On modelling the lithosphere in mantle convection with non-linear rheology
Article Sidebar
Published:
Oct 22, 1981
Keywords:
Mantle convection,
Finite-difference model,
Rheology,
Mantle temperatures,
Lithosphere
Volumes
Vols. 1-18 (1924-1944), ISSN 0044-2801
Main Article Content
Abstract
Numerical convection experiments were carried out with the aim of simulating the lithosphere as a strong mechanical boundary layer participating in the circulation, and to study its dynamical role and the governing parameters. The rheological model parameters were successively refined, effective viscosity depending on (1) depth, (2) temperature and pressure, and (3) temperature, pressure, and stress. In all cases a high-viscosity plate rested on a low-viscosity asthenosphere; in the two latter cases it could in principle subduct, but did so only if zones of weakness were built into it. It was possible to model active or inactive plates (moving faster or slower than the asthenosphere below). Because of a lack of numerical resolution it was however, not possible to simulate a narrow sinking slab; rather a broad zone of cooled and highly viscous material developed, often limiting the rate of descent and leading to non-steady convection. The circulation, including subduction, was stabilized by introduction of stress-dependence of viscosity (non-linearity), dissipation, and adiabatic heating. The parameter chiefly responsible for deciding the (active or passive) role of the plate is its decoupling from its neighbours, achieved in the models by assuming weakness zones. Another important result seems to be that the assumption of plausible mantle rheologies and heat input leads to equally plausible effective viscosities, plate velocities, and to upper-mantle temperatures which are relatively low by current ideas, but conforming to earlier estimates based on convection theory. Viscosity distribution and flow pattern are also in reasonable agreement with more detailed boundary layer computations. The main obstacles to our modelling are the numerical limitations, forcing upon us such artificialities as two-dimensionality, rectangular model boxes, coarse grids, and generalized weakness zones.
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How to Cite
Schmeling, H., & Jacoby, W. (1981). On modelling the lithosphere in mantle convection with non-linear rheology. Journal of Geophysics, 50(1), 89-100. Retrieved from https://journal.geophysicsjournal.com/JofG/article/view/176
Section
References
Anderson, O.L. (1980) The temperature profile of the upper mantle. J. Geophys. Res. 85:7003-7010
Andrews, D.J. (1972) Numerical simulation of sea-floor spreading. J. Geophys. Res. 77:6470-6481
Andrews, D.J., Sleep, N.H. (1974) Numerical modeling of tectonic flow behind island arcs. Geophys. J. R. Astron. Soc. 38:237-251
Artyushkov, E.V. (1968) Gravitational convection in the interior of the Earth. Izv. Earth Phys. 9:3-17 (trans. J. Buchner)
AveLallemant, H.G., Carter, N.L. (1970) Syntectonic recrystallisation of olivine and modes of flow in the upper mantle. Geol. Soc. Am. Bull. 81:2203-2220
Benard, H. (1900) Les tourbillons cellulaires dans une nappe liquide. Rev. Gen. Sci. 11:1261-1271
Busse, F.H. (1967) On the stability of two-dimensional convection in a layer heated from below. J. Math. Phys. 46:140-150
Busse, F.H., Whitehead, J.A. (1971) Instabilities of convection rolls in high Prandtl number fluid. J. Fluid Mech. 47:305-320
Chandrasekhar, S. (1953) The thermal instability in spherical shells. Phil. Mag., ser. 7, 44:233-241
Chandrasekhar, S. (1961) Hydrodynamic and Hydromagnetic Stability. Clarendon Pr., Oxford
