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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.
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