Abstract
Small-scale convection supplies heat flow of ∼17 mW m−2 to the base of stable continents where xenolith studies resolve the geotherm. However, effects of small-scale convection are difficult to resolve in ocean basins. On first pass, most seafloor appears to subside to an asymptote compatible with ∼40 mW m−2 convective heat flow. These common regions are tracked by hotspots so uplift associated with ponded mantle material is an attractive alternative. Unaffected seafloor in the North and South Atlantic continues to subside with the square root of age as expected from pure conduction. The theory of stagnant-lid convection provides good scaling relationships for heat flow. For linear viscosity, heat flow is proportional to the underlying “half-space” viscosity to the −1/3 power and the temperature to change viscosity by a factor of e to the 4/3 power. The formalism is easily modified to represent convection beneath a lid of highly viscous and buoyant cratonal lithosphere and to represent transient convection beneath thickening oceanic lithosphere. Asthenospheric mantle with linear, strongly temperature-dependent, and weakly depth-dependent viscosity is compatible with both oceanic and continental data. More complicated rheology may allow vigorous small-scale convection under most but not all old ocean basins. Still viable hypotheses require poorly understood global features, including lateral variations of asthenospheric temperature. Seismological studies have the potential to resolve the lithosphere-asthenosphere boundary, including local variations of its depth associated with small-scale convection.
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References
McKenzie D P. Some remarks on heat flow and gravity anomalies. J Geophys Res, 1967, 72: 6261–6273
McKenzie D P, Sclater J G. Heat flow in the eastern Pacific and sea-floor spreading. Bull Volcanol, 1969, 33: 101–117
Sleep N H. Sensitivity of heat flow and gravity to the mechanism of sea-floor spreading. J Geophys Res, 1969, 74: 542–549
Parker R L, Oldenburg D W. Thermal model of ocean ridges. Nature, 1973, 242: 137–139
Davis E E, Lister C R B. Fundamentals of ridge crest topography. Earth Planet Sci Lett, 1974, 21: 405–413
Isacks B, Oliver J, Sykes L R. Seismology and the new global tectonics. J Geophys Res, 1968, 73: 5855–5899
Parsons B, Sclater J G. An analysis of the variation of ocean floor bathymetry and heat flow with age. J Geophys Res, 1977, 82: 803–827
Doin M P, Fleitout L. Thermal evolution of the oceanic lithosphere: An alternative view. Earth Planet Sci Lett, 1996, 142: 121–136
Doin M P, Fleitout L. Flattening of the oceanic topography and geoid: Thermal versus dynamic origin. Geophys J Int, 2000, 143: 582–594
Doin M P, Fleitout L. Numerical simulations of the cooling of an oceanic lithosphere above a convective mantle. Phys Earth Planet Inter, 2001, 125: 45–64
Dumoulin C, Doin M P, Fleitout L. Numerical simulation of the cooling of an oceanic lithosphere above a convective mantle. Phys Earth Planet Int, 2001, 125: 45–64
Niu Y, Wilson M, Humphreys E R, et al. The origin of intra-plate ocean island basalts (OIB): The lid effect and its geodynamic implications. J Petrol, Peter J. Wyllie Volume, 2011 (in press)
Oldenburg D W. Physical model for creation of lithosphere. Geophys J R Astron Soc, 1975, 43: 425–451
Sleep N H. Thermal effects of the formation of Atlantic continental margins by continental break up. Geophys J R Astron Soc, 1971, 24: 325–350
McKenzie D. Some remarks on the development of sedimentary basins. Earth Planet Sci Lett, 1978, 40: 25–32
