No / Sulfate causes various health issues for human if on average daily intake of sulfate is more than 500 mg from drinking-water, air, and food. Moreover, the presence of sulfate in rainwater causes acid rains which has harmful effects on animals and plants. Food is the major source of sulfate intake; however, in areas of South-Punjab, Pakistan, the drinking-water containing high levels of sulfate may constitute the principal source of intake. The spatial behavior of sulfate in groundwater is recorded for South-Punjab province, Pakistan. The spatial dependence of the response variable (sulfate) is modeled by using various variograms models that are estimated by maximum likelihood method, restricted maximum likelihood method, ordinary least squares, and weighted least squares. The parameters of estimated variogram models are utilized in ordinary kriging, universal kriging, Bayesian kriging with constant trend, and varying trend and the above methods are used for interpolation of sulfate concentration. The K-fold cross validation is used to measure the performances of variogram models and interpolation methods. Bayesian kriging with a constant trend produces minimum root mean square prediction error than other interpolation methods. Concentration of sulfate in drinking water within the study area is increasing to the Northern part, and health risks are really high due to poor quality of water.

Résumé : Les barrages induisent un impact potentiellement important sur l'environnement et la société par la modification des écosystèmes, le déplacement des populations en amont et surtout par la présence d'un risque imposé aux populations situées à l'aval. Même si les ruptures de ces ouvrages ont une probabilité d'occurrence faible, la cause principale des accidents, à côté des submersions par des crues imprévues, a toujours été la rupture des fondations (ICOLD 1993) suite à des problèmes d'érosion, ou d'insuffisance de résistance au cisaillement le long des discontinuités rocheuses, des joints de levées ou de l'interface barrage-fondation. La fréquence de ruptures par défaut de résistance au cisaillement des discontinuités des fondations des barrages en béton est estimée à 21 % (ICOLD 1995). Les fondations rocheuses présentent souvent une variabilité verticale et horizontale des propriétés de résistance au cisaillement des discontinuités. Une variabilité verticale peut être matérialisée par une moyenne de la propriété de résistance qui varie en profondeur et dont la prise en compte réduit la variance de cette propriété de résistance. Aussi, la rupture des fondations rocheuses par défaut de résistance au cisaillement des discontinuités est un mécanisme qui mobilise les propriétés ponctuelles de résistance au cisaillement présentes sur cette discontinuité. La résistance au cisaillement mobilisée le long de cette discontinuité présente parfois une variance moins élevée que celle de la résistance ponctuelle au cisaillement (échelle de laboratoire). Ces phénomènes de variabilité spatiale ne sont pas pris en compte dans la justification du comportement en cisaillement des fondations ni dans les travaux de recherches publiées dans la littérature. L'objectif de la thèse est d'élaborer une démarche d'analyse de la variabilité spatiale de la résistance au cisaillement qui prend en compte cette réduction de la dispersion. Cette démarche a été élaborée dans le contexte de l'état de l'art actuel, avec la combinaison des impératifs suivants : • La démarche est basée sur une méthodologie expérimentale i)-alternative à l'essai de cisaillement direct (coûteux en temps et en argent) pouvant être relativement simple à mettre en œuvre ii)- qui permet de générer des données quantitatives de cisaillement suffisamment abondantes pour analyser la variabilité spatiale de la résistance au cisaillement. • Cette démarche a été mise en œuvre au contexte des outils numériques et des méthodes de justification de la résistance à l'effort tranchant d'une fondation rocheuse de barrage-poids. La méthodologie expérimentale définie dans la thèse a fait l'objet d'une validation par étude comparative avec 35 essais de cisaillement direct sur des joints à différents degrés de rugosité et d’altération, prélevés d'une fondation de barrage-poids en béton. Il a été développé une démarche d'analyse de la variabilité spatiale de la résistance au cisaillement des joints. Cette démarche repose sur l'utilisation des données géo référencées de paramètres de cisaillement caractérisant la même famille de discontinuité le long d'un forage vertical. Afin de valider la pertinence et l’applicabilité de cette démarche, nous l’avons implémentée dans un cas d'étude de fondation rocheuse de barrage. A l'aide d'un code de calcul numérique basé sur la méthode des éléments finis, une étude a permis d'illustrer la pertinence de l'analyse de la variabilité spatiale de la résistance au cisaillement des joints dans une étude