Non-linear rheology and return flow in the mantle
Article Sidebar
Main Article Content
Abstract
A simple model of mantle return flow in response to lithospheric plate motions is developed. Such a model is realistic if the buoyancy forces are concentrated in the plates. One-dimensionality is chosen as a simplification to study effects of mantle rheology in as much isolation as possible. Rheology is modelled as a combination of dislocation creep, diffusion creep and fluid phase transport; parameters are those appropriate for olivine. We have varied temperature, grain size, influence of partial melt, diffusivity and activation energy, grain deformation versus grain boundary sliding dominated creep, and surface plate velocity. A peculiar feature of non-linear rheology is the existence of low-stress high-viscosity regions, which, however, are of little dynamic importance because deformation there is very small. The main results are (1) that the model does not predict an excessive pressure gradient to be required by the return flow (which would be evident in a rise of the sea floor and strong increase in free air gravity anomalies toward the trenches); (2) that no excessive shear stresses at the plate bottom are predicted (which might result in observable heat flow effects and intra-plate seismicity and would require implausibly great driving forces at the plate ends); (3) that the model predicts the return flow to extend into the deeper mantle; this follows, however, from the simplifying assumption of olivine rheology below 400 km depth and would then argue for rather high temperatures, small grain sizes, possibly important fluid phase transport, and small activation volume. Recent work on the variation of activation volume with pressure and phase changes suggests a rather 'soft' lower mantle and thus supports the notion of 'deep' return flow. In interpreting the results one must, of course, keep in mind that the model is a purely mechanical one with a predetermined temperature profile (varied within plausible limits) and that the physics of the thermodynamic aspects of the flow problem is ignored.
ARK: https://n2t.net/ark:/88439/y009016
Permalink: https://geophysicsjournal.com/article/43
Article Details
Authors who publish with this journal as of Vol. 63 agree to the following terms:
a. Authors share the copyright with this journal in equal parts (50% to the journal, 50% to the lead author), and grant the journal right of first publication, with the work after publication simultaneously licensed under Creative Commons Attribution License CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
b. Authors may enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal, and a reference to this copyright notice.
c. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) during the submission process, as this can lead to productive exchanges and earlier and greater citation of published work and better sales of the copyright.
Author Self-archiving
Authors retain copyright and grant the Journal of Geophysics right of first publication, with the work three years after publication simultaneously licensed under the Creative Commons BY-NC-ND 4.0 License that allows others to share the work (with an acknowledgment of the work's authorship and initial publication in this journal), except for commercial purposes and for creating derivatives.
Authors can enter into separate, additional, but non-commercial contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository, but not publish it in a book), with an acknowledgment of its initial publication in this journal.
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) before and during the submission process, as that can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
Additional Notes
This journal is one of a handful of scholarly journals that publish original scientific works under CC BY-NC-ND 4.0 - the only Creative Commons license affording the authors' intellectual property absolute worldwide protection.
Journal of Geophysics is published under the scholar-publishers model, meaning authors do not surrender their copyright to us. Instead, and unlike corporate publishers like Elsevier or Springer Nature that resell copyright to third-parties for up to $80,000 (per paper, per transaction!), the Journal of Geophysics authors share copyright equally with this journal.
Therefore, all the proceeds from reselling copyright to third parties get shared to equal parts (50% to the journal, 50% to the lead author). Under the Berne Convention, this protection is an inheritable right that lasts for as long as the rightsholder lives + 50 years.
By submitting to this journal, the lead author, on behalf of all co-authors, grants permission to this journal to represent all co-authors in negotiating copyright sales and collecting proceeds. The lead author should negotiate with his/her co-authors the modalities of distributing the lead author's portion of the proceeds. Usually, this is per pre-agreed percentage of each co-author's contribution to creating the copyrighted work. (more...)
References
Ashby, M.F., Verrall, R.A. (1973) Diffusion-accommodated flow and superplasticity. Acta Metall. 21:149-163
Ashby, M.F., Verrall, R.A. (1977) Micromechanisms of deformation and fracture, and their relevance to the rheology of the upper mantle. Philos. Trans. R. Soc. London, Ser. A: 288:59-95
Brennen, C. (1974) IsostatiG recovery and the strain rate dependent viscosity of the earth's mantle. J. Geophys. Res. 79:3993-4001
Carter, N.L. (1976) Steady-state flow of rocks. Rev. Geophys. Space Phys. 14:301-360
Cathles, III, L.M. (1975) The viscosity of the earth's mantle. Princton, N.J.: Princton Univ. Press, 386 pp.
