This thesis deals with smooth discretization schemes and inverse problems, the former used in efficient yet accurate numerical solutions to forward models required in turn to solve inverse problems. The aims of the thesis include, (i) development of a stabilization techniques for a class of forward problems plagued by unphysical oscillations in the response due to the presence of jumps/shocks/high gradients, (ii) development of a smooth hybrid discretization scheme that combines certain useful features of Finite Element (FE) and Mesh-Free (MF) methods and alleviates certain destabilizing factors encountered in the construction of shape functions using the polynomial reproduction method and, (iii) a first of its kind attempt at the joint inversion of both static and dynamic source parameters of the 2004 Sumatra-Andaman earthquake using tsunami sea level anomaly data. Following the introduction in Chapter 1 that motivates and puts in perspective the work done in later chapters, the main body of the thesis may be viewed as having two parts, viz., the first part constituting the development and use of smooth discretization schemes in the possible presence of destabilizing factors (Chapters 2 and 3) and the second part involving solution to the inverse problem of tsunami source recovery (Chapter 4). In the context of stability requirements in numerical solutions of practical forward problems, Chapter 2 develops a new stabilization scheme. It is based on a stochastic representation of the discretized field variables, with a view to reduce or even eliminate unphysical oscillations in the MF numerical simulations of systems developing shocks or exhibiting localized bands of extreme plastic deformation in the response. The origin of the stabilization scheme may be traced to nonlinear stochastic filtering and, consistent with a class of such filters, gain-based additive correction terms are applied to the simulated solution of the system, herein achieved through the Element-Free Galerkin (EFG) method, in order to impose a set of constraints that help arresting the spurious oscillations. The method is numerically illustrated through its application to a gradient plasticity model whose response is often characterized by a developing shear band as the external load is gradually increased. The potential of the method in stabilized yet accurate numerical simulations of such systems involving extreme gradient variations in the response is thus brought forth. Chapter 3 develops the MF-based discretization motif by balancing this with the widespread adoption of the FE method. Thus it concentrates on developing a 'hybrid' scheme that aims at the amelioration of certain destabilizing algorithmic issues arising from the necessary condition of moment matrix invertibility en route to the generation of smooth shape functions. It sets forth the hybrid discretization scheme utilizing bivariate simplex splines as kernels in a polynomial reproducing approach adopted over a conventional FE-like domain discretization based on Delaunay triangulation. Careful construction of the simplex spline knotset ensures the success of the polynomial reproduction procedure at all points in the domain of interest, a significant advancement over its precursor, the DMS-FEM. The shape functions in the proposed method inherit the global continuity ( C p 1 ) and local supports of the simplex splines of degree p . In the proposed scheme, the triangles comprising the domain discretization also serve as background cells for numerical integration which here are near-aligned to the supports of the shape functions (and their intersections), thus considerably ameliorating an oft-cited source of inaccuracy in the numerical integration of MF-based weak forms. Numerical experiments establish that the proposed method can work with lower order quadrature rules for accurate evaluation of integrals in the Galerkin weak form, a feature desiderated in solving nonlinear inverse problems that demand cost-effective solvers for the forward models. Numerical demonstrations of optimal convergence rates for a few test cases are given and the hybrid method is also implemented to compute crack-tip fields in a gradient-enhanced elasticity model. Chapter 4 attempts at the joint inversion of earthquake source parameters for the 2004 Sumatra-Andaman event from the tsunami sea level anomaly signals available from satellite altimetry. Usual inversion for earthquake source parameters incorporates subjective elements, e.g. a priori constraints, posing and parameterization, trial-and-error waveform fitting etc. Noisy and possibly insufficient data leads to stability and non-uniqueness issues in common deterministic inversions. A rational accounting of both issues favours a stochastic framework which is employed here, leading naturally to a quantification of the commonly overlooked aspects of uncertainty in the solution. Confluence of some features endows the satellite altimetry for the 2004 Sumatra-Andaman tsunami event with unprecedented value for the inversion of source parameters for the entire rupture duration. A nonlinear joint inversion of the slips, rupture velocities and rise times with minimal a priori constraints is undertaken. Large and hitherto unreported variances in the parameters despite a persistently good waveform fit suggest large propagation of uncertainties and hence the pressing need for better physical models to account for the defect dynamics and massive sediment piles. Chapter 5 concludes the work with pertinent comments on the results obtained and suggestions for future exploration of some of the schemes developed here.