de stabilité au glissement des fondations rocheuses de barrage. Les résultats montrent que la prise en compte de la variabilité spatiale des paramètres de cisaillement permet d'augmenter la marge de sécurité mesurée à travers une hausse du coefficient de sécurité et une baisse significative de la probabilité de défaillance. // Abstract : Dams induce a potentially significant impact on the environment and society by changing ecosystems, by populations’ relocation upstream and especially by the presence of an imposed risk on populations located downstream. Although dam failures have a low probability, the main cause of accidents, near submersions by unexpected flood has been foundations failures (ICOLD 1993) due to problems of erosion, or insufficient shear strength along the rock discontinuities or the interface between dam and foundation. Among dam failures, 21% are related to lack of shear strength along the discontinuities of the foundations (ICOLD 1995). It is well known that rock, as soil, is a complex engineering material formed y natural process, which induces vertical and horizontal variability. Plus, the sliding process of a rock foundation discontinuity is a mechanism that mobilizes points shear properties of this discontinuity. The variability of shear properties averaged over the sheared discontinuities is less than that of their point shear properties. This is known as the average effect in spatial variability. These phenomena of spatial variability are not taken into account in the standards of stability analysis of dam foundations sliding or research work published in the literature. The aim of the thesis is to develop an analysis of the spatial variability of shear strength that takes into account the reduction of the variability by scaling up effect. This approach was developed in the context of the current state of the art. An experimental method, which aimed to investigate in a simple way the shear strength of joints, was suggested in the thesis and has been validated by comparative study with more than thirty direct shear tests on joints taken from a foundation of concrete gravity dam. It was developed a process to analyze the spatial variability of the shear strength of the joints using the input parameters of the model of Barton and Choubey (1977). This approach is based on the use of geo -referenced data on these parameters characterizing the family of discontinuity along a vertical borehole. To validate the relevance and applicability of this approach, we have implemented it in a case study of a rock dam foundation. Using finite element software, a study illustrates the relevance of the analysis of the spatial variability of the shear strength of the joints in the assessment of stability against rock dam foundations sliding. The results show that taking into account the spatial variability of shear parameters can increase the margin of safety measured through an increase in the safety factor and a significant decrease in the probability of failure.

La présence de dépendance spatiale des prix immobiliers impose aux méthodes d’estimation de prendre en compte cet élément. Les deux approches de la statistique spatiale sont l’économétrie spatiale et la géostatistique. La géostatistique estime directement la matrice de variance-covariance en supposant que la covariance entre les observations dépend inversement de la distance séparant leur localisation. L’économétrie spatiale définit et intègre la matrice d’interaction spatiale dans un modèle de régression hédonique. Si ces deux méthodes sont possibles pour étudier la dépendance spatiale des prix immobiliers dans des contextes variés, il n’existe cependant pas de règles très claires quant au choix de la méthode à sélectionner. Cette thèse procède à un examen détaillé de ces deux approches afin de pouvoir en distinguer les ressemblances et les différences, les avantages et les inconvénients. Des exemples d’application de chaque approche dans une étude immobilière sont présentés. La géostatistique est utilisée pour analyser la stationnarité du variogramme, ainsi que la sensibilité du variogramme aux paramètres de l’estimation hédonique. Le modèle d’économétrie spatiale est utilisé pour tenter d’identifier économétriquement le quartier dominant du marché immobilier d’une ville / Geostatistics and spatial econometrics are two spatial statistical approaches used to deal with spatial dependence. Geostatistics estimates directly the variance-covariance matrix by assuming that the covariance among observations depends inversely on the distance between their locations, called the covariogram. Spatial econometrics defines and integrates the spatial interaction matrix in a hedonic regression model. In real estate, price estimation should take into account these spatial characteristics because property prices are correlated. Hence, these two approaches are commonly used to study the spatial dependence of the real estate prices in many contexts. However, a definite rule in selection these statistic approaches has not been established. This thesis examined these two approaches in order to distinguish the similarities, differences, advantages, and disadvantages of each methodology. Some examples of their applications in a real estate study. The geostatistics is used to analyze the stationarity of the variogram and its sensitivity depending on the parameters added in hedonic estimation. The spatial econometric is used to define econometrically the real estate market dominant area