Jordan T H. The continental tectosphere. Rev Geophys, 1975, 13: 1–12
Sleep N H. Stagnant lid convection and the thermal subsidence of sedimentary basins with reference to Michigan. Geochem Geophys Geosyst, 2009, 10: Q12015, doi: 10.1029/2009GC002881
Crosby A G, Fishwick S, White N. Structure and evolution of the intracratonic Congo Basin. Geochem Geophys Geosyst, 2010, 11: Q06010, doi: 10.1029/2009GC003014
Sleep N H. Survival of Archean cratonal lithosphere. J Geophys Res, 2003, 108: 2302, doi: 10.1029/2001JB000169
Nyblade A A, Sleep N H. Long lasting epeirogenic uplift from mantle plumes and the origin of the Southern African Plateau. Geochem Geophys Geosyst, 2003, 4: 1105, doi: 10.1029/2003GC000573
Hofmeister A M, Criss R E. Earth’s heat flux revised and linked to chemistry. Tectonophysics, 2005, 395: 159–177
Hofmeister A M, Criss R E. Comment on “Estimates of heat flow from Cenozoic seafloor using global depth and age data” by M. Wei and D. Sandwell. Tectonophysics, 2006, 428: 95–100
Hofmeister A M, Criss R E. Model or measurements? A discussion of the key issue in Chapman and Pollack’s critique of Hamza et al.’s re-evaluation of oceanic heat flux and the global power. Int J Earth Sci (Geol Rundsch), 2008, 97: 241–244
Sleep N H, Phillips R J. Gravity and lithospheric stress on the terrestrial planets with reference to the Tharsis Region of Mars. J Geophys Res, 1985, 90: 4469–4489
Turcotte D L, Schubert G. Geodynamics. 2nd ed. New York: John Wiley, 2002. 456
Wei M, Sandwell D. Estimates of heat flow from Cenozoic seafloor using global depth and age data. Tectonophysics, 2006, 417: 325–335
Stein C A, Stein S. A model for the global variation in oceanic depth and heat flow with lithospheric age. Nature, 1992, 359: 123–129
Stein C A, Stein S. Constraints on hydrothermal heat flux through the oceanic lithosphere from global heat flow. J Geophys Res, 1994, 99: 3081–3095
Crosby A G, McKenzie D, Sclater J G. The relationship between depth, age and gravity in the oceans. Geophys J Int, 2006, 166: 553–573
Hillier J K. Subsidence of “normal” seafloor: Observations do indicate “flattening”. J Geophys Res, 2010, 115: B03102, doi:10.1029/2008JB005994
Zhong S, Ritzwoller M, Shapiro N, et al, Bathymetry of the Pacific plate and its implications for thermal evolution of lithosphere and mantle dynamics. J Geophys Res, 2007, 112: B06412, doi:10.1029/2006JB004628
Ballmer M D, van Hunen J, Ito G, et al. Non-hotspot volcano chains originating from small-scale sublithospheric convection. Geophys Res Lett, 2007, 34, doi:10.1029/2007GL031636.
Ballmer M D, van Hunen J, Ito G, et al., Intraplate volcanism with complex age-distance patterns: A case for small-scale sublithospheric convection. Geochem Geophys Geosyst, 2009, 10: Q06015, doi: 10. 1029/2009GC002386
Crosby A G, McKenzie D. An analysis of young ocean depth, gravity and global residual topography. Geophys J Int, 2009, 178: 1198
Korenaga T, Korenaga J. Subsidence of normal oceanic lithosphere, apparent thermal expansivity, and seafloor flattening. Earth Planet Sci Lett, 2008, 268: 41–51
Goutorbe B. Combining seismically derived temperature with heat flow and bathymetry to constrain the thermal structure of oceanic lithosphere. Earth Planet Sci Lett, 2010, 295: 390–400
Müller R D, Sdrolias M, Gaina C, et al. Age, spreading rates, and spreading asymmetry of the world’s ocean crust. Geochem Geophys Geosyst, 2008, 9: Q04006, doi:10.1029/2007GC001743
Sleep N H. Origins of the plume hypothesis and some of its implications. Geol Soc Am Spec Pap, 2007, 430: 29–45