The purpose of this study is to critically examine whether hospitals located in high seismic risk areas such as Vancouver can respond as post-disaster facilities in the aftermath of a major earthquake. Earthquake experience in California during the 1971 San Fernando and the 1989 Loma Prieta earthquakes in particular demonstrate that hospitals may be vulnerable and rendered unable to fully respond to their communities needs. In the case of earthquakes, risk management methods are limited to two strategies: pre-event mitigation to reduce the effects of the earthquake on life safety and loss of property; and providing recovery services after the event. In the case of post-disaster hospitals, experience shows that mitigation strategies ensure the functionality of the facility. Therefore, mitigation strategies must not only include structural mitigation to protect the life safety of its occupants, they must also include strategies which ensure the functionality of both the building operations as well as that of therapeutic and diagnostic medical equipment in the aftermath of an earthquake. Vancouver General Hospital is used as a case study to critically examine seismic pre-event mitigation strategies which include: the structures; building operation and medical equipment which are dependent on the supply of potable water and power. Findings of this study indicate that the current supply of potable water is not reliable and that some of VGH's essential building operations and medical equipment will not be functional due to losses in water pressures and disruptions in service. This study recommends that VGH should consider mitigation strategies which make the hospital independent of outside sources of both water and power supply in order to meet its emergency role as a post-disaster facility following an earthquake. The functionality of VGH in the aftermath of a major earthquake will be seriously curtailed unless there is adequate storage of potable water on site to meet the emergency needs of this hospital. / Applied Science, Faculty of / Community and Regional Planning (SCARP), School of / Graduate

In my doctoral thesis I have investigated earthquake swarms from two com- pletely different tectonic areas, West Bohemia/Vogtland and Southwest Iceland, with the aim of gaining a deeper insight into the nature of earthquake swarms in diverse tectonic environments. I analysed swarm-like activities from West Bo- hemia and Southwest Iceland from the perspective of statistical characteristics (magnitude-frequency distribution, interevent time distribution), seismic moment release, and space-time distribution of events. I found that the ratio of small to large events and the event rates are similar for all the activities in both areas, while the rate of the seismic moment release is significantly higher for the South- west Icelandic swarms. Seismic moment released step by step is characterised for the West Bohemia swarms, whereas seismic moment released in one dominant short-term phase is typical of Southwest Icelandic earthquake swarms. All the West Bohemian swarms took place in a bounded focal zone Nový Kostel that is fairly complex, consisting of several fault segments. The Southwest Icelandic swarms are distributed at much larger area along the Mid Atlantic Ridge up to its branching in the Hengill triple junction, the individual swarms clearly reflect a tectonic structure of respective focal areas. I have...

