Rozprawy doktorskie na temat „Geostatistics”

The objective of this thesis was to investigate the effectiveness of kriging as a predictor of future prices for copper, lead and zinc on the London Metal Exchange. The annual average metal prices from 1884 to 1986 were deflated into constant price series with reference to a base of 1984 prices. Analysis of the data showed that the requirement of stationarity was satisfied if the price series were divided into three distinct time periods viz. 1884 to 1917; 1918 to 1953; 1954 to 1986. For copper each of the three time periods were studied in detail, but for lead and zinc only the most recent period was included in this thesis. Spherical models gave a good fit to the experimental semi-variograms computed for each metal-time period and were used to predict future prices by ordinary kriging. Universal Kriging was applied to the most recent time period for each metal by fitting a polynomial curve to the price-time series, computing experimental semi-variograms from the residuals and then fitting spherical models which were used to predict future prices. Within the most recent price-time series, a further subdivision was made by taking that portion of the period from the highest price to 1986. Experimental semi-variograms from the residuals from fitted polynomial curves showed pure nugget effect and consequently extrapolation of the polynomial was used as the price predictor. The kriged and extrapolated future price estimates were compared to future prices estimated by a simple random walk using residual sums of squared differences. For four of the five time series analyzed, ordinary kriging produced the best future price estimates. For copper from 1918 to 1953 , the simple random walk was marginally better than ordinary kriging. This was probably due to the low price variability in this period resulting from the Great Depression and government price controls associated with the Second World War and the Korean War. Specific forecasts for 1985 and 1986 were most accurate for copper and lead by universal kriging and most accurate for zinc by ordinary kriging. The results are encouraging and future investigations should include: applying other kriging methods : analyzing daily and monthly prices : comparing results with more sophisticated time series analysis techniques.
Applied Science, Faculty of
Mining Engineering, Keevil Institute of
Graduate

With the ability to collect and store increasingly large datasets on modern computers comes the need to be able to process the data in a way that can be useful to a Geostatistician or application scientist. Although the storage requirements only scale linearly with the number of observations in the dataset, the computational complexity in terms of memory and speed, scale quadratically and cubically respectively for likelihood-based Geostatistics. Various methods have been proposed and are extensively used in an attempt to overcome these complexity issues. This thesis introduces a number of principled techniques for treating large datasets with an emphasis on three main areas: reduced complexity covariance matrices, sparsity in the covariance matrix and parallel algorithms for distributed computation. These techniques are presented individually, but it is also shown how they can be combined to produce techniques for further improving computational efficiency.

Assessment of river rehabilitation and restoration projects, as well as the monitoring of morphological changes in rivers requires collection of hydromorphological parameter data (i.e. depth, velocity and substrate). Field data collection is highly time and cost consuming and thus, effective and efficient monitoring programmes need to be designed. Interpolation techniques are often used to predict values of the variables under study at non measured locations. In this way, it is not necessary to collect detailed data sets of information. The accuracy of these predictions depends upon (i)the method used for the interpolation and/or extrapolation procedure and (ii) the sampling strategy applied for the collection of data. Even though the design of effective sampling strategies are of crucial importance when applying interpolation techniques, little work has been developed to determine the most effective way to collect hydromorphological data for this purpose. This project aimed to define a set of guidelines for effective and efficient hydromorphological data collection in rivers and relate this to the type of river site that is being sampled and to the objective for which the data are being collected. The project is structured in three main sections: spatial problem, the scaling problem and the temporal problem. Spatial problem refers to the location and number of points that need to be collected. Scaling problems focus on the study of the river length that needs to be sampled to characterise the spatial variability of a river site, whilst temporal problems determine how often a river site needs to be sampled to characterise the temporal variability associated with changes in discharge. Intensive depth data sets have been collected at a total of 20 river sites. These data sets have been used to investigate the spatial, temporal and scaling problems through geostatistical theory.

The competition in the world market for iron ore has increased lately. Therefore, an improved method of estimating the ore quality in small working areas has become an attractive cost-cutting strategy in short-term mine plans. Estimated grades of different working areas of a mine form the basis of any short-term mine plan. The generally sparse exploration data obtained during the development phase is not enough to accurately estimate the grades of small working areas. Therefore, additional sample information is often required in any operating mine. The findings of this case study show that better utilization of all available exploration information at this mine would improve estimation of small working areas even without additional face samples. Through the use of kriging variance, this study also determined the optimum face sampling grid, whose spacing turned out to be approximately 100 meters as compared to 50 meters in use today. (Abstract shortened with permission of author.)

A new concept of dispersion (cross) covariance has been introduced for the modeling of spatial scale dependent multivariate correlations. Such correlations between attributes depend on the spatial size of the domain and size of samples in the population and have been modeled by first time in this research. Modeled correlations have been used to introduce a new scale dependent principal component analysis (PCA) method. This method is based on computation of eigen values and vectors from dispersion covariance matrices or scale dependent correlations which can be modeled from integrals of matrix variograms. For second order stationary random functions this PCA converges for large domains to the classic PCA. A new technique for computing variograms from spatial variances have also been developed using derivatives. For completeness, a deeper analysis of the linear model of coregionalizations widely used in multivariate geostatistics has been included as well. This last part leads to a new more sophisticated model we termed "linear combinations coregionalization model." This whole research explains the relationship between different average states and the micro- state of vector random functions in the framework of geostatistics. Examples have been added to illustrate the practical application of the theory. This approach will be useful in all earth sciences and particularly in soil and environmental sciences.

Common implementations of geostatistical methods, kriging and simulation, ignore the fact that geochemical data are usually reported in weight percent, sum to a constant, and are thus compositional in nature. The constant sum implies that rescaling has occurred and this can be shown to produce spurious correlations. Compositional geostatistics is an approach developed to ensure that the constant sum constraint is respected in estimation while removing dependencies on the spurious correlations. This study tests the applicability of this method against the commonly implemented ordinary cokriging method. The sample data are production blast cuttings analyses drawn from a producing iron ore mine in Western Australia. Previous studies using the high spatial density blast hole data and compositional geostatistical approach returned encouraging results, results other practitioners suggested were due to the high spatial density. This assertion is tested through sub-sampling of the initial data to create four subsets of successively lower spatial densities representing densities, spacings, and orientations typical of the different stages of mine development. The same compositional geostatistical approach was then applied to the subsets using jack-knifing to produce estimates at the removed data locations. Although other compositional geostatistical solutions are available, the additive logratio (alr) approach used in this study is the simplest to implement using commercially available software. The advantages of the logratio methodology are the removal of the constant sum constraint, allowing the resulting quantities to range freely within the real space and, importantly, the use of many proven statistical and geostatistical methods. The back transformation of linear combinations of these quantities and associated estimation variances to the constrained sample space is known to be biased; this study used numerical integration by Gauss-Hermite quadrature to overcome this drawback. The Aitchison and Euclidean distances were used to quantify both the univariate and compositional errors between the estimates and original sample values from each estimation method. The errors of each method are analysed using common descriptive and graphical criteria including the standardised residual sum of squares and an assessment of the accuracy and precision. The highest spatial density dataset is equally well reproduced by either method. The compositional method is generally more accurate and precise than the conventional method. In general the compositional error analyses favour the compositional techniques, producing more geologically plausible results, and which sum to the required value. The results support the application of the logratio compositional methodology to low spatial density data over the commonly implemented ordinary cokriging.

Spatial modelling is examined in a model-based geostatistical context using the Gaussian linear mixed model in a likelihood framework. Complex spatial models developed provide practitioners with a practical and best-practice guide for spatial analysis. Adequate modelling theory and matrix algebra are provided to ground the methods demonstrated. A multivariate model over two time points and three-dimensional space is developed which is novel to the field of soil science. Soil organic carbon measurements at three soil depths and two time points from a cropping field with four soil classes are used. The spatial process is assessed for second-order stationarity and anisotropic correlation. Univariate spatial modelling is used to inform bivariate spatial modelling of pre- and post-harvest soil organic carbon at each soil depth. Bivariate modelling is extended to the multivariate level, where both time points and the three soil depths are incorporated in a single model to pool maximum information. A common correlation structure is tested and is supported for the response variable at each of the six time-depth combinations. Separable correlation structures are used for computational efficiency. The difficulty of estimating nugget effects suggests a sub-optimal sampling design. Preferred fitted models are all isotropic. Equations for predictions and the variance of prediction errors are extended from well-known results and maps of predicted values and variance of prediction errors are produced and show close correspondence with observed values. Finally, univariate models for spatially referenced seed counts from small sampling plots are examined within a Gaussian framework using Box-Cox transformations. The discrete nature of the data, small sample size and computational problems hamper model fitting. Anisotropy is examined using a variogram envelope diagnostic technique. ASReml-R software is shown to be a powerful analytical tool for spatial processes.

Knowledge of the spatial distribution of soil textural properties at the watershed scale is important for understanding spatial patterns of water movement, and in determining soil moisture storage and soil hydraulic transport properties. Capturing the heterogeneous nature of the subsurface without exhaustive and costly sampling presents a significant challenge. Soil scientists and geologists have adapted geophysical methods that measure a surrogate property related to the vital underlying process. Apparent electrical conductivity (ECa) is such a proxy, providing a measure of charge mobility due to application of an electric field, and is highly correlated to the electrical conductivity of the soil solution, clay percentage, and water content. Electromagnetic induction (EMI) provides the possibility of obtaining high resolution images of ECa across a landscape to identify subtle changes in subsurface properties. The aim of this study was to better characterize subsurface textural properties using EMI mapping and geostatistical analysis techniques. The effect of variable temperature environments on EMI instrumental response, and ECa - depth relationship were first determined. Then a procedure of repeated EMI mapping at varying soil water content was developed and integrated with temporal stability analysis to capture the time invariant properties of spatial soil texture on an agricultural field. In addition, an EMI imaging approach of densely sampling the subsurface of the Reynolds Mountain East watershed was presented using kriging to interpolate, and Sequential Gaussian Simulation to estimate the uncertainty in the maps. Due to the relative time-invariant characteristics of textural properties, it was possible to correlate clay samples collected over three seasons to ECa data of one mapping event. Kriging methods [ordinary kriging (OK), cokriging (CK), and regression kriging (RK)] were then used to integrate various levels of information (clay percentage, ECa, and spatial location) to produce clay percentage prediction maps. Leave-one-out cross-validation showed that the multivariate estimation methods CK and RK, incorporating the better sampled surrogate ECa, were able to improve the RMSE by 7% and 28%, respectively, relative to OK. Electromagnetic induction measurements provide an important exhaustive layer of information that can improve the quality and resolution of soil property maps used in hydrological and environmental research.

