Distribution of Mantle Up-welling Determined from Plate Motions: A Case for Large-scale Bénard Convection

—?The number and geometric distribution of putative mantle up-welling centers and the associated convection cell boundaries are determined from the lithospheric plate motions as given by the 14 Euler poles of the observational NUVEL model. For an assumed distribution of up-welling centers (called “cell-cores”) the corresponding cell boundaries are constructed by a Voronoi division of the spherical surface; the resulting polygons are called “Bénard cells.” By assuming the flow-kinematics within a cell, the viscous coupling between the flow and the plates is estimated, and the Euler poles for the plates are computed under the assumption of zero-net-torque. The positions of the cell-cores are optimized for the HS2-NUVEL1 Euler poles by a method of successive approximation (“subplex”); convergence to one of many local minima occurred typically after ～20,000 iterations. Cell-cores associated with the fourteen HS2-NUVEL1 Euler poles converge to a relatively small number of locations (8 to 10, depending on interpretation), irrespective of the number of convection cells submitted for optimized distribution (from 6 to 50). These locations are correlated with low seismic propagation velocities in tomography, uniformly occur within hotspot provinces, and may specifically be associated with the Hawaiian, Iceland, Reunion/Kerguelen (Indian Ocean), Easter Island, Melanesia/Society Islands (South Pacific), Azores/Cape Verde/Canary Islands, Tristan da Cunha (South Atlantic), Balleny Islands, and possibly Yellowstone hotspots. It is shown that arbitrary Euler poles cannot occur in association with mantle Bénard convection, irrespective of the number and the distribution of convection cells. Nevertheless, eight of the observational Euler poles – including the five that are accurately determined in HS2-NUVEL1 (Australia, Cocos, Juan de Fuca, Pacific, and Philippine) – are “Bénard-valid” (i.e., can be explained by our Bénard model). Five of the remaining six observational poles must be relocated within their error-ellipses to become Bénard-valid; the Eurasia pole alone appears to be in error by ～115°, and may actually lie near 40°N, 154°E. The collective results strongly suggest Bénard-like mantle convection cells, and that basal shear tractions are the primary factor in determining the directions of the plate motions as given by the Euler poles. The magnitudes of the computed Euler vectors show, however, that basal shear cannot be the exclusive driving force of plate tectonics, and suggest force contributions (of comparable magnitude for perhaps half of the plates) from the lithosphere itself, specifically subducting slab-pull and (continental) collision drag, which are provisionally evaluated. The relationship of the putative mantle Bénard polygons to dynamic chaos and turbulent flow is discussed.