Modeling of geodynamic influence of an anomalous body of variable density in the gravitational field of the Earth

Kosygin Vladimir Yuryevich

The problem of determining the stress-strain state of a highly viscous geological medium caused by the presence of density inhomogeneities in the gravitational field of the Earth is considered. The Navier equation, known from the theory of elasticity, is used as a model approximation. The solution of this equation for an elastic half-space containing density inhomogeneities is considered. At the upper boundary of this half-space, coinciding with the day surface of the Earth, the condition of a flat free surface was considered. In this formulation, it was possible to use the solution of the Mindlin problem for a unit force, which, when the Poisson's ratio tends to 0.5, turns into a solution of the corresponding hydrodynamic problem for a highly viscous medium. An analytical solution of the problem is obtained for a typical approximating element – a rectangular parallelepiped. Calculations are made on a model example.

Keywords:stresses, tectonosphere, highly viscous medium, Poisson's ratio, Navier equation, Mindlin problem, gravity, parallelepiped, viscosity coefficient, velocity vector.