O objetivo desse trabalho foi estabelecer planos de amostragem com redução no tamanho amostral, a partir de conjuntos de dados com dependência espacial, que fossem eficientes na predição de localizações não amostradas e que gerassem estimativas eficientes de características relacionadas na predição espacial. Esses planos amostrais reduzidos foram obtidos por processos de otimização denominados recozimento simulado e algoritmo genético híbrido, considerando a média da variância da predição espacial, obtida pelo método de interpolação chamado krigagem, como função objetivo minimizada. Para isso, utilizaram-se conjuntos de dados simulados, com diferentes valores de alcance e efeito pepita, cujo intuito foi identificar a influência que esses parâmetros exercem na escolha da configuração amostral otimizada. Para cada conjunto de dados simulados, foram obtidas amostras pelos processos de otimização e seus resultados foram comparados aos esquemas de amostragem: aleatório, sistemático, sistemático centrado adicionado de delineamentos menores e sistemático centrado adicionado de pontos próximos. Os resultados mostraram que os planos de amostragem otimizados, principalmente os planos obtidos pelo algoritmo genético híbrido, produziram menores estimativas para a média da variância da krigagem e melhores estimativas para a porcentagem e soma de valores preditos acima do terceiro quartil e do percentil 90, que s~ao características relacionadas na predição espacial. Observou-se, também, que o aumento do tamanho amostral produziu melhores estimativas para todos os resultados analisados e, independente do valor de alcance e efeito pepita, a amostragem otimizada pelo algoritmo genético híbrido produziu melhores resultados. Além disso, obtiveram-se conjuntos amostrais reduzidos de 128 parcelas pelo algoritmo genético híbrido, pelo processo de recozimento simulado e pelas amostragens aleatória e sistemática, para a propriedade química teor de potássio pertencente ao conjunto de dados, com 256 parcelas, de um experimento de agricultura de precisão em uma área experimental. Por intermédio dos dados resultantes dessas amostragens, realizou-se uma analise geoestatística para identificar o comportamento de dependência espacial da variável potássio na área e foram feitas predições espaciais do potássio em localizações n~ao amostradas nessa mesma área. Em todos os esquemas de amostragem utilizados, os valores preditos foram classificados segundo o critério de adubação do potássio no Paraná em culturas de soja (EMATER - Empresa Paranaense de Assistência Técnica e Extensão Rural, 1998). Esses resultados foram comparados com a analise realizada no conjunto de dados inicial e observou-se uma maior similaridade desses resultados com os obtidos pela analise realizada através dos dados da amostragem obtida pelo algoritmo genético híbrido. Assim, tiveram-se evidências de que a redução em 50% do tamanho amostral do conjunto de dados da variável potássio, utilizando nessa redução uma amostragem obtida pelo algoritmo genético híbrido, produziu resultados eficientes para a classificação de adubação de potássio na área em estudo, reduzindo em 50% os custos 8 com analise química do solo, sem grande perda de eficiência nas conclusões obtidas pela predição espacial.
The aim of this work was to establish plans for sampling with reduced in the sample size, from sets of dependent spatial data, and they are eficients in terms of prediction of the nonsampled observations and prediction of linear targets. These plans were obtained by sampling reduced processes optimization of the algorithm called simulated annealing and hybrid genetic algorithm, considering the average kriging variance as objective function to be minimised. Therefore, it was used simulated data sets, With diferent values of range and nugget efect, whose aim was to identify the in uence that these exercise parameters in choosing the sample configuration foptimized. For each set of data simulated samples were obtained through the optimization process and its results were compared to sampling schemes: random, systematic, lattice plus in ll and lattice plus close pairs. The results show that the sampling plans optimized, especially the plans obtained by hybrid genetic algorithm, produced lower estimates for the average kriging variance and best estimates for the percentage and amount of predicted values above the third quartile and the 90 percentile, which are characteristics related to spatial prediction. It was also observed that the increase of sample size produces best estimate for all results analyzed and independent of the value range and nugget efect, sampling optimized by the hybrid genetic algorithm produced better results. In addition, sets up sampling reduced of 128 samples by sampling schemes: hybrid genetic algorithm, simulated annealing, random and systematic, for the property belonging to the chemical potassium set data, with 256 samples, an experiment of precision agriculture, in an experimental area. Through these sampling data, an analysis was carried out geostatistics to identify the behavior of spatial dependence of the variable potassium in the area under study and predictions were made of potassium space in locations not sampled that same area. In all sampling schemes used, the predicted values were classified at the discretion of the potassium fertilization in the cultivation of soybeans in Parana (EMATER-PARANA, 1998). These results were compared with the analysis in the initial set of data and there was a greater similarity of these results with those obtained by the analysis performed by data obtained by the sampling hybrid genetic algorithm. So there has been evidence that the reduction by 50% of the sample size of the data set of variable potassium, using this reduction a sample obtained by the hybrid genetic algorithm, produced efective results for classification of potassium fertilizer in the area under study, reducing by 50% the costs with chemical analysis of soil, without much loss of eficiency in the conclusions obtained by predicting space.

In this dissertation, 3D surface seismic data was integrated with the well logs to be able to define the properties in every location for the reservoir under investigation. To accomplish this task, geostatistical and artificial neural networks (ANN) techniques were employed. First, missing log sets in the study area were estimated using common empirical relationships and ANN. Empirical estimations showed linear dependent results that cannot be generalized. On the other hand, ANNs predicted missing logs with an very high accuracy. Sonic logs were predicted using resistivity logs with 90% correlation coefficient. Second, acoustic impedance property was predicted in the study area. AI estimation first performed using sonic log with GRNN and 88% CC was obtained. AI estimation was repeated using sonic and resistivity logs and the result were improved to 94% CC. In the final part of the study, SGS technique was used with collocated cokriging techniques to estimate NPHI property. Results were varying due to nature of the algorithm. Then, GRNN and RNN algorithms were applied to predict NPHI property. Using optimized GRNN network parameters, NPHI was estimated with high accuracy. Results of the study were showed that ANN provides a powerful solution for reservoir parameter prediction in the study area with its flexibility to find out nonlinear relationships from the existing available data.

PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
PROGRAMA DE EXCELENCIA ACADEMICA
A modelagem de reservatórios consiste em uma tarefa de muita relevância na medida em que permite a representação de uma dada região geológica de interesse. Dada a incerteza envolvida no processo, deseja-se gerar uma grande quantidade de cenários possíveis para se determinar aquele que melhor representa essa região. Há, então, uma forte demanda de se gerar rapidamente cada simulação. Desde a sua origem, diversas metodologias foram propostas para esse propósito e, nas últimas duas décadas, Multiple-Point Geostatistics (MPS) passou a ser a dominante. Essa metodologia é fortemente baseada no conceito de imagem de treinamento (TI) e no uso de suas características, que são denominadas de padrões. No presente trabalho, é proposto um novo método de MPS que combina a aplicação de dois conceitos-chave: a técnica denominada Locality Sensitive Hashing (LSH), que permite a aceleração da busca por padrões similares a um dado objetivo; e a técnica de compressão Run-Length Encoding (RLE), utilizada para acelerar o cálculo da similaridade de Hamming. Foram realizados experimentos com imagens de treinamento tanto categóricas quanto contínuas que evidenciaram que o LSHSIM é computacionalmente eciente e produz realizações de boa qualidade, enquanto gera um espaço de incerteza de tamanho razoável. Em particular, para dados categóricos, os resultados sugerem que o LSHSIM é mais rápido do que o MS-CCSIM, que corresponde a um dos métodos componentes do estado-da-arte.
Reservoir modeling is a very important task that permits the representation of a geological region of interest. Given the uncertainty involved in the process, one wants to generate a considerable number of possible scenarios so as to find those which best represent this region. Then, there is a strong demand for quickly generating each simulation. Since its inception, many methodologies have been proposed for this purpose and, in the last two decades, multiple-point geostatistics (MPS) has been the dominant one. This methodology is strongly based on the concept of training image (TI) and the use of its characteristics, which are called patterns. In this work, we propose a new MPS method that combines the application of a technique called Locality Sensitive Hashing (LSH), which permits to accelerate the search for patterns similar to a target one, with a Run-Length Encoding (RLE) compression technique that speeds up the calculation of the Hamming similarity. We have performed experiments with both categorical and continuous images which showed that LSHSIM is computationally efficient and produce good quality realizations, while achieving a reasonable space of uncertainty. In particular, for categorical data, the results suggest that LSHSIM is faster than MS-CCSIM, one of the state-of-the-art methods.

Motivations and research objectives: During the passage of rain water through a forest canopy two main processes take place. First, water is redistributed; and second, its chemical properties change substantially. The rain water redistribution and the brief contact with plant surfaces results in a large variability of both throughfall and its chemical composition. Since throughfall and its chemistry influence a range of physical, chemical and biological processes at or below the forest floor the understanding of throughfall variability and the prediction of throughfall patterns potentially improves the understanding of near-surface processes in forest ecosystems. This thesis comprises three main research objectives. The first objective is to determine the variability of throughfall and its chemistry, and to investigate some of the controlling factors. Second, I explored throughfall spatial patterns. Finally, I attempted to assess the temporal persistence of throughfall and its chemical composition. Research sites and methods: The thesis is based on investigations in a tropical montane rain forest in Ecuador, and lowland rain forest ecosystems in Brazil and Panama. The first two studies investigate both throughfall and throughfall chemistry following a deterministic approach. The third study investigates throughfall patterns with geostatistical methods, and hence, relies on a stochastic approach. Results and Conclusions: Throughfall is highly variable. The variability of throughfall in tropical forests seems to exceed that of many temperate forests. These differences, however, do not solely reflect ecosystem-inherent characteristics, more likely they also mirror management practices. Apart from biotic factors that influence throughfall variability, rainfall magnitude is an important control. Throughfall solute concentrations and solute deposition are even more variable than throughfall. In contrast to throughfall volumes, the variability of solute deposition shows no clear differences between tropical and temperate forests, hence, biodiversity is not a strong predictor of solute deposition heterogeneity. Many other factors control solute deposition patterns, for instance, solute concentration in rainfall and antecedent dry period. The temporal variability of the latter factors partly accounts for the low temporal persistence of solute deposition. In contrast, measurements of throughfall volume are quite stable over time. Results from the Panamanian research site indicate that wet and dry areas outlast consecutive wet seasons. At this research site, throughfall exhibited only weak or pure nugget autocorrelation structures over the studies lag distances. A close look at the geostatistical tools at hand provided evidence that throughfall datasets, in particular those of large events, require robust variogram estimation if one wants to avoid outlier removal. This finding is important because all geostatistical throughfall studies that have been published so far analyzed their data using the classical, non-robust variogram estimator.
Motivation und Zielsetzung: Wenn Regen durch ein Kronendach fällt lassen sich zwei Prozesse beobachten: das Regenwasser wird umverteilt und die chemische Qualität des Wassers verändert sich erheblich. Die Prozesse im Kronenraum resultieren in einer hohen Variabilität des Bestandsniederschlags und dessen chemischer Zusammensetzung. Bestandsniederschlag beeinflusst eine Reihe von physikalischen, chemischen und biologischen Prozessen am Waldboden. Daher können Untersuchungen zur Variabilität und zu Mustern im Bestandsniederschlag helfen, bodennahe Prozesse besser zu verstehen. Diese Dissertation behandelt hauptsächlich drei Aspekte. Erstens, die Arbeit beschäftigt sich mit der Erfassung der Variabilität im Bestandsniederschlag und dessen chemischer Zusammensetzung, zudem werden Einflussfaktoren dieser Variabilität untersucht. Des Weiteren beschäftigt sich die Arbeit mit räumlichen Mustern des Bestandsniederschlagswassers, und drittens wird die zeitliche Stabilität des Bestandsniederschlags und dessen chemischer Zusammensetzung betrachtet. Untersuchungsgebiete und Methoden: Diese Dissertation basiert auf Untersuchungen in einem tropischen Bergregenwald in Ecuador, sowie Studien in tropischen Tieflandregenwäldern in Brasilien und Panama. Die ersten zwei Studien untersuchen Bestandsniederschlag und dessen chemische Zusammensetzung mit Hilfe deterministischer Methoden. Die Arbeit in Panama nutzt geostatistische Methoden zur Beschreibung von Bestandsniederschlagsmustern und verfolgt somit einen stochastischen Ansatz. Ergebnisse und Schlussfolgerungen: Die Variabilität des Bestandsniederschlages ist hoch; das heißt, die Menge des auf den Waldboden tropfenden Wassers kann sich je nach Standort stark unterscheiden. Diese räumliche Variabilität des Bestandsniederschlags ist in tropischen Wäldern höher als in vielen gemäßigten Waldökosystemen, was nicht allein auf verschiedenen Eigenschaften der Ökosysteme zurückzuführen ist. Vielmehr erklären sich die Unterschiede auch aus verschiedenen Waldnutzungen. Abgesehen von biologischen Faktoren beeinflusst die Regenmenge die Variabilität des Bestandsniederschlags erheblich. Die chemische Zusammensetzung des Bestandsniederschlags weist eine noch höhere Variabilität als der Bestandsniederschlag selbst auf. Unterschiede zwischen tropischen und gemäßigten Wäldern lassen sich hier allerdings nicht erkennen, weshalb die hohe Diversität tropischer Ökosysteme die Heterogenität der chemischen Zusammensetzung des Bestandsniederschlags nicht ausreichend erklärt. Eine Vielzahl anderer Faktoren kontrolliert deshalb die Variabilität der Bestandsniederschlagschemie, beispielsweise die Konzentration gelöster Stoffe im Regenwasser oder die Dauer von Trockenperioden. Deren hohe temporale Variabilität ist verantwortlich für die geringe zeitliche Stabilität von Depositionsmessungen. Im Gegensatz dazu ist die temporale Persistenz von Messungen der Bestandsniederschlagsmenge hoch. Insbesondere die Ergebnisse aus Panama zeigen, dass feuchte und trockene Messpunkte über einen Zeitraum von zwei Regenzeiten fortbestehen. Die räumlichen Bestandsniederschlagsmuster im letztgenannten Untersuchungsgebiet sind schwach bzw. weisen die Struktur eines reinen Nugget-Models auf. Die geostatistische Analyse zeigt, dass vor allem die Daten großer Regenereignisse eine robuste Modellierung des Variogramms erfordern, wenn die willkürliche Entfernung von Fernpunkten in den Daten vermieden werden soll. Dieses Resultat ist insbesondere deshalb von Bedeutung, da alle bisherigen Bestandsniederschlagsstudien den klassischen, nicht-robusten Schätzer benutzen, obwohl das Auftreten von Extremwerten in Bestandsniederschlagsdaten für viele Ökosysteme zu erwarten ist.

