A lucratividade da indústria mineira é diretamente dependente do planejamento adequado de todas as fases de extração e beneficiamento de minério. Cada passo deste processo por sua vez, também é dependente dos resultados da fase anterior. As usinas de beneficiamento, por exemplo, devem ser alimentadas por um material o mais homogêneo possível, o que é garantido por um planejamento adequado de lavra e de forma muito eficaz por pilhas de homogeneização. No entanto, os métodos de estimativa comumente utilizados para prever os teores dos blocos que formam esses sistemas, não medem adequadamente a incerteza associada a este processo de estimativa. Este estudo avalia a eficácia da simulação geoestatística na previsão da variabilidade in situ dos teores e planejamento de pilhas de homogeneização. O método gera múltiplos cenários equiprováveis para o depósito que devem reproduzir os parâmetros estatísticos das amostras, o histograma e o variograma do fenômeno. Para um dado plano de lavra, o conjunto de cenários simulados irá gerar um conjunto de valores equiprováveis para cada pilha de homogeneização. A metodologia proposta foi aplicada a um depósito de fosfato na região central do Brasil. Neste caso de estudo, os teores de P2O5 previstos pelo plano de lavra de curto prazo e amostrados na área industrial foram comparados com o grupo de valores gerados para as pilhas por meio da simulação. A reprodução dos resultados demonstrou a aplicabilidade da metodologia para o depósito em questão. Além disto, a simulação geoestatística demonstrou ser uma ferramenta muito eficiente na previsão da variabilidade in situ dos teores e planejamento de pilhas de homogeneização. / Profits in mineral industry strongly depend on proper planning at all stages of mining and ore processing, and every step of these processes depends on the results from the previous stage. These chains of events can be illustrated, for instance, by the processing plant. To maximize ore recovery, among various factors, the processing plant must be fed by a material as homogeneous as possible minimizing the variance of the head grades that can be achieved initially by a proper mining plan and optimal schedule and more effectively by homogenization piles. The key factor is to know the input grade variance to design a blending system capable of attenuating it. Estimation methods commonly used to predict block grades which form the geological model used for mine planning do not adequately measure the variance associated with these estimates. This study evaluates geostatistical simulation in predicting in situ grades variability and planning blending piles. The method generates multiple, equally probable grade scenarios for the deposit, which reproduce the values of the samples, the histogram, and the variograma of the attribute being simulated. For a given mining plan, the set of simulated scenarios will generate a group of equiprobable values for each homogenization pile. These results provide the means to assess a range of possible values each pile can have. To validate the suggested methodology, the contents of P2O5 obtained by the short-term mining plan and sampled at the processing plant from a large phosphate mine in central Brazil were compared against the simulated values. The results matched adequately demonstrating that geostatistical simulation and pile emulation methodology are efficient tools that could be applied in predicting grades in situ variability and in planning blending piles.

The collection of crop yield data has become much easier with the introduction of technologies such as the Global Positioning System (GPS), ground-based yield sensors, and Geographic Information Systems (GIS). This explosive growth and widespread use of spatial data has challenged the ability to derive useful spatial knowledge. In addition, outlier detection as one important pre-processing step remains a challenge because the technique and the definition of spatial neighbourhood remain non-trivial, and the quantitative assessments of false positives, false negatives, and the concept of region outlier remain unexplored. The overall aim of this study is to evaluate different spatial outlier detection techniques in terms of their accuracy and computational efficiency, and examine the performance of these outlier removal techniques in a site-specific management context. In a simulation study, unconditional sequential Gaussian simulation is performed to generate crop yield as the response variable along with two explanatory variables. Point and region spatial outliers are added to the simulated datasets by randomly selecting observations and adding or subtracting a Gaussian error term. With simulated data which contains known spatial outliers in advance, the assessment of spatial outlier techniques can be conducted as a binary classification exercise, treating each spatial outlier detection technique as a classifier. Algorithm performance is evaluated with the area and partial area under the ROC curve up to different true positive and false positive rates. Outlier effects in on-farm research are assessed in terms of the influence of each spatial outlier technique on coefficient estimates from a spatial regression model that accounts for autocorrelation. Results