Tsunami hazards were greatly underestimated along the coasts of countries bordering the northeastern Indian Ocean until the occurrence of the 26 December 2004, Mw 9.2 earthquake and its ensuing tsunami. Sourced off the coast of northern Sumatra, on the plate boundary between the Indo-Australian and Eurasian plates, the rupture of the 2004 earthquake propagated ~1300 km northward. The magnitude of this earthquake and the reach of its tsunami exceeded all known precedents, based on instrumental and historic records. The coseismic deformational and post-tsunami depositional features facilitated opportunities to conduct tsunami geology studies along the coasts of countries bordering the Indian Ocean. Several questions are being posed, the answers of which have implications for tsunami hazard assessment. How did this plate boundary behave prior to and after the great earthquake? Was the 2004 earthquake the first of its kind on the Sumatra-Andaman plate boundary? If it had a predecessor, when did it occur and was it a true predecessor in terms of its rupture dimensions and tsunamigenic potential? What types of depositional evidence are preserved and how can we use them to develop the history of past tsunamigenic earthquakes? Researchers are exploring the affected regions and using the imprints left by the 2004 event, to address these questions. There are two components to this study: one, a seismotectonic analysis of the region from the perspective of plate driving forces and their relative roles in the interseismic and post-seismic phases. This study uses global data catalogs like the NEIC PDE (National Earthquake Information Centre Preliminary Determination of Epicenters) and the Global Centroid Moment Tensor (CMT) solutions for earthquake source parameters to understand the along-strike variations in seismicity patterns before and after the 2004 earthquake. The 2004 experience was unprecedented in South Asia. Unaffected by tsunami hazards in the past, tsunami geology is a nascent field for most South Asian researchers. Very little background field data is available on the deformational features of great earthquakes along this plate boundary and the depositional characteristics of extreme coastal surges, such as tsunamis and storms. Where do we begin our search for evidence of past tsunamigenic earthquakes? How best can we use the 2004 tsunami and its deposits as a proxy? What problems are encountered in the interpretations? This thesis addresses these questions in part and presents observations from the Andaman Islands (the ~400 km, northern segment of the Sumatra-Andaman subduction zone) and the southeast coast of India, towards developing a reliable database of tsunami geology for 2004-type events. The premise is that regions affected by the 2004 earthquake are more likely to conserve signatures from older events. Based on the stratigraphic context of the proxy and quality of age estimates, this work presents evidence for past earthquake related deformation and tsunami deposition. In this work we use deformational and depositional features from the Andaman Islands, falling within the 2004 rupture zone and from one location on the Tamil Nadu coast of India (Kaveripattinam). From a perceptive understanding of the features related to tectonic deformation of the Sumatra-Andaman subduction zone, we have selected the Andaman segment that demonstrates explicit evidence for deformation and tsunami deposition through geomorphological and stratigraphic features, which are key to our exploration. A gist of each chapter is given below. The introduction (chapter 1) presents the background, motivation and scope of this work and the organization of this thesis, also summarizing the contents of each chapter. Chapter 2 provides a review of literature on subduction zone earthquakes and updates on tsunami geology, to place this study in the global context. The next two chapters discuss the seismotectonics of the Sumatra-Andaman plate boundary, the important earthquakes and their source processes. In chapter 3 we discuss the Andaman segment (from 10–15° N), characterized by relatively lower level seismicity, but distinctive, as it falls within the northern limit of the 2004 rupture. The deformational and depositional features here are better exposed due to availability of land straddling the hinge line separating the areas of 2004 uplift and subsidence. Here, the pre-2004 earthquakes used to occur along a gently dipping subducting slab, up to a depth of about 40 km. Post-2004, the earthquakes moved up-dip, extending also to the outer-rise and outer-ridge regions, expressing post-earthquake relaxation [Andrade and Rajendran, 2011]. The southern Nicobar segment (5–10° N) differs from the Andaman segment in its style of deformation and seismic productivity. The decreasing obliquity of convergence, the likely influence of a subducting ocean ridge on the subducting plate and the character of the subducting oceanic plate make this segment distinctly different. In chapter 4 we present an analysis of its seismotectonic environment based on the well-constrained focal mechanisms of historic and recent earthquakes. We report that left-lateral strike-slip faulting on near N-S oriented faults control the deformation and the style of faulting is consistent to ~80 km within the subducting slab [Rajendran, K. et al., 2011]. The 11 April 2012 sequence of earthquakes on the subducting oceanic plate, between the Sumatra Trench and the Ninety East Ridge are the more recent among the oceanic intraplate earthquakes that demonstrate the reactivation of N-S oriented fossil fractures. The limited availability of land and the 2004 coseismic deformation dominated by subsidence, followed by prolonged waterlogging makes exploration difficult in the Nicobar segment. Thus, we focus on the Andaman Islands for deformational and depositional evidence, using observations that can be corroborated through multiple proxies and depositional environments that are not prone to other coastal surges, such as cyclones and storms. The criteria for selection of sites, evaluation of deposits and determination of limiting ages are discussed in chapters 5 through 9. In chapter 5 we discuss different types of coastal environments and their