Cliff P D. Sedimentary evidence for moderate mantle temperature anomalies associated with hotspot volcanism. In: Foulger G R, Natland J H, Presnall D C, et al., eds. Plates, Plumes, and Paradigms. Geol Soc Am Spec Paper, 2005, 279–287
Humler E, Langmuir C, Daux V. Depth versus age: New perspective from the chemical compositions of ancient crust. Earth Planet Sci Lett, 1999, 173: 7–23
Géli L, Cochran J R, Lee T C, et al. Thermal regime of the Southeast Indian Ridge between 88°E and 140°E: Remarks on the subsidence of the ridge flanks. J Geophys Res, 2007, 112: B10101, doi:10.1029/2006JB004578
Hayes D E. Age-depth relationships and depth anomalies in the Southeast Indian Ocean and South Atlantic Ocean. J Geophys Res, 1988, 93: 2937–2954
Keen C E, Potter D P. Transition from volcanic to nonvolcanic rifted margin off eastern Canada. Tectonics, 1995, 14: 359–371
Ebinger C J, Tucholke B E. Marine geology of Sohm Plain, Canadian Atlantic margin. Am Assoc Petrol Geol Bull, 1988, 72: 1450–1468
Abbott D L, Burgess L, Longhi J, et al. An empirical thermal history of the Earth’s upper mantle. J Geophys Res, 1994, 99: 13835–13850
Galer S J G, Mezger K. Metamorphism denudation and sea level in the Archean and cooling of the Earth. Precambrian Res, 1998, 92: 389–412
Korenaga J. Urey ratio and the structure and evolution of Earth’s mantle. Rev Geophys, 2008, 46: RG2007, doi:10.1029/2007RG000241
Herzberg C, Condie K, Korenaga J. Thermal history of the Earth and its petrological expression. Earth Planet Sci Lett, 2010, 292: 79–88
Korenaga J. How does small-scale convection manifest in surface heat flux? Earth Planet Sci Lett, 2009, 287: 329–332
Solomatov V S. Scaling of temperature- and stress-dependent viscosity convection. Phys Fluids, 1995, 7: 266–274
Solomatov V S, Moresi L N. Scaling of time-dependent stagnant lid convection: Application to small-scale convection on Earth and other terrestrial planets. J Geophys Res, 2000, 105: 21795–21817
Sleep N H. Local lithospheric relief associated with fracture zones and ponded plume material. Geochem Geophys Geosyst, 2002, 3, doi: 10.1029/2002GC000376
Sleep N H, Jellinek A M. Scaling relationships for chemical lid convection with applications to cratonal lithosphere. Geochem Geophys Geosyst, 2008, 9: Q12025, doi:10.1029/2008GC002042
van Hunen J, Huang J, Zhong S. The effect of shearing on the onset and vigor of small-scale convection in a Newtonian rheology. Geophys Res Lett, 2003, 30, doi:10.1029/2003GL018101
van Hunen J, Zhong S. Influence of rheology on realignment of mantle convective structure with plate motion after a plate reorganization. Geochem Geophys Geosyst, 2006, 7, doi:10.1029/2005GC001209
Davaille A, Jaupart C. Thermal convection in lava lakes. Geophys Res Lett, 1993, 20: 1827–1830
Davaille A, Jaupart C. Transient high-Rayleigh number thermal convection with large viscosity variations. J Fluid Mech, 1993, 253: 141–166
Davaille, Jaupart C. The onset of thermal convection in fluids with temperature-dependent viscosity: Application to the oceanic mantle. J Geophys Res, 1994, 99: 19853–19866
Sleep N H. Edge-modulated stagnant-lid convection and volcanic passive margins, Geochem Geophys Geosyst, 2007, 8: Q12004, doi: 10.1029/2007GC001672
Francis D, Patterson M. Kimberlites and aillikites as probes of the continental lithospheric mantle. Lithos, 2009, 109: 72–80
Kopylova M G, Caro G. Mantle xenoliths from the Southeastern Slave Craton: Evidence for chemical zonation in a thick, cold lithosphere. J Petrol, 2004, 45: 1045–1067
