NUMERICAL APPROACH TO PROBLEMS OF GRAVITATIONAL-INSTABILITY OF GEOSTRUCTURES WITH ADVECTED MATERIAL BOUNDARIES

We present a numerical approach for solving 2-D mantle flow problems w here the chemical composition changes abruptly across intermediate bou ndaries. The method combines a Galerkin-spline technique with a method of integration over regions bounded by advected interfaces to represe nt discontinuous variations of material parameters. It allows direct a pproximation of a natural free surface position, instead of a posterio ri calculation of topography from the normal stress at the upper free- slip boundary. We formulate a model where a viscous incompressible flu id filling a square box is divided into layers (not necessarily horizo ntal) by advected boundaries, across which the density and viscosity c hange discontinuously. No-slip or free-slip conditions are assumed at the model sides. The suggested approach, being Eulerian, avoids the di fficulties due to material discontinuities at intermediate boundaries, like the Moho or the Earth's surface, and is also free from the defic iencies of the Lagrangian approach, always resulting in mesh distortio n. We present two geophysical cases analysed by this technique. The fi rst case concerns the formation of sedimentary basins under the effect s of heavy bodies sinking in the asthenosphere and of load due to sedi mentary infills. The second case demonstrates the evolution of salt di apirs and shows how their growth is affected by a laterally inhomogene ous sedimentary layer. This numerical approach is well suited for prob lems of gravitational instability with discontinuities of density and viscosity across advected boundaries.