Several epidemiological studies suggested that there is an association between incidence and exacerbation of adverse respiratory and cardiovascular health effects and air pollution. Accurate, high resolution maps of ground-level Particulate Matter (PM) are highly awaited for environmental policies and future monitoring stations design. Though the measurements made by the ground stations can ensure a high level of reliability, still they cannot provide full spatial coverage over an area, giving rise among other things to misclassified epidemiological studies. Fine particles are usually categorized by size distribution, known as fractions: PM10 represents the particles with aerodynamic diameter smaller than 10 µm and comprises the thoracic (or coarse) fraction – with diameter in the range 2.5-10 µm – and the smaller inhalable (or fine) fraction. Although including the less dangerous thoracic particles, PM10 measurements are usually far more available and hence lend themselves better for modelling. Spaceborne aerosols products like the ones offered by the polar-orbiting MODerate resolution Imaging Spectrometer (MODIS) are successfully finding practical applications for scientific research studies and, though not previously intended, the Aerosol Optical Thickness (AOT, or simply τ ) from MODIS revealed to have a leading role in the evaluation of surface air quality due to its full spatial (clear-sky constrained) coverage and daily overpasses almost throughout the globe. Despite the “promised land” has not been reached yet, researchers have verified an existing correlation between aerosols and particulate concentrations, rising expectation of air quality models for high-scale environmental characterization. Air quality modelling is generally a challenging application, due to the wide range of sources affecting this variable and the high spatial and temporal variability of the particles, especially over high populated areas with rugged topography and complex meteorological profiles. In this thesis, different variogram-based geostatistical techniques are evaluated to predict the concentrations of PM10, with a focus on the effective advantages brought by AOT from satellites. This work is meant as a guide for students and researchers who are taking their first steps in this specific application, as well as to experts of the field who want to overview geostatistical filling of PM concentrations, and weigh up the usefulness of MODIS imagery. Different areas of study and temporal resolutions will be considered, so as to propose directions and outline conclusions on how this task – still far from being definitively ruled out – should be approached. Aside from modelling, the interactive visualization, extraction and analysis of the model-based predicted maps are also covered, cutting-edge Web-based software architectures based on the Open Geospatial Consortium (OGC) standard services are proposed, giving rise to increased capabilities in the spatio-temporal elaboration of the model results. The availability of spaceborne maps of AOT at an increased nominal resolution of 1×1 km2 has been a unique occasion to experiment their role for air quality issues; the latest algorithmics from leading FOSS-like (Free and Open Source Software) modelling software where learned and used, resulting in several new testing results in a field where variogram-based geostatistics were lacking. Solutions for novel online analysis and visualization capabilities were explored, in order to approach an open and interconnected uncertainty-enabled Web.

In underground construction and foundation engineering uncertainties associated with subsurface properties are inevitable to deal with. Site investigations are expensive to perform, but a limited understanding of the subsurface may result in major problems; which often lead to an unexpected increase in the overall cost of the construction project. This study aims to optimize the pre-investigation program to get as much correct information out from a limited input of resources, thus making it as cost effective as possible. To optimize site investigation using soil-rock sounding three different sampling techniques, a varying number of sample points and two different interpolation methods (Inverse distance weighting and point Kriging) were tested on four modeled reference surfaces. The accuracy of rock surface predictions was evaluated using a 3D gridding and modeling computer software (Surfer 8.02®). Samples with continuously distributed data, resembling profile lines from geophysical surveys were used to evaluate how this could improve the accuracy of the prediction compared to adding additional sampling points. The study explains the correlation between the number of sampling points and the accuracy of the prediction obtained using different interpolators. Most importantly it shows how continuous data significantly improves the accuracy of the rock surface predictions and therefore concludes that geophysical measurement should be used combined with traditional soil rock sounding to optimize the pre-investigation program.

This thesis is concerned with environmental and hydrogeological issues approached by geostatistical methods. All the afforded issues have a common and difficult task to deal with. In particular, there is the need to build the complete spatial distribution of a studied property in a given spatial (or spatiotemporal) domain, using a limited number of unevenly spaced samples and using “expert knowledge”. Unfortunately this is a difficult task affected by uncertainty. Uncertainty about the real complete spatial distribution of the studied property arises from the complexity and heterogeneity of processes involved in the studied phenomena as well as from the characteristics of the available information that is fragmentary and heterogeneous. Uncertainty in the spatial distribution of the studied properties means that many scenarios, representing the spatial distribution of the studied properties, are compatible with the available information. Within a geostatistical framework, taking into account the random as well as the structured (fuzzy) behavior of the spatial phenomena, the spatial uncertainty may be conveniently quantified and analyzed, offering very useful tools for decision-making processes. The first part of the work is dedicated to presenting the geostatistical theory, giving more weight to those aspects (exploratory data analysis, indicator coding of information, use of secondary information, quantification of spatial uncertainty using simulations) that play an important role in hydrogeological and environmental issues. Then, four hydrogeological and environmental issues (figure), whose sites are all located in Veneto Region (Italy), are approached by using geostatistical methods. Case study 1. Stochastic geomodeling: “Porto Marghera” test site In this case study we are interested in quantifying the spatial uncertainty relative to the 3D geological architecture, in correspondence of the industrial site of “Porto Marghera” (lagoon of Venice, Italy). To perform this task 769 boreholes are available, permitting the geostatistical modeling of a 3D spatial domain with a area extension of some hectares and a vertical thickness of 18 m . The sedimentary environment investigated is mainly represented by Pleistocene fluvio-lacustrine deposits and secondarily by Holocene lagoonal and fluvial deposits. The information contained in the analyzed stratigraphic database is codified according to granulometric compositional classes. After performing an exploratory data analysis, the spatial continuity of each compositional class is studied calculating a 3D experimental indicator variogram. Then, the inference process of the continuity structures for each compositional class is conducted. Finally, indicator kriging and sequential indicator simulation procedures are performed to assess local as well as spatial uncertainty. The results of indicative estimations and simulations are discussed, with particular attention to the use of geostatistical geomodeling tools in the field of groundwater modeling. Case study 2. Soil pollution in a dismantled industrial area The study area is located in the city of Padova (Veneto region, NE Italy). The industrial activities present in this area since 1950 have produced very high concentrations of Pb down to a depth of 7 m, interesting the unsaturated as well as the saturated zones. In many studies of polluted sites, the geometry of the investigated volume is highly anisotropic. Generally we have an extension of some hectares in the horizontal plane and of a few meters in depth. It is likely that different horizontal spatial continuity structures in pollution distribution are found at different depths both for the layered nature of the medium and for the transition from unsaturated to saturated conditions. In such conditions the decision to divide a 3D problem into 1D and 2D problems can be useful. For this reason the study is approached in two phases. First, after analyzing the spatial distribution of Pb values along the vertical direction, a kriging with trend interpolation is performed along boreholes. Then, the geostatistical study is performed along seven horizontal layers, positioned at different depths between ground level and 5 m in depth, leading to the construction of 500 realizations of the Pb distribution, using a simulated annealing procedure. Finally, results are presented and discussed for each layer in terms of median and probability maps. Case study 3. Spatial distribution of temperature in the geothermal euganean field The Euganean geothermal reservoir is principally located in fractured Mesozoic limestone. The analysis of 186 ground water temperature measurements, ranging between 60°C and 86°C, reveals that the spatial distribution of temperatures along the geothermal area is characterized by some degree of spatial continuity. This pattern in the spatial distribution of temperatures to some extent seems related to the structural framework of the area and should be taken into account when quantifying the uncertainty in the spatial distribution of temperature. Geostatistical tools are good candidates for this task and in particular a simulated annealing procedure is used to build many scenarios (simulations) representing the spatial distribution of temperatures. These simulations reproduce the spatial continuity and the connectivity of high temperature values revealed from data analysis. The post processing of these simulations permits the evaluation of the uncertainty in the spatial distribution of temperature and above all the individuation of new potential exploitation areas. Case study 4. Nitrate pollution in groundwater The geostatistical methodology is applied to a groundwater pollution case in an area situated near Padova (northeast Italy). The study of pollution mainly involves the unconfined aquifer developed in an alluvial plain, with the subsoil consisting of an undifferentiated cover of gravel with sand, deposited by the Brenta river, locally interbedded with clay layers. Qualitative degradation of water is strongly related to industrial and agricultural activities. The water samples collected show the presence of relatively high concentrations of nitrate. The data set analyzed is composed of 3361 nitrate concentration values relative to water samples collected between the 1990 and 1994. Poor sampling strategy permits only a partial study of the spatiotemporal distribution of nitrate. After some consideration about the spatial and temporal variability of nitrate concentration it is possible to perform a complete geostatistical study for a densely sampled month (March ‘92). For this month a simulated annealing approach is used to build conditional simulations of the spatial distribution of nitrate. The simulations are post-processed and the results discussed.
In questa tesi una serie di problematiche di tipo idrogeologico ed ambientale vengono affrontate secondo la metodologia geostatistica. Le casistiche affrontate sono caratterizzate da un compito comune. In particolare, si e` interessati a conoscere in maniera esaustiva la distribuzione spaziale (o spazio-temporale) di una proprietà-fisico chimica a partire da un insieme frammentario ed eterogeneo di informazioni. Tale compito, inevitabilmente, e` caratterizzato da incertezza. L’incertezza circa la reale distribuzione spaziale della proprietà studiata deriva sia dalla complessità ed eterogeneità dei processi fisico-chimici coinvolti nei fenomeni analizzati sia dalla frammentarietà ed eterogeneità dell’informazione disponibile. In pratica, più scenari della distribuzione spaziale della proprietà fisico-chimica di interesse sono compatibili con le informazioni in nostro possesso. La metodologia geostatistica, permettendo di utilizzare la struttura sfumata che sovente caratterizza la distribuzione spaziale delle proprietà studiate, consente l’analisi e la quantificazione dell’incertezza spaziale, offrendo una serie di strumenti estremamente utili per operare eventuali processi decisionali. Nella parte iniziale della tesi, ci si dedica all’esposizione e all’approfondimento di quelle tematiche (analisi esplorativa dei dati, codifica indicativa dell’informazione, quantificazione dell’incertezza spaziale mediante la costruzioni di simulazioni condizionate) che risultano particolarmente rilevanti nel contesto idrogeologico ed ambientale. Quindi, quattro casistiche di studio (vedi figura) di ambito idrogeologico ed ambientale sono affrontate utilizzando gli strumenti geostatistici. Caso di studio 1. Ricostruzione probabilistiche del sottosuolo: il caso di Porto Marghera In questo caso di studio si e` interessati a quantificare l’incertezza spaziale circa la distribuzione spaziale 3D dei corpi sedimentari, in corrispondenza del sito industriale di “Porto Marghera”, posto ai margini della laguna di Venezia. Allo scopo vi sono a disposizione 769 carotaggi, ubicati su un’area di pochi ettari di estensione ed interessanti i primi 18 m del sottosuolo. Gli ambienti sedimentari incontrati sono rappresentati principalmente da depositi fluviali e fluvio-lacustri pleistocenici e solo marginalmente da depositi lagunari e fluviali olocenici. L’informazione contenuta nel database stratigrafico e` stata convenientemente codificata in termini di classi composizionali granulometriche. Conseguentemente, per ogni classe, si e` provveduto ad eseguire un’analisi esplorativa dei dati e lo studio della continuità spaziale, mediante il calcolo del variogramma indicativo 3D. Quindi, per le classi composizionali definite, e` stata eseguita l’inferenza dei modelli di variogramma. Infine, delle procedure di kriging indicativo e di simulazione sequenziale indicativa sono state utilizzate al fine della quantificazione dell’incertezza locale e dell’incertezza spaziale, relativamente alla distribuzione spaziale delle classi composizionali. I risultati delle elaborazioni sono analizzati e commentati, con particolar riguardo al loro utilizzo in ambito della modellistica del flusso sotterraneo. Caso di studio 2. Inquinamento del suolo in un area industriale dismessa L’area di studio e` situata nella città di Padova (Regione Veneto, Italia). Le attività industriali presenti nell’area dal 1950 hanno portato ad un degrado ambientale rilevante, come indicato, anche, dall’elevate concentrazioni di Piombo che si rinvengono nel suolo sino ad un profondità di 7 m, sia in corrispondenza della zona insatura sia della zona satura. Nella gran parte dei siti inquinati la geometria del dominio dimensionale investigato risulta notevolmente anisotropa. Generalmente e` caratterizzata da un’estensione nel piano orizzontale di alcuni ettari e un’estensione lungo la direzione verticale di pochi metri. Inoltre, le caratteristiche della distribuzione spaziale orizzontale degli inquinanti tendono a cambiare con la profondità, sia a causa della natura stratificata ed eterogenea del sottosuolo sia per effetto del passaggio tra condizioni insature e sature. In tali casi può risultare ragionevole suddividere il problema 3D in una serie di problemi 2D, scomponendo il dominio di studio in una serie di livelli orizzontali posti a differenti profondità. Per seguire tale approccio, in una prima fase e` stata studiata la distribuzione spaziale del piombo lungo la verticale e si e` utilizzato il kriging con deriva per eseguire delle stime lungo i carotaggi. Quindi, si e` proceduto alla studio geostatistico della distribuzione spaziale bidimensionale del piombo di una serie di livelli orizzontali, distribuiti dal piano campagna fino a 5 m di profondità. Per ognuno di tali livelli, utilizzando una procedura di “simulated annealing” sono state generate 500 simulazioni della distribuzione spaziale del piombo. Conseguentemente, i risultati delle post elaborazioni delle simulazioni sono presentati e commentati. Caso di studio 3. Distribuzione delle temperature nel bacino termale euganeo Il reservoir termale considerato e` principalmente localizzato nel calcare fratturato mesozoico dell’area euganea (Regione Veneto, Italia). L’analisi dei 186 valori di temperatura delle acque termali, oscillanti tra i 60 oC e gli 86 oC, evidenzia la presenza di una certa continuità nella distribuzione spaziale delle temperature. La struttura di continuità spaziale sembra in qualche modo relazionata alle caratteristiche tettonico-strutturali dell’area e deve essere presa in considerazione nel processo di quantificazione dell’incertezza della distribuzione spaziale delle temperature. Allo scopo le metodologie geostatistiche risultano particolarmente utili; a riguardo si e` utilizzata una procedura di “simulated annealing” al fine di costruire delle simulazioni condizionate riproducenti la continuità spaziale delle temperature e la connettività di valori elevati di temperatura. I risultati delle post-elaborazioni sono quindi presentati e commentati, con particolare riguardo all’individuazione di nuove aree di estrazione di acque termali. Caso di studio 4. Inquinamento da nitrati nelle acque sotterranee I metodi di analisi geostatistici sono applicati allo studio di un fenomeno inquinante delle acque sotterranee, di un area situata a nord di Padova (Italia). Lo studio dell’inquinamento riguarda, principalmente, l’acquifero non confinato che si sviluppa nella pianura alluvionale, costituito da depositi di ghiaia e sabbia, localmente interdigitati a depositi argillosi, deposti dal fiume Brenta. Il degrado qualitativo delle acque e` principalmente legato alle attività agricole ed industriali presenti nell’area. Il dataset analizzato e` composto da 3361 misurazioni delle concentrazioni di nitrati effettuate tra il 1990 ed il 1994. La cattiva strategia di campionamento permette solo uno studio solo parziale spazio-temporale del fenomeno. Oltre ad effettuare alcune considerazioni circa la variabilità spaziale e temporale dei nitrati e` stato possibile effettuare uno studio geostatistico per un mese (marzo `92) particolarmente campionato. Per tale subset e` stata utilizzata una procedura di “simulated annealing” per la costruzione di simulazioni condizionate, rappresentanti la distribuzione spaziale dei nitrati. I risultati delle post-elaborazioni sono presentati e commentati.