Chapman, D.S., Pollack, H.N. (1975) Global heat flow: A new bok. Earth Planet. Sci. Lett. 28:23-32
Chapple, W.M., Tullis, T.E. (1977) Evaluation of the forces that drive the plates. J. Geophys. Res. 82:1967-1984
Daly, S.F. (1980) The vagaries of variable viscosity convection. Geophys. Res. Lett. 7:841-844
Davies, G.F. (1977) Whole mantle convection and plate tectonics. Geophys. J. R. Astron. Soc. 49:459-486
DeBremaecker, J.C. (1977) Convection in the Earth's mantle. Tectonophysics 41:195-208
DeLaCruz, S. (1970) Asymmetric convection in the upper mantle. Rev. Union. Geofis. Mexico. 10:49-56
Forsyth, D., Uyeda, S. (1975) On the relative importance of the driving forces of plate motion. Geophys. J. R. Astron. Soc. 43:163-200
Foster, T.D. (1969) Convection in a variable viscosity fluid heated from within. J. Geophys. Res. 74:685-693
Froidevaux, C., Schubert, G. (1975) Plate motion and structure of the continental asthenosphere: a realistic model of the upper mantle. J. Geophys. Res. 80:2553-2564
Froidevaux, C., Schubert, G., Yuen, D.A. (1977) Thermal and mechanical structure of the upper mantle: a comparison between continental and oceanic models. Tectonophysics 37:233-246
Gebrande, H. (1975) Ein Beitrag zur Theorie thermischer Konvektion im Erdmantel mit besonderer Berucksichtigung der Moglichkeit eines Nachweises mit Methoden der Seismologie. Diss. Munich
Goetze, C., Brace, W.F. (1972) Laboratory observations of high-temperature rheology of rocks. Tectonophysics 13:583-600
Grohmann, N. (1980) Die 2-Scale Zellularkonvektion. Untersuchung Uber die Zusammenhange zwischen Orogenese, Kontinentaldrift und Magmatismus. Diss. Munich
Hager, B.H., O'Connell, R.J. (1978) Subduction zone dip angles and flow driven by plate motion. Tectonophysics 50:111-133
Harper, J.F. (1975) On the driving forces of plate tectonics. Geo phys. J. R. Astron. Soc. 40:465-474
Houston, M.H., DeBremaecker, J.C. (1974) ADI solution of free convection in variable viscosity fluid. J. Comp. Phys. 16:221-239
Houston, M.H., DeBremaecker, J.C. (1975) Numerical models of convection in the upper mantle. J. Geophys. Res. 80:742-751
Isacks, B., 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
Jacoby, W.R. (1970) Instability in the upper mantle and global plate movements. J. Geophys. Res. 75:5671-5680
Jacoby, W.R. (1978) One-dimensional modelling of mantle flow. Pure Appl. Geophys. 116:1231-1249
Jacoby, W.R., Ranalli, G. (1979) Non-linear rheology and return flow in the mantle. J. Geophys. 45:299-317
Jeffreys, H. (1926) The stability of a layer of fluid heated below. Philos. Mag. 57(2):833-844
Kaula, W.M. (1980) Material properties for mantle convection consistent with observed surface fields. J. Geophys. Res. 85:7031-7044
Kopitzke, U. (1979) Finite element convection models: Comparison of shallow and deep mantle convection, and temperatures in the mantle. J. Geophys. 46:97-121
Krishnamurti, R. (1970a) On the transition to turbulent convection. 1. The transition from two to three dimensional flow. J. Fluid Mech. 42:295-307
Krishnamurti, R. (1970b) On the transition to turbulent convection. 2. The transition to time dependent flow. J. Fluid Mech. 42:309-320
McConnell, R.K. (1968) Viscosity of the mantle from relaxation time spectra of isostatic adjustment. J. Geophys. Res. 73:7089-7105
McKenzie, D.P. (1969) Speculations on the consequences and causes of plate motions. Geophys. J. R. Astron. Soc. 18:1-32
McKenzie, D.P. (1977) Surface deformation, gravity anomalies and convection. Geophys. J. R. Astron. Soc. 48:211-238
McKenzie, D.P., Watts, A., Parsons, B., Roufosse, M. (1980) Planform of mantle convection beneath the Pacific Ocean. Nature 288:442-446
