Resonances in the two centers Coulomb system

In this work we investigate the existence of resonances for two-centers Coulomb systems with arbitrary charges in two and three dimensions, defining them in terms of generalized complex eigenvalues of a non-selfadjoint deformation of the two-center Schrödinger operator. After giving a description of the bifurcation of the classical system for positive energies, we construct the resolvent kernel of the operators and we prove that they can be extended analytically to the second Riemann sheet. The resonances are then defined and studied with numerical methods and perturbation theory.

A comprehensive study of the 26th December 2004 Sumatra earthquake: possible implications on Earth rotation and investigations on the coseismic and postseismic stress diffusion associated with the seismic rupture

In this work a multidisciplinary study of the December 26th, 2004 Sumatra earthquake has been carried out. We have investigated both the effect of the earthquake on the Earth rotation and the stress field variations associated with the seismic event. In the first part of the work we have quantified the effects of a water mass redistribution associated with the propagation of a tsunami wave on the Earth’s pole path and on the length-of-day (LOD) and applied our modeling results to the tsunami following the 2004 giant Sumatra earthquake. We compared the result of our simulations on the instantaneous rotational axis variations with some preliminary instrumental evidences on the pole path perturbation (which has not been confirmed yet) registered just after the occurrence of the earthquake, which showed a step-like discontinuity that cannot be attributed to the effect of a seismic dislocation. Our results show that the perturbation induced by the tsunami on the instantaneous rotational pole is characterized by a step-like discontinuity, which is compatible with the observations but its magnitude turns out to be almost one hundred times smaller than the detected one. The LOD variation induced by the water mass redistribution turns out to be not significant because the total effect is smaller than current measurements uncertainties. In the second part of this work of thesis we modeled the coseismic and postseismic stress evolution following the Sumatra earthquake. By means of a semi-analytical, viscoelastic, spherical model of global postseismic deformation and a numerical finite-element approach, we performed an analysis of the stress diffusion following the earthquake in the near and far field of the mainshock source. We evaluated the stress changes due to the Sumatra earthquake by projecting the Coulomb stress over the sequence of aftershocks taken from various catalogues in a time window spanning about two years and finally analyzed the spatio-temporal pattern. The analysis performed with the semi-analytical and the finite-element modeling gives a complex picture of the stress diffusion, in the area under study, after the Sumatra earthquake. We believe that the results obtained with the analytical method suffer heavily for the restrictions imposed, on the hypocentral depths of the aftershocks, in order to obtain the convergence of the harmonic series of the stress components. On the contrary we imposed no constraints on the numerical method so we expect that the results obtained give a more realistic description of the stress variations pattern.

Sviluppo di metodologie di localizzazione nel contesto del Comprehensive Nuclear Test-Ban Treaty