Rock physical properties are usually associated with important geologic features within mineral deposits and can be used to define the location, depth and size of the deposit, type of ore, or physical property contrast between the host and country rock. Geophysical surveys are sensitive to physical properties and therefore are widely used in mining exploration, especially in concealed terrains. The surveys can be performed at multiple scales, resulting in corresponding physical property datasets at different scales. Survey scale can vary from core or hand sample, involving few cubic centimeters, to regional-scale surveys providing information about physical property contrasts between distinct regional geological features. The understanding of the relationship between the physical property distributions with the sample volume (e.g. district, deposit, and drill-hole scale) is required where point scale physical property measurements are going to be consistent with measurements at larger volumetric scales during the integration of data for geophysical modeling The approach used to address the problem of understanding the scaling relations of physical properties, was achieved by considering them as second order stationary regionalized variables and then applying the random function formalism, provided by geostatistics theory. Geostatistics provide the required framework to characterize, quantify, model and link the spatial variability of the random variable at the different volumetric scales. The aim of this study is to apply geostatistics to effectively integrate data collected at several scales and bring knowledge to the understanding of the scaling relations of magnetic susceptibility. For this purpose, measurements of magnetic susceptibility available from Flin Flon copper-zinc district in Canada will be used. The data available at point scale were collected with hand portable magnetic susceptibility meter. The larger volumetric scale dataset were acquired using frequency domain electromagnetic instruments capable of measuring larger sample volumes, and then used to obtain magnetic susceptibility models using geophysical inversion algorithms. Once different scale models of magnetic susceptibility were available, quantification of the scaling relation using geostatistics, specifically variogram models and dispersion variance were determined. The understanding provided by the scaling analysis of the Flin-Flon magnetic data is applied to data from the Rio Blanco copper district in central Chile. Magnetic susceptibility measurements collected with a hand magnetic susceptibility meter on drill-core is integrated in larger scale volumes used for geophysical inversion modeling of regional scale airborne magnetic field measurements to recover magnetic susceptibility models. The methodology resulting from this application of geostatistics is used to address the problem of integrating multiple scales of physical property data in an effective way. The resulting physical property models capture the small-scale magnetic susceptibility variability observed and can guide larger-scale variability within geophysical inversion models. Establishing reliable statistical correlations between physical properties and rock units controlling ore within deposits are crucial steps leading predictive mine exploration tools. Any numerical modeling approach to establish these correlations should consider in some way the scaling nature of both physical property and ore content.

Characterization of aquifers hydraulic parameters is a difficult task that requires field information. Most of the time the hydrogeologist relies on a group of values coming from different test to interpret the hydrogeological setting and possibly, generate a model. However, getting the best from this information can be challenging. In this thesis, three cases are explored. First, hydraulic conductivities associated with measurement scale of the order of 10−1 m and collected during an extensive field campaign near Tübingen, Germany, are analyzed. Estimates are provided at coinciding locations in the system using: the empirical Kozeny-Carman formulation, providing conductivity values, based on particle size distribution, and borehole impeller-type flowmeter tests, which infer conductivity from measurements of vertical flows within a borehole. Correlation between the two sets of estimates is virtually absent. However, statistics of the natural logarithm of both sets at the site are similar in terms of mean values and differ in terms of variogram ranges and sample variances. This is consistent with the fact that the two types of estimates can be associated with different (albeit comparable) measurement (support) scales. It also matches published results on interpretations of variability of geostatistical descriptors of hydraulic parameters on multiple observation scales. The analysis strengthens the idea that hydraulic conductivity values and associated key geostatistical descriptors inferred from different methodologies and at similar observation scales (of the order of tens of cm) are not readily comparable and should not be embedded blindly into a flow (and eventually transport) prediction model. Second, a data-adapted kernel regression method, originally developed for image processing and reconstruction is modified and used for the delineation of facies. This non-parametric methodology uses both the spatial and the sample value distribution, to produce for each data point a locally adaptive steering kernel function, self-adjusting the kernel to the direction of highest local spatial correlation. The method is shown to outperform the nearest-neighbor classification (NNC) in a number of synthetic aquifers whenever the available number of data is small and randomly distributed. Still, in the limiting case, when the domain is profusely sampled, both the steering kernel method and the NNC method converge to the true solution. Simulations are finally used to explore which parameters of the locally adaptive kernel function yield optimal reconstruction results in typical field settings. It is shown that, in practice, a rule of thumb can be used to get suboptimal results, which are best when key prior information such as facies proportions is used. Third, the effect of water temperature fluctuation on the hydraulic conductivity profile of coarse sediments beneath an artificial recharge facility is model and compared with field data. Due to the high permeability, water travels at a high rate, and therefore also water with different temperature is also present on the sediment under the pond at different moments, this translates into different hydraulic conductivity values within the same layer, even though all the other parameters are the same for this layer. Differences of almost 79% in hydraulic conductivity were observed for the model temperatures (2 °C – 25 °C). This variation of hydraulic conductivity in the sediment below the infiltration pond when water with varying temperature enters the sediment, causes the infiltration velocity to change with time and produces the observed fluctuation on the field measurements.
La caracterización de los parámetros hidráulicos de los acuíferos es una tarea difícil que requiere información de campo. La mayoría de las veces el hidrogeólogo se basa en un grupo de valores procedentes de diferentes pruebas para interpretar la configuración hidrogeológica y posiblemente , generar un modelo . Sin embargo, obtener lo mejor de esta información puede ser un reto. En esta tesis se analizan tres casos. Primero, se analizan las conductividades hidráulicas asociadas a una escala de medición del orden de 10 m− 1 y obtenidas durante una extensa campaña de campo cerca de Tübingen, Alemania. Las estimaciones se obtuvieron en puntos coincidentes en el sitio, mediante: la formulación empírica de Kozeny - Carman, proporcionando valores de conductividad, con base en la distribución de tamaño de partículas y las pruebas del medidor de caudal de tipo impulsor en el pozo, el cual infiere las medidas de conductividad a partir de los flujos verticales dentro de un pozo. La correlación entre los dos conjuntos de estimaciones es prácticamente ausente. Sin embargo, las estadísticas del logaritmo natural de ambos conjuntos en el lugar son similares en términos de valores medios y difieren en términos de rangos del variograma y varianzas de muestra. Esto es consecuente con el hecho de que los dos tipos de estimaciones pueden estar asociados con escalas de apoyo de medición diferentes (aunque comparables). También coincide con los resultados publicados sobre la interpretación de la variabilidad de los descriptores geoestadísticos de parámetros hidráulicos en múltiples escalas de observación . El análisis refuerza la idea de que los valores de conductividad hidráulica y descriptores geoestadísticos clave asociados al inferirse de diferentes metodologías y en las escalas de observación similares (en el caso del orden de decenas de cm) no son fácilmente comparables y debe ser utilizados con cuidado en la modelación de flujo (y eventualmente, el transporte) del agua subterránea. En segundo lugar, un método de regresión kernel adaptado a datos, originalmente desarrollado para el procesamiento y la reconstrucción de imágenes se modificó y se utiliza para la delimitación de las facies. Esta metodología no paramétrica utiliza tanto la distribución espacial como el valor de la muestra, para producir en cada punto de datos una función kernel de dirección localmente adaptativo, con ajuste automático del kernel a la dirección de mayor correlación espacial local. Se demuestra que este método supera el NNC (por su acrónimo en inglés nearest-neighbor classification) en varios casos de acuíferos sintéticos donde el número de datos disponibles es pequeño y la distribución es aleatoria. Sin embargo, en el caso límite, cuando hay un gran número de muestras, tanto en el método kernel adaptado a la dirección local como el método de NNC convergen a la solución verdadera. Las simulaciones son finalmente utilizadas para explorar cuáles parámetros de la función kernel localmente adaptado dan resultados óptimos en la reconstrucción de resultados en escenarios típicos de campo. Se demuestra que, en la práctica, una regla general puede ser utilizada para obtener resultados casi óptimos, los cuales mejoran cuando se utiliza información clave como la proporción de facies. En tercer lugar, se modela el efecto de la fluctuación de la temperatura del agua sobre la conductividad hidráulica de sedimentos gruesos debajo de una instalación de recarga artificial y se compara con datos de campo. Debido a la alta permeabilidad, el agua se desplaza a alta velocidad alta, y por lo tanto, agua con temperatura diferente también está presente en el sedimento bajo el estanque en diferentes momentos, esto se traduce en diferentes valores de conductividad hidráulica dentro de la misma capa, a pesar de que todos los demás parámetros son los mismos para esta capa. Se observaron diferencias de casi 79 % en la conductividad hidráulica en el modelo, para las temperaturas utilizadas (2 º C - 25 º C ). Esta variación de la conductividad hidráulica en el sedimento por debajo de la balsa de infiltración cuando el agua de temperatura variable entra en el sedimento, causa un cambio en la velocidad de infiltración con el tiempo y produce las fluctuacciones observadas en las mediciones de campo.

PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
Na área de Exploração e Produção (EeP) de petróleo, o estudo minucioso das características de um reservatório é imperativo para a criação de modelos de simulação que representem adequadamente as suas propriedades petrofísicas. A disponibilidade de um modelo adequado é fundamental para a obtenção de previsões acertadas acerca da produção do reservatório, e isso impacta diretamente a tomada de decisões gerenciais. Devido às incertezas inerentes ao processo de caracterização, ao longo da vida produtiva do reservatório, periodicamente o seu modelo de simulação correspondente precisa ser ajustado. Todavia, a tarefa de ajustar as propriedades do modelo se traduz em um problema de otimização complexo, onde o número de variáveis envolvidas é tão maior quanto maior for a quantidade de blocos que compõem a malha do modelo de simulação. Na maioria das vezes esses ajustes envolvem processos empíricos que demandam elevada carga de trabalho do especialista. Esta pesquisa investiga e avalia uma nova técnica computacional híbrida, que combina Algoritmos Genéticos e Geoestatística Multiponto, para a otimização de propriedades em modelos de reservatórios. Os resultados obtidos demonstram a robustez e a confiabilidade da solução proposta, uma vez que, diferentemente das abordagens tradicionalmente adotadas, é capaz de gerar modelos que não apenas proporcionam um ajuste adequado das curvas de produção, mas também que respeitam as características geológicas do reservatório.
In the Exploration and Production (EeP) of oil, the detailed study of reservoir characteristics is imperative for the creation of simulation models that adequately represent their petrophysical properties. The availability of an appropriate model is fundamental to obtaining accurate predictions about the reservoir production. In addition, this impacts directly the management decisions. Due to the uncertainties inherent in the characterization process, along the productive period of the reservoir, its corresponding simulation model needs to be matched periodically. However, the task of matching the model properties represents a complex optimization problem. In this case, the number of variables involved increases with the number of blocks that make up the grid of the simulation model. In most cases these matches involve empirical processes that take too much time of an expert. This research investigates and evaluates a new hybrid computer technique, which combines Genetic Algorithms and Multipoint Geostatistics, for the optimization of properties in reservoir models. The results demonstrate the robustness and reliability of the proposed solution. Unlike traditional approaches, it is able to generate models that not only provide a proper match of the production curves, but also satisfies the geological characteristics of the reservoir.

A geostatistical inverse method of estimating hydraulic parameters of a heterogeneous porous medium at discrete points in space, called pilot points, is presented. In this inverse method the parameter estimation problem is posed as a nonlinear optimization problem with a likelihood based objective function. The likelihood based objective function is expressed in terms of head residuals at head measurement locations in the flow domain, where head residuals are the differences between measured and model-predicted head values. Model predictions of head at each iteration of the optimization problem are obtained by solving a forward problem that is based on nonlocal conditional ensemble mean flow equations. Nonlocal moment equations make possible optimal deterministic predictions of fluid flow in randomly heterogenous porous media as well as assessment of the associated predictive uncertainty. In this work, the nonlocal moment equations are approximated to second order in the standard deviation of log-transformed hydraulic conductivity, and are solved using the finite element method. To enhance computational efficiency, computations are carried out in the complex Laplace-transform space, after which the results are inverted numerically to the real temporal domain for analysis and presentation. Whereas a forward solution can be conditioned on known values of hydraulic parameters, inversion allows further conditioning of the solution on measurements of system state variables, as well as for the estimation of unknown hydraulic parameters. The Levenberg-Marquardt algorithm is used to solve the optimization problem. The inverse method is illustrated through two numerical examples where parameter estimates and the corresponding predictions of system state are conditioned on measurements of head only, and on measurements of head and log-transformed hydraulic conductivity with prior information. An example in which predictions of system state are conditioned only on measurements of log-conductivity is also included for comparison. A fourth example is included in which the estimation of spatially constant specific storage is demonstrated. In all the examples, a superimposed mean uniform and convergent transient flow field through a bounded square domain is used. The examples show that conditioning on measurements of both head and hydraulic parameters with prior information yields more reliable (low uncertainty and good fit) predictions of system state, than when such information is not incorporated into the estimation process.

Carbonate strata preserve indicators of local marine environments through time. Such indicators often include microfossils that have relatively unique conditions under which they can survive, including light, nutrients, salinity, and especially water temperature. As such, microfossils are environmental proxies. When these microfossils are preserved in the rock record, they constitute key components of depositional facies. Spence et al. (2004, 2007) has proposed several approaches for determining the facies of a given stratigraphic succession based upon these proxies. Cluster analysis can be used to determine microfossil groups that represent specific environmental conditions. Identifying which microfossil groups exist through time can indicate local environmental change. When new observations (microfossils) are found, classification analysis can be used to predict group membership. Kristen Briggs (2005) identified the microfossils present in sedimentary strata within a specific time interval (Morrowan) of Pennsylvanian-age rocks. In this study we expand analysis to overlying Atokan and Desmoinesian strata. The Bird Spring Formation in Arrow Canyon, Nevada records cycles of environmental change as evidenced by changes in microfossils. Our research investigates cluster and classification analyses as tools for determining the marine facies succession. Light, nutrients, salinity, and water temperature are very dependent on water depth; therefore, our analyses essentially indicate the relative rise and fall of sea-level during Early to Middle Pennsylvanian time.

One critical consideration in the design of buildings constructed in the western United States is the weight of settled snow on the roof of the structure. Engineers are tasked with selecting a design snow load that ensures that the building is safe and reliable, without making the construction overly expensive. Western states use historical snow records at weather stations scattered throughout the region to estimate appropriate design snow loads. Various mapping techniques are then used to predict design snow loads between the weather stations. Each state uses different mapping techniques to create their snow load requirements, yet these different techniques have never been compared. In addition, none of the current mapping techniques can account for the uncertainty in the design snow load estimates. We address both issues by formally comparing the existing mapping techniques, as well as creating a new mapping technique that allows the estimated design snow loads to be represented as an interval of values, rather than a single value. In the process, we have improved upon existing methods for creating design snow load requirements and have produced a new tool capable of handling uncertain climate data.