indicate that for point outliers, spatial outlier techniques that account for spatial autocorrelation tend to be better than standard spatial outlier techniques in terms of higher sensitivity, lower false positive detection rate, and consistency in performance. They are also more resistant to changes in the neighbourhood definition. In terms of region outliers, standard techniques tend to be better than spatial autocorrelation techniques in all performance aspects because they are less affected by masking and swamping effects. In particular, one spatial autocorrelation technique, Averaged Difference, is superior to all other techniques in terms of both point and region outlier scenario because of its ability to incorporate spatial autocorrelation while at the same time, revealing the variation between nearest neighbours. In terms of decision-making, all algorithms led to slightly different coefficient estimates, and therefore, may result in distinct decisions for site-specific management. The results outlined here will allow an improved removal of crop yield data points that are potentially problematic. What has been determined here is the recommendation of using Averaged Difference algorithm for cleaning spatial outliers in yield dataset. Identifying the optimal nearest neighbour parameter for the neighbourhood aggregation function is still non-trivial. The recommendation is to specify a large number of nearest neighbours, large enough to capture the region size. Lastly, the unbiased coefficient estimates obtained with Average Difference suggest it is the better method for pre-processing spatial outliers in crop yield data, which underlines its suitability for detecting spatial outlier in the context of on-farm research.

The collection of crop yield data has become much easier with the introduction of technologies such as the Global Positioning System (GPS), ground-based yield sensors, and Geographic Information Systems (GIS). This explosive growth and widespread use of spatial data has challenged the ability to derive useful spatial knowledge. In addition, outlier detection as one important pre-processing step remains a challenge because the technique and the definition of spatial neighbourhood remain non-trivial, and the quantitative assessments of false positives, false negatives, and the concept of region outlier remain unexplored. The overall aim of this study is to evaluate different spatial outlier detection techniques in terms of their accuracy and computational efficiency, and examine the performance of these outlier removal techniques in a site-specific management context. In a simulation study, unconditional sequential Gaussian simulation is performed to generate crop yield as the response variable along with two explanatory variables. Point and region spatial outliers are added to the simulated datasets by randomly selecting observations and adding or subtracting a Gaussian error term. With simulated data which contains known spatial outliers in advance, the assessment of spatial outlier techniques can be conducted as a binary classification exercise, treating each spatial outlier detection technique as a classifier. Algorithm performance is evaluated with the area and partial area under the ROC curve up to different true positive and false positive rates. Outlier effects in on-farm research are assessed in terms of the influence of each spatial outlier technique on coefficient estimates from a spatial regression model that accounts for autocorrelation. Results indicate that for point outliers, spatial outlier techniques that account for spatial autocorrelation tend to be better than standard spatial outlier techniques in terms of higher sensitivity, lower false positive detection rate, and consistency in performance. They are also more resistant to changes in the neighbourhood definition. In terms of region outliers, standard techniques tend to be better than spatial autocorrelation techniques in all performance aspects because they are less affected by masking and swamping effects. In particular, one spatial autocorrelation technique, Averaged Difference, is superior to all other techniques in terms of both point and region outlier scenario because of its ability to incorporate spatial autocorrelation while at the same time, revealing the variation between nearest neighbours. In terms of decision-making, all algorithms led to slightly different coefficient estimates, and therefore, may result in distinct decisions for site-specific management. The results outlined here will allow an improved removal of crop yield data points that are potentially problematic. What has been determined here is the recommendation of using Averaged Difference algorithm for cleaning spatial outliers in yield dataset. Identifying the optimal nearest neighbour parameter for the neighbourhood aggregation function is still non-trivial. The recommendation is to specify a large number of nearest neighbours, large enough to capture the region size. Lastly, the unbiased coefficient estimates obtained with Average Difference suggest it is the better method for pre-processing spatial outliers in crop yield data, which underlines its suitability for detecting spatial outlier in the context of on-farm research.

