A numerical model of three-dimensional convection in the upper mantle

Results of 3-D modeling of thermal convection in the upper mantle with viscosity depending on temperature and pressure are presented. The numerical model is realized in the vorticity-vector potential variables. Testing with the use of the model developed by Busse et al. [1993] yielded an error of no more than 1-3%. Model results are obtained for thermal convection beneath a lithosphere of variable thickness. The modeling of convection beneath a plate of variable thickness represented by a long band showed that the structure of convective flows is essentially three-dimensional and, therefore, the application of two-dimensional modeling to the investigation of mantle dynamics even beneath extended structures can hardly be justified. The main result of the three-dimensional modeling of thermal convection beneath a thick craton is the determination of spatial characteristics of a small-scale convection mode immediately under the lithosphere in the "asthenospheric" interval depths (200350 km). The small-scale convection exists in the form of elongated cells of a lateral size of 500 kin between ascending and descending convective flows. This mode develops on the periphery of a thickened region of the lithosphere and can account for the properties of trap magmatism in ancient cratons and their peripheral parts.