31259 - Foundations of Geophysics 1

Learning outcomes

At the end of the course the student will possess a solid background in continuum mechanics, the basic concepts of tensor algebra, the main properties of the strain and stress tensors and the constitutive relationships of elastic materials, their use to describe elastic waves, the state of stress within the Earth, faulting and intrusion processes.  In particular, the student will be able - to distinguish and characterize the stress regimes present in different regions of the Earth - to solve 2-D dislocation problems and problems of fracture mechanics.

Course contents

The course is organized into two moduli, each dealing with different subjects within the following list.

Mechanics of continuum media. Stress and strain. Conservation laws. Thermo-Elastic materials. Elastic and adiabatic moduli.

Isotropic elastic media. Constraints on elastic moduli. Equations of motion (Cauchy-Navier). Elastic waves.

Stress within the Earth, theories of faulting. Elastostatic problems in a half-space: the Airy stress function.

Potentials in the theory of elasticity, the Love strain function, the Galerkin vector. Elastic dislocations and their representation.

Fracture mechanics, the Cauchy integral equation: the elliptic crack, the stress intensity factor and the fracture criteria. Darcy's law and poroelasticity.

Readings/Bibliography

Lecture notes (Prof. Maurizio Bonafede) and slides will be available online (Insegnamenti online IOL).

Teaching methods

Classroom lectures and tutorials

Assessment methods

Oral examination: typically 3 questions are proposed to assess the student's theoretical knowledge of the Mechanics of elastic solids and its application to the study of the interior of the Earth. The candidate is likely to be requested both to prove the main theoretical results and to estimate some of the physical parameters of the Earth interior.

Office hours

See the website of Maria Elina Belardinelli

See the website of Letizia Anderlini