usp. Fiz. Nauk 170 535 (2000); Brazhkin V V, Lyapin A G Phys. Usp. 43 493 (2000)
Poirier J P Geophys. J. 92 99 (1988)
Jeffreys H Mon. Not. R. Astron. Soc. Geophys. Suppl. 1 371 (1926)
Garland G D Introduction To Geophysics: Mantle, Core And Crust (Philadelphia: Saunders, 1971) p. 42
Bullen K E, Bolt B A An Introduction To The Theory Of Seismology 4th ed. (Cambridge: Cambridge Univ. Press, 1985) p. 322
Poincaré H Bull. Astron. 27 321 (1910)
Aldridge K D "An experimental study of axisymmetric inertial oscillations of a rotating liquid sphere" Ph.D. Thesis (Cambridge, Mass.: MIT, 1967)
Smylie D E et al. Geophys. J. Int. 108 465 (1992)
Jiang X "Wobble-nutation modes of the Earth" Ph.D. Thesis (Toronto: York Univ., 1993)
Jiang X, Smylie D E Phys. Earth Planet. Inter. 90 91 (1995)
Jiang X, Smylie D E Phys. Earth Planet. Inter. 94 159 (1996)
Greenspan H P The Theory Of Rotating Fluids (London: Cambridge Univ. Press, 1968) p. 66
Crossley D, Smylie D E Geophys. J. R. Astron. Soc. 42 1011 (1975)
Acheson D J Geophys. J. R. Astron. Soc. 43 253 (1975)
Smylie D E, Szeto A M K, Rochester M G Rep. Prog. Phys. 47 855 (1984)
Smylie D E "Electromagnetic excitation of the Chandler Wobble" Ph.D. Thesis (Toronto: Univ. of Toronto, 1963)
Rochester M G, Smylie D E Geophys. J. Int. 10 289 (1965)
Buffett B A, Mathews P M, Herring T A J. Geophys. Res. 107 (B4) 2070 (2002)
Runcorn S K Trans. Am. Geophys. Union 36 191 (1955)
Smylie D E Geophys. J. Int. 9 169 (1965)
Johnson I M, Smylie D E Geophys. J. Int. 22 41 (1970)
Mathews P M et al. J. Geophys. Res. 96 (B5) 8219 (1991)
de Vries D, Wahr J M J. Geophys. Res. 96 (B5) 8275 (1991)
Palmer A, Smylie D E Phys. Earth Planet. Inter. 148 285 (2005)
Slichter L B Proc. Natl. Acad. Sci. USA 47 186 (1961)
Smylie D E et al. Phys. Earth Planet. Inter. 80 135 (1993)
Courtier N et al. Phys. Earth Planet. Inter. 117 3 (2000)
Smylie D E, Francis O, Merriam J P J. Geodetic Soc. Jpn. 47 364 (2001)
Moore D W "Homogeneous fluids in rotation" In Rotating Fluids In Geophysics (Eds P H Roberts, A M Soward) (New York: Academic Press, 1978)
Smylie D E, McMillan D G Phys. Earth Planet. Inter. 117 71 (2000)
Smylie D E Science 284 461 (1999)
Smylie D E, McMillan D G Phys. Earth Planet. Inter. 117 71 (2000)
Widmer R, Masters G, Gilbert F in 17th Inter. Conf. on Mathematical Geophysics, Blanes, Spain, IUGG, June 1988
Dziewonski A M, Anderson D L Phys. Earth Planet. Inter. 25 297 (1981)
Gilbert F, Dziewonski A M Philos. Trans. R. Soc. London A 278 187 (1975)
Bolt B A, Urhammer R Geophys. R. Astron. Soc. J. 42 419 (1975)
Bolt B A, Urhammer R A In Evolution Of The Earth (Geodynamics Series, Vol. 5, Eds R J O’Connell, W S Fyfe) (Washington, DC: American Geophysical Union, 1981) p. 28
Smylie D E, Palmer A arXiv:0709.3333
Stacey F D Physics Of The Earth 3rd ed. (Brisbane: Brookfield Press, 1992)
Mineev V N, Funtikov A I Usp. Fiz. Nauk 174 727 (2004); Mineev V N, Funtikov A I Phys. Usp. 47 671 (2004)
Alfe D, Gillan M J, Price G D Nature 401 462 (1999)
Boehler R Nature 363 534 (1993)
Braginskii S I Dokl. Akad. Nauk SSSR 149 8 (1963)
Loper D E, Roberts P H Phys. Earth Planet. Inter. 24 302 (1981)
Olson P, Christensen U R Geophys. J. Int. 151 809 (2002)