Karmalkar N R, Duraiswami R A, Chalapathi Rao N V, et al. Mantle-derived mafic-ultramafic xenoliths and the nature of Indian sub-continental lithosphere. J Geol Soc India, 2009, 73: 657–679
Saltzer R L, Chatterjee N, Grove T L, et al. The spatial distribution of garnets and pyroxenes in mantle peridoties: Pressure-temperature history of peridotites from the Kaapvaal craton. J Petrol, 2001, 42: 2215–2229
Dumoulin C, Doin M P, Fleitout L, et al. Onset of small scale instabilities at the base of the lithosphere: Scaling laws and role of preexisting lithospheric structures. Geophys J Int, 2005, 160: 344–356
Choblet G, Sotin C. 3D thermal convection with variable viscosity: Can transient cooling be described by a quasi-static scaling law? Phys Earth Planet Inter, 2000, 119: 321–336
Dumoulin C, Chobet G, Doin M P. Convective interactions between oceanic lithosphere and asthenosphere: Influence of a transform fault. Earth Planet Sci Lett, 2008, 274: 301–309
Colin P, Fleitout L. Topography of the ocean floor: Thermal evolution of the lithosphere and interaction of deep mantle heterogeneities with the lithosphere. Geophys Res Lett, 1990, 17: 1961–1964
Lévy F, Jaupart C, Mareschal J C, et al. Low heat flux and large variations of lithospheric thickness in the Canadian Shield. J Geophys Res, 2010, 115: B06404, doi:10.1029/2009JB006470
Perry H K C, Jaupart C, Mareschal J C, et al. Crustal heat production in the Superior Province, Canadian Shield, and in North America inferred from heat flow data. J Geophys Res, 2006, 111: B04401, doi: 10.1029/2005JB003893
Doin M P, Fleitout L, Christensen U. Mantle convection and stability of depleted and undepleted continental lithosphere. J Geophys Res, 1997, 102: 2771–2787
Dumoulin C, Doin M P, Fleitout L. Heat transport in stagnant lid convection with temperature- and depth-dependent Newtonian or non-Newtonian rheology. J Geophys Res, 1999, 104: 12759–12777
Sleep N H. Plate tectonics through time. In: Schubert G, ed. Treatise on Geophysics. Oxford: Elsevier, 2007. 101–117
Cooper C M, Conrad C P. Does the mantle control the maximum thickness of cratons? Lithosphere, 2009, 1: 67–72
Sleep N H. Geodynamic implications of xenolith geotherms. Geochem Geophys Geosyst, 2003, 4: 1079
Moucha R, Forte A M, Mitrovica J X, et al. Dynamic topography and long-term sea-level variations: There is no such thing as a stable continental platform. Earth Planet Sci Lett, 2008, 271: 101–108
Spasojevic S, Liu L, Gurnis M. Adjoint models of mantle convection with seismic, plate motion, and stratigraphic constraints: North America since the Late Cretaceous. Geochem Geophys Geosyst, 2009, 10: Q05W02, doi:10.1029/2008GC002345
Richards M A, Hager B H, Sleep N H. Dynamically supported geoid highs and hotspots: Observation and theory. J Geophys Res, 1988, 93: 7690–7708
Huang J, Zhong S. Sublithospheric small-scale convection and its implications for residual topography at old ocean basins and the plate model. J Geophys Res, 2005, 110: B05404, doi:10.1029/2004JB003153
Bunge H P. Low plume excess temperature and high core heat flux inferred from non-adiabatic geotherms in internally heated mantle circulation models. Phys Earth Planet Int, 2005, 153: 3–10
Phillips B R, Coltice N. Temperature beneath continents as a function of continental cover and convective wavelength. J Geophys Res, 2010, 115: B04408, doi:10.1029/2009JB006600
Petersen K D, Nielsen S B, Clausen O R, et al. Small-scale mantle convection produces stratigraphic sequences in sedimentary basins. Science, 2010, 329: 827–830
