Lecture details - MaIn IP 2014
TITLEEstimation of Seismic Losses in Urban Regions within an Interdisciplinary Mathematical Framework: A Case Study
Aysegul Askan, Middle East Technical University, Turkey
ABSTRACTRisk mitigation in urban regions starts with identification of potential seismic losses in future earthquakes. Estimation of seismic losses concerns a wide range of authorities varying from geophysical and earthquake engineers, physical and economic planners to insurance companies while the process naturally involves inputs from multiple disciplines. In this study a city model is constructed where potential seismic losses are expressed in terms of building vulnerabilities and regional seismic hazard. The main components of the study are probabilistic and deterministic seismic hazard assessment and estimation of potential ground motions, regional building vulnerability and fragility information, casualty and economic loss functions. Each stage involves mathematical modeling with well-defined input parameters regarding the physical process involved.
In this seminar, description of the multiple stages of the algorithm will be presented followed by a case study.
As the study area, Erzincan, a city on the eastern part of the North Anatolian Fault zone, Turkey is selected. Located within a triple conjunction of major fault systems within a basin structure, and experienced a major event (Ms=8.3) in 1939, this city has significant hazard potential. I will present the initial results in terms of key components such as construction of a 2D velocity model, ground motion simulations of past earthquakes and scenario events, site-specific probabilistic seismic hazard analyses and fragility functions derived using regional building characteristics along with simulated regional ground motion data.
Interacting particle systems in social sciences. Microscopic and macroscopic descriptions.
Marco Di Francesco, University of Bath
The goal of this mini course is to introduce deterministic particle methods and continuum partial differential equations for systems of interacting agents in animal biology and sociology. We will first introduce the concept of gradient flow in finite dimensions. We shall then construct gradient flows of systems of interacting particles subject to nonlocal forces, which consist of systems of ODEs. We shall show with simple examples that simple qualitative properties of the interaction potentials account for phenomena such as finite time collapse (or consensus), clustering, confinement. In the second part of the course we shall introduce continuum systems, consisting of PDEs with nonlocal fluxes. We shall then provide a short introduction to transport distances in spaces of probability measures, and prove that some properties of the particle systems can be proven for the continuum counterpart. Finally, I will consider models with nonlinear diffusion, and prove the existence of stationaty states under suitable conditions on the interaction potentials.
TITLEA Tectonic model of the Earth and earthquakes
Carlo Doglioni, INGV
The mechanisms of geodynamics are still unclear. We will revise the main geometric and kinematic constraints of plate tectonics in order to formulate some new dynamical inferences. The astronomical effects on plate motion will be discussed. This framework allows to present a new model also for the generation of earthquakes as being controlled by stress and strain gradients occurring within the Earth’s outer shell.
Inverse problems: a tale of adventure
Antonio Emolo, University of Naples "Federico II"
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.
Earthquake source mechanics
Gaetano Festa, University of Naples "Federico II", Italy
In the course I will present theoretical description of the earthquake source, as a nucleating and propagating rupture, its kinematic and dynamic modelling, numerical, analogical and theoretical challenges.
An earthquake source can be modelled as a developing rupture, propagating along weak interfaces inside the Earth, where the tectonic stress concentrates. Nevertheless, a fracture cannot nucleate if a sufficiently large zone does not coherently move in the initial part of an earthquake. I will discuss the physical ingredients that control an earthquake rupture (the friction, the cohesion), present the mathematical formulation of an advancing rupture for nucleation and dynamic propagation, show some theoretical results, solutions and expectation for a realistic propagating earthquake.
As far, I will connect the physical parameters of an earthquake to the data and discuss the inverse problem of characterizing an earthquake rupture from the seismic/geodetic and other geophysical data recorded immediately after a large earthquake. I will discuss the ill posedness of the inverse problem and actual trials of regularization for the problem.
Finally, I will discuss the challenges of numerical methods in describing a propagating rupture, with specific application toward high-order finite element methods.
An introduction to statistical seismology
Eugenio Lippiello, Second University of Naples, Caserta (Italy)
Statistical seismology is the application of rigorous statistical methods to earthquake occurrence. Its main scope is the improvement of our scientific understanding of physical mechanisms responsible of earthquakes and of the evaluation and testing of earthquake forecasts and seismic hazards assessments. Within this course, seismic occurrence will be framed within the general statistical mechanical approach to complex phenomena. The most relevant statistical models for seismic occurrence will be presented as well as a general framework where seismic occurrence is described as a stochastic process. Within this scheme the evolution of seismic occurrence probability is given by the superposition of a deterministic part plus a random fluctuating contribution. The implications for seismic hazard evaluation will be discussed and some examples of forecasting maps will be presented.