Entre as técnicas de análise exploratória de dados espaciais encontram-se os indicadores de associação espacial, que mensuram o grau de dependência espacial dos dados analisados e são aplicáveis apenas a dados quantitativos. Outro procedimento disponível é a geoestatística, a qual se baseia no variograma, descrevendo quantitativa e qualitativamente a estrutura espacial de determinada variável. Neste trabalho, utilizam-se conceitos do variograma para desenvolver um indicador de associação espacial global (SIVAR-G) e um indicador de associação espacial local (SIVAR-L). São utilizados dois bancos de dados: dados binários de escolha modal de uma Cidade Fictícia e dados de média de viagens por modo automóvel por domicílio para um recorte da região central da cidade de São Paulo (Pesquisa de Mobilidade 2012). Em ambos os casos, o indicador global, para diferentes vizinhanças, foi calculado com base em valores padronizados, provenientes do variograma experimental e teórico. Em seguida, aplicou-se um teste de hipótese baseado em pseudo-significância para avaliar a significância do indicador proposto previamente. Por fim, os resultados do indicador proposto foram comparados ao índice de Moran, calculado com os mesmos parâmetros. Para o indicador local, foi elaborado um procedimento similar, porém os cálculos foram feitos pontualmente. Cada observação do banco de dados teve um variograma experimental calculado e um variograma teórico modelado para uma análise omniderecional. Um teste de hipótese similar ao do indicador global foi desenvolvido e aplicado. Assim obtiveram-se indicadores de associação espacial local ponto a ponto. Conclui-se que o indicador SIVAR-G possui desempenho satisfatório na estimação de associação espacial para dados contínuos e binários, mostrando-se sensível a anisotropia dos dados. O indicador SIVAR-L é capaz de identificar \"bolsões\" de associação espacial. É aplicável a dados contínuos e binários. Os indicadores propostos permitem a modelagem de variogramas teóricos globais e locais, fornecendo uma maior riqueza de detalhes da estrutura espacial dos dados. Os indicadores SIVAR baseiam-se na dissimilaridade espacial, enquanto o índice de Moran e LISA baseiam-se na similaridade espacial. / Among the exploratory spatial data analysis tools, there are the indicators of spatial association, which measure the degree of spatial dependence of the analyzed data and can be applied to quantitative data. Other procedure available is the geoestatistics, which is based on the variogram, describing quantitatively and qualitatively the spatial structure of a variable. The aim of this thesis is to use the concept of the variogram to develop a global indicator of spatial association (SIVAR-G) and a local indicator of spatial association (SIVAR-L). Two data bases were used: binary data of travel mode choice of a hypothetical city and mean of automobile trips by household to a region of São Paulo\'s center (Mobility Survey, 2012). In both cases, the global indicator, for different neighborhoods, was calculated based on standardized values, derived from the experimental and theoretical variogram. Then, a pseudo-significance test was applied to evaluate the significance of the previously proposed indicator. The results of the proposed indicator were compared to Moran\'s I, calculated with the same parameters. For the local indicator, it was made a similar procedure, however the calculation was punctual. For each observation of the database, it was calculated experimental variogram and adjusted a theoretical variogram for a omnidirectional analysis. A hypothesis test similar to the one applied in the global indicator was developed and applied. Therefore, it was obtained local indicators point by point. It was concluded that the indicator SIVAR-G has a satisfactory performance for spatial association of binary and continuous data, with sensibility for anisotropy cases. The SIVAR-L indicator is able to identify spatial association pockets and outliers. The local indicator is suitable for continuous and binary data. The developed indicators allow the modeling of theoretical global and local variograms, providing more details of the spatial structure of the data. The SIVAR indicators are based on spatial dissimilarity, while the Moran and LISA index are based on spatial similarity.

