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.

The port-Hamiltonian framework as a comprehensive approach to model and simulate complex systems

This thesis describes modelling tools and methods suited for complex systems (systems that typically are represented by a plurality of models). The basic idea is that all models representing the system should be linked by well-defined model operations in order to build a structured repository of information, a hierarchy of models. The port-Hamiltonian framework is a good candidate to solve this kind of problems as it supports the most important model operations natively. The thesis in particular addresses the problem of integrating distributed parameter systems in a model hierarchy, and shows two possible mechanisms to do that: a finite-element discretization in port-Hamiltonian form, and a structure-preserving model order reduction for discretized models obtainable from commercial finite-element packages.