Stability of heavy inclusions in the Earth’s crust

Abstract

Stability of a heavy inclusion in the Earth’s upper crust is studied by the linear theory method for small perturbations. The presence of such inclusions with an increased density is associated with chemical inhomogeneity or phase transformations. The problem of the stability of a heavy elastic layer above a less dense elastic layer that represents the lower crust and mantle lithosphere is solved. It is shown that such a system is stable: small initial perturbations produce low-amplitude oscillations. The corrections to the oscillation frequency that arise due to the density jump at the boundary between the layers are calculated. The changes in the solution due to the consideration of creep, which is present even in cold geomaterials, are discussed. Creep leads to instability of heavy inclusions in the upper crust. However, because the effective viscosity of the cold upper crust is very high, this instability is of a formal nature, since it develops so slowly that heavy inclusions in the upper crust hardly change their position over a timescale comparable to the age of the Earth.