Physics of the Earth and Laboratory

A.Y. 2019/2020
Overall hours
Learning objectives
To provide students with the capacity of comprehending the major processes occurring in our planet from the physico-mathematical perspective. In order to score this target, the formulation of continuum mechanics is the most advanced, deeply a mathematical one. The physical processes over which attention is focused are relative to the crust and Earth's mantle and those responsible for the structure of the oceanic lithosphere and subduction. Major attention is also devoted to the most relevant processes in the field of the Earth's gravity.
Expected learning outcomes
Acquiring capabilities in the mathematical and physical modelling of the processes occurring on the surface of the Earth and in its interior, in a modern and advanced fashion, in order to allow the students to compete in the labour market with a solid know-how, representing a solid basis also in the field of applications for informatics and computer science.
Course syllabus and organization

Single session

Lesson period
Second semester
Course syllabus
Continuum mechanics.
Strain and stress tensor. Cauchy formula. Maximum shear stress. Mohr's circle. Eigen values and eigen directions of the stress tensor. Wave equation, body and surface waves.
Linear elasticity for homogeneous and isotropic media, Hooke's law. Viscous behavious of rocks, Maxwell and Kelvin-Voigt viscoelastic solid. Crystal defects underlying the viscous behaviour of rocks, voids and dislocations. Navier-Stokes equation.
Heat transport.
Steady-state and time-dependent heat conduction. Geotherm for continental and oceanic lithospheres. Heat flow. Thermal boundary layer. Negative buoyancy forces at subduction zones. Cooling and subsidence of the oceanic lithosphere and of a sedimentary basin.
Gravity field.
Gravity and geopotential, zero and first order term, the latter due to the Earth's flattening. J2 and the ratio between centrifugal and gravitational potentials.
Geophysical processes responsible for the present-day J2 reduction. First-order expression of the geoid, as a function of latitude. Gravity and geoid anomalies, due to anomalous mass distributions.
Isostatic compensation. Bouguer and free-air gravity anomalies. Geoid anomalies, for Airy and Pratt topography isostatic compensation.
Magnetic field
Basic concepts (magneto-hydrodynamics) on the Earth's magnetic field. Equivalent magnetic dipole. Self-exciting dynamo. Magnetic field as a function of the latitude.

Numerical Solution of Partial Differential Equations. Outlines of finiteelements
methods. Introduction to discrete systems. Discretisation of a
continuum into a discrete set of elements. Application of MatLab for
numerical modelling and visualization. Energy Conservation Equation.
Numerical Solution of the Heat Stationary and time dependent
Conservation Equation: Numerical solution of Steady-state continental
geotherm. Numerical solution of Steady-state oceanic geotherm.
Numerical implementation of thermal boundary conditions: constant
temperature, constant heat flow, combined boundary conditions.
Numerical implementation of initial thermal conditions.
GEO/10 - SOLID EARTH GEOPHYSICS - University credits: 9
Practicals: 36 hours
Lessons: 48 hours
Professor: Sabadini Roberto
Every day by e-mail appointment
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