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 stability problem of a heavy elastic layer above a less dense elastic layer representing 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 of oscillation frequencies for the density jump at the boundary between the layers are calculated. The changes introduced to the solution by the consideration of creep, which is present even in cold geomaterials, are discussed. Creep causes instability of heavy inclusions in the upper crust. However, due to the very high effective viscosity of the cold upper crust, this instability is of a formal nature, since it develops so slowly that heavy inclusions in the upper crust hardly change their position on timescales comparable to the age of the Earth.