Entre as técnicas de análise exploratória de dados espaciais encontram-se os indicadores de associação espacial, que mensuram o grau de dependência espacial dos dados analisados e são aplicáveis apenas a dados quantitativos. Outro procedimento disponível é a geoestatística, a qual se baseia no variograma, descrevendo quantitativa e qualitativamente a estrutura espacial de determinada variável. Neste trabalho, utilizam-se conceitos do variograma para desenvolver um indicador de associação espacial global (SIVAR-G) e um indicador de associação espacial local (SIVAR-L). São utilizados dois bancos de dados: dados binários de escolha modal de uma Cidade Fictícia e dados de média de viagens por modo automóvel por domicílio para um recorte da região central da cidade de São Paulo (Pesquisa de Mobilidade 2012). Em ambos os casos, o indicador global, para diferentes vizinhanças, foi calculado com base em valores padronizados, provenientes do variograma experimental e teórico. Em seguida, aplicou-se um teste de hipótese baseado em pseudo-significância para avaliar a significância do indicador proposto previamente. Por fim, os resultados do indicador proposto foram comparados ao índice de Moran, calculado com os mesmos parâmetros. Para o indicador local, foi elaborado um procedimento similar, porém os cálculos foram feitos pontualmente. Cada observação do banco de dados teve um variograma experimental calculado e um variograma teórico modelado para uma análise omniderecional. Um teste de hipótese similar ao do indicador global foi desenvolvido e aplicado. Assim obtiveram-se indicadores de associação espacial local ponto a ponto. Conclui-se que o indicador SIVAR-G possui desempenho satisfatório na estimação de associação espacial para dados contínuos e binários, mostrando-se sensível a anisotropia dos dados. O indicador SIVAR-L é capaz de identificar \"bolsões\" de associação espacial. É aplicável a dados contínuos e binários. Os indicadores propostos permitem a modelagem de variogramas teóricos globais e locais, fornecendo uma maior riqueza de detalhes da estrutura espacial dos dados. Os indicadores SIVAR baseiam-se na dissimilaridade espacial, enquanto o índice de Moran e LISA baseiam-se na similaridade espacial. / Among the exploratory spatial data analysis tools, there are the indicators of spatial association, which measure the degree of spatial dependence of the analyzed data and can be applied to quantitative data. Other procedure available is the geoestatistics, which is based on the variogram, describing quantitatively and qualitatively the spatial structure of a variable. The aim of this thesis is to use the concept of the variogram to develop a global indicator of spatial association (SIVAR-G) and a local indicator of spatial association (SIVAR-L). Two data bases were used: binary data of travel mode choice of a hypothetical city and mean of automobile trips by household to a region of São Paulo\'s center (Mobility Survey, 2012). In both cases, the global indicator, for different neighborhoods, was calculated based on standardized values, derived from the experimental and theoretical variogram. Then, a pseudo-significance test was applied to evaluate the significance of the previously proposed indicator. The results of the proposed indicator were compared to Moran\'s I, calculated with the same parameters. For the local indicator, it was made a similar procedure, however the calculation was punctual. For each observation of the database, it was calculated experimental variogram and adjusted a theoretical variogram for a omnidirectional analysis. A hypothesis test similar to the one applied in the global indicator was developed and applied. Therefore, it was obtained local indicators point by point. It was concluded that the indicator SIVAR-G has a satisfactory performance for spatial association of binary and continuous data, with sensibility for anisotropy cases. The SIVAR-L indicator is able to identify spatial association pockets and outliers. The local indicator is suitable for continuous and binary data. The developed indicators allow the modeling of theoretical global and local variograms, providing more details of the spatial structure of the data. The SIVAR indicators are based on spatial dissimilarity, while the Moran and LISA index are based on spatial similarity.

