The course aims to deepen the knowledge of the physical mechanisms that regulate the dynamics of the deformation processes involving the crust-mantle system at small and large-scales, both spatial and temporal.
Expected learning outcomes
Capability to understand the physical laws that govern the processes that take place at different scales on our Planet. Capability to solve a complex problem using appropriate mathematical tools.
PHYSICS OF EARTH'S INTERIOR Hooke's Law. Lamé's parameters. Rigidity, Young Modulus, Poisson ratio. Uniaxial stress. Application: Deformation under mountain under its own weight. Uniaxial strain. Application: Stress induced by instantaneous sedimentation and erosion. Plane stress and its validity for the Earth's lithosphere. Elasticity and the interatomic forces. Variation of potential energy with interatomic spacing. Two-dimensional flexure of a thin elastic plate. Fiber stress. Neutral plane. Equations of forces and bending moment equilibrium. General equation for the deflection of a thin elastic plate. Flexural Rigidity. Application: Deformation of strata overlying an igneous intrusion. Buckling of a thin elastic plate under an end horizontal force. Application of the theory of elastic flexure to the Earth's Lithosphere. Hydrostatic Restoring Force. Stability of the Earth's Lithosphere under an end load. Deflection of the Lithosphere under a Periodic load. Degree of Compensation of a periodic Topographic load. Bending of the Elastic lithosphere under the Loads of Island Chains. Flexural Parameter. Flexural Forebulge. Continuous lithosphere model and Broken Lithosphere model. Variation of the Flexural moment and Fiber stress with distance along the bended Lithosphere for the continuum lithosphere and for the broken lithosphere models. Bending of the elastic lithosphere at the ocean trench. The universal flexure profile. Application of the universal flexure profile to the Mariana Trench and to the Tonga Trench. Strain Energy Function. Elastic strain energy. Lattice Potential Energy. Number of atoms per unit volume with energy greater than the barrier potential energy. Fick law. Diffusion coefficient for Vacancies and Atoms. Diffusion Creep. Strain rate induced by deviatoric stress. Dynamic viscosity and its dependence on pressure and temperature. Coble Creep. Unidirectional flow. Variation of stress with depth for an unidirectional flow. Astenospheric counterflow. Viscous dissipation. Frictional heating in Couette flow. Prandtl number. Eckert number. Velocity profile foe Couette flow with a temperature dependent viscosity. Frictional heating in a flow with a strongly temperature dependent viscosity. Dislocation creep. Effective viscosity. Continuity equation for an incompressible fluid. Momentum equation for an incompressible fluid. Energy equation for an incompressible fluid. Linear stability analysis for the onset of thermal convection in a layer of fluid heated from below. Rayleigh number. Critical value of the Rayleigh number and its dependence on disturbance wavelength. Rayleigh number for Earth mantle. Brittle and ductile behavior of rocks. Stress hardening and stress softening. Variation of fracture stress and ductile yield stress with pressure and temperature. Brittle/ductile transition. Lithosphere strength envelope: 1-layer and 2-layer models. Maxwell viscoelasticity. Relaxation time.