Estimating local site effects and modifying the uncertainty in ground motion predictions are two indispensable parts of partially non-ergodic site-specific PSHA. Local site effects can be estimated using site response simulations or recorded ground motions at the site. When such predictions are available, the aleatory variability of ground motions used in PSHA can be changed to the single station sigma value. However, in these cases, the epistemic uncertainty in predicting site effects must be incorporated into the hazard analyses. This research focuses on the challenges specific to conducting partially non-ergodic site-specific PSHA using recorded ground motions or site response analysis. The main challenge in estimating local site effects using recorded data is whether ground motions collected in a relatively short time can be used to estimate site effects for long return period events. We first develop a database for recorded ground motions at the KiK-net array to investigate this question and use this database to develop a predictive model for the Fourier Amplitude Spectra of ground motions. The ground motion model (GMM) residuals are used to investigate the stability of site terms across different tectonic regimes. We observe that empirical site terms are stable across different tectonic regimes. This observation allows the use of ground motions from any tectonic regime (whether they belong to the tectonic regime that controls the hazard or not) to estimate local site effects. Moreover, in Fourier amplitude, site effects are not dependent on event magnitude and source to site distance; therefore, estimates of site effects from low magnitude events can be easily extrapolated to larger events. The Fourier amplitude GMM developed in this study adds to the library of Fourier amplitude models to be used in future partially non-ergodic site-specific PSHAs. In practice, one of the most common tools for simulating wave propagation is 1-D site response analysis. Two central assumptions in 1-D site response analysis are that the soil profile is comprised of horizontal soil layers of infinite extent and that the vertically propagating SH-waves control the horizontal component of ground motion. SH-waves tend to propagate vertically near the surface because as earthquake waves hit softer layers traveling from the source to the site, they refract until the path becomes steeply inclined. The validity of both assumptions in 1-D site response depends on the geological setting at the site and the geology between the earthquake source and the site, raising the question of which sites are suitable for 1-D site response analysis and what the model error in 1-D site response analysis is. We use the GMM developed for FAS to estimate observed and empirical site terms. The empirical site effects are then compared with the theoretical site effects to determine whether sites are amenable to 1-D site response analyses, and to quantify the model error in the analyses. / Doctor of Philosophy / It is impossible to predict future earthquake-induced ground motions due to randomness in the process and a lack of knowledge. In fact, there are significant uncertainties not only in predicting the location, time, and magnitude of a future earthquake but also in predicting the intensity of ground motion induced by a given future earthquake. Therefore, assessing the safety of the human environment against earthquake hazards requires a method that considers all sources of uncertainties. To this end, Earthquake Engineers have developed Probabilistic Seismic Hazard Analysis(PSHA) framework. Structural engineers use the results of PSHA to design a new structure or assess the safety of an existing building. The accuracy of PSHA estimations leads to designs that are both safe and cost-efficient. The distribution of possible ground motions induced by a given earthquake scenario significantly controls the result of PSHA. This distribution should consider the effect of source, source to site path, and local site effects. This research focuses on improving PSHA results by estimating local site effects using recorded ground motions or simulating wave propagation in the site. In estimating local site effects using recorded data, the local site effect observed in ground motions collected in a relatively short time window is used to estimate hazards from all scenarios. However, the collected ground motions usually belong to frequent low magnitude events that are different from large magnitude events that control the hazard. This difference requires either using a measure of local site effect that is independent of the magnitude and distance of the earthquake or considering the effect of magnitude and distance on the local site effect estimate. Moreover, since frequent events sample different sources and paths than large events, we need to make sure the local site effect is consistent across different sources and paths. This research develops Ground Motion Models(GMMs) for Fourier amplitude, a linear function of ground motion times series, using Japanese ground motions. The ratio of Fourier amplitude at the surface over bedrock is a measure of local site effect that is not dependant on magnitude and distance. The model is then used to see if the trade-off between source and site effect and path and site effect is significant or not. In practice, one of the most common tools for simulating wave propagation is 1-D site response analysis. Two central assumptions in 1-D site response analysis are that the soil profile comprises horizontal soil layers of infinite extent and that the vertically propagating horizontal shear waves (SH-waves) control the horizontal component of ground motion. SH-waves tend to propagate vertically near the surface because as earthquake waves hit softer layers traveling from the source to the site, they refract until the path becomes vertically inclined. The validity of both assumptions in 1-D site response depends on the geological setting at the site and the geology between the earthquake source and the site, raising the question of which sites are suitable for 1-D site response analysis and what the model error in 1-D site response analysis is. We use the GMM developed for FAS to estimate empirical local site effects. The empirical site effects are then compared with the theoretical site effects to determine whether sites are amenable to 1-D site response analyses and quantify the model error in the analyses.

