Mantle heterogeneities, geoid, and plate motion: A Monte Carlo inversion

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Abstract
Seismic tomography in both the upper and the lower mantle, as well as subducting oceanic slabs defined by seismicity, has been translated into density heterogeneities to generate models of mantle circulation. These models can predict both the surface velocities and the geoid, which can be compared with plate tectonics and gravity data. A given model is specified by 6 parameters related to the viscosities of 3 mantle layers and the absolute amplitudes of density variations in the upper and lower mantle as well as in the slabs. The values of these parameters are chosen at random within an acceptable range. Each model is submitted to an appropriate test comparing observations with predictions. The results of the most successful models selected by this Monte Carlo inversion are displayed. They yield preferred mantle viscosity structures exhibiting large variations at depth. With a physical interface between upper and lower mantle, i.e., with the possibility for the circulation to penetrate the 650 km discontinuity, two classes of viscosity profiles stand out. The first one implies a regular increase of the viscosity in the sublithospheric mantle, with reasonable values for the density parameters. The second one is unexpected in the sense that it predicts a very stiff bottom for the upper mantle. It also requires vanishingly small amplitudes for the upper mantle density heterogeneities defined by tomography, which would thus have to be of lithological rather than thermal origin. With a chemical interface at 650 km the outcome is very similar: the same two classes of viscosity structures do yield a satisfactory geoid prediction. However only the class of models with a stiff layer at midmantle depths predicts acceptable surface velocities. Altogether the best models out of some 60,000 which have been tested only explain one third of the geoid and two thirds of the surface divergence for spherical harmonic degrees 1 to 6. Nevertheless the main features of these two observed patterns are present in the computed maps, and 4 out of 6 correlation coefficients lie close to the 90% confidence level. This is true for the geoid as well as for the surface divergence of the displacement velocity. However, as the internal viscosity structure has been assumed to have spherical symmetry, the rotational component of the surface velocities cannot be predicted.

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