As land-cover conversion continues to expand into ever more remote areas in the humid tropics, montane rainforests are increasingly threatened. In the south Ecuadorian Andes, they are not only subject to man-made disturbances but also to naturally occurring landslides. I was interested in the impact of this ecosystem dynamics on a key parameter of the hydrologic cycle, the soil saturated hydraulic conductivity (synonym: permeability; Ks from here on), because it is a sensitive indicator for soil disturbances. My general objective was to quantify the effects of the regional natural and human disturbances on the saturated hydraulic conductivity and to describe the resulting spatial-temporal patterns. The main hypotheses were: 1) disturbances cause an apparent displacement of the less permeable soil layer towards the surface, either due to a loss of the permeable surface soil after land-sliding, or as a consequence of the surface soil compaction under cattle pastures; 2) ‘recovery’ from disturbance, either because of landslide re-vegetation or because of secondary succession after pasture abandonment, involves an apparent displacement of the less permeable layer back towards the original depth an 3) disturbances cause a simplification of the Ks spatial structure, i.e. the spatially dependent random variation diminishes; the subsequent recovery entails the re-establishment of the original structure. In my first study, I developed a synthesis of recent geostatistical research regarding its applicability to soil hydraulic data, including exploratory data analysis and variogram estimation techniques; I subsequently evaluated the results in terms of spatial prediction uncertainty. Concerning the exploratory data analysis, my main results were: 1) Gaussian uni- and bivariate distributions of the log-transformed data; 2) the existence of significant local trends; 3) no need for robust estimation; 4) no anisotropic variation. I found partly considerable differences in covariance parameters resulting from different variogram estimation techniques, which, in the framework of spatial prediction, were mainly reflected in the spatial connectivity of the Ks-field. Ignoring the trend component and an arbitrary use of robust estimators, however, would have the most severe consequences in this respect. Regarding variogram modeling, I encouraged restricted maximum likelihood estimation because of its accuracy and independence on the selected lags needed for experimental variograms. The second study dealt with the Ks spatial-temporal pattern in the sequences of natural and man-made disturbances characteristic for the montane rainforest study area. To investigate the disturbance effects both on global means and the spatial structure of Ks, a combined design-and model-based sampling approach was used for field-measurements at soil depths of 12.5, 20, and 50 cm (n=30-150/depth) under landslides of different ages (2 and 8 years), under actively grazed pasture, fallows following pasture abandonment (2 to 25 years of age), and under natural forest. Concerning global means, our main findings were 1) global means of the soil permeability generally decrease with increasing soil depth; 2) no significant Ks differences can be observed among landslides and compared to the natural forest; 3) a distinct permeability decrease of two orders of magnitude occurs after forest conversion to pasture at shallow soil depths, and 4) the slow regeneration process after pasture abandonment requires at least one decade. Regarding the Ks spatial structure, we found that 1) disturbances affect the Ks spatial structure in the topsoil, and 2) the largest differences in spatial patterns are associated with the subsoil permeability. In summary, the regional landslide activity seems to affect soil hydrology to a marginal extend only, which is in contrast to the pronounced drop of Ks after forest conversion. We used this spatial-temporal information combined with local rain intensities to assess the partitioning of rainfall into vertical and lateral flowpaths under undisturbed, disturbed, and regenerating land-cover types in the third study. It turned out that 1) the montane rainforest is characterized by prevailing vertical flowpaths in the topsoil, which can switch to lateral directions below 20 cm depth for a small number of rain events, which may, however, transport a high portion of the annual runoff; 2) similar hydrological flowpaths occur under the landslides except for a somewhat higher probability of impermeable layer formation in the topsoil of a young landslide, and 3) pronounced differences in runoff components can be observed for the human disturbance sequence involving the development of near-surface impeding layers for 24, 44, and 8 % of rain events for pasture, a two-year-old fallow, and a ten-year-old fallow, respectively.
Der tropische Bergregenwald in den Südecuadorianischen Anden unterliegt sowohl anthropogenen Eingriffen, d.h. der Umwandlung von Naturwald in Rinderweiden, als auch natürlichen Störungen in der Form von Hangrutschen. Ziel meiner Arbeit war es, die Auswirkungen dieser regionalen Störungsdynamik auf einen Schlüsselparameter des hydrologischen Kreislaufs, die gesättigte hydraulische Wasserleitfähigkeit (Ks), zu untersuchen und die resultierenden raum-zeitlichen Muster zu beschreiben. In der ersten Studie habe ich eine Synthese aktueller geostatistischer Forschung hinsichtlich ihrer Eignung für die Analyse bodenhydrologischer Daten entwickelt. Diese beinhaltet explorative Datenanalyse und verschiedene Techniken zur Schätzung der Kovarianzparameter; die Ergebnisse habe ich in Bezug auf die Ungenauigkeit räumlicher Vorhersagen bewertet. Es hat sich dabei herausgestellt, dass die Schätztechniken teilweise beachtliche Unterschiede in den Parametern hervorrufen, welche sich hauptsächlich in der räumlichen Konnektivität widergespiegeln. Die wichtigste Rolle im Zusammenhang mit der räumlichen Vorhersage kommt jedoch den vorgeordneten explorativen Analyseschritten zu. In der zweiten Studie habe ich mich mit der Beschreibung des raum-zeitlichen Muster der Wasserleitfähigkeit in den anthropogenen und natürlichen Störungsgradienten beschäftigt. Wichtigste Ergebnisse waren, dass es keine signifikanten Unterschiede der Wasserleitfähigkeit zwischen den verschieden alten Hangrutschen und dem Naturwald gibt. Daraus lässt sich schließen, dass die natürlichen Störungen im Untersuchungsgebiet lediglich marginale Auswirkungen auf die Bodenhydrology haben. Das steht in starkem Kontrast zum anthropogenen Störungskreislauf: die Wasserleitfähigkeit im Weideboden hat gegenüber dem Naturwald um zwei Größenordnungen abgenommen; eine „Erholung“ nach Nutzungsaufgabe scheint mindestens ein Jahrzehnt in Anspruch zu nehmen. Die räumlichen Abhängigkeit von Ks in den Oberböden von Wald und einer alten Brache ist stärker als in jenen der gestörten Flächen, was auf eine störungsbedingte Beeinträchtigung der räumlichen Struktur in geringer Bodentiefe schließen lässt. In der dritten Studie habe ich diese raum-zeitlichen Informationen mit dem örtlichen Niederschlagsregime in Verbindung gebracht, um Rückschlüsse auf die Auswirkungen der störungsbedingten Änderungen von Ks auf hydrologische Fließwege zu ziehen. Es hat sich gezeigt, dass im tropischen Bergregenwald und unter Hangrutschen ubiquitäre Tiefenversickerung dominiert, es allerdings zu einer Verschiebung in laterale Fließrichtungen für die seltenen intensiven Regenereignisse kommen kann. Anthropogene Störungen gehen mit einer um bis zu 50 Prozent erhöheren Wahrscheinlichkeit des Auftretens oberflächennaher Stauschichten einher, was die Bedeutung lateraler Fließwege erhöht. Dies trifft in vergleichbarer Größenordnung auch auf ein Vergleichsökosystem im Tieflandregenwald zu.

Aquesta tesi estudia com estimar la distribució de les variables regionalitzades l'espai mostral i l'escala de les quals admeten una estructura d'espai Euclidià. Apliquem el principi del treball en coordenades: triem una base ortonormal, fem estadística sobre les coordenades de les dades, i apliquem els output a la base per tal de recuperar un resultat en el mateix espai original. Aplicant-ho a les variables regionalitzades, obtenim una aproximació única consistent, que generalitza les conegudes propietats de les tècniques de kriging a diversos espais mostrals: dades reals, positives o composicionals (vectors de components positives amb suma constant) són tractades com casos particulars. D'aquesta manera, es generalitza la geostadística lineal, i s'ofereix solucions a coneguts problemes de la no-lineal, tot adaptant la mesura i els criteris de representativitat (i.e., mitjanes) a les dades tractades. L'estimador per a dades positives coincideix amb una mitjana geomètrica ponderada, equivalent a l'estimació de la mediana, sense cap dels problemes del clàssic kriging lognormal. El cas composicional ofereix solucions equivalents, però a més permet estimar vectors de probabilitat multinomial. Amb una aproximació bayesiana preliminar, el kriging de composicions esdevé també una alternativa consistent al kriging indicador. Aquesta tècnica s'empra per estimar funcions de probabilitat de variables qualsevol, malgrat que sovint ofereix estimacions negatives, cosa que s'evita amb l'alternativa proposada. La utilitat d'aquest conjunt de tècniques es comprova estudiant la contaminació per amoníac a una estació de control automàtic de la qualitat de l'aigua de la conca de la Tordera, i es conclou que només fent servir les tècniques proposades hom pot detectar en quins instants l'amoni es transforma en amoníac en una concentració superior a la legalment permesa.
This Thesis presents an estimation procedure for the distribution of regionalized variables with sample space and scale admitting an Euclidean structure. We apply the principle of working on coordinates: choose an orthonormal basis; do statistics on the coordinates of your observations on that basis; and, by applying the output to the basis, you will recover a result within the original space. Applying this procedure to regionalized variables, we obtain a unified, consistent method, with the same properties of classical linear kriging techniques, but valid for several sample spaces: real data, positive data and compositions (vectors of positive components summing up to a constant) are regarded as particular cases. In this way we generalize the linear kriging techniques, and offer a solution to several well-known problems of the non-linear ones, by adapting the measure of the space and the averaging criterion (the way means are computed) to the data. The obtained estimator for positive variables is a weighted geometric mean, equivalent to estimate the median, which has none of the drawback of classical lognormal kriging. For compositional data, equivalent results are obtained, but which also serve to treat multinomial probability vectors. By combining this with a preliminary Bayesian estimation, our kriging for compositions become also a valid alternative to indicator kriging, without its order-relation problems (i.e. the rather-usual negative estimates of some probabilities). These techniques are validated by studying the ammonia pollution hazard in an automatic water quality control station placed in a small Mediterranean river. Only the proposed techniques allow us to assess when the secondary pollution by ammonia exceeds the existing legal threshold.