response to high-energy sea surges. We also give a brief review of the comparative analyses of storm and tsunami deposits, a highly debated issue and then discuss important characteristics of these two deposits, using examples from the 2004 tsunami and the 2011 Thane cyclone that affected parts of the Tamil Nadu coast. An important component of tsunami geology is the ability to identify and select datable material from tsunami deposits and chose an appropriate method for dating (chapter 6). The types of material used vary from peat layers, peat-rich soil, gastropod shells, wood, charcoal, organic remains such as bones, coral fragments, pottery sherds and buried soil. Techniques such as AMS Carbon-14 and Thermoluminescence are commonly used with appropriate calibrations and corrections. In addition to the dates generated in this study (based on wood and shell dates) we use some previous dates from the entire stretch of the rupture within the Indian Territory and assign a relative grading to these ages, based on the quality criterion evolved in this study. We believe that this is the first attempt to segregate age data obtained from coastal deposits, and assign them a specific quality grading based on their environment of deposition and the type of material dated. Chapter 7 presents results of our investigations in the Andaman Islands, which cover ~30% of the rupture area. A coseismically subsided mangrove from Rangachanga (Port Blair, east coast of South Andaman) led us to a former subsidence during AD 770–1040, which we believe is the most convincing evidence for a previous tectonic event. Data based on inland deposits of coral and organic debris yielded a younger age in the range of AD 1480–1660. Both these dates fall in the age brackets reported from other regions of this plate boundary (mainly Sumatra) as well as distant shores of Sri Lanka, Thailand and mainland India. To understand the nature of distant deposits, we present observations from Kaveripattinam, an ancient port city on the east coast of India, where a high-energy sea surge deposit, found 1 km inland is attributed to a paleotsunami. The inland location of this archeological site at an elevation of 2 m and characteristics of the deposit that help discriminate it from typical storm deposition provide clinching evidence in favor of a 1000-year old regional tsunami (chapter 8). In chapter 9 we discuss the results of our study. We evaluate the nature of deformation/deposition and the calibrated age data in the context of their environments. Ages based on the organic material associated with coral debris (at Hut Bay and Interview Island) and the remains of mangrove roots, 1 m below the present ground level (at Port Blair) are considered as reliable estimates, due to their sheltered inland location and the in situ root horizon used for dating. Age data from Kaveripattinam is also considered reliable, based on its inland location beyond the reach of storm surges, sediment characteristics typical of tsunami deposition and ages based on multiple methods and samples. The age data based on the sites presented in this thesis are more conclusive about the 800 to 1100 AD and 1250 to 1450 AD tsunamis, and the former is represented from regions closer to the 2004 source as well as distant shores reached by its tsunami. Chapter 10 presents our conclusions and the scope for future studies. We present this as the first study of its kind in the northeastern Bay of Bengal, wherein the coseismic vertical coastal deformation features along an interplate subduction boundary and a variety of tsunami deposits are used to categorize depositional environments and ages of paleoearthquakes and tsunamis. To our knowledge, this is the first study of its kind where the effects of a recent tsunami have been used to evaluate paleodeposits based on their respective environments of occurrence. Our results have implications for tsunami geology studies in coastal regions prone to tsunami hazard.

The great social and economic impact of earthquakes has made necessary the development of novel structural health monitoring (SHM) solutions for increasing the level of structural safety and assessment. SHM is the process of comparing the current state of a structure’s condition relative to a healthy baseline state to detect the existence, location, and degree of likely damage during or after a damaging input, such as an earthquake. Many SHM algorithms have been proposed in the literature. However, a large majority of these algorithms cannot be implemented in real time. Therefore, their results would not be available during or immediately after a major event for urgent post-event response and decision making. Further, these off-line techniques are not capable of providing the input information required for structural control systems for damage mitigation. The small number of real-time SHM (RT-SHM) methods proposed in the past, resolve these issues. However, these approaches have significant computational complexity and typically do not manage nonlinear cases directly associated with relevant damage metrics. Finally, many available SHM methods require full structural response measurement, including velocities and displacements, which are typically difficult to measure. All these issues make implementation of many existing SHM algorithms very difficult if not impossible. This thesis proposes simpler, more suitable algorithms utilising a nonlinear Bouc-Wen hysteretic baseline model for RT-SHM of a large class of nonlinear hysteretic structures. The RT-SHM algorithms are devised so that they can accommodate different levels of the availability of design data or measured structural responses, and therefore, are applicable to both existing and new structures. The second focus of the thesis is on developing a high-speed, high-resolution, seismic structural displacement measurement sensor to enable these methods and many other SHM approaches by using line-scan cameras as a low-cost and powerful means of measuring structural displacements at high sampling rates and high resolution. Overall, the results presented are thus significant steps towards developing smart, damage-free structures and providing more reliable information for post-event decision making.

