Simple plate models of mantle convection
Article Sidebar
Published:
Dec 12, 1977
Keywords:
Plate dynamics,
Mantle convection,
Mantle viscosity
Volumes
Vols. 1-18 (1924-1944), ISSN 0044-2801
Main Article Content
Abstract
A simple convective model that can maintain observed plate motions consists of a viscous upper mantle of uniform density overlain by denser rigid plates. In the absence of density differences within the upper mantle the viscous stresses exerted by the flow are easily obtained and demonstrate that the buoyancy forces associated with plate creation and destruction can maintain plate motions. A model having a uniform viscosity upper mantle is, however, unsatisfactory because it predicts gravity and residual depth anomalies two orders of magnitude larger than those observed. This problem can be overcome by introducing a thin low viscosity layer beneath the plates. The resulting model is then similar to that proposed by Forsyth and Uyeda and by Chapple and Tullis despite a very different approach. This agreement suggests that the energetics of plate motion are now understood in outline. The model cannot, however, account for the existence of the longwavelength gravity anomalies which are not associated with plate motions.
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Article Details
How to Cite
Richter, F., & McKenzie, D. (1977). Simple plate models of mantle convection. Journal of Geophysics, 44(1), 441-471. Retrieved from https://journal.geophysicsjournal.com/JofG/article/view/139
Section
References
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Chapple, W.M., Tullis, T.E. (1977) Evaluation of the forces that drive the plates. J. Geophys. Res. 82:1967-1984
Christoffel, D.A., Calhaem, I.M. (1973) Upper mantle viscosity determined from Stokes' Law. Nature Phys. Sci. 243:51-52
Davies, G.F. (1977a) Whole mantle convection and plate tectonics. Geophys. J. Roy. Astron. Soc. 49:459-486
Davies, G.F. (1977) Viscous mantle flow under moving lithospheric plates and under subduction zones. Geophys. J. Roy. Astron. Soc. 49:557-563
Elsasser, W.M. (1969) Convection and stress propagation in the upper mantle. In: Runcorn, S.K. (Ed.) The Application of Modern Physics to the Earth and Planetary Interiors, pp. 223-246. Interscience, New York
Fisher, O. (1881) Physics of the Earth's Crust. MacMillan, London
Forsyth, D., Uyeda, S. (1975) On the relative importance of the driving forces of plate motion. Geophys. J. Roy. Astron. Soc. 43:163-200
Fukao, Y. (1972) Source process of a large deep-focus earthquake and its tectonic implications. -The western Brazil earthquake of 1963. Phys. Earth Planet. Inter. 5:61-76
Fukao, Y. (1973) Thurst faulting at a lithospheric plate boundary: The Portugal earthquake of 1969. Earth Planet. Sci. Lett. 18:205-216
Gaposchkin, E.M. (1974) Earth's gravity field to the eighteenth degree and geocentric coordinates for 204 stations from satellite and terrestrial data, J. Geophys. Res. 79:5377-5411
Green, D.H. (1972) Magmatic activity as the major process in the chemical evolution of the earth's crust and mantle. In. The Upper Mantle, A.R. Ritsema, ed. pp. 47-71, Amsterdam: Elsevier
Hager, B.H., O'Connell, R.J. (1977) Benioff zone dip angles and flow driven by moving planes. Trans. Am. Geophys. Union 58:499 (abstract)
Hewitt, J.M., McKenzie, D.P., Weiss, N.O. (1975) Dissipative heating in convective flows. J. Fluid Mech. 68:721-738
Isacks, B.L., Molnar, P. (1971) Distribution of stresses in the descending lithosphere from a global survey of focal-mechanism solutions of mantle earthquakes. Rev. Geophys. Space Phys. 9:103-174
Isacks, B.L., Oliver, J., Sykes, L.R. (1968) Seismology and the new global tectonics. J. Geophys. Res. 73:5855-5899
Kanamori, H. (1970a) Synthesis of long-period surface waves and its application to earthquake source studies. - Kurile Islands earthquake of October 13, 1963. J. Geophys. Res. 75:5011-5027
Kanamori, H. (l970b) The Alaskan earthquake of 1964: radiation of longperiod surface waves and source mechanism. J. Geophys. Res. 75:5029-5040
Kanamori, H. (1971) Focal mechanism of the Takachi-Oki earthquake of May 16, 1968: contortion of the lithosphere at a junction between two trenches, Tectonophysics 12:l-13
