Programme

Surface forces and volume forces. Traction vector or strain vector.
Traction applied to a free body. Cauchy's relation and Cauchy's tetrahedron. Stress tensor property. Diagonalization of stress matrix
Principal axes and planes. Principal stresses. Invariantes. Maximun shear stesses. Spherical, deviatory, hydrostatic, lithostatic stress.
The tensor deformation. The antisymmetric tensor of rigid rotations. Principal deformations. Dilatation. Relationships between stress and
deformation. Constitutive equations.

Rheological function. Linear elasticity. Hooke's Law
Generalized. Hooke's law for homogeneous and isotropic media. Duhamel-Neumann equations.
Stress-dependent rheological function, deformation and time. Linear viscoelasticity.
Time-deformation. Boltzmann Linear Solids with Memory Mechanism. Constitutive equations. Boltzmann's Integral-Differential Equation.
Creep and relaxation functions, complex module and quality factor. Linear viscoelastic models of Maxwell, Kelvin-Voigt, SLS.

Dynamic theory of elasticity. Elastic waves. Helmholtz-Lamé's elastic potential and theorem. Plane and
Spherical waves. Horizontal and vertical slowness. Volume waves. Waves P, S, SH, SV. Phase velocity and
Group velocity. Partition and conversion of seismic energy to a surface of discontinuity. Reflection and transmission coefficients.
Geometric spreading. Attenuation and scattering of a seismic wave. Surface Waves. Rayleigh and Love Waves.
Dispersion of surface waves. Equation and dispersion curve. Fundamental and overtones mode.
Free oscillations of the Earth. Spheroidal and toroidal (or torsional) modes.

Seismology and earth structure. Refraction seismology. Reflection seismology. Travel times. Travel times
In a layered Earth. Direct waves, head wave,
Reflected wave, diffracted wave. Shadow zones. Dromocron.
Seismic waves in a spherical earth.

Short and long-term seismometers. Seismograms and their interpretation.
Determination of the epicenter. Volume waves nomenclature. Determination of
Hypocentric parameters. The inverse problem. Origin Time.
The Seismic Source: radation pattern and Focal Mechanism.
Seismic: focal point and focal mechanism.
Seismic Moment and Magnitude.
Determination of the seismic moment. Earthquake magnitude. Local magnitude, for volume waves, for the
Superficial waves. Saturation of magnitude scales. Seismic energy and magnitude momentum.

Core Documentation

- An introduction to seismology: earthquakes and earth structure. Stein and Wysession. Blakwell publishing.
- Terremoti e onde. Metodi e pratica della sismologia moderna. Zollo e Emolo. Liguori.
- Modern global seismology. Lay Thorne AND Terry C. Wallace. Vol. 58. Elsevier, 1995.

Reference Bibliography

Aki Keiiti and Paul G. Richards. Quantitative seismology. 2002.

Type of delivery of the course

The course is mainly held with lectures on the blackboard so that the student can follow the reasoning made by the teacher slavishly. During the course the teacher performs the demonstrations on the blackboard trying to convey to the student what are the mathematical tools to be used and the physical meaning of what is obtained. During the course teacher-student dialogue and students' questions are encouraged. For some more descriptive topics (such as the propagation of the different seismic phases inside the Earth, the normal ways ...) there are also power point presentations and computer simulations that complete the lectures on the blackboard on the same topics.

Attendance

Attendance is not mandatory, but is strongly recommended.

Type of evaluation

The exam takes place in oral mode aimed at verifying the level of effective understanding of the concepts and the ability to describe both the formal aspects and the physical implications of the topics covered. During the test, the commission verifies the completeness and methodological rigor used by the student in describing the phenomenology and the basic principles of the physics of continuous media in Earth and Environmental Physics and in seismology.