A lucratividade da indústria mineira é diretamente dependente do planejamento adequado de todas as fases de extração e beneficiamento de minério. Cada passo deste processo por sua vez, também é dependente dos resultados da fase anterior. As usinas de beneficiamento, por exemplo, devem ser alimentadas por um material o mais homogêneo possível, o que é garantido por um planejamento adequado de lavra e de forma muito eficaz por pilhas de homogeneização. No entanto, os métodos de estimativa comumente utilizados para prever os teores dos blocos que formam esses sistemas, não medem adequadamente a incerteza associada a este processo de estimativa. Este estudo avalia a eficácia da simulação geoestatística na previsão da variabilidade in situ dos teores e planejamento de pilhas de homogeneização. O método gera múltiplos cenários equiprováveis para o depósito que devem reproduzir os parâmetros estatísticos das amostras, o histograma e o variograma do fenômeno. Para um dado plano de lavra, o conjunto de cenários simulados irá gerar um conjunto de valores equiprováveis para cada pilha de homogeneização. A metodologia proposta foi aplicada a um depósito de fosfato na região central do Brasil. Neste caso de estudo, os teores de P2O5 previstos pelo plano de lavra de curto prazo e amostrados na área industrial foram comparados com o grupo de valores gerados para as pilhas por meio da simulação. A reprodução dos resultados demonstrou a aplicabilidade da metodologia para o depósito em questão. Além disto, a simulação geoestatística demonstrou ser uma ferramenta muito eficiente na previsão da variabilidade in situ dos teores e planejamento de pilhas de homogeneização. / Profits in mineral industry strongly depend on proper planning at all stages of mining and ore processing, and every step of these processes depends on the results from the previous stage. These chains of events can be illustrated, for instance, by the processing plant. To maximize ore recovery, among various factors, the processing plant must be fed by a material as homogeneous as possible minimizing the variance of the head grades that can be achieved initially by a proper mining plan and optimal schedule and more effectively by homogenization piles. The key factor is to know the input grade variance to design a blending system capable of attenuating it. Estimation methods commonly used to predict block grades which form the geological model used for mine planning do not adequately measure the variance associated with these estimates. This study evaluates geostatistical simulation in predicting in situ grades variability and planning blending piles. The method generates multiple, equally probable grade scenarios for the deposit, which reproduce the values of the samples, the histogram, and the variograma of the attribute being simulated. For a given mining plan, the set of simulated scenarios will generate a group of equiprobable values for each homogenization pile. These results provide the means to assess a range of possible values each pile can have. To validate the suggested methodology, the contents of P2O5 obtained by the short-term mining plan and sampled at the processing plant from a large phosphate mine in central Brazil were compared against the simulated values. The results matched adequately demonstrating that geostatistical simulation and pile emulation methodology are efficient tools that could be applied in predicting grades in situ variability and in planning blending piles.

A lucratividade da indústria mineira é diretamente dependente do planejamento adequado de todas as fases de extração e beneficiamento de minério. Cada passo deste processo por sua vez, também é dependente dos resultados da fase anterior. As usinas de beneficiamento, por exemplo, devem ser alimentadas por um material o mais homogêneo possível, o que é garantido por um planejamento adequado de lavra e de forma muito eficaz por pilhas de homogeneização. No entanto, os métodos de estimativa comumente utilizados para prever os teores dos blocos que formam esses sistemas, não medem adequadamente a incerteza associada a este processo de estimativa. Este estudo avalia a eficácia da simulação geoestatística na previsão da variabilidade in situ dos teores e planejamento de pilhas de homogeneização. O método gera múltiplos cenários equiprováveis para o depósito que devem reproduzir os parâmetros estatísticos das amostras, o histograma e o variograma do fenômeno. Para um dado plano de lavra, o conjunto de cenários simulados irá gerar um conjunto de valores equiprováveis para cada pilha de homogeneização. A metodologia proposta foi aplicada a um depósito de fosfato na região central do Brasil. Neste caso de estudo, os teores de P2O5 previstos pelo plano de lavra de curto prazo e amostrados na área industrial foram comparados com o grupo de valores gerados para as pilhas por meio da simulação. A reprodução dos resultados demonstrou a aplicabilidade da metodologia para o depósito em questão. Além disto, a simulação geoestatística demonstrou