Lerch, F.J., Wagner, C.A., Richardson, J.A., Brownd, J.E. (1974) Goddard earth models (5 and 6). Goddard Space Flight Centre report no. x-921-74.145
McKenzie, D.P. (1968) The influence of the boundary conditions and rotation on convection in the earth's mantle. Geophys. J. Roy. Astron. Soc. 15:457-500
McKenzie, D.P. (1969) Speculations of the causes and consequences of plate motions. Geophys. J. Roy. Astron. Soc. 18:1-32
McKenzie, D.P. (1976) The orientation of the stress within sinking slabs. Earth Planet. Sci. Lett. 31:305-307
McKenzie, D.P. (1977) Surface deformation, gravity anomalies and convection. Geophys. J. Roy. Astron. Soc. 48:211-238
McKenzie, D.P., Roberts, J.M., Weiss, N.O. (1974) Convection in the earth's mantle: towards a numerical simulation. J. Fluid Mech. 62:465-538
McKenzie, D.P., Weiss, N.O. (1975) Speculations on the thermal and tectonic history of the earth. Geophys. J. Roy. Astron. Soc. 42:131-174
Mikumo, T. (1972) Focal process of deep and intermediate earthquakes around Japan as inferred from long-period P and S waveforms. Phys. Earth Planet. Inter. 6:293-299
Minister, J.B., Jordan, T.H., Molnar, P., Haines, E. (1974) Numerical modelling of instantaneous plate tectonics. Geophys. J. Roy. Astron. Soc. 36:541-576
Molnar, P., Atwater, T., Mammerickx, J., Smith, S.M. (1975) Magnetic anomalies, bathymetry and the tectonic evolution of the South Pacific since the late Cretaceous. Geophys. J. Roy. Astron. Soc.
40:383-420
Molnar, P., Tapponnier, P. (1975) Cenozoic tectonics of Asia: effects of a continental collision. Science 189:419-426
Morgan, W.J. (1971) Convection plumes in the lower mantle. Nature 230:42-43
Morgan, W.J. (1972) Deep mantle convection plumes and plate motions. Bull. Amer. Ass. Petrol. Geol. Bull. 56:203-213
O'Connell, R.J. (1977) On the scale of mantle convection. Tectonophysics 38:119-136
Parsons, B., Sclater, J.G. (1977) An analysis of the variation of ocean floor bathymetry and heat flow with age. J. Geophys. Res. 82:803-827
Pekeris, C.L. (1935) Thermal convection in the interior of the earth, Monthly Notices Roy. Astron. Soc. Geophys. Suppl. 3:343-367
Peltier, W.R., Andrews, J.T. (1976) Glacial-isostatic adjustment I: the forward problem. Geophys. J. Roy. Astron. Soc. 46:605-646
Prothero, W.A., Reid, I., Reickle, M.S., Brune, J.N. (1976) Ocean bottom seismic measurements on the East Pacific Rise and Rivera Fracture Zone. Nature 262:121-124
Rayleigh, C.B., Healy, J.H., Bredehoeft, J.D. (1972) Faulting and crustal stress at Rangely, Colorado. In: Heard, H.C. et al. (Ed.) Flow and Fracture of Rocks, AGU monograph 16, pp. 275-284
Richter, F.M. (1973a) Dynamical models for sea-floor spreading. Rev. Geophys. Space Phys. 11:223-287
Richter, F.M. (1973b) Convection and the large scale circulation of the mantle. J. Geophys. Res. 78:8735-8745
Richter, F.M. (1977) On the driving mechanism of plate tectonics. Tectonophysics 38:61-88
Richter, F.M., Parsons, B. (1975) On the interaction of two scales of convection in the mantle. J. Geophys. Res. 80:2529-2541
Sbar, M.L., Sykes, L.R. (1973) Contemporary compressive stress and seismicity in eastern North America: an example of intra-plate tectonics. Bull. Geol. Soc. Am. 84:1861-1882
Schubert, G., Turcotte, D.L. (1972) One-dimensional model of shallow-mantle convection. J. Geophys. Res. 77:945-951
Sclater, J.G., Lawver, L.A., Parsons, B. (1975) Comparison of Jong-wavelength residual elevation and free air gravity anomalies in the North Atlantic and possible implications for the thickness of the lithospheric plate. J. Geophys. Res. 80:1031-1052
Stocker, R.L., Ashby, M.F. (1973) On the rheology of the upper mantle, Rev. Geophys. Space Phys. 11:391-426
Weertman, J. (1970) The creep strength of the earth's mantle. Rev. Geophys. Space Phys. 8:145-168
Weidner, D.J., Aki, K. (1973) Focal depth and mechanism of mid-ocean ridge earthquakes. J. Geophys. Res. 78:1818-1831
Wu, F., Kanamori, H. (1973) Source mechanism of February 4, 1965, Rat Island earthquake. J. Geophys. Res. 78:6082-6092
Wyllie, P.J. (1971) The Dynamic Earth. New York: J. Wiley & Sons
Wyss, M. (1970) Apparent stresses of earthquakes on ridges compared to apparent stress of earthquakes in trenches. Geophys. J. Roy. Astron. Soc. 19:479-484