Since the first underground nuclear explosion, carried out in 1958, the analysis of seismic signals generated by these sources has allowed seismologists to refine the travel times of seismic waves through the Earth and to verify the accuracy of the location algorithms (the ground truth for these sources was often known). Long international negotiates have been devoted to limit the proliferation and testing of nuclear weapons. In particular the Treaty for the comprehensive nuclear test ban (CTBT), was opened to signatures in 1996, though, even if it has been signed by 178 States, has not yet entered into force, The Treaty underlines the fundamental role of the seismological observations to verify its compliance, by detecting and locating seismic events, and identifying the nature of their sources. A precise definition of the hypocentral parameters represents the first step to discriminate whether a given seismic event is natural or not. In case that a specific event is retained suspicious by the majority of the State Parties, the Treaty contains provisions for conducting an on-site inspection (OSI) in the area surrounding the epicenter of the event, located through the International Monitoring System (IMS) of the CTBT Organization. An OSI is supposed to include the use of passive seismic techniques in the area of the suspected clandestine underground nuclear test. In fact, high quality seismological systems are thought to be capable to detect and locate very weak aftershocks triggered by underground nuclear explosions in the first days or weeks following the test. This PhD thesis deals with the development of two different seismic location techniques: the first one, known as the double difference joint hypocenter determination (DDJHD) technique, is aimed at locating closely spaced events at a global scale. The locations obtained by this method are characterized by a high relative accuracy, although the absolute location of the whole cluster remains uncertain. We eliminate this problem introducing a priori information: the known location of a selected event. The second technique concerns the reliable estimates of back azimuth and apparent velocity of seismic waves from local events of very low magnitude recorded by a trypartite array at a very local scale. For the two above-mentioned techniques, we have used the crosscorrelation technique among digital waveforms in order to minimize the errors linked with incorrect phase picking. The cross-correlation method relies on the similarity between waveforms of a pair of events at the same station, at the global scale, and on the similarity between waveforms of the same event at two different sensors of the try-partite array, at the local scale. After preliminary tests on the reliability of our location techniques based on simulations, we have applied both methodologies to real seismic events. The DDJHD technique has been applied to a seismic sequence occurred in the Turkey-Iran border region, using the data recorded by the IMS. At the beginning, the algorithm was applied to the differences among the original arrival times of the P phases, so the cross-correlation was not used. We have obtained that the relevant geometrical spreading, noticeable in the standard locations (namely the locations produced by the analysts of the International Data Center (IDC) of the CTBT Organization, assumed as our reference), has been considerably reduced by the application of our technique. This is what we expected, since the methodology has been applied to a sequence of events for which we can suppose a real closeness among the hypocenters, belonging to the same seismic structure. Our results point out the main advantage of this methodology: the systematic errors affecting the arrival times have been removed or at least reduced. The introduction of the cross-correlation has not brought evident improvements to our results: the two sets of locations (without and with the application of the cross-correlation technique) are very similar to each other. This can be commented saying that the use of the crosscorrelation has not substantially improved the precision of the manual pickings. Probably the pickings reported by the IDC are good enough to make the random picking error less important than the systematic error on travel times. As a further justification for the scarce quality of the results given by the cross-correlation, it should be remarked that the events included in our data set don’t have generally a good signal to noise ratio (SNR): the selected sequence is composed of weak events ( magnitude 4 or smaller) and the signals are strongly attenuated because of the large distance between the stations and the hypocentral area. In the local scale, in addition to the cross-correlation, we have performed a signal interpolation in order to improve the time resolution. The algorithm so developed has been applied to the data collected during an experiment carried out in Israel between 1998 and 1999. The results pointed out the following relevant conclusions: a) it is necessary to correlate waveform segments corresponding to the same seismic phases; b) it is not essential to select the exact first arrivals; and c) relevant information can be also obtained from the maximum amplitude wavelet of the waveforms (particularly in bad SNR conditions). Another remarkable point of our procedure is that its application doesn’t demand a long time to process the data, and therefore the user can immediately check the results. During a field survey, such feature will make possible a quasi real-time check allowing the immediate optimization of the array geometry, if so suggested by the results at an early stage.

Crustal heterogeneities and complexities of fault processes

In this work we study the relation between crustal heterogeneities and complexities in fault processes. The first kind of heterogeneity considered involves the concept of asperity. The presence of an asperity in the hypocentral region of the M = 6.5 earthquake of June 17-th, 2000 in the South Iceland Seismic Zone was invoked to explain the change of seismicity pattern before and after the mainshock: in particular, the spatial distribution of foreshock epicentres trends NW while the strike of the main fault is N 7◦ E and aftershocks trend accordingly; the foreshock depths were typically deeper than average aftershock depths. A model is devised which simulates the presence of an asperity in terms of a spherical inclusion, within a softer elastic medium in a transform domain with a deviatoric stress field imposed at remote distances (compressive NE − SW, tensile NW − SE). An isotropic compressive stress component is induced outside the asperity, in the direction of the compressive stress axis, and a tensile component in the direction of the tensile axis; as a consequence, fluid flow is inhibited in the compressive quadrants while it is favoured in tensile quadrants. Within the asperity the isotropic stress vanishes but the deviatoric stress increases substantially, without any significant change in the principal stress directions. Hydrofracture processes in the tensile quadrants and viscoelastic relaxation at depth may contribute to lower the effective rigidity of the medium surrounding the asperity. According to the present model, foreshocks may be interpreted as induced, close to the brittle-ductile transition, by high pressure fluids migrating upwards within the tensile quadrants; this process increases the deviatoric stress within the asperity which eventually fails, becoming the hypocenter of the mainshock, on the optimally oriented fault plane. In the second part of our work we study the complexities induced in fault processes by the layered structure of the crust. In the first model proposed we study the case in which fault bending takes place in a shallow layer. The problem can be addressed in terms of a deep vertical planar crack, interacting with a shallower inclined planar crack. An asymptotic study of the singular behaviour of the dislocation density at the interface reveals that the density distribution has an algebraic singularity at the interface of degree ω between -1 and 0, depending on the dip angle of the upper crack section and on the rigidity contrast between the two media. From the welded boundary condition at the interface between medium 1 and 2, a stress drop discontinuity condition is obtained which can be fulfilled if the stress drop in the upper medium is lower than required for a planar trough-going surface: as a corollary, a vertically dipping strike-slip fault at depth may cross the interface with a sedimentary layer, provided that the shallower section is suitably inclined (fault "refraction"); this results has important implications for our understanding of the complexity of the fault system in the SISZ; in particular, we may understand the observed offset of secondary surface fractures with respect to the strike direction of the seismic fault. The results of this model also suggest that further fractures can develop in the opposite quadrant and so a second model describing fault branching in the upper layer is proposed. As the previous model, this model can be applied only when the stress drop in the shallow layer is lower than the value prescribed for a vertical planar crack surface. Alternative solutions must be considered if the stress drop in the upper layer is higher than in the other layer, which may be the case when anelastic processes relax deviatoric stress in layer 2. In such a case one through-going crack cannot fulfil the welded boundary conditions and unwelding of the interface may take place. We have solved this problem within the theory of fracture mechanics, employing the boundary element method. The fault terminates against the interface in a T-shaped configuration, whose segments interact among each other: the lateral extent of the unwelded surface can be computed in terms of the main fault parameters and the stress field resulting in the shallower layer can be modelled. A wide stripe of high and nearly uniform shear stress develops above the unwelded surface, whose width is controlled by the lateral extension of unwelding. Secondary shear fractures may then open within this stripe, according to the Coulomb failure criterion, and the depth of open fractures opening in mixed mode may be computed and compared with the well studied fault complexities observed in the field. In absence of the T-shaped decollement structure, stress concentration above the seismic fault would be difficult to reconcile with observations, being much higher and narrower.