[eng] The main objective proposed in this doctoral thesis was focused on the study and development of a solution for the remote sensing of the submarine topographic relief, using for this, inexpensive equipment. Here we focus in three works that altogether will improve the remote sensing process for underwater medium using sonars as the main relief data acquisition system. The problem was systematically addressed since the previous work in the master thesis, constituting three stages: 1) building a prototype data extraction platform, 2) data acquisition and 3) data processing. In the first stage was developed a prototype taking as a reference the modular structure and the software design applied in AUVI project (Acosta 2008), and besides it was used the model of autonomous navigation system developed to AutoTracker project (Acosta et al., 2005), this stage and part of the following one were developed in the master thesis. In the second stage, it was done the survey planning and the acoustic data extraction including navigational data in three different places: i) On the cove “Estancia”, located in Palma, Mallorca island/Spain, where we used the prototype developed in the first stage of this work as a platform to data extraction; ii) “Alfeite Arsenal” Port, located on the Tejo River, in Almada/Portugal into the context of robotics exercises promoted by the Navy of Portugal (REX2014). In this location, it was used the robotic vehicle ZARCO from the Oceansys Lab, through cooperative work with the Oceansys Lab. research group at the University of Porto (UP)/INESC in Portugal and finally, iii) in the “Bay of All Saints”, near the city of Salvador/Brazil, where were performed some missions to collect data using hydrographic survey boats in cooperation with the Federal University of Bahia (UFBA) and Belov Engineering - Port Engineering and Hydrographic Services Company, both located in Salvador/Bahia. Finally, the third stage, that is the main body of this thesis, was characterized by the data analysis and comparison between several datasets. In this stage, studies had been conducted to verify the feasibility of the use of spatial statistical algorithms in the process of bathymetric data interpolation without any ancillary information to support the prediction. We determined an optimized procedure for estimating the unsampled points, hence it was validated using a regular cross-validation method and a comparative validation method to compare the estimated data with a second dataset acquired in the same region and acting as a Merit Figure. The average discrepancy between the estimated data and Merit Figure data value was 25 cm, it is below the acceptable error for bathymetric data at depths below 30m (IHO 2012). In addition, an algorithm based on the Stochastic Resonance (SR) theory was developed. It consists in applying white noise in an optimal intensity level to improve the contrasts of acoustic images generated by a side Sonar Scan (SSS). The SR theory also, was used as a basis for development of a weak signals detection algorithm in sensing applications. Regarding the sensors application for measure remote sensing physical variables, we could cite the magnetic field meters (magnetometers), and inertial sensors (accelerometers and gyroscopes), in this study was performed a simulation of Chua's circuit operating in a chaotic regime as a sensor, where we could determine successfully the region of system solution into the strange attractor, using, for this, the technique of residence time, which will be defined along this thesis. The entire set of modules, techniques and processes described in this work proposed one solution to the remote sensing problem applied to the underwater environment, and give the opportunity to develop in more deep way future works in sensor integration, algorithms and data acquisition platform.
[cat] L'objectiu principal proposat en aquesta tesi doctoral es va centrar en l'estudi i desenvolupament d'una solució per a la detecció remota del relleu topogràfic submarí, utilitzant per a això un equip econòmic. Aquí ens centrem en tres treballs que en total milloraran el procés de teledetecció per al medi submarí utilitzant sonars com el principal sistema d'adquisició de dades de relleu. El problema es va abordar sistemàticament des del treball anterior a la tesi de màster, que constava de tres etapes: 1) construcció d'una plataforma d'extracció de dades prototip, 2) adquisició de dades i 3) tractament de dades. En la primera etapa es va desenvolupar un prototip prenent com a referència l'estructura modular i el disseny de programari aplicat en el projecte AUVI (Acosta 2008), a més d'utilitzar el model de sistema de navegació autònom desenvolupat per al projecte AutoTracker (Acosta et al., 2005 ), aquesta etapa i una part de la següent es van desenvolupar en la tesi de màster. En la segona etapa, es va realitzar la planificació de l'enquesta i l'extracció de dades acústiques, incloses les dades de navegació en tres llocs diferents: i) A la cala "Estancia", situada a Palma, illa de Mallorca / Espanya, on utilitzem el prototip desenvolupat a la primera etapa d'aquest treball com a plataforma d'extracció de dades; ii) Port "Alfeite Arsenal", ubicat al riu Tajo, a Almada / Portugal, en el context dels exercicis de robòtica promoguts per l'Armada de Portugal (REX2014). En aquesta ubicació, es va utilitzar el vehicle robotitzat ZARCO del laboratori Oceansys, a través del treball cooperatiu amb l'Oceansys Lab. grup d'investigació de la Universitat de Porto (UP) / INESC a Portugal i, finalment, iii) a la "Badia de Tots Sants", a prop de la ciutat de Salvador / Brasil, on es van realitzar algunes missions per recollir dades utilitzant vaixells d'enquestes hidrogràfiques en cooperació amb la Universitat Federal de Bahia (UFBA) i Belov Engineering - Port Engineering and Hydrographic Services Company, ambdós ubicats a Salvador / Bahia. Finalment, la tercera etapa, que és el cos principal d'aquesta tesi, es va caracteritzar per l'anàlisi de dades i la comparació entre diversos conjunts de dades. En aquesta etapa, s'han realitzat estudis per verificar la viabilitat de l'ús d'algoritmes estadístics espacials en el procés d'interpolació de dades batimètriques sense cap tipus d'informació auxiliar per a la predicció. Es va determinar un procediment optimitzat per estimar els punts sense mostrejar, per tant, es va validar mitjançant un mètode de validació de mètodes regular i un mètode de validació comparatiu per comparar les dades estimades amb un segon conjunt de dades adquirit a la mateixa regió i actuant com a Figura de mèrit. La discrepància mitjana entre les dades estimades i el valor de dades de Merit Figure va ser de 25 cm, per sota de l'error acceptable per a dades batimètriques a profunditats inferiors a 30 m (IHO 2012). A més, es va desenvolupar un algorisme basat en la teoria de la ressonància estocàstica (SR). Consisteix en aplicar soroll blanc en un nivell d'intensitat òptima per millorar els contrastos d'imatges acústiques generades per un costat Sonar Scan (SSS). La teoria del SR també es va utilitzar com a base per al desenvolupament d'un algoritme de detecció de senyals feble en la detecció d'aplicacions. Pel que fa a l'aplicació de sensors per a la mesura de les variables físiques de control remot, podríem citar els mesuradors de camp magnètic (magnetòmetres) i els sensors inercials (acceleròmetres i giroscopis), en aquest estudi es va realitzar una simulació del circuit de Chua que funciona en un règim caòtic com a sensor, on podríem determinar amb èxit la regió de la solució del sistema en l'estrany atractor, utilitzant, per a això, la tècnica del temps de residència, que es definirà al llarg d'aquesta tesi. Tot el conjunt de mòduls, tècniques i processos descrits en aquest treball proposen una solució al problema de teledetecció aplicat a l'entorn submarí i permeten desenvolupar de manera més profunda futurs treballs en integració de sensors, algorismes i plataforma d'adquisició de dades..
[spa] El principal objetivo propuesto en esta tesis doctoral se centró en el estudio y desarrollo de una solución para la detección remota del relieve topográfico submarino, utilizando para esto, equipos de bajo costo. Aquí nos enfocamos en tres trabajos que en conjunto mejorarán el proceso de detección remota para medios subacuáticos usando sonares como el principal sistema de adquisición de datos de alivio. El problema fue abordado sistemáticamente desde el trabajo anterior en la tesis de maestría, constituyendo tres etapas: 1) construcción de una plataforma prototipo de extracción de datos, 2) adquisición de datos y 3) procesamiento de datos. En la primera etapa se desarrolló un prototipo tomando como referencia la estructura modular y el diseño de software aplicado en el proyecto AUVI (Acosta 2008), y además se utilizó el modelo de sistema de navegación autónomo desarrollado para el proyecto AutoTracker (Acosta et al., 2005 ), esta etapa y parte de la siguiente se desarrollaron en la tesis de maestría. En la segunda etapa, se realizó la planificación de la encuesta y la extracción de datos acústicos, incluyendo datos de navegación en tres lugares diferentes: i) En la cala "Estancia", ubicada en Palma, isla de Mallorca / España, donde utilizamos el prototipo desarrollado en el primera etapa de este trabajo como una plataforma para la extracción de datos; ii) Puerto "Alfeite Arsenal", ubicado en el río Tajo, en Almada / Portugal en el contexto de ejercicios de robótica promovidos por la Armada de Portugal (REX2014). En esta ubicación, se utilizó el vehículo robótico ZARCO del Laboratorio Oceansys, a través del trabajo cooperativo con el Laboratorio Oceansys. grupo de investigación en la Universidad de Oporto (UP) / INESC en Portugal y finalmente, iii) en la "Bahía de Todos los Santos", cerca de la ciudad de Salvador / Brasil, donde se realizaron algunas misiones para recopilar datos utilizando barcos hidrográficos en cooperación con la Universidad Federal de Bahía (UFBA) y Belov Engineering - Compañía de Ingeniería Portuaria y Servicios Hidrográficos, ambas ubicadas en Salvador / Bahía. Finalmente, la tercera etapa, que es el cuerpo principal de esta tesis, se caracterizó por el análisis de datos y la comparación entre varios conjuntos de datos. En esta etapa, se realizaron estudios para verificar la viabilidad del uso de algoritmos estadísticos espaciales en el proceso de interpolación de datos batimétricos sin ninguna información auxiliar para respaldar la predicción. Determinamos un procedimiento optimizado para estimar los puntos no muestreados, por lo que se validó utilizando un método de validación cruzada regular y un método de validación comparativa para comparar los datos estimados con un segundo conjunto de datos adquiridos en la misma región y actuando como una figura de mérito. La discrepancia promedio entre los datos estimados y el valor de los datos de Merit Figure fue de 25 cm, está por debajo del error aceptable para los datos batimétricos a profundidades por debajo de 30 m (OHI 2012). Además, se desarrolló un algoritmo basado en la teoría de la Resonancia Estocástica (SR). Consiste en aplicar ruido blanco en un nivel de intensidad óptimo para mejorar los contrastes de las imágenes acústicas generadas por un Sonar Scan lateral (SSS). La teoría SR también se usó como base para el desarrollo de un algoritmo de detección de señales débiles en aplicaciones de detección. En cuanto a la aplicación de sensores para medir variables físicas de teledetección, podríamos citar los medidores de campo magnético (magnetómetros) y sensores inerciales (acelerómetros y giroscopios), en este estudio se realizó una simulación del circuito de Chua operando en un régimen caótico como sensor, donde pudimos determinar con éxito la región de la solución del sistema en el atractor extraño, utilizando, para ello, la técnica del tiempo de residencia, que se definirá a lo largo de esta tesis. El conjunto completo de módulos, técnicas y procesos descritos en este trabajo propuso una solución al problema de teledetección aplicado al entorno subacuático, y brinda la oportunidad de desarrollar de manera más profunda futuros trabajos de integración de sensores, algoritmos y plataforma de adquisición de datos.
[por] O objetivo principal proposto nesta tese de doutorado foi focado no estudo e desenvolvimento de uma solução para o sensoriamento remoto do alívio topográfico submarino, usando para isso, equipamentos baratos. Aqui nos concentramos em três trabalhos que, em conjunto, melhorarão o processo de sensoriamento remoto para o meio subaquático, utilizando os sonares como o principal sistema de aquisição de dados de alívio. O problema foi sistematicamente abordado desde o trabalho anterior na tese de mestrado, constituindo três etapas: 1) construção de um protótipo de plataforma de extração de dados, 2) aquisição de dados e 3) processamento de dados. Na primeira etapa foi desenvolvido um protótipo tomando como referência a estrutura modular e o projeto de software aplicado no projeto AUVI (Acosta 2008), e além disso, utilizou-se o modelo de sistema de navegação autônomo desenvolvido para o projeto AutoTracker (Acosta et al., 2005 ), este estágio e parte do seguinte foram desenvolvidos na tese de mestrado. Na segunda etapa, foi feito o planejamento da pesquisa e a extração de dados acústicos, incluindo dados de navegação em três lugares diferentes: i) Na enseada "Estancia", localizada em Palma, Ilha de Maiorca / Espanha, onde usamos o protótipo desenvolvido no primeira etapa deste trabalho como plataforma para a extração de dados; ii) Porto do "Alfeite Arsenal", localizado no rio Tejo, em Almada / Portugal no contexto de exercícios de robótica promovidos pela Marinha de Portugal (REX2014). Nessa localização, utilizou-se o veículo robotizado ZARCO do Laboratório Oceansys, através do trabalho cooperativo com o Oceansys Lab. grupo de pesquisa na Universidade do Porto (UP) / INESC em Portugal e, finalmente, iii) na "Baía de Todos os Santos", perto da cidade de Salvador / Brasil, onde foram realizadas algumas missões para coletar dados usando embarcações hidrográficas em cooperação com a Universidade Federal da Bahia (UFBA) e a Engenharia Belov - Empresa de Engenharia de Portos e Hidrográficos, ambos localizados em Salvador / Bahia. Finalmente, o terceiro estágio, que é o corpo principal desta tese, foi caracterizado pela análise de dados e comparação entre vários conjuntos de dados. Nesta fase, foram realizados estudos para verificar a viabilidade do uso de algoritmos estatísticos espaciais no processo de interpolação de dados batimétricos sem qualquer informação auxiliar para sustentar a predição. Determinamos um procedimento otimizado para estimar os pontos não amostrados, portanto, foi validado usando um método de validação cruzada regular e um método de validação comparativa para comparar os dados estimados com um segundo conjunto de dados adquirido na mesma região e atuando como uma Figura de mérito. A discrepância média entre os dados estimados eo valor de dados da Figura de Mérito foi de 25 cm, está abaixo do erro aceitável para dados batimétricos a profundidades abaixo de 30 m (IHO 2012). Além disso, um algoritmo baseado na teoria da Ressonância Estocástica (SR) foi desenvolvido. Consiste na aplicação de ruído branco em um nível de intensidade ótimo para melhorar os contrastes de imagens acústicas geradas por um lado de Sonar Scan (SSS). A teoria SR também foi utilizada como base para o desenvolvimento de um algoritmo de detecção de sinais fracos em aplicações de detecção. Em relação ao aplicativo de sensores para medir as variáveis físicas de sensoriamento remoto, podemos citar os medidores de campo magnético (magnetômetros) e sensores inerciais (acelerômetros e giroscópios), neste estudo realizou-se uma simulação do circuito de Chua operando em regime caótico como sensor, onde podemos determinar com sucesso a região da solução do sistema no atrativo estranho, usando, para isso, a técnica de tempo de residência, que será definida ao longo desta tese. Todo o conjunto de módulos, técnicas e processos descritos neste trabalho propôs uma solução para o problema de sensoriamento remoto aplicado ao ambiente subaquático e oferece a oportunidade de desenvolver de forma mais profunda os futuros trabalhos em integração de sensores, algoritmos e plataforma de aquisição de dados.