名古屋大学博士学位論文 学位の種類:工学博士 (論文) 学位授与年月日:平成1年12月8日

Les barrages induisent un impact potentiellement important sur l'environnement et la société par la modification des écosystèmes, le déplacement des populations en amont et surtout par la présence d'un risque imposé aux populations situées à l'aval. Même si les ruptures de ces ouvrages ont une probabilité d'occurrence faible, la cause principale des accidents, à côté des submersions par des crues imprévues, a toujours été la rupture des fondations (ICOLD 1993) suite à des problèmes d'érosion, ou d'insuffisance de résistance au cisaillement le long des discontinuités rocheuses, des joints de levées ou de l'interface barrage-fondation. La fréquence de ruptures par défaut de résistance au cisaillement des discontinuités des fondations des barrages en béton est estimée à 21 % (ICOLD 1995). Les fondations rocheuses présentent souvent une variabilité verticale et horizontale des propriétés de résistance au cisaillement des discontinuités. Une variabilité verticale peut être matérialisée par une moyenne de la propriété de résistance qui varie en profondeur et dont la prise en compte réduit la variance de cette propriété de résistance. Aussi, la rupture des fondations rocheuses par défaut de résistance au cisaillement des discontinuités est un mécanisme qui mobilise les propriétés ponctuelles de résistance au cisaillement présentes sur cette discontinuité. La résistance au cisaillement mobilisée le long de cette discontinuité présente parfois une variance moins élevée que celle de la résistance ponctuelle au cisaillement (échelle de laboratoire). Ces phénomènes de variabilité spatiale ne sont pas pris en compte dans la justification du comportement en cisaillement des fondations ni dans les travaux de recherches publiées dans la littérature. L'objectif de la thèse est d'élaborer une démarche d'analyse de la variabilité spatiale de la résistance au cisaillement qui prend en compte cette réduction de la dispersion. Cette démarche a été élaborée dans le contexte de l'état de l'art actuel, avec la combinaison des impératifs suivants : 1. La démarche est basée sur une méthodologie expérimentale i)-alternative à l'essai de cisaillement direct (coûteux en temps et en argent) pouvant être relativement simple à mettre en œuvre ii)- qui permet de générer des données quantitatives de cisaillement suffisamment abondantes pour analyser la variabilité spatiale de la résistance au cisaillement. 2. Cette démarche a été mise en œuvre au contexte des outils numériques et des méthodes de justification de la résistance à l'effort tranchant d'une fondation rocheuse de barrage-poids. La méthodologie expérimentale définie dans la thèse a fait l'objet d'une validation par étude comparative avec 35 essais de cisaillement direct sur des joints à différents degrés de rugosité et d’altération, prélevés d'une fondation de barrage-poids en béton. Il a été développé une démarche d'analyse de la variabilité spatiale de la résistance au cisaillement des joints. Cette démarche repose sur l'utilisation des données géo référencées de paramètres de cisaillement caractérisant la même famille de discontinuité le long d'un forage vertical. Afin de valider la pertinence et l’applicabilité de cette démarche, nous l’avons implémentée dans un cas d'étude de fondation rocheuse de barrage. A l'aide d'un code de calcul numérique basé sur la méthode des éléments finis, une étude a permis d'illustrer la pertinence de l'analyse de la variabilité spatiale de la résistance au cisaillement des joints dans une étude de stabilité au glissement des fondations rocheuses de barrage. Les résultats montrent que la prise en compte de la variabilité spatiale des paramètres de cisaillement permet d'augmenter la marge de sécurité mesurée à travers une hausse du coefficient de sécurité et une baisse significative de la probabilité de défaillance. / Dams induce a potentially significant impact on the environment and society by changing ecosystems, by populations’ relocation upstream and especially by the presence of an imposed risk on populations located downstream. Although dam failures have a low probability, the main cause of accidents, near submersions by unexpected flood has been foundations failures (ICOLD 1993) due to problems of erosion, or insufficient shear strength along the rock discontinuities or the interface between dam and foundation. Among dam failures, 21% are related to lack of shear strength along the discontinuities