Faculty of Science School of Statistics snd Acturial Science 9907894x craig.morgan@goldfields.co.za / This dissertation presents a detailed study of geostatistics. Included in this work are details of the development of geostatistics and its usefulness both in and outside of the mining industry, a comprehensive presentation of the theory of geostatistics, and a discussion of the application of this theory to practical situations. A published debate over the validity of geostatistics is also examined. The ultimate goal of this dissertation is to provide a thorough investigation of geostatistics from both a theoretical and a practical perspective. The theory presented in this dissertation is thus tested on various spatial data sets, and from these tests it is concluded that geostatistics can be effectively used in practice provided that the practitioner fully understands the theory of geostatistics and the spatial data being analyzed. A particularly interesting conclusion to come out of this dissertation is the importance of using additive regionalized variables in all geostatistical analyses.

To overcome the limit of topography and manpower, vegetation prediction is an important method in vegetation mapping. There can be used in model prediction that concern about environment factor or in data interpolation that only consider about spatial distribution. In this research, indicator kriging was used to predict the spatial distribution of the vegetation of Laonong river basin. The distributions of associations were combined from the species in these associations which had been selected by Cluster analyst and TWINSPAN. Indicator kriging used presence/absence data to calculate the distribution pattern of these species, and the each species predicted raster had its own distinctly distribution. The distribution pattern of associations were related to species distribution directly. The stability of prediction pattern were evaluated by jackknife method. All standard errors of the prediction were under 0.01, with no significant difference in 4 different sampling measures.

The variogram plays a central role in the analysis of geostatistical data. A valid variogram model is selected and the parameters of that model are estimated before kriging (spatial prediction) is performed. These inference procedures are generally based upon examination of the empirical variogram, which consists of average squared differences of data taken at sites lagged the same distance apart in the same direction. The ability of the analyst to estimate variogram parameters efficiently is affected significantly by the sampling design, i.e., the spatial configuration of sites where measurements are taken. In this paper, we propose design criteria that, in contrast to some previously proposed criteria oriented towards kriging with a known variogram, emphasize the accurate estimation of the variogram. These criteria are modifications of design criteria that are popular in the context of (nonlinear) regression models. The two main distinguishing features of the present context are that the addition of a single site to the design produces as many new lags as there are existing sites and hence also produces that many new squared differences from which the variograrn is estimated. Secondly, those squared differences are generally correlated, which inhibits the use of many standard design methods that rest upon the assumption of uncorrelated errors. Several approaches to design construction which account for these features are described and illustrated with two examples. We compare their efficiency to simple random sampling and regular and space-filling designs and find considerable improvements. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

Chemnitz, Techn. Univ., Diplomarb., 2007.

Any natural surface is in essence non-smooth, consisting of more or less regular roughness and/or mobile structures of different scales. From a fluid mechanics point of view, these natural surfaces offer better aerodynamic performances when they cover moving bodies, in terms of drag reduction, lift enhancement or control of boundary layer separation; this has been shown for boundary layer or wake flows around thick bodies. The numerical simulation of microscopic flows around "natural" surfaces is still out of reach today. Therefore, the goal of this thesis is to study the modeling of the apparent flow slip occurring on this kind of surfaces, modeled as a porous medium, applying Whitaker's volume averaging theory. This mathematical model makes it possible to capture details of the microstructure while preserving a satisfactory description of the physical phenomena which occur. The first chapter of this manuscript provides an overview of previous efforts to model these surfaces, detailing the most important results from the literature. The second chapter presents the mathematical derivation of the volume-averaged Navier-Stokes equations (VANS) in a porous medium. In the third chapter the flow stability at the interface between a free fluid and a porous medium, formed by a series of rigid cylinders, is studied. The presence of this porous layer is treated by including a drag term in the fluid equations. It is shown that the presence of this term reduces the rates of amplification of the Kelvin-Helmholtz instability over the whole range of wavenumbers, thus leading to an increase of the wavelength of the most amplified mode. In this same context, the difference between the isotropic model and a tensorial approach for the drag term has been evaluated, to determine the most consistent approach to study these flow instabilities. This has led to the conclusion that the model that uses the apparent permeability tensor is the most relevant one. In the following chapter, based on this last result, the apparent permeability tensor, based on over one hundred direct numerical simulations carried out over microscopic unit cells, has been identified for a three-dimensional porous medium consisting of rigid cylinders. In these configurations the tensor varies according to four parameters: the Reynolds number, the porosity and the direction of the average pressure gradient, defined by two Euler angles. This parameterization makes it possible to capture local three-dimensional effects. This database has been set up to create, based on a kriging-type approach, a behavioral metamodel for estimating all the components of the apparent permeability tensor. In the fifth chapter, simulations of the VANS equations are carried out on a macroscopic scale after the implementation of the metamodel, to get reasonable computing times. The validation of the macroscopic approach is performed on a closed cavity flow covered with a porous layer and a comparison with the results of a very accurate DNS, homogenized a posteriori, has shown a very good agreement and has demonstrated the relevance of the approach. The next step has been the study of the passive control of the separation of the flow past a hump which is placed on a porous wall, by the same macroscopic VANS approach. Finally, general conclusions and possible directions of research in the field are presented in the last chapter.

