Intensive Programme - Mathematical Models in Seismology
27 August - 7 September 2012, University of L'Aquila
SeisMath IP 2012
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Welcome to the 2012 Intensive Programme (IP) in
Mathematical Models in Seismology
27 August - 7 September 2012, University of L'Aquila (Italy)
Coordinators: Armin Iske and Bruno Rubino
Coordinating Institutions: University of Hamburg and University of L'Aquila
Venue: University of L'Aquila (Italy)
Scientific Committee
- Alvaro Corral (Centre de Recerca Matematica, Barcelona, Catalonia, Spain),
- Armin Iske (Department of Mathematics, University of Hamburg, Germany),
- Antonino Morassi (Department of Georesources and Territory, University of Udine, Italy),
- Roberto Paolucci (Structural Engineering Department, Politecnico di Milano, Italy),
- Mircea Radulian (Scientific Director National Institute for Earth Physics, Bucharest, Romania),
- Bruno Rubino (Department of Pure and Applied Mathematics, University of L'Aquila, Italy),
List of Partner Institutions and Local Coordinators of the SeisMath IP 2013
University of L'Aquila (Italy) - Coordinator, Prof. Bruno Rubino
Brno University of Technology (Czech Republic), Prof. Josef Slapal
University of Hamburg (Germany), Prof. Armin Iske
National and Kapodistrian University of Athens (Greece), Prof. Nicholas Alikakos
University of Crete (Greece), Prof. Chrysoula Tsogka
Politecnico di Milano (Italy), Prof. Roberto Paolucci
University of Udine (Italy), Prof. Antonino Morassi
Tehnical University of Cluj Napoca (Romania), Prof. Petrica Pop
Autonomous University of Barcelona (Catalunia, Spain), Prof. Aureli Alabert
Middle East Technical University (Turkey), Prof. Sinan Akkar
University of Maine (France), Prof. Sohbi Sahraoui
Second University of Naples (Italy), Prof. Eugenio Lippiello
University of Naples (Italy), Prof. Aldo Zollo
Presentation
Earthquakes occur nearly constantly around Europe in places like Greece, Italy, Portugal, Romania and Turkey. But earthquakes can occur almost anywhere. Italy is a well-known complex earthquake zone. In Italy there is the collision of Africa and Europe, it is highly fractured and broken up, there are a lot of micro plates moving around, which create a lot of different types of fault action.
An earthquake measuring 5.8 on the Richter scale and 6.3 in the moment magnitude scale hit L'Aquila on April 6th, 2009. There have been a large number of minor tremors since December 2008. Along with the stories of tragedy in L'Aquila, there are also stories that the earthquake was predicted, and that the predictions were ignored. Earthquake prediction remains an elusive goal of seismology. Earthquake source mechanisms are complex and involve many variables and factors. Earthquake prediction can be divided into long-, medium- and short-term phases. The short-term prediction of earthquakes has considerable allure. However, it is beset by problems. Although earthquakes are complex multi-scale phenomena, we now have much better models for earthquake nucleation and rupture processes, associated phenomena such as tsunamis, and tools with which earthquakes can be carefully studied from both deterministic and statistical points of view.
The Intensive Programme (IP) called "Mathematical Models in Seismology - SeisMath 2012" will consist of a set of short courses and seminars. Contributors will take into account methods, modelling and simulations related to above mentioned aspects of seismology. Although the need for newly developed mathematical modelling within seismology is very strong, its clear identification as an interdisciplinary research/training context at a European level is still in progress. This programme aims to provide a relevant contribution to this process by exploiting the scientific competencies of the partners. The short courses will be taught by physicians, geologists, engineers and mathematicians.The programme is addressed mainly to MSc and PhD students in Applied Mathematics, but also in Civil and Environmental Engineering and Applied Physics.
The participation of students and teachers will be supported by the LLP Erasmus Programme (see the partner universities) and by the DFG Priority Program 1324.
Reimbursement
Reimbursement for DFG Priority Program 1324 participants
Students and teacher supported by the DFG Priority Program 1324 will have to follow the standard procedures adopted by that program. For further information you may contact Prof Armin Iske.
Reimbursement for LLP participants
Applicants from LLP partner institutions are eligible for a reimbursement of living and travel expenses.
This contribution is offered by the LLP Italian National Agency. 
We assume to select:
- around 30 students (MSc or PhD) for the contribution for travel costs and the contribution for accommodation and subsistence costs: this corresponds to about 3 students for each partner institution.
- around 10 teachers for the contribution for travel costs and the contribution for accommodation and subsistence costs.
