Spot core from the San Andreas Fault Observatory at Depth (SAFOD) borehole provides the opportunity to characterize and quantify damage and mineral alteration of siliciclastics within an active, large-displacement plate-boundary fault zone. Deformed arkosic, coarse-grained, pebbly sandstone, and fine-grained sandstone and siltstone retrieved from 2.55 km depth represent the western damaged zone of the San Andreas Fault, approximately 130 m west of the Southwest Deforming Zone (SDZ). The sandstone is cut by numerous subsidiary faults that display extensive evidence of repeating episodes of compaction, shear, dilation, and cementation. The subsidiary faults are grouped into three size classes: 1) small faults, 1 to 2 mm thick, that record an early stage of fault development, 2) intermediate-size faults, 2 to 3 mm thick, that show cataclastic grain size reduction and flow, extensive cementation, and alteration of host particles, and 3) large subsidiary faults that have cemented cataclastic zones up to 10 mm thick. The cataclasites contain fractured host-rock particles of quartz, oligoclase, and orthoclase, in addition to albite and laumontite produced by syn-deformation alteration reactions. Five structural units are distinguished in the subsidiary fault zones: fractured sandstones, brecciated sandstones, microbreccias, microbreccias within distinct shear zones, and principal slip surfaces. We have quantified the particle size distributions and the particle shape of the host rock mineral phases and the volume fraction of the alteration products for these representative structural units. Shape characteristics vary as a function of shear strain and grain size, with smooth, more circular particles evolving as a result of increasing shear strain. Overall, the particle sizes are consistent with a power law distribution over the particle size range investigated (0.3 µm < d < 400 µm). The exponent (fractal dimension, D) is found to increase with shear strain and volume fraction of laumontite. This overall increase in D and evolution of shape with increasing shear strain reflects a general transition from constrained comminution, active at low shear strains to abrasion processes that dominate at high shear strains.

Generating samples from multivariate distributions efficiently is an important task in Monte Carlo integration and many other stochastic simulation problems. Markov chain Monte Carlo has been shown to be very efficient compared to "conventional methods", especially when many dimensions are involved. In this article we propose a Hit-and-Run sampler in combination with the Ratio-of-Uniforms method. We show that it is well suited for an algorithm to generate points from quite arbitrary distributions, which include all log-concave distributions. The algorithm works automatically in the sense that only the mode (or an approximation of it) and an oracle is required, i.e., a subroutine that returns the value of the density function at any point x. We show that the number of evaluations of the density increases slowly with dimension. An implementation of these algorithms in C is available from the <a href="http://statmath.wu-wien.ac.at/software/hitro/">authors</a>. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

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.

Le terme d'énergie de symétrie (Csym) contenu à l'intérieur de l'équation d'état de la matière nucléaire est étudié via l'isoscaling et les formes des distributions isotopiques pour les réactions 40,48Ca+40,48Ca à une énergie incidente de 35 MeV/A. Les collisions périphériques et semi-périphériques sont étudiées. Un couplage entre deux appareils expérimentaux, le spectromètre VAMOS et le multidétecteur INDRA, a été fait. VAMOS a permis de mesurer la charge et la masse des résidus d'évaporation du quasi-projectile (PLF) avec grande précision. Les particules légères chargées ont été mesurées simultanément avec INDRA, permettant d'estimer le paramètre d'impact et l'énergie d'excitation ainsi que de reconstruire le fragment primaire, parent du PLF. L'étude des PLF montre la présence d'un effet pair-impair associé aux effets de désintégrations secondaires. L'extraction d'une information concernant Csym par l'étude des PLF, dans le cadre de cette thèse, est donc difficile, d'où la nécessité de reconstruire le fragment primaire. En étudiant les fragments primaires reconstruits, nous observons une évolution du paramètre Csym/T en fonction de la charge. Cette évolution est attribuée au degré d'excitation des fragments. De plus, la forme des distributions globales de Csym/T nous permet d'extraire le rapport des contributions de surface et de volume à l'énergie de symétrie. Ces rapports nous montrent des effets de surface importants, appuyés par les calculs théoriques. À partir des températures extraites par les spectres en énergie des protons, une valeur de Csym est extraite. Ces valeurs, autour de 30 MeV, sont cohérentes avec des valeurs autour de la densité de saturation.

Bayesian principle is conceptually simple and intuitively plausible to carry out but its numerical implementation is not always straightforward. Most of the times we have posterior distributions in terms of complicated analytical funs ions and be known only up to a multiplicative constant. Hence it becomes computationally difficult to attain the marginal densities and the moments of the posterior distributions in closed form. In the present study the leading methods, both analytical and numerical, for implementing Bayesian inference has been explored. In particular, the non-iterative Monte Carlo method known as Importance Sampling has been applied to approximate the posterior expectations of the Lognormal and Cauchy distributions, belonging to the Exponential family and the non-Exponential family of distributions respectively. Sample values from these distributions have been simulated through computer programming. Calculations are done mostly by C++ programming language and Mathematica. / Department of Mathematical Sciences

This thesis shows how to test the fit of a data set to a number of different models, using Watson’s U2 statistic for both grouped and continuous data. While Watson’s U2 statistic was introduced for continuous data, in recent work, the statistic has been adapted for grouped data. However, when using Watson’s U2 for continuous data, the asymptotic distribution is difficult to obtain, particularly, for some skewed circular distributions that contain four or five parameters. Until now, U2 asymptotic points are worked out only for uniform distribution and the von Mises distribution among all circular distributions. We give U2 asymptotic points for the wrapped exponential distributions, and we show that U2 asymptotic points when data are grouped is usually easier to obtain for other more advanced circular distributions. In practice, all continuous data is grouped into cells whose width is decided by the accuracy of the measurement. It will be found useful to treat such data as grouped with sufficient number of cells in the examples to be analyzed. When the data are treated as grouped, asymptotic points for U2 match well with the points when the data are treated as continuous. Asymptotic theory for U2 adopted for grouped data is given in the thesis. Monte Carlo studies show that, for reasonable sample sizes, the asymptotic points will give good approximations to the p-values of the test.

In Geostatistical modelling of the spatial distribution of rock attributes, the multivariate distribution of a Random Function defines the range of possible values and the spatial relationships among them. Under a decision of stationarity, the Random Function distribution and its statistics are inferred from data within a spatial domain deemed statistically homogenous. Assuming stationary multiGaussianity allows spatial prediction techniques to take advantage of this simple parametric distribution model. These techniques compute the local distributions with surrounding data and global spatially invariant statistics. They often fail to reproduce local changes in the mean, variability and, particularly, the spatial continuity, that are required for geologically realistic modelling of rock attributes. The proposed alternative is to build local Random Function models that are deemed stationary only in relation to the locations where they are defined. The corresponding location-dependent distributions and statistics are inferred by weighting the samples inversely proportional to their distance to anchor locations. These distributions are locally Gaussian transformed. The transformation models carry information on the local histogram. The distance weighted experimental measures of spatial correlation are able to adapt to local changes in the spatial continuity and are semi-automatically fitted by locally defined variogram models. The fields of local variogram and transformation parameters are used in locally stationary spatial prediction algorithms. The resulting attribute models are rich in non-stationary spatial features. This process implies a higher computational demand than the traditional techniques, but, if data is abundant enough to allow a reliable inference of the local statistics, the proposed locally stationary techniques outperform their stationary counterparts in terms of accuracy and precision. These improved models have the potential of providing better decision support for engineering design. / Mining Engineering

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 97-104).

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