Depending on their nature and severity, disasters can create large volumes of debris and waste. Waste volumes from a single event can be the equivalent of many times the annual waste generation rate of the affected community. These volumes can overwhelm existing solid waste management facilities and personnel. Mismanagement of disaster waste can affect both the response and long term recovery of a disaster affected area. Previous research into disaster waste management has been either context specific or event specific, making it difficult to transfer lessons from one disaster event to another. The aim of this research is to develop a systems understanding of disaster waste management and in turn develop context- and disaster-transferrable decision-making guidance for emergency and waste managers. To research this complex and multi-disciplinary problem, a multi-hazard, multi-context, multi-case study approach was adopted. The research focussed on five major disaster events: 2011 Christchurch earthquake, 2009 Victorian Bushfires, 2009 Samoan tsunami, 2009 L’Aquila earthquake and 2005 Hurricane Katrina. The first stage of the analysis involved the development of a set of ‘disaster & disaster waste’ impact indicators. The indicators demonstrate a method by which disaster managers, planners and researchers can simplify the very large spectra of possible disaster impacts, into some key decision-drivers which will likely influence post-disaster management requirements. The second stage of the research was to develop a set of criteria to represent the desirable environmental, economic, social and recovery effects of a successful disaster waste management system. These criteria were used to assess the effectiveness of the disaster waste management approaches for the case studies. The third stage of the research was the cross-case analysis. Six main elements of disaster waste management systems were identified and analysed. These were: strategic management, funding mechanisms, operational management, environmental and human health risk management, and legislation and regulation. Within each of these system elements, key decision-making guidance (linked to the ‘disaster & disaster waste’ indicators) and management principles were developed. The ‘disaster & disaster waste’ impact indicators, the effects assessment criteria and management principles have all been developed so that they can be practically applied to disaster waste management planning and response in the future.

The Canterbury Earthquakes of 2010-2011, in particular the 4th September 2010 Darfield earthquake and the 22nd February 2011 Christchurch earthquake, produced severe and widespread liquefaction in Christchurch and surrounding areas. The scale of the liquefaction was unprecedented, and caused extensive damage to a variety of man-made structures, including residential houses. Around 20,000 residential houses suffered serious damage as a direct result of the effects of liquefaction, and this resulted in approximately 7000 houses in the worst-hit areas being abandoned. Despite the good performance of light timber-framed houses under the inertial loads of the earthquake, these structures could not withstand the large loads and deformations associated with liquefaction, resulting in significant damage. The key structural component of houses subjected to liquefaction effects was found to be their foundations, as these are in direct contact with the ground. The performance of house foundations directly influenced the performance of the structure as a whole. Because of this, and due to the lack of research in this area, it was decided to investigate the performance of houses and in particular their foundations when subjected to the effects of liquefaction. The data from the inspections of approximately 500 houses conducted by a University of Canterbury summer research team following the 4th September 2010 earthquake in the worst-hit areas of Christchurch were analysed to determine the general performance of residential houses when subjected to high liquefaction loads. This was followed by the detailed inspection of around 170 houses with four different foundation types common to Christchurch and New Zealand: Concrete perimeter with short piers constructed to NZS3604, concrete slab-on-grade also to NZS3604, RibRaft slabs designed by Firth Industries and driven pile foundations. With a focus on foundations, floor levels and slopes were measured, and the damage to all areas of the house and property were recorded. Seven invasive inspections were also conducted on houses being demolished, to examine in more detail the deformation modes and the causes of damage in severely affected houses. The simplified modelling of concrete