Kinematic models of large‐scale flow in the Earth's mantle

Abstract

It is likely that the motions of the lithospheric plates strongly influence the accompanying large‐scale flow in the earth's mantle. In order to isolate and understand the effects of the plate motions on the large scale flow, we calculate simple kinematic models in which the observed plate motions and geometries are imposed as boundary conditions; thermal buoyancy forces are ignored and the flow is determined by the mass flux imposed by the moving plates. With the assumption of a layered, radially symmetric, Newtonian rheology, the flow accompanying the observed plate motions is calculated analytically. The flow is in general complicated, but for models in which whole‐mantle flow occurs, the dips of subduction zones are predicted remarkably well by the flow modesl. Circulation does not from simple closed cells and flow under slowly moving plates is not closely related to the direction of plate motion. There is little return flow under the Pacific unless the lithosphere is essentially decoupled from the mantle by an extremely weak low viscosity layer. Only viscosity contrasts between the upper and lower mantle of three to four orders of magnitude are sufficient to confine flow to the upper mantle. For a wide range of mantle viscosity structures, significant mixing between the upper and lower mantle is expected over geologic time. On the basis of these models, the source rock for oceanic ridge basalt probably lies below the asthenosphere. A comparison of the magnitude of the deviatoric stress with theoretical flow mechanism calculations and with models of postglacial rebound indicate that the assumption of Newtonian viscosity is plausible. The drag on the lithosphere is compared to that calculated assuming simple shear. On a regional basis, the stresses can differ by up to 90°, e.g., in eastern North America. Small plates have higher apparent drag coefficients than larger ones. The normal stress at the base of the lithosphere is excessive in models in which the flow is confined to the upper 700 km of the mantle unless the lithosphere is decoupled from the mantle by an extremely low viscosity layer.