Minster, J.B., Jordan, T.H., Molnar, P., Haines, E. (1974) Numerical modeling of instantaneous plate tectonics. Geophys. J. R. Astron. Soc. 36:541-576
Minster, J.B., Jordan, T.H. (1978) Present-day plate motions. J. Geophys. Res. 83:5331-5354
Morgan, W.J. (1971) Convection plumes in the lower mantle. Nature 230:42-43
Parmentier, E.M., Turcotte, D.L., Torrance, K.E. (1976) Studies of finite amplitude non-Newtonian thermal convection with application to convection in the Earth's mantle. J. Geophys. Res. 81:1839-1846
Rabinowicz, M., Lago, B., Froidevaux, C. (1980) Thermal transfer between the continental asthenosphere and the oceanic subducting lithosphere: its effect on subcontinental convection. J. Geophys. Res. 85:1839-1853
Rayleigh, J.W.S. (1916) On convection currents in a horizontal layer of fluid when the higher temperature is on the under side. Philos. Mag. VI, ser. 32:529-546
Richardson, R.M., Solomon, S.C., Sleep, N.H. (1979) Tectonic stress in the plates. Rev. Geophys. Space Phys. 17:981-1019
Richter, F.M. (1973a) Dynamical models for sea floor spreading. Rev. Geophys. Space Phys. 11:223-287
Richter, F.M. (1973b) Finite amplitude convection through a phase boundary. Geophys. J. R. Astron. Soc. 35:265-276
Richter, F.M., Daly, S.F. (1978) Convection models having a multiplicity of large horizontal scales. J. Geophys. Res. 83:4951-4956
Richter, F.M., McKenzie, D.P. (1978) Simple plate models of mantle convection. J. Geophys. 44:441-471
Richter, F.M., Parsons, B. (1975) On the interaction of two scales of convection in the mantle. J. Geophys. Res. 80:2529-2541
Roberts, P.H. (1967) Convection in horizontal layers with internal heat generation. Theory. J. Fluid Mech. 30:33-49
Ross, J.V., Nielsen, K.C. (1978) High temperature flow of wet polycrystalline enstatite. Tectonophysics 44:233-261
Schmeling, H. (1980) N umerische Konvektionsrechnungen unter Annahme verschiedener Viskositatsverteilungen und Rheologien im Mantel. Diplomarb. Frankfurt, 1979 - also: Ber. Inst. Met. Geophys. Un.
Frankfurt, Nr. 41
Schubert, G., Turcotte, D.L. (1971) Phase changes and mantle convection. J. Geophys. Res. 76:1424-1432
Schubert, G., Yuen, D.A., Turcotte, D.L. (1975) Role of phase transitions in a dynamic mantle. Geophys. J. R. Astron. Soc. 42:705-735
Schubert, G., Yuen, D.A. (1978) Shear heating instability in the Earth's upper mantle. Tectonophysics 50:197-205
Schubert, G., Froidevaux, C., Yuen, D.A. (1976) Oceanic lithosphere and asthenosphere: thermal and mechanical structure. J. Geophys. Res. 81:3525-3540
Schubert, G., Yuen, D.A., Froidevaux, C., Fleitout, L., Souriau, M. (1978) Mantle circulation with partial shallow return flow: effects on stresses in oceanic plates and topography of the sea floor. J. Geophys. Res. 83:745-758
Sclater, J.G., Jaupart, C., Galson, D. (1980) The heat flow through the oceanic and continental crust and the heat loss of the Earth. Rev. Geophys. Space Phys. 18:269-311
Solomon, S.C. (1976) Geophysical constraints on radial and lateral temperature variations in the upper mantle. Am. Mineral. 61:788-803
Solomon, S.C., Sleep, N.H., Richardson, R.M. (1975) On the forces driving plate tectonics: Inferences from absolute plate velocities and intra-plate stress. Geophys. J. R. Astron. Soc. 42:769-801
Stocker, R.L., Ashby, M.F. (1973) On the rheology of the upper mantle. Rev. Geophys. Space Phys. 11:391-426
Takeuchi, H., Sakata, S. (1970) Convection in a mantle with variable viscosity. J. Geophys. Res. 75:921-927
Thirlby, R. (1970) Convection in an internally heated layer. J. Fluid Mech. 44:673-693
Torrance, K.E., Turcotte, D.L. (1971) Structure of convection cells in the mantle. J. Geophys. Res. 76:1154-1161
Tozer, D.C. (1967a) Some aspects of thermal convection theory for the Earth's mantle. Geophys. J. R. Astron. Soc. 14:395-402