perimeter sections subjected to a variety of liquefaction-related scenarios was also performed, to examine the comparative performance of foundations built in different periods, and the loads generated under various bearing loss and lateral spreading cases. It was found that the level of foundation damage is directly related to the level of liquefaction experienced, and that foundation damage and liquefaction severity in turn influence the performance of the superstructure. Concrete perimeter foundations were found to have performed most poorly, suffering high local floor slopes and being likely to require foundation repairs even when liquefaction was low enough that no surface ejecta was seen. This was due to their weak, flexible foundation structure, which cannot withstand liquefaction loads without deforming. The vulnerability of concrete perimeter foundations was confirmed through modelling. Slab-on-grade foundations performed better, and were unlikely to require repairs at low levels of liquefaction. Ribraft and piled foundations performed the best, with repairs unlikely up to moderate levels of liquefaction. However, all foundation types were susceptible to significant damage at higher levels of liquefaction, with maximum differential settlements of 474mm, 202mm, 182mm and 250mm found for concrete perimeter, slab-on-grade, ribraft and piled foundations respectively when subjected to significant lateral spreading, the most severe loading scenario caused by liquefaction. It was found through the analysis of the data that the type of exterior wall cladding, either heavy or light, and the number of storeys, did not affect the performance of foundations. This was also shown through modelling for concrete perimeter foundations, and is due to the increased foundation strengths provided for heavily cladded and two-storey houses. Heavy roof claddings were found to increase the demands on foundations, worsening their performance. Pre-1930 concrete perimeter foundations were also found to be very vulnerable to damage under liquefaction loads, due to their weak and brittle construction.

Earthquake engineering is increasingly focusing on large international collaborations to address complex problems. Recent computing advances have greatly contributed to the way scientific collaborations are conducted, where web-based solutions are an emerging trend to manage and present results to the scientific community and the general public. However, collaborations in earthquake engineering lack a common interoperability framework, resulting in tedious and complex processes to integrate results, which cannot be efficiently used by third-party institutions. The work described in this thesis applies novel computing techniques to enable the interoperability of earthquake engineering resources, by integrating data, distributed simulation services and laboratory facilities. This integration focuses on distributed approaches rather than centralised solutions, and has been materialised in a platform called Celestina, that supports the integration of hazard mitigation resources. The prototype of Celestina has been implemented and validated within the context of two of the current largest earthquake engineering networks, the SERIES network in Europe and the NEES network in the USA. It has been divided into three sub-systems to address different problems: (i) Celestina Data, to develop best methods to define, store, integrate and share earthquake engineering experimental data. Celestina Data uses a novel approach based on Semantic Web technologies, and it has accomplished the first data integration between earthquake engineering institutions from the United States and Europe by means of a formalised infrastructure. (ii) Celestina Tools, to research applications that can be implemented on top of the data integration, in order to provide a practical benefit for the end user. (iii) Celestina Simulations, to create the most efficient methods to integrate distributed testing software and to support the planning, definition and execution of the experimental workflow from a high-level perspective. Celestina Simulations has been implemented and validated by conducting distributed simulations between the Universities of Oxford and Kassel. Such validation has demonstrated the feasibility to conduct both flexible, general-purpose and high performance simulations under the framework. Celestina has enabled global analysis of data requirements for the whole community, the definition of global policies for data authorship, curation and preservation, more efficient use of efforts and funding, more accurate decision support systems and more efficient sharing and evaluation of data results in scientific articles.