The influence of atmospheric parameters on radon level: A time series approach
Umberto Triacca, University of L'Aquila
Lesson 1. Univariate autoregressive moving average (ARMA) models
Lesson 2. Vector autoregressive (VAR) models
Lesson 3. Granger causality analysis
TITLEGNSS monitoring of strain rates in the Italian area
Federica Riguzzi, INGV
The Italian peninsula is a rather interesting natural laboratory for geodynamical investigations since its tectonic evolution is affected by the interaction of the African and Eurasian plates. The entire area is characterized by a complex tectonic setting generating slow crustal deformations (at the few mm/yr level) and velocity spatial gradients (strain rates) changing rapidly from point to point. In this perspective, the rapid development of Global Navigation Satellite System (GNSS) networks, with relatively low cost and high accuracy positioning, provides great advances in geodynamical studies. Since the first attempts to measure the convergence rate between Africa and Eurasia at large scale, based on space geodetic methods, current GNSS networks allow to study the deformation process at fault scale level and the seismic cycle evolution.
Modelling and Simulation of Crowd Dynamics
Monika Twarogowska, IAC-CNR
Growing population densities combined with easier transport lead to greater accumulation of people and increasing number of life threatening situations due to accidents and panic. Modern designs of walking facilities follow optimal requirements regarding flow efficiency and pedestrians comfort and security. Numerous engineering projects welcome the support of mathematical modelling and simulations in optimization processes. Pedestrians moving within a given walking area can be described at a microscopic scale by a system of ordinary differential equations. However, when the distance between individuals becomes much smaller than the walking area crowd may be considered as a continuum medium and macroscopic models can be applied. In this lecture we will give a general description of the microscopic social force model introduced by Helbing (1) and some macroscopic models: Hughes model (2) and the second order model (3). Then we will present basic numerical methods used to approximate the solutions of the above systems on two dimensional domains. Finally we will give some examples of numerical simulations of evacuation of pedestrians from walking facilities such as a large room, university campus or airport.
1. D.Helbing, P.Molnár. Social force model for pedestrian dynamics. Physical Review E, 4282-4286, 1995.
2. R.L.Hughes. A continuum theory for the flow of pedestrians. Transportation research Part B: methodological, 36(6):507-535, 2002.
3. Y.Q.Jiang, P.Zhang, S.C.Wong, R.X.Liu. A higher-order macroscopic model for pedestrian flows. Physica A: Statistical Mechanics and its Applications, 389(21):4623-4635, 2010
TITLEThe Modeling procedures in Earthquake Engineering
Doina Verdes, TU Cluj-Napoca (Romania)
2. The ground movement
3. The structural system: modeling in 1D, 2D, 3D of space dimensions
4. Numerical methods
5. Experimental methods
The lecture presents some procedures used to model and design earthquake resisting buildings. It is starting with the ground movement which is modeled by seismologists, geologists and mathematicians. The engineer uses the accelerograms real or artificial into computation of seismic response of building.
The building is a very complex system which is studied and designed by a multidisciplinary team involving: the architect, the structural engineer, the building facility engineer, the IT engineer, the mechanical engineer into certain environment conditions.
The seismic response of building is the task of structural engineer who is able to model adequately the resistance structure and to find as call seismic response of it and compute on this base the dimensions of structural elements which accomplish the appropriate performance level. Many procedures have been developed to solve this task; these are depending on what type of structure is the building - one level or multistory building - what is the material used to build the structure - steel, reinforced concrete, masonry, wood or is it a simple form or a complicated one, like the bio-mimetic building or high rise building.
The modeling is referring to structure or to structure interacting with nonstructural elements of the building. These are dynamic computation or in certain cases static one. The process is beginning with creation of the dynamic model of the building involving the characteristics of mass, damping and stiffness of the structural system. From this step the equations of seismic equilibrium can be obtained and the mathematics is called again to solve the system of numerous equations.
There are structural systems which need an experimental study in order to validate the theoretical modeling and the seismic response. On this raison are developed the installations to test models at reduced scale of dimensions and masses subjected to accelerograms ; the engineers asked tests on as call shake table which can move in the one to three or six directions on space.
The procedure presented will have examples of computation and the applications on case study buildings. Experimental test on shake table will be also presented in order to better understand the complexity of the modeling of seismic response of the building.