The contact person of each institution in the Organizing Committee is responsible for the selection of students in their universities.
Details about Reimbursement
Reservation for lodging and contribution for subsistence costs.
Please notice that students and teachers from LLP partner universities will be hosted in university premises free of charge for the whole period of the IP. Unfortunately, the Erasmus agency applies a very low daily amount for subsistence costs of students (24 euro per day, both for lodging and full board). That's why, in addition to the accommodation, we can confirm that we will only be able to offer students free access to the university canteen (open on working days). We hope we'll be able to offer some additional support to students, but we cannot guarantee anything at the moment.
Reimbursement for travel costs.
- We are allowed to reimburse travel costs only to teachers and students (MSc and PhD) who are from LLP partner institutions.
- The Erasmus Agency requires each single participant to certify they bought the cheapest flight ticket they could find. In addition, only tickets from/to the town of your home institution can be reimbursed.
- Please upload a copy of your electronic ticket as soon as possible. If you have an online check-in, please upload a pdf copy of it, as well. Otherwise, please keep the boarding pass with you and give it to us when you arrive. Without that, we will not be able to reimburse your travel expenses!
- As for the participants who need a visa, please contact the organizers at info[AT]seismath.eu to ask for a specific invitation letter. The cost of the visa will be reimbursed if the participant provides the original receipt of payment.
- For any additional tickets (or not electronic ones), when you are here, you'll have to provide us with the original one. In addition, you will be requested to provide us with the original boarding pass (if you have not uploaded the electronic one).
Lectures
Lecture 1
TITLE
Forward and Inverse Earthquake Ground Motion Simulations: Mathematical Models and Applications to Engineering
HOURS
2
LECTURER
Aysegul Askan (Turkey)
ABSTRACT
Ground motion simulations are essential for studying the source, path and site effects of the earthquakes. Forward simulations involve solution of the wave equation in addition to high-frequency synthetics. Inversions are performed to retrieve the velocity structure and/or the source properties. In this talk, I will focus on forward and inverse theory with example simulations of previous large events (including the 2009 L'Aquila earthquake). Applications of results to engineering and disaster mitigation will also be presented.
Lecture 2
TITLE
Classification and Regression for Data Analysis
HOURS
8
LECTURER
Jochen Garcke (Germany)
ABSTRACT
The main focus of the course will be on supervised learning for classification and regression. Attention will be given to generalisability and predictive accuracy and the practical contexts in which methods are applied. Relevant statistical theory will mostly be assumed and described rather than derived mathematically. There will be more attention to the mathematical derivation and description of the algorithms. Topics to be covered include linear and additive models, support vector machines, Gaussian processes, Bayesian Classifiers, training/test approach to assessing accuracy, and covariance shift.
Lecture 3
TITLE
Modern Methods in Dimensionality Reduction and Persistent Homology for Signal and Data Analysis
HOURS
8
LECTURER
Mijail Guillemard (Germany)
ABSTRACT
Over the last decade, new advances in signal and data analysis have been achieved with the application of geometrical and topological concepts. In this lecture, we will learn about modern developments in dimensionality reduction and manifold learning by studying important algorithms such as Kernel PCA, Isomap, Laplacian Eigenmanps, Local Tangent Space Alignment, etc. Additionally, we study important trends for data analysis based on powerful methods of persistent homology which has emerged as an important subfield of computational topology. Concrete applications in audio and image analysis will be covered both from a theoretical and computational point of view.
Lecture 4
TITLE
An Introduction to Compressive Sensing
HOURS
8
LECTURER
Holger Rauhut (Germany)
ABSTRACT
Compressive sensing is a recent area in mathematical signal processing that predicts that certain signals (vectors, functions) can be recovered from what was previously believed to be incomplete information. The key observation is that many real-world signals are sparse in the sense that they can be well-represented by an expansion with only a small number of non-zero terms. Sparse signals can be accurately reconstructed from a small number of linear measurements via efficient algorithms such as l1-minimization. Remarkably, all known provably optimal measurement matrices in this context are random matrices. Of particular interest for applications are structured random matrices such as random partial Fourier matrices, or partial random circulant matrices. Applications of compressed sensing include medical imaging, geophysical imaging, analog to digital conversion, statistics and more.