Avec le développement rapide des modèles mathématiques et des outils de simulation, le besoin des processus de quantification des incertitudes a été bien augmenté. L'incertitude paramétrique et la groupe des nombreux décisions sont aujourd’hui les deux barrières principales dans la résolution des grandes problèmes systématiques.Capable de proportionner l'incertitude de la sortie sur celle des entrées, l’Analyse de Sensibilité Globale (GSA) est une solution fiable pour la quantification de l’incertitude. Parmi plusieurs algorithmes de GSA, Fourier Amplitude Sensitivity Analysis (FAST) est l’un des choix les plus populaires des chercheurs. Basé sur ANOVA-HDMR (ANalysis Of VAriance - High Dimensional Model Representation), il est solide en mathématique est efficace en calcul.Malheureusement, la décomposition unique d’ANOVA-HDMR se dépend sur l’indépendance des entrées. À cause de cela, il y a pas mal de cas industriels qui ne peut pas se traiter par FAST, particulièrement pour ceux qui donnent uniquement les échantillons mais sans lois de distribution. Sous cette demande, deux méthode extensifs de FAST avec design de corrélation sont proposées et étudiées dans la recherche. Parmi les deux méthodes, FAST-c s’est basé sur les distributions et FAST-orig s’est basé sur les échantillons.Comme applications et validations, multiples problèmes vibroacoustiques se sont traités dans la recherche. Les matériaux acoustiques avec soustructures, sont des candidats parfaits pour tester FAST-c et FAST-orig. Deux application sont présentées dans la première partie de la thèse, après l’état de l’arts. Les modèles choisis sont matérial poroélastique et structures composite sandwich, dont les propriétés mécaniques sont tous fortement influencées par les paramètres géométriques microscopique ou mesoscopique. D’avoir la méthode de FAST originale comparée avec les deux nouvelles, on trouve bien plus d’information sur la performance vibroacoustique de ces matériaux.Déjà répondu à la demande de GSA sur les modèles avecs les variables dépendantes, la deuxième partie de la thèse contient plus de recherches reliées avec FAST. D’abord FAST est pris en comparaison avec Random Forest, une algorithme bien connu de data-mining. Leurs erreurs potentiels et la possibilité de fonctioner ensemble sont discutés. Et dans les chapitres suivies, plus d’application de FAST sont présentées. Les méthodes sont appliquées sous plusieurs différente conditions. Une modèle de structure périodique qui contient des corrélation parmi les unités nous a en plus forcé à développer une nouvelle FAST-pe méthode. Dans ces applications, les designs des processus préliminaires et les stratégies d’échantillonages sont des essences à présenter. / With rapid development of mathematical models and simulation tools, the need of uncertainty quantification process has grown higher than ever before. Parametric uncertainties and overall decision stacks are nowadays the two main barriers in solving large scale systematic problem.Global Sensitivity Analysis (GSA) is one reliable solution for uncertainty quantification which is capable to assess the uncertainty of model output on its inputs’. Among several GSA algorithms, Fourier Amplitude Sensitivity Test (FAST) is one of the most popular choices of researchers. Based on ANOVA-HDMR (ANalysis Of VAriance - High Dimensional Model Representation), it is both mathematically solid and computationally efficient.One unfortunate fact is that the uniqueness of ANOVA-HDMR relies on the independency of input variables. It makes FAST unable to treat many industrial cases especially for those with only datasets but not distribution functions to be found. To answer the needs, two extended FAST methods with correlation design are proposed and further studied in this research. Among them FAST-c is distribution-based and FAST-orig is data-based.As a frame of validation and application, a number of vibroacoustic problems are