Tozer, D.C. (1967b) Towards a theory of thermal convection in the mantle. In: Gaskell, T.F. (Ed.) The Earth's Mantle, pp. 327-353. Academic Press, New York
Tritton, D.J., Zarraga, M.N. (1967) Convection in horizontal layers with internal heat generation, Experiments. J. Fluid Mech. 30:21-31
Turcotte, D.L., Torrance, K.E., Hsui, A.T. (1973) Convection in the Earth's mantle. Meth. Comp. Phys. 13:431-454
Vetter, U.R. (1978) Stress and viscosity in the asthenosphere. J. Geophys. 44:231-244
Zienkewicz, O.L. (1971) The Finite Element Method in Engineering Science. McGraw-Hill, London
Andrews, D.J. (1972) Numerical simulation of sea-floor spreading. J. Geophys. Res. 77:6470-6481
Andrews, D.J., Sleep, N.H. (1974) Numerical modeling of tectonic flow behind island arcs. Geophys. J. R. Astron. Soc. 38:237-251
Artyushkov, E.V. (1968) Gravitational convection in the interior of the Earth. Izv. Earth Phys. 9:3-17 (trans. J. Buchner)
AveLallemant, H.G., Carter, N.L. (1970) Syntectonic recrystallisation of olivine and modes of flow in the upper mantle. Geol. Soc. Am. Bull. 81:2203-2220
Benard, H. (1900) Les tourbillons cellulaires dans une nappe liquide. Rev. Gen. Sci. 11:1261-1271
Busse, F.H. (1967) On the stability of two-dimensional convection in a layer heated from below. J. Math. Phys. 46:140-150
Busse, F.H., Whitehead, J.A. (1971) Instabilities of convection rolls in high Prandtl number fluid. J. Fluid Mech. 47:305-320
Chandrasekhar, S. (1953) The thermal instability in spherical shells. Phil. Mag., ser. 7, 44:233-241
Chandrasekhar, S. (1961) Hydrodynamic and Hydromagnetic Stability. Clarendon Pr., Oxford
Chapman, D.S., Pollack, H.N. (1975) Global heat flow: A new bok. Earth Planet. Sci. Lett. 28:23-32
Chapple, W.M., Tullis, T.E. (1977) Evaluation of the forces that drive the plates. J. Geophys. Res. 82:1967-1984
Daly, S.F. (1980) The vagaries of variable viscosity convection. Geophys. Res. Lett. 7:841-844
Davies, G.F. (1977) Whole mantle convection and plate tectonics. Geophys. J. R. Astron. Soc. 49:459-486
DeBremaecker, J.C. (1977) Convection in the Earth's mantle. Tectonophysics 41:195-208
DeLaCruz, S. (1970) Asymmetric convection in the upper mantle. Rev. Union. Geofis. Mexico. 10:49-56
Forsyth, D., Uyeda, S. (1975) On the relative importance of the driving forces of plate motion. Geophys. J. R. Astron. Soc. 43:163-200
Foster, T.D. (1969) Convection in a variable viscosity fluid heated from within. J. Geophys. Res. 74:685-693
Froidevaux, C., Schubert, G. (1975) Plate motion and structure of the continental asthenosphere: a realistic model of the upper mantle. J. Geophys. Res. 80:2553-2564
Froidevaux, C., Schubert, G., Yuen, D.A. (1977) Thermal and mechanical structure of the upper mantle: a comparison between continental and oceanic models. Tectonophysics 37:233-246
Gebrande, H. (1975) Ein Beitrag zur Theorie thermischer Konvektion im Erdmantel mit besonderer Berucksichtigung der Moglichkeit eines Nachweises mit Methoden der Seismologie. Diss. Munich
Goetze, C., Brace, W.F. (1972) Laboratory observations of high-temperature rheology of rocks. Tectonophysics 13:583-600
Grohmann, N. (1980) Die 2-Scale Zellularkonvektion. Untersuchung Uber die Zusammenhange zwischen Orogenese, Kontinentaldrift und Magmatismus. Diss. Munich
Hager, B.H., O'Connell, R.J. (1978) Subduction zone dip angles and flow driven by plate motion. Tectonophysics 50:111-133
Harper, J.F. (1975) On the driving forces of plate tectonics. Geo phys. J. R. Astron. Soc. 40:465-474
Houston, M.H., DeBremaecker, J.C. (1974) ADI solution of free convection in variable viscosity fluid. J. Comp. Phys. 16:221-239