Davies, G.F. (1977a) Whole mantle convection and plate tectonics. Geophys. J. R. Astron. Soc. 49:459-486
Davies, G.F. (1977b) Viscous mantle flow under moving lithospheric plates and under subduction zones. Geophys. J. R. Astron. Soc., 49:557-563
Durham, W.B., Goetze, C. (1977) Plastic flow of oriented single crystals of olivine. J. Geophys. Res. 82:5737-5753
Duschenes, J.D., Solomon, S.C. (1977) Shear wave travel time residuals from oceanic earthquakes and the evolution of the oceanic lithosphere. J. Geophys. Res. 82:1985-2000
Elliott, D. (1973) Diffusion flow laws in metamorphic rocks. Bull. Geol. Soc. Am. 84:2645-2664
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
Goetze, C. (1977) A brief summary of our present-day understanding of the effect of volatiles and partial melt of the upper mantle. In: High Pressure Research Applications in Geophysics, M. Manghnani and S. Akimoto (Eds.), pp. 3-23. New York: Academic Press
Jacoby, W.R. (1978) One-dimensional modelling of mantle flow. Pure Appl. Geophys. 116:1231-1249
Jordan, T.H. (1975) The continental tectosphere. Rev. Geophys. Space Phys. 13:1-12
Kirby, S.H., Raleigh, C.B. (1973) Mechanisms of high-temperature, solid-state flow in minerals and ceramics and their bearing on the creep behaviour of the mantle. Tectonophysics 19:165-194
Kushiro, I., Yoder, H.S. Jr., Mysen, B.O. (1976) Viscosities of basalt and andesite melts at high pressures. J. Geophys. Res. 81:6351-6356
Murase, T., McBirney, A.R. (1973) Properties of some common igneous rocks and their melts at high temperatures. Bull. Geol. Soc. Am. 84:3563-3592
Nicolas, A. (1976) Flow in upper mantle rocks: some geophysical and geodynamical consequences. Tectonophysics 32:93-106
O'Connell, R.J. (1977) On the scale of mantle convection. Tectonophysics 38:119-136
Peltier, W.R. (1974) The impulse response of a Maxwell earth. Rev. Geophys. Space Phys. 12:649-669
Peltier; W.R., Andrews, J.T. (1976) Glacial-isostatic adjustment - I. The forward problem. Geophys. J. Roy. Astron. Soc. 46:605-646
Peltier, W.R., Farrell, W.E., Clark, J.A. (1978) Glacial isostasy and relative sea level: a global finite element model. Tectonophysics 50:81-110
Post, R.L., Griggs, D.T. (1973) The earth's mantle: evidence for non-Newtonian flow. Science 181:1242-1244
Ranalli, G. (1978) Regional models of the steady-state rheology of the upper mantle. In: Earth rheology, isostasy and eustasy, N.A. Marner (ed.) New York: Wiley (in press)
Rutter, E. H. (1976) The kinetics of rock deformation by pressure solution. Philos. Trans. R. Soc. London, Ser. A.: 283:203-219
Sammis, C.G., Smith, J.C., Schubert, G., Yuen, D.A. (1977) Viscosity-depth profile of the earth's mantle: effects of polymorphic phase transitions. J. Geophys. Res. 82:3747-3761
Schubert, G., Turcotte, D.L. (1972) One-dimensional model of shallow convection. J. Geophys. Res. 77:945-951
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
Solomon, S.C. (1976) Geophysical constraints on radial and lateral temperature variations in the upper mantle. Am. Mineral. 61:788-803
Stocker, R.L., Ashby, M.F. (1973) On the rheology of the upper mantle. Rev. Geophys. Space Phys. 11:391-426
Twiss, R.J. (1976) Structural superplastic creep and linear viscosity in the earth's mantle. Earth Planet. Sci Lett. 33:86-100
Walcott, R.I. (1973) Structure of the earth from glacio-isostatic rebound. Ann. Rev. Earth Planet. Sci. I:15-37
Weertman, J. (1970) The creep strength of the earth's mantle. Rev. Geophys. Space Phys. 8:145-168
Woollard, G.P. (1975) The interrelationship of crustal and upper mantle parameter values in the Pacific. Rev. Geophys. Space Physics 13:87-137
Yuen, D.A., Tovish A., Schubert, G. (1978) Shear flow beneath oceanic plates: local nonsimilarity boundary layers for olivine rheology. J. Geophys. Res. 83:759-765