The bursting behavior of gas slugs: laboratory and analytical insights into Strombolian volcanic eruptions.

The aim of this thesis is to study how explosive behavior and geophysical signals in a volcanic conduit are related to the development of overpressure in slug-driven eruptions. A first suite of laboratory experiments of gas slugs ascending in analogue conduits was performed. Slugs ascended into a range of analogue liquids and conduit diameters to allow proper scaling to the natural volcanoes. The geometrical variation of the slug in response to the explored variables was parameterised. Volume of gas slug and rheology of the liquid phase revealed the key parameters in controlling slug overpressure at bursting. Founded on these results, a theoretical model to calculate burst overpressure for slug-driven eruptions was developed. The dimensionless approach adopted allowed to apply the model to predict bursting pressure of slugs at Stromboli. Comparison of predicted values with measured data from Stromboli volcano showed that the model can explain the entire spectrum of observed eruptive styles at Stromboli – from low-energy puffing, through normal Strombolian eruptions, up to paroxysmal explosions – as manifestations of a single underlying physical process. Finally, another suite of laboratory experiments was performed to observe oscillatory pressure and forces variations generated during the expansion and bursting of gas slugs ascending in a conduit. Two end-member boundary conditions were imposed at the base of the pipe, simulating slug ascent in closed base (zero magma flux) and open base (constant flux) conduit. At the top of the pipe, a range of boundary conditions that are relevant at a volcanic vent were imposed, going from open to plugged vent. The results obtained illustrate that a change in boundary conditions in the conduit concur to affect the dynamic of slug expansion and burst: an upward flux at the base of the conduit attenuates the magnitude of the pressure transients, while a rheological stiffening in the top-most region of conduit changes dramatically the magnitude of the observed pressure transients, favoring a sudden, and more energetic pressure release into the overlying atmosphere. Finally, a discussion on the implication of changing boundary on the oscillatory processes generated at the volcanic scale is also given.

Sviluppo di una metodologia per la modellazione geologica-geomeccanica ed il monitoraggio di reservoir adibiti a siti di stoccaggio di gas naturale