Houston, M.H., DeBremaecker, J.C. (1975) Numerical models of convection in the upper mantle. J. Geophys. Res. 80:742-751
Isacks, B., 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
Jacoby, W.R. (1970) Instability in the upper mantle and global plate movements. J. Geophys. Res. 75:5671-5680
Jacoby, W.R. (1978) One-dimensional modelling of mantle flow. Pure Appl. Geophys. 116:1231-1249
Jacoby, W.R., Ranalli, G. (1979) Non-linear rheology and return flow in the mantle. J. Geophys. 45:299-317
Jeffreys, H. (1926) The stability of a layer of fluid heated below. Philos. Mag. 57(2):833-844
Kaula, W.M. (1980) Material properties for mantle convection consistent with observed surface fields. J. Geophys. Res. 85:7031-7044
Kopitzke, U. (1979) Finite element convection models: Comparison of shallow and deep mantle convection, and temperatures in the mantle. J. Geophys. 46:97-121
Krishnamurti, R. (1970a) On the transition to turbulent convection. 1. The transition from two to three dimensional flow. J. Fluid Mech. 42:295-307
Krishnamurti, R. (1970b) On the transition to turbulent convection. 2. The transition to time dependent flow. J. Fluid Mech. 42:309-320
McConnell, R.K. (1968) Viscosity of the mantle from relaxation time spectra of isostatic adjustment. J. Geophys. Res. 73:7089-7105
McKenzie, D.P. (1969) Speculations on the consequences and causes of plate motions. Geophys. J. R. Astron. Soc. 18:1-32
McKenzie, D.P. (1977) Surface deformation, gravity anomalies and convection. Geophys. J. R. Astron. Soc. 48:211-238
McKenzie, D.P., Watts, A., Parsons, B., Roufosse, M. (1980) Planform of mantle convection beneath the Pacific Ocean. Nature 288:442-446
Minster, J.B., Jordan, T.H., Molnar, P., Haines, E. (1974) Numerical modeling of instantaneous plate tectonics. Geophys. J. R. Astron. Soc. 36:541-576
Minster, J.B., Jordan, T.H. (1978) Present-day plate motions. J. Geophys. Res. 83:5331-5354
Morgan, W.J. (1971) Convection plumes in the lower mantle. Nature 230:42-43
Parmentier, E.M., Turcotte, D.L., Torrance, K.E. (1976) Studies of finite amplitude non-Newtonian thermal convection with application to convection in the Earth's mantle. J. Geophys. Res. 81:1839-1846
Rabinowicz, M., Lago, B., Froidevaux, C. (1980) Thermal transfer between the continental asthenosphere and the oceanic subducting lithosphere: its effect on subcontinental convection. J. Geophys. Res. 85:1839-1853
Rayleigh, J.W.S. (1916) On convection currents in a horizontal layer of fluid when the higher temperature is on the under side. Philos. Mag. VI, ser. 32:529-546
Richardson, R.M., Solomon, S.C., Sleep, N.H. (1979) Tectonic stress in the plates. Rev. Geophys. Space Phys. 17:981-1019
Richter, F.M. (1973a) Dynamical models for sea floor spreading. Rev. Geophys. Space Phys. 11:223-287
Richter, F.M. (1973b) Finite amplitude convection through a phase boundary. Geophys. J. R. Astron. Soc. 35:265-276
Richter, F.M., Daly, S.F. (1978) Convection models having a multiplicity of large horizontal scales. J. Geophys. Res. 83:4951-4956
Richter, F.M., McKenzie, D.P. (1978) Simple plate models of mantle convection. J. Geophys. 44:441-471
Richter, F.M., Parsons, B. (1975) On the interaction of two scales of convection in the mantle. J. Geophys. Res. 80:2529-2541
Roberts, P.H. (1967) Convection in horizontal layers with internal heat generation. Theory. J. Fluid Mech. 30:33-49
Ross, J.V., Nielsen, K.C. (1978) High temperature flow of wet polycrystalline enstatite. Tectonophysics 44:233-261
Schmeling, H. (1980) N umerische Konvektionsrechnungen unter Annahme verschiedener Viskositatsverteilungen und Rheologien im Mantel. Diplomarb. Frankfurt, 1979 - also: Ber. Inst. Met. Geophys. Un.