Wyss, M., Molnar, P. (1972) Source parameters of intermediate and deep focus earthquakes in the Tonga Arc. Phys. Earth Planet. Inter. 6:279-292
Chapple, W.M., Tullis, T.E. (1977) Evaluation of the forces that drive the plates. J. Geophys. Res. 82:1967-1984
Christoffel, D.A., Calhaem, I.M. (1973) Upper mantle viscosity determined from Stokes' Law. Nature Phys. Sci. 243:51-52
Davies, G.F. (1977a) Whole mantle convection and plate tectonics. Geophys. J. Roy. Astron. Soc. 49:459-486
Davies, G.F. (1977) Viscous mantle flow under moving lithospheric plates and under subduction zones. Geophys. J. Roy. Astron. Soc. 49:557-563
Elsasser, W.M. (1969) Convection and stress propagation in the upper mantle. In: Runcorn, S.K. (Ed.) The Application of Modern Physics to the Earth and Planetary Interiors, pp. 223-246. Interscience, New York
Fisher, O. (1881) Physics of the Earth's Crust. MacMillan, London
Forsyth, D., Uyeda, S. (1975) On the relative importance of the driving forces of plate motion. Geophys. J. Roy. Astron. Soc. 43:163-200
Fukao, Y. (1972) Source process of a large deep-focus earthquake and its tectonic implications. -The western Brazil earthquake of 1963. Phys. Earth Planet. Inter. 5:61-76
Fukao, Y. (1973) Thurst faulting at a lithospheric plate boundary: The Portugal earthquake of 1969. Earth Planet. Sci. Lett. 18:205-216
Gaposchkin, E.M. (1974) Earth's gravity field to the eighteenth degree and geocentric coordinates for 204 stations from satellite and terrestrial data, J. Geophys. Res. 79:5377-5411
Green, D.H. (1972) Magmatic activity as the major process in the chemical evolution of the earth's crust and mantle. In. The Upper Mantle, A.R. Ritsema, ed. pp. 47-71, Amsterdam: Elsevier
Hager, B.H., O'Connell, R.J. (1977) Benioff zone dip angles and flow driven by moving planes. Trans. Am. Geophys. Union 58:499 (abstract)
Hewitt, J.M., McKenzie, D.P., Weiss, N.O. (1975) Dissipative heating in convective flows. J. Fluid Mech. 68:721-738
Isacks, B.L., Molnar, P. (1971) Distribution of stresses in the descending lithosphere from a global survey of focal-mechanism solutions of mantle earthquakes. Rev. Geophys. Space Phys. 9:103-174
Isacks, B.L., Oliver, J., Sykes, L.R. (1968) Seismology and the new global tectonics. J. Geophys. Res. 73:5855-5899
Kanamori, H. (1970a) Synthesis of long-period surface waves and its application to earthquake source studies. - Kurile Islands earthquake of October 13, 1963. J. Geophys. Res. 75:5011-5027
Kanamori, H. (l970b) The Alaskan earthquake of 1964: radiation of longperiod surface waves and source mechanism. J. Geophys. Res. 75:5029-5040
Kanamori, H. (1971) Focal mechanism of the Takachi-Oki earthquake of May 16, 1968: contortion of the lithosphere at a junction between two trenches, Tectonophysics 12:l-13
Lerch, F.J., Wagner, C.A., Richardson, J.A., Brownd, J.E. (1974) Goddard earth models (5 and 6). Goddard Space Flight Centre report no. x-921-74.145
McKenzie, D.P. (1968) The influence of the boundary conditions and rotation on convection in the earth's mantle. Geophys. J. Roy. Astron. Soc. 15:457-500
McKenzie, D.P. (1969) Speculations of the causes and consequences of plate motions. Geophys. J. Roy. Astron. Soc. 18:1-32
McKenzie, D.P. (1976) The orientation of the stress within sinking slabs. Earth Planet. Sci. Lett. 31:305-307
McKenzie, D.P. (1977) Surface deformation, gravity anomalies and convection. Geophys. J. Roy. Astron. Soc. 48:211-238
McKenzie, D.P., Roberts, J.M., Weiss, N.O. (1974) Convection in the earth's mantle: towards a numerical simulation. J. Fluid Mech. 62:465-538
McKenzie, D.P., Weiss, N.O. (1975) Speculations on the thermal and tectonic history of the earth. Geophys. J. Roy. Astron. Soc. 42:131-174
Mikumo, T. (1972) Focal process of deep and intermediate earthquakes around Japan as inferred from long-period P and S waveforms. Phys. Earth Planet. Inter. 6:293-299
Minister, J.B., Jordan, T.H., Molnar, P., Haines, E. (1974) Numerical modelling of instantaneous plate tectonics. Geophys. J. Roy. Astron. Soc. 36:541-576
Molnar, P., Atwater, T., Mammerickx, J., Smith, S.M. (1975) Magnetic anomalies, bathymetry and the tectonic evolution of the South Pacific since the late Cretaceous. Geophys. J. Roy. Astron. Soc.