ser uma ferramenta muito eficiente na previsão da variabilidade in situ dos teores e planejamento de pilhas de homogeneização. / Profits in mineral industry strongly depend on proper planning at all stages of mining and ore processing, and every step of these processes depends on the results from the previous stage. These chains of events can be illustrated, for instance, by the processing plant. To maximize ore recovery, among various factors, the processing plant must be fed by a material as homogeneous as possible minimizing the variance of the head grades that can be achieved initially by a proper mining plan and optimal schedule and more effectively by homogenization piles. The key factor is to know the input grade variance to design a blending system capable of attenuating it. Estimation methods commonly used to predict block grades which form the geological model used for mine planning do not adequately measure the variance associated with these estimates. This study evaluates geostatistical simulation in predicting in situ grades variability and planning blending piles. The method generates multiple, equally probable grade scenarios for the deposit, which reproduce the values of the samples, the histogram, and the variograma of the attribute being simulated. For a given mining plan, the set of simulated scenarios will generate a group of equiprobable values for each homogenization pile. These results provide the means to assess a range of possible values each pile can have. To validate the suggested methodology, the contents of P2O5 obtained by the short-term mining plan and sampled at the processing plant from a large phosphate mine in central Brazil were compared against the simulated values. The results matched adequately demonstrating that geostatistical simulation and pile emulation methodology are efficient tools that could be applied in predicting grades in situ variability and in planning blending piles.

O planejamento de curto prazo em minas a céu aberto exige a definição de poligonais, que representam os sucessivos avanços de lavra. As poligonais, tradicionalmente, são desenhadas em um processo laborioso na tentativa de delinear como minério em qualidade e quantidade de acordo com os limites determinados. O minério delimitado deve apresentar a menor variabilidade em qualidade possível, com o objetivo de maximizar a recuperação na usina de processamento. Essa dissertação visa desenvolver um fluxo do trabalho para definir poligonais de curto prazo de forma automática, além disso, sequenciar todos os blocos de minério de cada polígono de modo a definir uma sequência interconectada lavrável de poligonais. O fluxo do trabalho foi aplicada à incerteza de teores, obtida através de simulações estocásticas. Algoritmos genéticos foram desenvolvidos em linguagem de programação Python e implementados na forma de plug-in no software geoestatístico Ar2GeMS. Múltiplas iterações são criadas para cada avanço individual, gerando regiões (ou poligonais). Então, a região que apresenta menor variabilidade de teores é selecionada. A distribuição de probabilidade dos teores dos blocos em cada avanço é comparada com a distribuição global de teores, calculada a partir de todos os blocos do corpo de minério. Os resultados mostraram que os teores dos blocos abrangidos pelas poligonais criadas dessa forma apresentam teores similares à distribuição de referência, permitindo o sequenciamento de lavra com distribuição de teores mais próximo possível da distribuição global. Modelos equiprováveis permitem avaliar a incerteza associada à solução proposta. / Open-pit short-term planning requieres the definition of polygons identifying the successive mining advances. These polygons are drawn in a labour intensive task attempting to delineate ore with the quantity and quality within established ranges. The ore delineated by the polygons should have the least possible quality variability among them, helping in maximizing ore recovery at the processing plant. This thesis aims at developíng a workflow for drawing short-term polygons automatically, sequencing all ore blocks within each polygon and leading to a mineable and connected sequence of polygons. This workflow is also tested under grade uncertainty obtained through multiple syochastic simulated models. For this, genetics algorithms were developed in Python programming language and pluged in Ar2GeMS geostatistical software. Multiple iterations were generated for each of the individual advances, generating regions or polygons, and selecting the regions of lower grade variability. The blocks probability distribution within each advance were compared to the global distribution, including all blocks within the ore body. Results show that the polygons generated are comprised by block grades similar to the ones from the reference distribution, leading to mining sequence as close as possible to the global maintaining a quasi-satationarity. Equally probable models provide the means to access the uncertainy in the solution provided.