Le premier chapitre présente les axes principaux de recherche ainsi que les problèmes traités dans cette thèse. Plus précisément, il expose une synthèse sur le sujet, en y donnant les propriétés essentielles pour la bonne compréhension de cette étude, accompagnée des références bibliographiques les plus importantes. Il présente également les motivations de ce travail en précisant les contributions originales dans ce domaine. Le deuxième chapitre est composé d’une recherche originale sur l’estimation du risque sismique, dans la zone du nord de la mer Egée (Grèce), en faisant usage de la théorie des processus semi-markoviens à temps continue. Il propose des estimateurs des mesures importantes qui caractérisent les processus semi-markoviens, et fournit une modélisation dela prévision de l’instant de réalisation d’un séisme fort ainsi que la probabilité et la grandeur qui lui sont associées. Les chapitres 3 et 4 comprennent une première tentative de modélisation du processus de génération des séismes au moyen de l’application d’un temps discret des modèles cachés markoviens et semi-markoviens, respectivement. Une méthode d’estimation non paramétrique est appliquée, qui permet de révéler des caractéristiques fondamentales du processus de génération des séismes, difficiles à détecter autrement. Des quantités importantes concernant les niveaux des tensions sont estimées au moyen des modèles proposés. Le chapitre 5 décrit les résultats originaux du présent travail à la théorie des processus stochastiques, c’est- à-dire l’étude et l’estimation du « Intensité du temps d’entrée en temps discret (DTIHT) » pour la première fois dans des chaînes semi-markoviennes et des chaînes de renouvellement markoviennes cachées. Une relation est proposée pour le calcul du DTIHT et un nouvel estimateur est présenté dans chacun de ces cas. De plus, les propriétés asymptotiques des estimateurs proposés sont obtenues, à savoir, la convergence et la normalité asymptotique. Le chapitre 6 procède ensuite à une étude de comparaison entre le modèle markovien caché et le modèle semi-markovien caché dans un milieu markovien et semi-markovien en vue de rechercher d’éventuelles différences dans leur comportement stochastique, déterminé à partir de la matrice de transition de la chaîne de Markov (modèle markovien caché) et de la matrice de transition de la chaîne de Markov immergée (modèle semi-markovien caché). Les résultats originaux concernent le cas général où les distributions sont considérées comme distributions des temps de séjour ainsi que le cas particulier des modèles qui sont applique´s dans les chapitres précédents où les temps de séjour sont estimés de manière non-paramétrique. L’importance de ces différences est spécifiée à l’aide du calcul de la valeur moyenne et de la variance du nombre de sauts de la chaîne de Markov (modèle markovien caché) ou de la chaîne de Markov immergée (modèle semi-markovien caché) pour arriver dans un état donné, pour la première fois. Enfin, le chapitre 7 donne des conclusions générales en soulignant les points les plus marquants et des perspectives pour développements futurs. / The first chapter describes the definition of the subject under study, the current state of science in this area and the objectives. In the second chapter, continuous-time semi-Markov models are studied and applied in order to contribute to seismic hazard assessment in Northern Aegean Sea (Greece). Expressions for different important indicators of the semi- Markov process are obtained, providing forecasting results about the time, the space and the magnitude of the ensuing strong earthquake. Chapters 3 and 4 describe a first attempt to model earthquake occurrence by means of discrete-time hidden Markov models (HMMs) and hidden semi-Markov models (HSMMs), respectively. A nonparametric estimation method is followed by means of which, insights into features of the earthquake process are provided which are hard to detect otherwise. Important indicators concerning the levels of the stress field are estimated by means of the suggested HMM and HSMM. Chapter 5 includes our main contribution to the theory of stochastic processes, the investigation and the estimation of the discrete-time intensity of the hitting time (DTIHT) for the first time referring to semi-Markov chains (SMCs) and hidden Markov renewal chains (HMRCs). A simple formula is presented for the evaluation of the DTIHT along with its statistical estimator for both SMCs and HMRCs. In addition, the asymptotic properties of the estimators are proved, including strong consistency and asymptotic normality. In chapter 6, a comparison between HMMs and HSMMs in a Markov and a semi-Markov framework is given in order to highlight possible differences in their stochastic behavior partially governed by their transition probability matrices. Basic results are presented in the general case where specific distributions are assumed for sojourn times as well as in the special case concerning the models applied in the previous chapters, where the sojourn time distributions are estimated non-parametrically. The impact of the differences is observed through the calculation of the mean value and the variance of the number of steps that the Markov chain (HMM case) and the EMC (HSMM case) need to make for visiting for the first time a particular state. Finally, Chapter 7 presents concluding remarks, perspectives and future work.