40:383-420
Molnar, P., Tapponnier, P. (1975) Cenozoic tectonics of Asia: effects of a continental collision. Science 189:419-426
Morgan, W.J. (1971) Convection plumes in the lower mantle. Nature 230:42-43
Morgan, W.J. (1972) Deep mantle convection plumes and plate motions. Bull. Amer. Ass. Petrol. Geol. Bull. 56:203-213
O'Connell, R.J. (1977) On the scale of mantle convection. Tectonophysics 38:119-136
Parsons, B., Sclater, J.G. (1977) An analysis of the variation of ocean floor bathymetry and heat flow with age. J. Geophys. Res. 82:803-827
Pekeris, C.L. (1935) Thermal convection in the interior of the earth, Monthly Notices Roy. Astron. Soc. Geophys. Suppl. 3:343-367
Peltier, W.R., Andrews, J.T. (1976) Glacial-isostatic adjustment I: the forward problem. Geophys. J. Roy. Astron. Soc. 46:605-646
Prothero, W.A., Reid, I., Reickle, M.S., Brune, J.N. (1976) Ocean bottom seismic measurements on the East Pacific Rise and Rivera Fracture Zone. Nature 262:121-124
Rayleigh, C.B., Healy, J.H., Bredehoeft, J.D. (1972) Faulting and crustal stress at Rangely, Colorado. In: Heard, H.C. et al. (Ed.) Flow and Fracture of Rocks, AGU monograph 16, pp. 275-284
Richter, F.M. (1973a) Dynamical models for sea-floor spreading. Rev. Geophys. Space Phys. 11:223-287
Richter, F.M. (1973b) Convection and the large scale circulation of the mantle. J. Geophys. Res. 78:8735-8745
Richter, F.M. (1977) On the driving mechanism of plate tectonics. Tectonophysics 38:61-88
Richter, F.M., Parsons, B. (1975) On the interaction of two scales of convection in the mantle. J. Geophys. Res. 80:2529-2541
Sbar, M.L., Sykes, L.R. (1973) Contemporary compressive stress and seismicity in eastern North America: an example of intra-plate tectonics. Bull. Geol. Soc. Am. 84:1861-1882
Schubert, G., Turcotte, D.L. (1972) One-dimensional model of shallow-mantle convection. J. Geophys. Res. 77:945-951
Sclater, J.G., Lawver, L.A., Parsons, B. (1975) Comparison of Jong-wavelength residual elevation and free air gravity anomalies in the North Atlantic and possible implications for the thickness of the lithospheric plate. J. Geophys. Res. 80:1031-1052
Stocker, R.L., Ashby, M.F. (1973) On the rheology of the upper mantle, Rev. Geophys. Space Phys. 11:391-426
Weertman, J. (1970) The creep strength of the earth's mantle. Rev. Geophys. Space Phys. 8:145-168
Weidner, D.J., Aki, K. (1973) Focal depth and mechanism of mid-ocean ridge earthquakes. J. Geophys. Res. 78:1818-1831
Wu, F., Kanamori, H. (1973) Source mechanism of February 4, 1965, Rat Island earthquake. J. Geophys. Res. 78:6082-6092
Wyllie, P.J. (1971) The Dynamic Earth. New York: J. Wiley & Sons
Wyss, M. (1970) Apparent stresses of earthquakes on ridges compared to apparent stress of earthquakes in trenches. Geophys. J. Roy. Astron. Soc. 19:479-484
Wyss, M., Molnar, P. (1972) Source parameters of intermediate and deep focus earthquakes in the Tonga Arc. Phys. Earth Planet. Inter. 6:279-292