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Geomechanical analysis is one of the fundamental pillars to build up the confidence of geological sequestration of CO2. Large scale CO2 sequestration in deep carbonate formation is a complicated geological process, which will non-reversibly transform the presumed equivalent and stable status of a sedimentary basin that formed over millions of years: chemically, hydraulically, geothermally, and geomechanically. In this dissertation, thermoporoelasticity guides the theoretical establishment of a conservative baseline for the geomechanical stability analysis of CO2 sequestration.Extensive laboratory tests, including CO2 flooding tests, permeability tests, uniaxial and triaxial tests, Brazilian tensile strength tests, poroelasticity tests, point load tests, and fracture toughness tests, etc, were conducted on Indiana limestone and Pierre shale to investigate the effects of CO2 sequestration on storage rock and caprock. Numerical simulations using finite difference method of FLAC3D were also conducted to understand the mechanism of strain localization due to pore pressure fluctuation.Based on these laboratory and numerical tests, it is concluded that two mechanisms are competing for rock failures in deep carbonate formations during CO2 sequestration. One is the faulting induced by pore-pressure buildup, and another is the compaction failure because of rock quality deterioration due to exposure to CO2 enriched solution.Fracture toughness measurements on limestone and shale suggest that the fracture toughness of target formation may not be necessarily lower than that of cap rock formation; then the fractures developed in target formation may be easily extended to the cap rock formation, ruining the sealing mechanism. As such, preventing extensive fracturing, and monitoring the seismicity in target formation are essential.Finally, the potential problems of CO2 sequestration in the Williston Basin were investigated. The in-situ stress regime of the Williston Basin was estimated as a mixture of normal and strike-slip faulting regimes, in favor of a vertical or sub-vertical fracture development pattern, which is negative to the CO2 sequestration. However, as the basin is not very close to an incipient failure, compaction failures are expected to be more pronounced, and naturally occurred geological phenomena, stylolites, will help to understand the CO2 sequestration in deep carbonate formation in the long run.

Soft independent modelling of class analogy (SIMCA) is a widely used subspacebased classification technique for spectral data analysis. The principal component (PC) subspace is built for each class separately through principal components analysis (PCA). The squared orthogonal distance (OD2) between the test sample and the class subspace of each class, and the squared score distance (SD2) between the projection of the test sample to the class subspace and the centre of the class subspace, are usually used in the classification rule of SIMCA to classify the test sample. Although it is commonly used to classify high-dimensional spectral data, SIMCA suffers from several drawbacks and some misleading calculations in literature. First, modelling classes separately makes the discriminative between-class information neglected. Second, the literature of SIMCA fail to explore the potential benefit of using geometric convex class models, whose superior classification performance has been demonstrated in face recognition. Third, based on our experiments on several real datasets, calculating OD2 using the formulae in a highlycited SIMCA paper (De Maesschalck et al., 1999) results in worse classification performance than using those in the original SIMCA paper (Wold, 1976) for some high-dimensional data and provides misleading classification results. Fourth, the distance metrics used in the classification rule of SIMCA are predetermined, which are not adapted to different data. Hence the research objectives of my PhD work are to reinforce SIMCA from the following four perspectives: O1) to make its feature space more discriminative; O2) to use geometric convex models as class models in SIMCA for spectral data classification and to study the classification mechanism of classification using different class models; O3) to investigate the equality and inequality of the calculations of OD2 in De Maesschalck et al. (1999) and Wold (1976) for low-dimensional and high-dimensional scenarios; and O4) to make its distance metric adaptively learned from data. In this thesis, we present four contributions to achieve the above four objectives, respectively: First, to achieve O1), we propose to first project the original data to a more discriminative subspace before applying SIMCA. To build such discriminative subspace, we propose the discriminatively ordered subspace (DOS) method, which selects the eigenvectors of the generating matrix with high discriminative ability between classes to span DOS. A paper of this work, "Building a discriminatively ordered subspace on the generating matrix to classify high-dimensional spectral data", has been recently published by the journal of "Information Sciences". Second, to achieve O2), we use the geometric convex models, convex hull and convex cone, as class models in SIMCA to classify spectral data. We study the dual of classification methods using three class models: the PC subspace, convex hull and convex cone, to investigate their classification mechanism. We provide theoretical results of the dual analysis, establish a separating hyperplane classification (SHC) framework and provide a new data exploration scheme to analyse the properties of a dataset and why such properties make one or more of the methods suitable for the data. Third, to achieve O3), we compare the calculations of OD2 in De Maesschalck et al. (1999) and Wold (1976). We show that the corresponding formulae in the two papers are equivalent, only when the training data of one class have more samples than features. When the training data of one class have more features than samples (i.e. high-dimensional), the formulae in De Maesschalck et al. (1999) are not precise and affect the classification results. Hence we suggest to use the formulae in Wold (1976) to calculate OD2, to get correct classification results of SIMCA for highdimensional data. Fourth, to achieve O4), we learn the distance metrics in SIMCA based on the derivation of a general formulation of the classification rules used in literature. We define the general formulation as the distance metric from a sample to a class subspace. We propose the method of learning distance to subspace to learn this distance metric by making the samples to be closer to their correct class subspaces while be farther away from their wrong class subspaces. Lastly, at the end of this thesis we append two pieces of work on hyperspectral image analysis. First, the joint paper with Mr Mingzhi Dong and Dr Jing-Hao Xue, "Spectral Nonlocal Restoration of Hyperspectral Images with Low-Rank Property", has been published by the IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing. Second, the joint paper with Dr Fei Zhou and Dr Jing-Hao Xue, "MvSSIM: A Quality Assessment Index for Hyperspectral Images", has been in revision for Neurocomputing. As these two papers do not focus on the research objectives of this thesis, they are appended as some additional work during my PhD study.

Principal components regression (PCR) and partial least squares regression (PLS) are widely used in multivariate calibration in the fields of chemometrics, econometrics, social science and so forth, serving as alternative solutions to the problems which arise in ordinary least squares regression when explanatory variables are either collinear, or there are hundreds of explanatory variables with a relatively small sample size. Both PCR and PLS tackle the problems by constructing lower dimensional factors based on the explanatory variables. The extra step of factor construction makes the standard prediction uncertainty theory of ordinary least squares regression not directly applicable to the two reduced dimension methods. In the thesis, we start by reviewing the ordinary least squares regression prediction uncertainty theory, and then investigate how the theory performs when it extends to PCR and PLS, aiming at potentially better approaches. The first main contribution of the thesis is to clarify the quantification of prediction uncertainty for PLS. We rephrase existing methods with consistent mathematical notations in the hope of giving a clear guidance to practitioners. The second main contribution is to develop a new linearisation method for PLS. After establishing the theory, simulation and real data studies have been employed to understand and compare the new method with several commonly used methods. From the studies of simulations and a real dataset, we investigate the properties of simple approaches based on the theory of ordinary least squares theory, the approaches using resampling of data, and the local linearisation approaches including a classical and our improved new methods. It is advisable to use the ordinary least squares type prediction variance with the estimated regression error variance from the tuning set in both PCR and PLS in practice.