O planejamento de curto prazo em minas a céu aberto exige a definição de poligonais, que representam os sucessivos avanços de lavra. As poligonais, tradicionalmente, são desenhadas em um processo laborioso na tentativa de delinear como minério em qualidade e quantidade de acordo com os limites determinados. O minério delimitado deve apresentar a menor variabilidade em qualidade possível, com o objetivo de maximizar a recuperação na usina de processamento. Essa dissertação visa desenvolver um fluxo do trabalho para definir poligonais de curto prazo de forma automática, além disso, sequenciar todos os blocos de minério de cada polígono de modo a definir uma sequência interconectada lavrável de poligonais. O fluxo do trabalho foi aplicada à incerteza de teores, obtida através de simulações estocásticas. Algoritmos genéticos foram desenvolvidos em linguagem de programação Python e implementados na forma de plug-in no software geoestatístico Ar2GeMS. Múltiplas iterações são criadas para cada avanço individual, gerando regiões (ou poligonais). Então, a região que apresenta menor variabilidade de teores é selecionada. A distribuição de probabilidade dos teores dos blocos em cada avanço é comparada com a distribuição global de teores, calculada a partir de todos os blocos do corpo de minério. Os resultados mostraram que os teores dos blocos abrangidos pelas poligonais criadas dessa forma apresentam teores similares à distribuição de referência, permitindo o sequenciamento de lavra com distribuição de teores mais próximo possível da distribuição global. Modelos equiprováveis permitem avaliar a incerteza associada à solução proposta. / Open-pit short-term planning requieres the definition of polygons identifying the successive mining advances. These polygons are drawn in a labour intensive task attempting to delineate ore with the quantity and quality within established ranges. The ore delineated by the polygons should have the least possible quality variability among them, helping in maximizing ore recovery at the processing plant. This thesis aims at developíng a workflow for drawing short-term polygons automatically, sequencing all ore blocks within each polygon and leading to a mineable and connected sequence of polygons. This workflow is also tested under grade uncertainty obtained through multiple syochastic simulated models. For this, genetics algorithms were developed in Python programming language and pluged in Ar2GeMS geostatistical software. Multiple iterations were generated for each of the individual advances, generating regions or polygons, and selecting the regions of lower grade variability. The blocks probability distribution within each advance were compared to the global distribution, including all blocks within the ore body. Results show that the polygons generated are comprised by block grades similar to the ones from the reference distribution, leading to mining sequence as close as possible to the global maintaining a quasi-satationarity. Equally probable models provide the means to access the uncertainy in the solution provided.

O planejamento de curto prazo em minas a céu aberto exige a definição de poligonais, que representam os sucessivos avanços de lavra. As poligonais, tradicionalmente, são desenhadas em um processo laborioso na tentativa de delinear como minério em qualidade e quantidade de acordo com os limites determinados. O minério delimitado deve apresentar a menor variabilidade em qualidade possível, com o objetivo de maximizar a recuperação na usina de processamento. Essa dissertação visa desenvolver um fluxo do trabalho para definir poligonais de curto prazo de forma automática, além disso, sequenciar todos os blocos de minério de cada polígono de modo a definir uma sequência interconectada lavrável de poligonais. O fluxo do trabalho foi aplicada à incerteza de teores, obtida através de simulações estocásticas. Algoritmos genéticos foram desenvolvidos em linguagem de programação Python e implementados na forma de plug-in no software geoestatístico Ar2GeMS. Múltiplas iterações são criadas para cada avanço individual, gerando regiões (ou poligonais). Então, a região que apresenta menor variabilidade de teores é selecionada. A distribuição de probabilidade dos teores dos blocos em cada avanço é comparada com a distribuição global de teores, calculada a partir de todos os blocos do corpo de minério. Os resultados mostraram que os teores dos blocos abrangidos pelas poligonais criadas dessa forma apresentam teores similares à distribuição de referência, permitindo o sequenciamento de lavra com distribuição de teores mais próximo possível da distribuição global. Modelos equiprováveis permitem avaliar a incerteza associada à solução proposta. / Open-pit short-term planning requieres the definition of polygons identifying the successive mining advances. These polygons are drawn in a labour intensive task attempting to delineate ore with the quantity and quality within established ranges. The ore delineated by the polygons should have the least possible quality variability among them, helping in maximizing ore recovery at the processing plant. This thesis aims at developíng a workflow for drawing short-term polygons automatically, sequencing all ore blocks within each polygon and leading to a mineable and connected sequence of polygons. This workflow is also tested under grade uncertainty obtained through multiple syochastic simulated models. For this, genetics algorithms were developed in Python programming language and pluged in Ar2GeMS geostatistical software. Multiple iterations were generated for each of the individual advances, generating regions or polygons, and selecting the regions of lower grade variability. The blocks probability distribution within each advance were compared to the global distribution, including all blocks within the ore body. Results show that the polygons generated are comprised by block grades similar to the ones from the reference distribution, leading to mining sequence as close as possible to the global maintaining a quasi-satationarity. Equally probable models provide the means to access the uncertainy in the solution provided.