La valutazione dei rischi associati all’operatività dei sistemi di stoccaggio, quali la sismicità indotta e la subsidenza, è requisito basilare per una loro corretta gestione e progettazione, e passa attraverso la definizione dell’influenza sullo stato tensionale delle variazioni di pressione di poro nel sottosuolo. Principale scopo di questo progetto è lo sviluppo di una metodologia in grado di quantificare le deformazioni dei reservoir in funzione della pressione di poro, di tarare i modelli utilizzati con casi studio che presentino dati di monitoraggio reali, tali da consentire un confronto con le previsioni di modello. In questa tesi, la teoria delle inomogeneità è stata utilizzata, tramite un approccio semianalitico, per definire le variazioni dei campi elastici derivanti dalle operazioni di prelievo e immissione di fluidi in serbatoi geologici. Estensione, forma e magnitudo delle variazioni di stress indotte sono state valutate tramite il concetto di variazione dello sforzo critico secondo il criterio di rottura di Coulomb, tramite un’analisi numerica agli elementi finiti. La metodologia sviluppata è stata applicata e tarata su due reservoir sfruttati e riconvertiti a sistemi di stoccaggio che presentano dataset, geologia, petrofisica, e condizioni operative differenti. Sono state calcolate le variazioni dei campi elastici e la subsidenza; è stata mappata la variazione di sforzo critico di Coulomb per entrambi i casi. I risultati ottenuti mostrano buon accordo con le osservazioni dei monitoraggi, suggerendo la bontà della metodologia e indicando la scarsa probabilità di sismicità indotta. Questo progetto ha consentito la creazione di una piattaforma metodologica di rapido ed efficace utilizzo, per stimare l’influenza dei sistemi di stoccaggio di gas sullo stato tensionale della crosta terrestre; in fase di stoccaggio, permette di monitorare le deformazioni e gli sforzi indotti; in fase di progettazione, consente di valutare le strategie operative per monitorare e mitigare i rischi geologici associati a questi sistemi.

Hydrodynamical simulations of early-type galaxies: effects of galaxy shape and stellar dynamics on hot coronae

Early-Type galaxies (ETGs) are embedded in hot (10^6-10^7 K), X-ray emitting gaseous haloes, produced mainly by stellar winds and heated by Type Ia supernovae explosions, by the thermalization of stellar motions and occasionally by the central super-massive black hole (SMBH). In particular, the thermalization of the stellar motions is due to the interaction between the stellar and the SNIa ejecta and the hot interstellar medium (ISM) already residing in the ETG. A number of different astrophysical phenomena determine the X-ray properties of the hot ISM, such as stellar population formation and evolution, galaxy structure and internal kinematics, Active Galactic Nuclei (AGN) presence, and environmental effects. With the aid of high-resolution hydrodynamical simulations performed on state-of-the-art galaxy models, in this Thesis we focus on the effects of galaxy shape, stellar kinematics and star formation on the evolution of the X-ray coronae of ETGs. Numerical simulations show that the relative importance of flattening and rotation are functions of the galaxy mass: at low galaxy masses, adding flattening and rotation induces a galactic wind, thus lowering the X-ray luminosity; at high galaxy masses the angular momentum conservation keeps the central regions of rotating galaxies at low density, whereas in non-rotating models a denser and brighter atmosphere is formed. The same dependence from the galaxy mass is present in the effects of star formation (SF): in light galaxies SF contributes to increase the spread in Lx, while at high galaxy masses the halo X-ray properties are marginally sensitive to SF effects. In every case, the star formation rate at the present epoch quite agrees with observations, and the massive, cold gaseous discs are partially or completely consumed by SF on a time-scale of few Gyr, excluding the presence of young stellar discs at the present epoch.

Application of Submerged Grouted Anchors in Sheet Pile Quay Walls

Sheet pile walls are one of the oldest earth retention systems utilized in civil engineering projects. They are used for various purposes; such as excavation support system, cofferdams, cut-off walls under dams, slope stabilization, waterfront structures, and flood walls. Sheet pile walls are one of the most common types of quay walls used in port construction. The worldwide increases in utilization of large ships for transportation have created an urgent need of deepening the seabed within port areas and consequently the rehabilitation of its wharfs. Several methods can be used to increase the load-carrying capacity of sheet-piling walls. The use of additional anchored tie rods grouted into the backfill soil and arranged along the exposed wall height is one of the most practical and appropriate solutions adopted for stabilization and rehabilitation of the existing quay wall. The Ravenna Port Authority initiated a project to deepen the harbor bottom at selected wharves. An extensive parametric study through the finite element program, PLAXIS 2D, version 2012 was carried out to investigate the enhancement of using submerged grouted anchors technique on the load response of sheet-piling quay wall. The influence of grout-ties area, length of grouted body, anchor inclination and anchor location were considered and evaluated due to the effect of different system parameters. Also a comparative study was conducted by Plaxis 2D and 3D program to investigate the behavior of these sheet pile quay walls in terms of horizontal displacements induced along the sheet pile wall and ground surface settlements as well as the anchor force and calculated factor of safety. Finally, a comprehensive study was carried out by using different constitutive models to simulate the mechanical behavior of the soil to investigate the effect of these two models (Mohr-Coulomb and Hardening Soil) on the behavior of these sheet pile quay walls.