of the foundations (ICOLD 1995). It is well known that rock, as soil, is a complex engineering material formed y natural process, which induces vertical and horizontal variability. Plus, the sliding process of a rock foundation discontinuity is a mechanism that mobilizes points shear properties of this discontinuity. The variability of shear properties averaged over the sheared discontinuities is less than that of their point shear properties. This is known as the average effect in spatial variability. These phenomena of spatial variability are not taken into account in the standards of stability analysis of dam foundations sliding or research work published in the literature. The aim of the thesis is to develop an analysis of the spatial variability of shear strength that takes into account the reduction of the variability by scaling up effect. This approach was developed in the context of the current state of the art. An experimental method, which aimed to investigate in a simple way the shear strength of joints, was suggested in the thesis and has been validated by comparative study with more than thirty direct shear tests on joints taken from a foundation of concrete gravity dam. It was developed a process to analyze the spatial variability of the shear strength of the joints using the input parameters of the model of Barton and Choubey (1977). This approach is based on the use of geo -referenced data on these parameters characterizing the family of discontinuity along a vertical borehole. To validate the relevance and applicability of this approach, we have implemented it in a case study of a rock dam foundation. Using finite element software, a study illustrates the relevance of the analysis of the spatial variability of the shear strength of the joints in the assessment of stability against rock dam foundations sliding. The results show that taking into account the spatial variability of shear parameters can increase the margin of safety measured through an increase in the safety factor and a significant decrease in the probability of failure.

MSCAGR / Department of Soil Science / Soil hydraulic and hydraulic-related physical properties are key to soil productivity and these properties are widely studied. Nevertheless, their spatial variability is least understood. Two sites were selected for this study (University of Venda Experimental farm and Roodeplaat, Agricultural Research Council farm). The objectives of this study were to determine the spatial variability of soil water content, water infiltration and hydraulic conductivity on selected soils. Field measurements were done on a 20 m × 20 m. Soil hydraulic and hydraulic-related physical properties were studied at two depths, 0 – 0.2 m top soil and 0.2 – 0.4 m sub soil. The field was irrigated to saturation and let to drain freely for two days. The soil was quickly secured in water cans to avoid further loss of water by evaporation and taken to the laboratory for analysis. Data was analysed using ordinary kriging method in ArcMap® software version 10.4 to generate spatial variability maps and semi variograms. The University of Venda Experimental farm had lesser spatial variability with coefficient of variation ranging from 9.6 to 33.4%. The spatial variability of soil was very low confirmed by contour maps depicting slightly homogeneity. Whereas, the soil hydro-physical properties displayed greater spatial variability at Roodeplaat, Agricultural Research Council Experimental farm. The empirical variograms of spherical model fits were also assuming weak spatial dependence with a curve variogram. The coefficient of variation ranged from 10.5 to 51.9%. Therefore, the greater variability at Roodeplaat, Agricultural Research Council Experimental farm indicated that coarse soil texture under conventional tillage has a greater influence on the spatial variability of the soil hydro-physical properties. / NRF