Korenaga J, Jordan T H. Physics of multiscale convection in Earth’s mantle: Onset of sublithospheric convection. J Geophys Res, 2003, 108: 2333
Morency C, Doin M P, Dumoulin C. Three-dimensional numerical simulations of mantle flow beneath mid-ocean ridges. J Geophys Res, 2005, 110: B11407
Till C B, Elkins-Tanton L T, Fischer K M. A mechanism for low extent melts at the lithosphere-asthenosphere boundary. Geochem Geophys Geosyst, 2010, 11: Q11XXX, doi:10.1029/2010GC003234
Kawakatsu H, Kumar P, Takei Y, et al. Seismic evidence for sharp lithosphere-asthenosphere boundaries of oceanic plates. Science, 2009, 324: 499–502
Sandwell D T, Winterer E L, Mammerickx J, et al. Evidence for diffuse extension of the Pacific Plate from Pukapuka ridges and cross-grain gravity lineations. J Geophys Res, 1995, 100: 15087–15099
Mittelstaedt E, Ito G. Plume-ridge interaction, lithospheric stresses, and the origin of near-ridge volcanic lineaments. Geochem Geophys Geosyst, 2005, 6: Q06002, doi: 10.1029/2004GC000860
Holmes R C, Webb S C, Forsyth D W. Crustal structure beneath the gravity lineations in the Gravity Lineations, Intraplate Melting, Petrologic and Seismic Expedition (GLIMPSE) study area from seismic refraction data. J Geophys Res, 2007, 112: B07316, doi: 10.1029/2006 JB004685
Sleep N H. Channeling at the base of the lithosphere during the lateral flow of plume material beneath flow line hot spots. Geochem Geophys Geosyst, 2008, 9: Q08005, doi:10.1029/2008GC002090
Yuan H, Romanowicz B. Lithosphere layering in the North American craton. Nature, 2010, 466: 1063–1069
Sleep N H. Segregation of magma from a mostly crystalline mush. Geol Soc Am Bull, 1974, 85: 1225–1232
Sleep N H. Formation of oceanic crust: Some thermal constraints. J Geophys Res, 1975, 80: 4037–4042
Morton J, Sleep N H. A mid-ocean ridge thermal model: Constraints on the volume of axial hydrothermal heat flux. J Geophys Res, 1985, 90: 11345–11353
Pollack H N. On the use of the volume thermal expansion coefficient in models of ocean floor topography. Tectonophysics, 1980, 64: T45–T47
Raterron P, Wu Y, Weider D J, et al. Low-temperature olivine rheology at high pressure. Phys Earth Planet Int, 2004, 145: 149–159
Hunt S A, Dobson D P, Wood I G, et al. Deformation of olivine at 5 GPa and 350–900°C. Phys Earth Planet Int, 2009, 172: 84–90
Korenaga J. Effective thermal expansivity of Maxwellian oceanic lithosphere. Earth Planet Sci Lett, 2007, 257: 343–349
Korenaga J, Karato S. A new analysis of experimental data on olivine rheology. J Geophys Res, 2008, 113: B02403, doi: 10.1029/2007 JB005100
Turcotte D. Are Transform faults thermal contraction cracks? J Geophys Res, 1974, 79: 2573–2577
Kumar R R, Gordon R G. Horizontal thermal contraction of oceanic lithosphere: The ultimate limit to the rigid plate approximation. J Geophys Res, 2009, 114: B01403, doi:10.1029/2007JB005473
Sleep N H, Snell N S. Thermal contraction and flexure of mid-continent and Atlantic marginal basins. Geophys J R Astron Soc, 1976, 45: 125–154
Sleep N H. Stagnant lid convection and carbonate metasomatism of the deep continental lithosphere. Geochem Geophys Geosyst, 2009, 10: Q11010, doi:10.1029/2009GC002702
Sandwell D T, Smith W H F. Marine gravity anomaly from Geosat and ERS1 satellite altimetry. J Geophys Res, 1997, 102: 10039–10054
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Sleep, N.H. Small-scale convection beneath oceans and continents. Chin. Sci. Bull. 56, 1292–1317 (2011). https://doi.org/10.1007/s11434-011-4435-x
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DOI: https://doi.org/10.1007/s11434-011-4435-x