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Week 2
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Lecture 5
TITLE
An introduction to one-dimensional inverse problems in vibration
HOURS
8
LECTURER
Antonio Morassi (Italy)
ABSTRACT
Classical vibration theory is concerned with the determination of the response of a given dynamical system to a prescribed input. These are called direct problems in vibration. However, when one studies a phenomenon which is governed by the equations of classical dynamics, the application of the model to real life situations often requires the knowledge of constitutive and/or geometrical parameters which are not completely known or are inaccessible to direct measurements. Therefore, in several areas in applied science and technology, one has to deal with inverse problems in vibration. Examples concern with the determination of the mass density of the Earth by its natural frequencies; with the determination of the profile of a thin rod or beam by its eigenproperties, and so on. The main focus of the course will be the presentation of classical uniqueness, stability and reconstruction approaches for Sturm-Liouville and fourth-order (Euler-Bernoulli) operators governing the longitudinal vibration and flexural vibration of a thin rod, respectively. Topics to be covered include the construction of isospectral/quasi-isospectral systems and damage identification in mechanical systems by real data.
Lecture 6
TITLE
Inverse problems: a tale of adventure
HOURS
8
LECTURER
Antonio Emolo (Italy)
ABSTRACT
Let us imagine we find ourselves on a gleaming white beach somewhere in the Caribbean with time in our hands, a device that measures changes in gravitational acceleration, and a certain conviction that a golden blob of pirate booty lies somewhere beneath us. In pursuit of wealth, we make a series of measurements of gravity at several points along the beach. How can we use these observations to decide where the pirate gold lies and how much gold is present? Generally speaking, an inverse problem is one in which you want to derive inferences on a physical model from a finite set of observations containing errors. Some examples will be used to discuss the non-uniqueness of solution and the role of data uncertainties. Particular attention will be devoted to linear discrete inverse problems, deriving the least-squares solution and discussing its association with the maximum likelihood. Once the fitted model parameters have been obtained, further investigations have to be done in order to assess the quality of fit and estimating how errors in the data propagate into the model. The issue of data outliers is handled introducing the 1-norm minimization as a robust estimation technique. Some insight about linearized inverse problems will be finally provided.
Lecture 7
TITLE
Earth's tectonic asymmetry and seismicity
HOURS
4
LECTURER
Carlo Doglioni (Italy)
ABSTRACT
The lecture will review the main structure of the Earth, the kinematics at the surface and in the underlying mantle. It will be shown as the upper 700 km of the Earth are geometrically and tectonically asymmetric. The main mechanisms invoked to explain the geodynamics of the planet will be discussed. The system appears as a chaotic self-organized system as indicated by the Gutenberg-Richter law, which supports the occurrence of a common force acting contemporaneously all over the Earth's lithosphere. The only possible explanation for this observation is the contribution of the astronomical forces. The final interpretation is that the dynamics of the Earth is controlled by the combination of the dissipation of the primordial and the ongoing radiogenic heat, the internal heterogeneities in the mantle, and the Earth's rotational and related tidal mechanisms. The decoupling of the lithosphere relative to the underlying mantle can be explained by the occurrence of a low viscosity layer, corresponding to the Low Velocity Zone of the seismic waves which has been detected at about 100-200 km depth, in the upper part of the asthenosphere. This decoupling can be explained by the torque exerted on the lithosphere by the Earth's rotation and the related body tides. The seismicity of the Earth is concentrated where the decoupling of the lithosphere relative to the underlying mantle varies. Moreover it will be shown as the transition between the upper elastic behavior of the lithosphere and the underlying ductile layer acts as a sort of switch for the generation of the earthquakes, which have a magnitude proportional to the involved volume and the amount of its motion. The volumes locked above the brittle-ductile transition are sort of accumulators of elastic energy during the interseismic period, which is suddenly released during the coseismic stage, i.e., the earthquakes.
Lecture 8
TITLE
Methods for determining seismic moment rate: examples from Italy
HOURS
4
LECTURER
Salvatore Barba (Italy).
ABSTRACT
To be announced.
Lecture 9
TITLE
Space geodesy, plate kinematics and earthquake cycle
HOURS
4
LECTURER
Federica Riguzzi (Italy)
ABSTRACT
The determination of Earth’s plate motion has been a major research area since the formulation of plate tectonics. Space geodesy observations have become a key tool in geodynamics studies since they have demonstrated that plate motions on time scale of years are very similar to those averaged over the last millions of years. These results have considerable implications for global geodynamics and regional tectonic studies, including analysis of the seismic cycle.
The aim of the lecture is to show the contribution provided by space geodetic methods, focusing in particular on Global Positioning System (GPS) networks which are currently employed to study the kinematics and deformation rates of the Italian peninsula, allowing more detailed studies of seismogenic structures. Some concrete applications of the recent earthquakes occurred on 2009 (L’Aquila) and 2012 (Emilia region) will be shown.