In modern mining industry, new resource efficient and climate resilient methods have been gaining traction. Commissioned efforts to improve the efficiency of European mining is further helping us to such goals. Orexplore AB's X-ray technology for analyzing drill cores is currently involved in two such project. Orexplore AB wishes to incorporate geostatistics (spatial statistics) into their analyzing process in order to further extend the information gained from the mineral data. The geostatistical method implemented here is ordinary kriging which is an interpolation method that, given measured data, predicts intermediate values governed by prior covariance models. Ordinary kriging facilitates prediction of mineral concentrations on a continuous grid in 1-D up to 3-D. Intermediate values are predicted on a Gaussian process regression line, governed by prior covariances. The covariance is modeled by fitting a model to a calculated experimental variogram. Mineral concentrations are available along the lateral surface of the drill core. Ordinary kriging is implemented to sequentially predict mineral concentrations on shorter sections of the drill core, one mineral at a time. Interpolation of mineral concentrations is performed on the data considered in 1-D and 3-D. The validation is performed by calculating the corresponding density at each section that concentrations are predicted on and compare each such value to measured densities. The performance of the model is evaluated by subjective visual evaluation of the fit of the interpolation line, its smoothness, together with the variance. Moreover, the fit is tested through cross-validation using different metrics that evaluates the variance and prediction errors of different models. The results concluded that this method accurately reproduces the measured concentrations while performing well according to the above mentioned metrics, but does not outperform the measured concentrations when evaluated against the measured densities. However, the method was successful in providing information of the minerals in the drill core by producing mineral concentrations on a continuous grid. The method also produced mineral concentrations in 3-D that reproduced the measured densities well. It can be concluded that ordinary kriging implemented according to the methodology described in this report efficiently produces mineral concentrations that can be used to obtain information of the distribution of concentrations in the interior of the drill core. / I den moderna gruvindustrin har nya resurseffektiva och klimatbeständiga metoder ökat i efterfråga. Beställda projekt för att förbättra effektiviteten gällande den europeiska gruvdriften bidrar till denna effekt ytterligare. Orexplore AB:s röntgenteknologi för analys av borrkärnor är för närvarande involverad i två sådana projekt. Orexplore AB vill integrera geostatistik (spatial statistik) i sin analysprocess för att ytterligare vidga informationen från mineraldatan. Den geostatistiska metoden som implementeras här är ordinary kriging, som är en interpolationsmetod som, givet uppmätta data, skattar mellanliggande värden betingade av kovariansmodeller. Ordinary kriging tillåter skattning av mineralkoncentrationer på ett kontinuerligt nät i 1-D upp till 3-D. Mellanliggande värden skattas enligt en Gaussisk process-regressionslinje. Kovariansen modelleras genom att passa en modell till ett beräknat experimentellt variogram. Mineralkoncentrationer är tillgängliga längs borrkärnans mantelyta. Ordinary kriging implementeras för att sekventiellt skatta mineralkoncentrationer på kortare delar av borrkärnan, ett mineral i taget. Interpolering av mineralkoncentrationer utförs på datan betraktad i 1-D och 3-D. Valideringen utförs genom att utifrån de skattade koncentrationerna beräkna den motsvarande densiteten vid varje sektion som koncentrationer skattas på och jämföra varje sådant värde med uppmätta densiteter. Undersökning av modellen utförs genom subjektiv visuell utvärdering av interpolationslinjens passning av datan, dess mjukhet, tillsammans med variansen. Dessutom testas passformen genom korsvalidering med olika mätvärden som utvärderar varians- och skattningsfel för olika modeller. Slutsatsen från resultaten är att denna metod reproducerar de uppmätta koncentrationerna väl samtidigt som den presterar bra enligt de mätvärden som utvärderas, men överträffar ej de uppmätta koncentrationerna vid utvärdering mot de uppmätta densiteterna. Metoden var emellertid framgångsrik med att tillhandahålla information om mineralerna i borrkärnan genom att producera mineralkoncentrationer på ett kontinuerligt rutnät. Metoden producerade också mineralkoncentrationer i 3-D som reproducerade de uppmätta densiteterna väl. Slutsatsen dras att ordinary kriging, implementerad enligt den metod som beskrivs i denna rapport, effektivt skattar mineralkoncentrationer som kan användas för att få information om fördelningen av koncentrationer i det inre av borrkärnan.

No description available.