L’objectif de ce travail est double : d’une part, il s’agit de développer une méthodologie intégrée pour la construction d’un modèle géomécanique ainsi que la représentation des incertitudes associées aux propriétés poro-élastiques des roches constitutives, en exploitant l’ensemble des données disponibles et en s’appuyant de façon cohérente sur les modèles de réservoir statique et dynamique classiquement utilisés par les géologues et les ingénieurs réservoir ; d’autre part, il s’agit d’analyser quel est l’impact des hétérogénéités géologiques, souvent négligées, dans la réponse mécanique du réservoir sollicité par son exploitation, et d’aboutir à des incertitudes sur les champs de contraintes et de déplacements, issues des incertitudes sur ces hétérogénéités et leurs paramètres mécaniques. Pour ce faire, une méthodologie intégrée s’appuyant sur des simulations géostatistiques a été développée. Après la construction du cadre géométrique 3D, le remplissage des propriétés au sein du réservoir suit une démarche de simulations géostatistiques 3D emboîtées, dans laquelle la représentation des hétérogénéités lithologiques conditionne la génération des propriétés poro-élastiques. La démarche consiste ensuite à représenter les incertitudes sur le modèle géomécanique par des ensembles de réalisations géostatistiques dont la réponse mécanique est alors calculée avec un simulateur mécanique aux éléments finis. Les incertitudes sur les champs de contraintes et de déformations sont déduites ensuite des différentes réponses mécaniques obtenues. La démarche a été mise en œuvre sur un réservoir réel, dans un environnement fluvio-deltaïque, produisant en Mer du Nord. Dans ce cadre, il a été démontré que les hétérogénéités du réservoir et leurs incertitudes influencent significativement les calculs des champs de contraintes et de déformations, ainsi que les risques mécaniques de rupture. Des incertitudes sur les quantités mécaniques analysées (premier invariant du tenseur des contraintes et subsidence) ont été aussi estimées / This work has two main objectives. The first one is to develop an integrated methodology allowing to build a 3D geomechanical model and also to image the uncertainties attached to the poro-mechanical properties of the constitutive rocks. This geomechanical model should be based on all related available data and should be consistent with the static and dynamic models, currently built by reservoir geologists and engineers. The second objective is to analyse the impact of geological heterogeneities, which are often neglected, in the mechanical response of the reservoir induced by its exploitation, and furthermore to derive uncertainties on the stress and deformation fields related to the uncertainties on the input properties of the geomechanical model. An integrated methodology based on geostatistical simulations is developed. First, the geometric frame is built; then an approach of embedded stochastic simulations is carried out to infill the different reservoir properties, the lithological description constraining the petrophysical and poro-elastic descriptions. The next step is to generate the mechanical responses of the stochastic realisations, using a finite-element mechanical simulator. The uncertainties on the resulting stress and displacement fields are then deduced from the multiple mechanical responses which are computed. This approach is demonstrated on a real field case, a fluvio-deltaic reservoir in North Sea. It is shown on this example that the reservoir heterogeneities and their uncertainties significantly influence the calculations of stress and strain fields, and also the risks of mechanical failure. Uncertainties on the mechanical quantities under analysis (first invariant of the stress tensor and subsidence) are also derived

