Seismology and laboratory

The course aims to provide the necessary knowledges for understanding the generation and effects of earthquakes and the modelling of propagation of seismic wave through the planet. The course also discusses applications of such a knowledge in order to assess the seismic hazard and the current legislation for seismic risk.

The frontal lessons will cover the following main topics:

SEISMOTECTONICS

We discuss how brittle shear fractures occur on the basis of the main (Tresca and Coulomb-Navier) empirical criteria of rock failure, taking advantage of their Mohr plane representation, and how they evolve in time, until stop, on the basis of 1-D models of rupture dynamic. Applying the Coulomb-Navier criterion to extensional, compressional and strike-slip tectonic regimes, we discuss also the main fault (normal, thrust and strike-slip) geometries on the basis of the Anderson theory of faulting.

· Tresca and Coulomb-Navier empirical criteria
· Mohr plane representation
· Rupture dynamics
· Anderson theory of faulting

SEISMIC SOURCE

We review the Hooke law and the momentum equation and understand how ruptures are taken into account on the basis of the Volterra representation theorem. It thus defines the concepts of point-like forces and dipole and double couple, and of seismic moment tensor.
In order to understand how earthquakes generate seismic waves, as well as static (co-seismic) deformations left after their passage, we obtain the closed form expression for the displacement field caused by a point-like seismic source in an infinite homogeneous elastic space. Investigating the time-dependent displacement field, we understand how to define and calculate the focal mechanism.

· Momentum equation
· Hooke law
· Volterra representation theorem
· Helmholtz representation theorem
· Seismic moment tensor
· Double couple and focal mechanism
· Body waves and co-seismic deformations

SEISMIC WAVES

On the basis of simple plane seismic waves and suitable boundary conditions, we derive the Snell law and understand how seismic waves reflect and refract at internal interfaces and at the Earth surface. This offers us the possibility of understanding in detail some cases of site effects leading to seismic wave amplification and to introduce (Love and Rayleigh) surface waves. The ray theory in stratified and spherical Earth model is also discussed, as well as the definition of the different seismic phase.

· Plane seismic waves
· Snell law
· Reflection and refraction of seismic waves
· Surface (Love and Rayleigh) waves
· Amplification due to shallow stratification
· Eikonal approximation
· Rays theory in stratified and spherical Earth models

SEISMIC HAZARD

In order to understand the fundamental concepts of the probabilistic seismic hazard assessment (PSHA), the course discuss how we can describe the temporal distribution of earthquakes and the seismic moment-frequency relation (Poisson distribution, and Guttenberg-Richter and Omori laws) and the peak ground acceleration caused by earthquakes (attenuation laws). Combining these probabilistic descriptions, we then define a simple procedure for calculate seismic hazard maps, taking into account for seismogenic zonation.

Through a series of example of site effects and the definition of the elastic response spectrum in acceleration, the course also shows how implement the current (Italian) legislation for defining the seismic risk as function of the natural period of the building, its reference period and the target state limit.

· Binomial and Poisson distributions
· Omori, Guttenberg-Richter and attenuation laws
· Seismogenic zonation
· Seismic risk map
· Site effects
· Elastic response spectrum
· "Nuove Norme Tecniche per le Costruzioni" (DM 14.01.08 NTC)

The laboratory lessons aim to provide the students with a first understanding of how a seismometer works, by making their own recordings with the seismometers of the laboratory, and with the tools necessary for processing raw waveforms and retrieving the ground motion. The students will access to the main seismological data center and download the waveform required for locating a selected earthquake and for estimating its (local) magnitude. Furthermore, the students will learn also how to get and deal with information about seismic stations.

The students will practice with some of the basic ingredients of the seismic hazard and risk assessment, making some statistical analysis of seismic catalogs and verifying the validity of the attenuation laws, as well as simulating the response of a building to given ground motions.

For a better understanding of all the above topics, the course will first review the definition of Fourier transform and series and the discrete Fourier transform, together with the response function of damped harmonic oscillator.

· Fourier transform and series
· Discrete Fourier transform
· Damped harmonic oscillator
· Taper and high, low and band pass filters.
· Waveform analysis and picking
· Earthquake location
· Estimate of the local magnitude
· Statistical analysis of earthquake catalogs
· Simulation of the response of a building

All the algorithms will exploit the state of the art "Obspy" module and developed in Python language.