On modelling the lithosphere in mantle convection with non-linear rheology

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H. Schmeling
W.R. Jacoby


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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Schmeling, H., and W.R. Jacoby. 1981. “On Modelling the Lithosphere in Mantle Convection With Non-Linear Rheology”. Journal of Geophysics 50 (1), 89-100. https://journal.geophysicsjournal.com/JofG/article/view/176.
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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