Simple considerations on forces driving plate motion and on the plate-tectonic contribution to the long-wavelength geoid

SUMMARY In order to gain some insights into the role of deep mass anomalies on surface velocity and geoid anomalies, Cartesian models involving strong lateral viscosity contrasts and where plate boundaries are mimicked by zones of very low viscosity are performed. The response of the system to mass anomalies at various depths and various distances from the plate boundary is computed. It is compared with the responses obtained using the three other methods used in global geoid models for mimicking the mobility of the lithosphere: models with layered viscosity and a uniform low-viscosity lithosphere; models computing plate velocities from horizontal force balance; and models where the surface velocities are set equal to the observed ones with plates ‘moved by the hand of God’. Contrary to what occurs in models with layered viscosity, the geoid response for the weak-zone model proposed here changes drastically from positive to negative, depending upon the position of the mass anomaly with respect to the plate boundary. This arises from the fact that only mass anomalies situated close to the plate boundary are able to move the plates efficiently. Changing the location of an upper-mantle mass anomaly by a few hundred kilometres considerably modifies the amplitude of the predicted plate velocities and geoid anomalies. Consequently, upper-mantle density anomalies deduced from global tomography analysis, or density anomalies assumed to be known a priori (subducted slabs) but truncated by a spherical harmonic decomposition should not be used in models aimed at computing plate motions and the associated geoid. When a mass anomaly is situated just below a plate boundary, the sign of the predicted geoid anomalies can be the same as for models with a layered viscosity and a low-viscosity lithosphere. However, the shape of the predicted geoid anomaly and its amplitude as a function of the depth of the mass anomaly cannot be mimicked by models with a uniform-viscosity lithosphere, whatever the lithospheric viscosity. For mass anomalies situated at a large distance from the plate boundaries, the induced plate velocities are small and the geoid is equal to that computed for a highly viscous continuous lithosphere. The ‘force-balance method’ is strongly affected by the cut-off in the harmonic decomposition. Only models with a lithospheric layer below the surface reproduce the geoid successfully for mass anomalies situated away from a plate boundary. The plate velocities for the force-balance method and for the weak-zone model proposed here are not proportional, due to differences in the structure of the plate boundary. In short, only mass anomalies very close to a plate boundary are able to influence the plate velocities, but these velocities depend strongly on the mechanical details of the plate boundary. As a consequence, we believe that it is impossible to compute plate velocities from what we know from mass anomalies in the Earth precisely enough to include them in a geoid model. On the other hand, actual plate velocities are known. We show that an accurate geoid can be computed by imposing the observed plate velocities onto the Earth's surface, even if the details of the mechanical structure of the lithosphere are not respected. It is this method that is suggested for introducing the effect of plate tectonics in global geoid models.