Cette thèse a pour objectif d’explorer la relation entre les caractéristiques socio-culturelles et les politiques de reconstruction post-séisme dans les zones rurales de Azad Jammu et du Cachemire, au Pakistan. L’objet principal est d’examiner les pratiques architecturales traditionnelles : dhajji-dewari et la composition sociale de la communanuté pendant et après la reconstruction. Différents processus sont analysés: comment les aspects socio-culturels des sociétés rurales sont affectés par les politiques de reconstruction? Comment les politiques sont touchées par les aspects socio-culturels des commmunautés? Comment la combinaison des deux influence le processus final?Ce travail de thèse part du constat que 80% des 600 000 bâtiments endommagés ou détruits lors du séisme du 8 octobre 2005 au Cachemire, étaient des maisons rurales provisoires (Katcha). Il s’agit d’examiner jusqu’où le Programme de Reconstruction de Logement Rural (RHRP) qui a concerné quelque 100 000 maisons dhajji, a réduit ou augmenté la vulnérabilité de la zone pour l'avenir. Ce programme a été initié à partir de l’expérience de précédents programmes de reconstruction post-tremblements de terre, qui ont été d’une grande utilité pour les experts. Il restait à analyser les erreurs commises ou répétées par les différents acteurs pendant les phases d’élaboration, de validation, de mise en œuvre, et de suivi des politiques de reconstruction. Les principaux résultats de la thèse couvrent trois thèmes relatifs aux différentes étapes de la reconstruction : la durabilité de la reconstruction ; la réduction de la vulnérabilité de la reconstruction ; les résultats qui n’entrent pas dans les catégories “durabilité” et “vulnérabilité” selon les experts du Cachemire rural. La satisfaction des communautés est l’indicateur principal permettant d’évaluer les principaux résultats. L'étude conclut que la non-prise en compte des aspects socioculturels des communautés pendant la reconstruction peut augmenter la vulnérabilité du scénario de post-reconstruction. Le suivi du programme de reconstruction consiste à évaluer les tendances liées aux maisons en construction. En présentant par des illustrations les détails architecturaux de ces maisons reconstruites, l’écart avec les recommandations est évalué. Après que quelques années, les populations oublient les impacts du séisme et leurs besoins immédiats dictent leurs priorités de décision. Il est suggéré qu'à la fin du programme de reconstruction, la présence des autorités dans la zone reconstruite permette d’assister les populations dans leurs besoins actuels et futurs, et de contrôler le développement des constructions non conformes. / This thesis is aimed at exploring the relation of socio-cultural characteristics and policies with post-quake reconstruction of rural areas of Azad Jammu & Kashmir, Pakistan. The primary concern of the study is limited to examine the traditional architectural practice ; dhajji-dewari and social composition of the community during and after reconstruction. It is analyzed that how the socio-cultural aspects of rural communities are affected by the policies, how policies are affected by the socio-cultural aspects of the community and how both of these can influence the final product. The thesis was rooted in the fact that 80% of the 600,000 damaged/destroyed buildings during 8th October, 2005 Kashmir earthquake were rural temporary (Katcha) houses. It was hence to be investigated that how far the Rural Housing Reconstruction Program (RHRP) has reduced (or increased) the vulnerability of the area for future. The impact of any policy launched during this program was not limited to few housing units rather more than 0.1 million dhajji houses could be affected through this. The rural Kashmir reconstruction was commenced with the in-hand knowledge of several previous post-quake reconstruction programs and was appreciated widely by experts. It was yet to be explored that which mistakes were committed/repeated by the stakeholders during policy making, delivery, implementation and post implementation phases. Covering the phases of policy making, delivery and implementation, the major findings of the thesis are categorized into three sections ; the sustainability generating aspects of reconstruction, vulnerability enhancing dimensions of reconstruction, and, those outcomes of reconstruction which are not yet categorized under ”sustainability” or ”vulnerability” by the experts focusing particularly rural Kashmir. Community satisfaction is given primary focus to rate different outcomes.The study concludes that ignoring socio-cultural aspects of the community during reconstruction may lead to vulnerability in post-reconstruction scenario. Considering the post implementation phase, the current trends are observed by examining under-construction houses. By pictorially presenting the architectural details of these houses it is examined that deviations from guidelines are in practice. People start forgetting the disaster impacts after few years and their immediate needs drive their decision priorities. It is suggested that after reconstruction program ends up, some authorities must be present in the reconstructed area to guide people for their current requirements and future needs and also to control the spread of non compliant construction.