Syllabus
* Small motions in a medium with a finite pre-stress
Total, initial and incremental fields, Lagrangian and Eulerian increments, material and local forms of the equations for the incremental fields, kinematic and dynamic interface conditions, increments in gravitation, linearized Poisson's equation for gravitational potential increments, linearized interface conditions for increments in gravitation.
* Free elastic-gravitational oscillations of the Earth
Excitation of free oscillations, equations of motion, boundary and interface conditions, SNREI Earth model, toroidal and spheroidal oscillations, rotational and elliptical splitting, splitting due to the Earth's lateral heterogeneities, calculations of the eigenfrequencies.
* Postglacial viscoelastic rebound
Maxwell solid, theory of initial and boundary-value viscoelastic problem for spherically symmetric sphere, the model of ice-load, implicit and explicit time integration, solution in the Laplace domain, Love numbers, effect of compressibility and gravitation, viscoelastic problem with 3-D viscosity, its numerical solution, synthetic test examples.
* Thermal convection in the Earth's mantle
Formulation of the problem, methods of solution, review of the results.
Annotation
Deformation, deformation tensors, polar decomposition, volume and area deformation, geometric linearization. Kinematics, material time derivative, Reynold's theorem. Surface and volume forces, Cauchy traction principle, stress tensors. Basic axioms, mass conservation, balance of linear momemtum and angular momentum, energy conservation. Integral and differential forms. Interface conditions. Classical linear elasticity. Fluid dynamics.
Weak motions of viscoelastic prestressed self-graviting body.
Examples: Earth free oscillations, postglacial rebound, tidal and rotational deformation, convection in Earth mantle.