Frankfurt, Nr. 41
Schubert, G., Turcotte, D.L. (1971) Phase changes and mantle convection. J. Geophys. Res. 76:1424-1432
Schubert, G., Yuen, D.A., Turcotte, D.L. (1975) Role of phase transitions in a dynamic mantle. Geophys. J. R. Astron. Soc. 42:705-735
Schubert, G., Yuen, D.A. (1978) Shear heating instability in the Earth's upper mantle. Tectonophysics 50:197-205
Schubert, G., Froidevaux, C., Yuen, D.A. (1976) Oceanic lithosphere and asthenosphere: thermal and mechanical structure. J. Geophys. Res. 81:3525-3540
Schubert, G., Yuen, D.A., Froidevaux, C., Fleitout, L., Souriau, M. (1978) Mantle circulation with partial shallow return flow: effects on stresses in oceanic plates and topography of the sea floor. J. Geophys. Res. 83:745-758
Sclater, J.G., Jaupart, C., Galson, D. (1980) The heat flow through the oceanic and continental crust and the heat loss of the Earth. Rev. Geophys. Space Phys. 18:269-311
Solomon, S.C. (1976) Geophysical constraints on radial and lateral temperature variations in the upper mantle. Am. Mineral. 61:788-803
Solomon, S.C., Sleep, N.H., Richardson, R.M. (1975) On the forces driving plate tectonics: Inferences from absolute plate velocities and intra-plate stress. Geophys. J. R. Astron. Soc. 42:769-801
Stocker, R.L., Ashby, M.F. (1973) On the rheology of the upper mantle. Rev. Geophys. Space Phys. 11:391-426
Takeuchi, H., Sakata, S. (1970) Convection in a mantle with variable viscosity. J. Geophys. Res. 75:921-927
Thirlby, R. (1970) Convection in an internally heated layer. J. Fluid Mech. 44:673-693
Torrance, K.E., Turcotte, D.L. (1971) Structure of convection cells in the mantle. J. Geophys. Res. 76:1154-1161
Tozer, D.C. (1967a) Some aspects of thermal convection theory for the Earth's mantle. Geophys. J. R. Astron. Soc. 14:395-402
Tozer, D.C. (1967b) Towards a theory of thermal convection in the mantle. In: Gaskell, T.F. (Ed.) The Earth's Mantle, pp. 327-353. Academic Press, New York
Tritton, D.J., Zarraga, M.N. (1967) Convection in horizontal layers with internal heat generation, Experiments. J. Fluid Mech. 30:21-31
Turcotte, D.L., Torrance, K.E., Hsui, A.T. (1973) Convection in the Earth's mantle. Meth. Comp. Phys. 13:431-454
Vetter, U.R. (1978) Stress and viscosity in the asthenosphere. J. Geophys. 44:231-244
Zienkewicz, O.L. (1971) The Finite Element Method in Engineering Science. McGraw-Hill, London