While there has been significant progress in modeling radial mantle viscosity structure, there has also been a growth in the study of lateral variations in viscosity. The correlation of long wavelength gravity anomalies in northern Eurasia with seismic tomography points strongly toward a lateral variation in upper mantle viscosity [ Kogan and McNutt, 1993]. The change in sign of the correlation from western to eastern Eurasia can best be explained by a low-viscosity zone in the upper mantle beneath eastern Eurasia that is absent in the west. At this stage, most of this work is in the theoretical stage of understanding how lateral variations in viscosity affect surface observables. As yet, no studies have been bold enough to produce maps of lateral viscosity variations.
A simple scaling theory has been developed by Solomatov [1995], in which he finds three convective regimes: (1) a small viscosity contrast regime, (2) a transitional regime, and (3) a stagnant lid regime. Through scaling relations he shows that regime (1) is similar to constant viscosity convection while in regime (2) is controlled by the dynamics of the cold boundary layer and the properties of convection depend on the value of the surface viscosity. None of these regimes resembles the mobile, rigid plates and narrow deformation zones as are expected from plate tectonics; however regime (3) has been applied to Venus with some success [ Solomatov, 1993].