Das Ziel der vorliegenden Arbeit war die Erstellung eines dreidimensionalen Untergrundmodells der Region Göttingen basierend auf einer geotechnischen Klassifikation der unkosolidierten Sedimente. Die untersuchten Materialen reichen von Lockersedimenten bis hin zu Festgesteinen, werden jedoch in der vorliegenden Arbeit als Boden, Bodenklassen bzw. Bodenkategorien bezeichnet. Diese Studie evaluiert verschiedene Möglichkeiten durch geostatistische Methoden und Simulationen heterogene Untergründe zu erfassen. Derartige Modellierungen stellen ein fundamentales Hilfswerkzeug u.a. in der Geotechnik, im Bergbau, der Ölprospektion sowie in der Hydrogeologie dar. Eine detaillierte Modellierung der benötigten kontinuierlichen Parameter wie z. B. der Porosität, der Permeabilität oder hydraulischen Leitfähigkeit des Untergrundes setzt eine exakte Bestimmung der Grenzen von Fazies- und Bodenkategorien voraus. Der Fokus dieser Arbeit liegt auf der dreidimensionalen Modellierung von Lockergesteinen und deren Klassifikation basierend auf entsprechend geostatistisch ermittelten Kennwerten. Als Methoden wurden konventionelle, pixelbasierende sowie übergangswahrscheinlichkeitsbasierende Markov-Ketten Modelle verwendet. Nach einer generellen statistischen Auswertung der Parameter wird das Vorhandensein bzw. Fehlen einer Bodenkategorie entlang der Bohrlöcher durch Indikatorparameter beschrieben. Der Indikator einer Kategorie eines Probepunkts ist eins wenn die Kategorie vorhanden ist bzw. null wenn sie nicht vorhanden ist. Zwischenstadien können ebenfalls definiert werden. Beispielsweise wird ein Wert von 0.5 definiert falls zwei Kategorien vorhanden sind, der genauen Anteil jedoch nicht näher bekannt ist. Um die stationären Eigenschaften der Indikatorvariablen zu verbessern, werden die initialen Koordinaten in ein neues System, proportional zur Ober- bzw. Unterseite der entsprechenden Modellschicht, transformiert. Im neuen Koordinatenraum werden die entsprechenden Indikatorvariogramme für jede Kategorie für verschiedene Raumrichtungen berechnet. Semi-Variogramme werden in dieser Arbeit, zur besseren Übersicht, ebenfalls als Variogramme bezeichnet. IV Durch ein Indikatorkriging wird die Wahrscheinlichkeit jeder Kategorie an einem Modellknoten berechnet. Basierend auf den berechneten Wahrscheinlichkeiten für die Existenz einer Modellkategorie im vorherigen Schritt wird die wahrscheinlichste Kategorie dem Knoten zugeordnet. Die verwendeten Indikator-Variogramm Modelle und Indikatorkriging Parameter wurden validiert und optimiert. Die Reduktion der Modellknoten und die Auswirkung auf die Präzision des Modells wurden ebenfalls untersucht. Um kleinskalige Variationen der Kategorien auflösen zu können, wurden die entwickelten Methoden angewendet und verglichen. Als Simulationsmethoden wurden "Sequential Indicator Simulation" (SISIM) und der "Transition Probability Markov Chain" (TP/MC) verwendet. Die durchgeführten Studien zeigen, dass die TP/MC Methode generell gute Ergebnisse liefert, insbesondere im Vergleich zur SISIM Methode. Vergleichend werden alternative Methoden für ähnlichen Fragestellungen evaluiert und deren Ineffizienz aufgezeigt. Eine Verbesserung der TP/MC Methoden wird ebenfalls beschrieben und mit Ergebnissen belegt, sowie weitere Vorschläge zur Modifikation der Methoden gegeben. Basierend auf den Ergebnissen wird zur Anwendung der Methode für ähnliche Fragestellungen geraten. Hierfür werden Simulationsauswahl, Tests und Bewertungsysteme vorgeschlagen sowie weitere Studienschwerpunkte beleuchtet. Eine computergestützte Nutzung des Verfahrens, die alle Simulationsschritte umfasst, könnte zukünftig entwickelt werden um die Effizienz zu erhöhen. Die Ergebnisse dieser Studie und nachfolgende Untersuchungen könnten für eine Vielzahl von Fragestellungen im Bergbau, der Erdölindustrie, Geotechnik und Hydrogeologie von Bedeutung sein.