Realizar una estimación precisa de los recursos minerales de un yacimiento es fundamental para el éxito de un proyecto minero, debido a los altos montos de inversión involucrados. La estimación se realiza a partir de información obtenida en una toma de muestras y la posterior aplicación de técnicas geoestadísticas de kriging o de simulación, que permiten crear escenarios plausibles dada la información disponible del yacimiento. Los métodos de simulación geoestadística buscan cuantificar la incertidumbre en las leyes de los minerales y en los volúmenes de las distintas unidades geológicas que posee el yacimiento. Esta memoria se enfoca en determinar la incertidumbre en los contactos de las unidades geológicas que existen en el yacimiento Mansa Mina, mediante métodos de simulación de variables categóricas. Específicamente, se utilizan los métodos de simulación secuencial de indicadores y simulación plurigaussiana, con los cuales es posible generar realizaciones de las distintas unidades geológicas que posee el yacimiento Mansa Mina (brecha, stockwork C5, C1 y estéril), con el objetivo de determinar un rango entre los escenarios más optimistas y más pesimistas para cada unidad geológica. Se define una zona de interés y una grilla de prueba en la que se realizan todas las simulaciones de las distintas unidades geológicas. Dado que los escenarios posibles de generar son numerosos, se debe realizar una etapa de validación que permita estudiar la calidad de los modelos generados. Se comparan ambos modelos para establecer cuál de los dos proporciona los mejores resultados en las estimaciones y en los contactos litológicos. Se cuenta con un modelo litológico del yacimiento Mansa Mina propuesto por Codelco, el que es comparado con los modelos simulados, obteniendo una diferencia importante de volúmenes y tonelajes para cada una de las unidades litológicas. Esto se debe principalmente a la existencia de un sector que el modelo de Codelco estima como unidad estéril, mientras que las simulaciones realizadas lo identifican parcialmente como mineral. Como recomendación se establece que se debe refinar el modelo geológico en las zonas del yacimiento en donde la diferencia encontrada es notable.

No description available.

El presente trabajo tiene como objetivos comparar cuatro métodos de simulación geoestadística de leyes minerales en depósitos polimetálicos, de modo de reproducir su variabilidad espacial y sus relaciones de dependencias, y determinar las ventajas e inconvenientes que presenta cada método. Estos métodos son la simulación de cada ley por separado, la co-simulación bajo un modelo lineal de coregionalización (MLC), la simulación de factores obtenidos por análisis en componentes principales (ACP), y la simulación condicional paso a paso. Los métodos se han aplicado a dos bases de datos, una de las cuales es heterotópica (es decir, no todas las leyes son conocidas en todos los sitios muestreados), mientras que la otra es homotópica. La primera base de datos corresponde a un deposito de pórfido cuprífero y posee ocho variables medidas (relativas a leyes de Cu, Fe, Mn, Mo, Cl), mientras que la segunda base de datos corresponde a un deposito de lateritas que contiene seis variables de interés (leyes de Al2O3, Cr, Fe, Mgo, Ni, SiO2). De los resultados obtenidos se desprende las siguientes conclusiones. Primero, la simulación por separado no permite reproducir las dependencias entre variables y, por lo tanto, no es recomendada. Segundo, la co-simulación bajo un modelo lineal de corregionalización considera las correlaciones entre variables y proporciona mejores resultados para ambos casos de estudio. Sin embargo el método es complejo, en particular para ajustar el MLC cuando el número de variables a trabajar es grande. Tercero, la simulación por la factorización de ACP es difícil de aplicar en el caso heterotópico, ya que el método sólo permite trabajar con bases de datos homotópicas, por lo que se debe eliminar aquellas variables que presentan menor información. A pesar de ello, este método proporciona la mejor reproducción de las dependencias entre variables y es recomendable para casos homotópicos ya que no se pierde variables para el análisis. Cuarto, la simulación paso a paso reproduce de buena manera las correlaciones entre variables; sin embargo está restringida a un número limitado de variables (4) por el programa utilizado. Quinto, ninguno de los métodos es capaz de reproducir relaciones de desigualdad, como la que existe entre las leyes de cobre total y sus solubles.

Kriging techniques are regression methods used for evaluation of continuous spatial processes. If the covariance structure of process is unknown, then it's necessary to estimate it from the data. The first part of this Master's thesis is devoted to description the kriging method and to estimate of a variogram fuction, which describes the covariance structure of considered process. The second part includes the implementation of kriging method in MATLAB for simulated and real data.

In-house windrow composting of broiler litter has been studied to reduce microbial populations between flocks. Published time-temperature goals are used to determine the success of the composting process for microbial reductions. Spatial and temporal density of temperature measurement can influence the ability to determine what portion of a windrow pile has achieved specified time-temperature goals. Based on this motivation, an investigation of the heating profile in windrowed litter and the identification of the effects of spatial and temporal sampling densities on the prediction of the heating profile in windrowed broiler litter were executed. Likewise, an investigation of the effects of moisture content on heat generation during composting of broiler litter was conducted. Ultimately, the research projects were designed with the goal of determining the efficacy of windrow composting as a treatment method for reducing microbial populations in broiler litter and to produce recommendations for the implementation of future windrow temperature monitoring investigations. While past investigations have reported success of windrow composting for microbial population reductions, a lack of intense spatial and temporal temperature monitoring has likely mis-represented the pile heating profile and resultant effects on microbial populations.