dealt with in this research. Vibroacoustic materials with substructures, are perfect test candidates for FAST-c and FAST-orig. Two application cases are presented in the first part of this thesis, following the literature review. The models chosen here are poroelastic material and sandwich composite structures, both having their mechanical properties hugely influenced by their microscopic and mesoscopic geometric parameters. Getting the original FAST method compared to the two with correlation design, many different features on materials’ vibroacoustic performance are latter discovered.Having got an answer for GSA on models with dependent variables, the second part of this thesis contains more extended researches related to FAST. It is taken into comparison with Random Forest, a well-known data-mining algorithm. The potential error of both algorithms are analyzed and the possibility of joint application is discussed. In the following chapters, more applications of FAST-series methods are reported. They are applied under various conditions where another improved version named FAST-pe is developed to treat a model of periodic structures with correlation among each units. Upon these FAST application cases, the design of preliminary process and the sampling strategies is the core part to be introduced.

Understanding the effects of uncertainty on modeling has seen an increased focus as engineering disciplines rely more heavily on computational modeling of complex physical processes to predict system performance and make informed engineering decisions. These computational methods often use simplified models and assumptions with models calibrated using uncertain, averaged experimental data. This commonplace method ignores the effects of uncertainty on the variation of modeling output. Qualitatively, uncertainty is the possibility of error existing from experiment to experiment, from model to model, or from experiment to model. Quantitatively, uncertainty quantification (UQ) methodologies seek to determine the how variable an engineering system is when subjected to variation in the factors that control it. Often performed in conjunction, sensitivity analysis (SA) methods seek to describe what model factor contributes the most to variation in model output. UQ and SA methodologies were employed in the analysis of the Modified Embedded Atom Method (MEAM) model for a pure aluminum, a microstructure sensitive fatigue crack growth model for polycarbonate, and the MultiStage Fatigue (MSF) model for AZ31 magnesium alloy. For the MEAM model, local uncertainty and sensitivity measures were investigated for the purpose of improving model calibrations. In polycarbonate fatigue crack growth, a Monte Carlo method is implemented in code and employed to investigate how variations in model input factors effect fatigue crack growth predictions. Lastly, in the analysis of fatigue life predictions with the MSF model for AZ31, the expected fatigue performance range due to variation in experimental parameters is investigated using both Monte Carlo Simple Random Sampling (MCSRS) methods and the estimation of first order effects indices using the Fourier Amplitude Sensitivity Test (FAST) method.

A number of topics related to Fourier imaging are investigated. Relationships between the magnitude of errors in the amplitude and phase of the Fourier transform of images and the mean square error in reconstructed images are derived. The differing effects of amplitude and phase errors are evaluated, and "equivalent" amplitude and phase errors are derived. A model of the probability density function of the Fourier amplitudes of images is derived. The fundamental basis of phase dominance is studied and quantitated. Inconsistencies in published counter-examples of phase dominance are highlighted. The key characteristics of natural images that lead to their observed power spectral behaviour with spatial frequency are determined.

This thesis addresses two fundamental topics in Engineering Seismology; the application of Probabilistic Seismic Hazard Analysis (PSHA) methodology, and the estimation of measures of Strong Ground Motion. These two topics, while being related, are presented as separate sections. In the first section, state-of-the-art PSHA methodologies are applied to various sites in the Buller Region, South Island, New Zealand. These sites are deemed critical to the maintenance of economic stability in the region. A fault-source based seismicity model is developed for the region that is consistent with the governing tectonic loading, and seismic moment release of the region. In attempting to ensure this consistency the apparent anomaly between the rates of activity dictated by deformation throughout the Quaternary, and rates of activity dictated by observed seismicity is addressed. Individual fault source activity is determined following the application of a Bayesian Inference procedure in which observed earthquake events are attributed to causative faults in the study region. The activity of fault sources, in general, is assumed to be governed by bounded power law behaviour. An exception is made for the Alpine Fault which is modelled as a purely characteristic source. The calculation of rates of exceedance of various ground motion indices is made using a combination of Poissonian and time-dependent earthquake occurrence models. The various ground motion indices for which rates of exceedance are determined include peak ground acceleration, ordinates of 5% damped Spectral Acceleration, and Arias Intensity. The total hazard determined for each of these ground motion measures is decomposed using a four dimensional disaggregation procedure. From this disaggregation procedure, design earthquake scenarios are specified for the sites that are considered. The second part of the thesis is concerned with the estimation of ground motion measures that are more informative than the existing scalar measures that are available for use in New Zealand. Models are developed for the prediction of Fourier Amplitude Spectra (FAS) as well as Arias Intensity for use in the New Zealand environment. The FAS model can be used to generate ground motion time histories for use in structural and geotechnical analyses. Arias Intensity has been shown to be an important strong motion measure due to its positive correlation with damage in short period structures as well as its utility in predicting the onset of liquefaction and landslides. The models are based upon the analysis of a dataset of New Zealand Strong Motion records as well as supplementary near field records from major overseas events. While the two measures of ground motion intensity are strongly related, different methods have been adopted in order to develop the models. As part of the methodology used for the FAS model, Monte Carlo simulation coupled with a simple ray tracing procedure is employed to estimate source spectra from various New Zealand earthquakes and, consequently, a magnitude - corner-frequency relationship is obtained. In general, the parameters of the predictive equations are determined using the most state-of-the-art mixed effects regression procedures.

One of the most difficult tasks towards designing earthquake resistant structures is the determination of critical earthquakes. Conceptually, these are the ground motions that would induce the critical response in the structures being designed. The quantification of this concept, however, is not easy. Unlike the linear response of a structure, which can often be obtained by using a single spectrally modified ground acceleration history, the nonlinear response is strongly dependent on the phasing of ground motion and the detailed shape of its spectrum. This necessitates the use of a suite (bin) of ground acceleration histories having phasing and spectral shapes appropriate for the characteristics of the earthquake source, wave propagation path, and site conditions that control the design spectrum. Further, these suites of records may have to be scaled to match the design spectrum over a period range of interest, rotated into strike-normal and strike-parallel directions for near-fault effects, and modified for local site conditions before they can be input into time-domain nonlinear analysis of structures. The generation of these acceleration histories is cumbersome and daunting. This is especially so due to the sheer magnitude of the data processing involved. The purpose of this thesis is the development and documentation of PC-based computational tools (hereinafter called EQTools) to provide a rapid and consistent means towards systematic assembly of representative strong ground motions and their characterization, evaluation, and modification within a performance-based seismic design framework. The application is graphics-intensive and every effort has been made to make it as user-friendly as possible. The application seeks to provide processed data which will help the user address the problem of determination of the critical earthquakes. The various computational tools developed in EQTools facilitate the identification of severity and damage potential of more than 700 components of recorded earthquake ground motions. The application also includes computational tools to estimate the ground motion parameters for different geographical and tectonic environments, and perform one-dimensional linear/nonlinear site response analysis as a means to predict ground surface motions at sites where soft soils overlay the bedrock. While EQTools may be used for professional practice or academic research, the fundamental purpose behind the development of the software is to make available a classroom/laboratory tool that provides a visual basis for learning the principles behind the selection of ground motion histories and their scaling/modification for input into time domain nonlinear (or linear) analysis of structures. EQTools, in association with NONLIN, a Microsoft Windows based application for the dynamic analysis of single- and multi-degree-of-freedom structural systems (Charney, 2003), may be used for learning the concepts of earthquake engineering, particularly as related to structural dynamics, damping, ductility, and energy dissipation. / Master of Science