Near infrared reflectance spectroscopy (NIRS) and geostatistical techniques were used to predict diet quality of sub-Saharan African (SSA) livestock, and to create cokriged estimated diet quality maps for cattle across a landscape. Rations of native vegetation were stall-fed to cattle (Bos indicus), sheep (Ovis aries), and goats (Capra hircus) to generate diet-fecal pair data. Trials were conducted in Ethiopia, Kenya, Uganda, Tanzania, and Ghana. Historical data from Ethiopia, Nigeria, and Niger were included. Diet samples were analyzed for crude protein (CP%), and digestible organic matter (DOM%), while feces were scanned for NIR spectra. NIRS equations were developed from data using modified partial least square (MPLS) regression. Coefficients of determination (R2) of CP for cattle, sheep, and goats were 0.92, 0.95, and 0.97, with corresponding standard errors of calibration (SEC) being 0.90, 0.79, and 0.80, respectively. Standard errors of cross validation (SECV) for CP were 1.12%, 1.08%, and 1.03% for cattle, sheep, and goats, respectively. R2 and SEC values for DOM were 0.88, 0.94, 0.94 and 2.82%, 1.68%, and 2.65%, for cattle, sheep, and goats, respectively. Corresponding SECV values for DOM were 3.26%, 2.07%, and 3.30%, respectively. The statistics reported were within the acceptable limits for NIRS calibrations. The results indicate that dietary CP and DOM of free-ranging SSA livestock can be predicted with the same precision as that of conventional wet chemistry methods. The cattle equation was used to predict cattle fecal samples collected, from February to August 2000, from selected households located within the northern Ghana savanna. The predicted CP% and DOM% were used with Normalized Differential Vegetation Index (NDVI) data, and cokriging technique to create diet quality maps for March and July 2000 for the northern Ghana savanna. Cross validation results indicated a moderate capability of cokriging to estimate predicted CP% for March (r2 = 0.687, SEp = 1.736) and July (r2 = 0.513, SEp = 1.558). Cokriged-estimated DOM value for July was above average (r2 = 0.584, SEp = 3.611), while March DOM% estimation was rather poor (r2 = 0.132, SEp = 3.891). The techniques of cokriging and creation of diet quality maps were moderately successful in this study.

We sampled forest stands in upland forests of the Southeastern US along a chronosequence of a replicated successional forest sere (1, 6, 10, 25, and 80 years) to elucidate the temporal changes in soil spatial heterogeneity. Samples were collected from loblolly pine plantations representing reorganization through aggradation phases of succession, and from one set of oak-hickory stands to signify the steady-state phase of the model. These trends are characterized and compared to a conceptual model of pattern dynamics. Variability in soil properties (NO3, NH4, pH, Total N, Total C) and forest floor litter at scales relevant to individual plants was quantified using univariate and geostatistical procedures. Global variation (using both coefficient of variation and standard deviation), patch size and proportion of spatially structured variation were examined for individual variables at each successional stage. These patterns were also averaged to produce a generalized model of spatial heterogeneity change during succession. Individual variables often showed differing patterns. However, when patterns from individual variables were averaged, overall patterns emerged. Early in succession global variability was largest and patch sizes were smallest. As succession progressed, trends in the data showed that global variability decreased and patch sizes increased to the middle stage of succession. Both of these trends fit our conceptual model of pattern dynamics. However, the slopes in these trends were not significant at alpha=0.05.
Master of Science

Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2009.
Title from electronic title page (viewed Sep. 3, 2009). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Environmental Sciences and Engineering." Discipline: Environmental Sciences and Engineering; Department/School: Public Health.

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

Understanding how soil variability changes with spatial scale is critical to our ability to understand and model soil processes at scales relevant to decision makers. This thesis uses legacy data to address the ongoing challenge of understanding soil spatial variability in a number of complementary ways. We use a range of information: precision agriculture studies; compiled point datasets; and remotely observed raster datasets. We use classical geostatistics, but introduce a new framework for comparing variability of spatial properties across scales. My thesis considers soil spatial variability from a number of geostatistical angles. We find the following: • Field scale variograms show differing variance across several magnitudes. Further work is required to ensure consistency between survey design, experimental methodology and statistical methodology if these results are to become useful for comparison. • Declustering is a useful tool to deal with the patchy design of legacy data. It is not a replacement for an evenly distributed dataset, but it does allow the use of legacy data which would otherwise have limited utility. • A framework which allows ‘roughness’ to be expressed as a continuous variable appears to fit the data better than the mono-fractal or multi-fractal framework generally associated with multi–scale modelling of soil spatial variability. • Soil appears to have a similar degree of stochasticity to short range topographic variability, and a higher degree of stochasticity at short ranges (less than 10km and 100km) than vegetation and Radiometrics respectively. • At longer ranges of variability (i.e. around 100km) only rainfall and height above sea level show distinctly different stochasticity. • Global variograms show strong isotropy, unlike the variograms for the Australian continent.

The support of a soil sample defines the size and shape of the volume of soil material that is collected and then analysed to give a single datum. This includes both the horizontal and vertical dimensions of the sampled material. For instance, in the vertical dimension some samples might be collected over 10-cm intervals, whilst others might be over 30-cm intervals, giving data with different supports. In horizontal space, data might represent the value of a soil property in a single soil core, whilst others might be measurements of a sample composed of multiple composited soil cores collected from locations across a sampling unit. Support can refer to that on which the data are collected, or to that on which predictions are required, and in both cases can play an important role in mapping soil properties. Generally, the larger the extent of the sample support, the more variation is averaged out of the data. Hence composite soil samples are often collected to reduce noise in the data, and predictions calculated on block support to produce smoother maps. Geostatistical approaches have proven to be extremely useful for modelling and mapping the spatial distributions of soil properties, although they have most commonly been applied under the assumption that the sample supports of all data are identical. In this thesis, we investigate some aspects of sample support, and how data from different sample supports might be used in the same geostatistical analysis. We consider four specific types of support, two where the data differ in their vertical supports, and two where they differ in their horizontal supports. Our general strategy is to employ a model-based geostatistical approach, based on the formulation of a statistical model that describes the distribution of all raw measurements whilst accounting for their different supports. This same statistical model is also applied for prediction, again accounting for prediction sample support. Our aim in each research chapter is to describe and test methods that can adequately deal with each sample-support issue, and to investigate whether the proposed methods can be used to analyse such data and give (i) reliable inference, (ii) competitive predictions when compared with existing methods and (iii) a fair assessment of prediction uncertainty.

Geographic Information Systems (GIS) used in concert with statistical and geostatistical software provide the geologist with a powerful tool for processing, visualizing and analysing geoscience data for mineral exploration applications. This thesis focuses on different methods for analysing, visualizing and integrating geochemical data sampled from various media (rock, till, soil, humus), with other types of geoscience data. Different methods for defining geochemical anomalies and separating geochemical anomalies due to mineralization from other lithologic or surficial factors (i.e. true from false anomalies) are investigated. With respect to lithogeochemical data, this includes methods to distinguish between altered and un-altered samples, methods (normalization) for identifying lithologic from mineralization effects, and various statistical and visual methods for identifying anomalous geochemical concentrations from background. With respect to surficial geochemical data, methods for identifying bedrock signatures, and scavenging effects are presented. In addition, a new algorithm, the dispersal train identification algorithm (DTIA), is presented which broadly helps to identify and characterize anisotropies in till data due to glacial dispersion and more specifically identifies potential dispersal trains using a number of statistical parameters. The issue of interpolation of geochemical data is addressed and methods for determining whether geochemical data should or should not be interpolated are presented. New methods for visualizing geochemical data using red-green-blue (RGB) ternary displays are illustrated. Finally data techniques for integrating geochemical data with other geoscience data to produce mineral prospectivity maps are demonstrated. Both data and knowledge-driven GIS modeling methodologies are used (and compared) for producing prospectivity maps. New ways of preparing geochemical data for input to modeling are demonstrated with the aim of getting the most out of your data for mineral exploration purposes. Processing geochemical data by sub-populations, either by geographic unit (i.e., lithology) or by geochemical classification and alteration style was useful for better identification of geochemical anomalies, with respect to background, and for assessing varying alteration styles. Normal probability plots of geochemical concentrations based on spatial (lithologic) divisions and Principal Component Analysis (PCA) were found to be particularly useful for identifying geochemical anomalies and for identifying associations between major oxide elements that in turn reflect different alteration styles. (Abstract shortened by UMI.)

Spatial uncertainty modelling and prediction of a set of regionalized dependent variables from various sample spaces (e.g. continuous and categorical) is a common challenge for geoscience modellers and many geoscience applications such as evaluation of mineral resources, characterization of oil reservoirs or hydrology of groundwater. To consider the complex statistical and spatial relationships, categorical data such as rock types, soil types, alteration units, and continental crustal blocks should be modelled jointly with other continuous attributes (e.g. porosity, permeability, seismic velocity, mineral and geochemical compositions or pollutant concentration). These multivariate geospatial data normally have complex statistical and spatial relationships which should be honoured in the predicted models. Continuous variables in the form of percentages, proportions, frequencies, and concentrations are compositional which means they are non-negative values representing some parts of a whole. Such data carry just relative information and the constant sum constraint forces at least one covariance to be negative and induces spurious statistical and spatial correlations. As a result, classical (geo)statistical techniques should not be implemented on the original compositional data. Several geostatistical techniques have been developed recently for the spatial modelling of compositional data. However, few of these consider the joint statistical and/or spatial relationships of regionalized compositional data with the other dependent categorical information. This PhD thesis explores and introduces approaches to spatial modelling of regionalized compositional and categorical data. The first proposed approach is in the multiple-point geostatistics framework, where the direct sampling algorithm is developed for joint simulation of compositional and categorical data. The second proposed method is based on two-point geostatistics and is useful for the situation where a large and representative training image is not available or difficult to build. Approaches to geostatistical simulation of regionalized compositions consisting of several populations are explored and investigated. The multi-population characteristic is usually related to a dependent categorical variable (e.g. rock type, soil type, and land use). Finally, a hybrid predictive model based on the advanced geostatistical simulation techniques for compositional data and machine learning is introduced. Such a hybrid model has the ability to rank and select features internally, which is useful for geoscience process discovery analysis. The proposed techniques were evaluated via several case studies and results supported their usefulness and applicability.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
A emissão de CO2 do solo (FCO2) apresenta alta variabilidade espacial, sendo devida a grande dependência espacial existente nas propriedades do solo que a influenciam. Neste estudo objetivou-se (i) caracterizar e relacionar a variabilidade e a distribuição espacial da FCO2, temperatura do solo, porosidade livre de água (PLA), teor de matéria orgânica do solo (MO) e densidade do solo (Ds), (ii) avaliar a acurácia dos resultados fornecidos pelo método da krigagem ordinária (KO) e simulação sequencial Gaussiana (SSG), e (iii) avaliar a incerteza na predição da variabilidade espacial das FCO2 e demais propriedades utilizando a SSG. O estudo foi conduzido em uma malha amostral regular de 60 x 60 m2 com 141 pontos, com espaçamento mínimo variando de 0,50 a 10 m, instalada em área de cana-de-açúcar. Nestes pontos foram avaliados a FCO2, temperatura do solo, PLA, determinadas com base na média de 07 dias de avaliação, MO e Ds. Todas as variáveis apresentaram estrutura de dependência espacial, sendo ajustados modelos Gaussianos, esféricos e exponenciais. A configuração da malha amostral e possivelmente a presença de espessa camada de resíduos da cultura sobre o solo influenciaram a estrutura de variabilidade espacial da FCO2, temperatura e MO. FCO2 apresentou correlações positivas com a MO (r = 0,25, p < 0,05) e PLA (r = 0,27, p < 0,01) e negativa com a Ds (r = - 0,41, p < 0,01). No entanto, quando os valores digitais estimados espacialmente (N=8.833) são considerados, a PLA passa a ser a principal variável responsável pelas características espaciais da FCO2, apresentando correlação de 0,26 (p < 0,01). As simulações individuais propiciaram, para todas as variáveis analisadas, melhor reprodução das funções de distribuição acumuladas (fdac), e dos variogramas em comparação...
The soil CO2 emission (FCO2) has high spatial variability, which caused due to the strong spatial dependence in soil properties that influence it. This study aimed to (i) to characterize the variability and spatial distribution of FCO2, soil temperature, air-filled pore space (AFPS), soil organic matter (OM) and soil bulk density (BD) and related properties, (ii) evaluate the accuracy of the results provided by the method of ordinary kriging (OK) and sequential Gaussian simulation (SGS), and (iii) evaluate the uncertainty in predicting the spatial variability of FCO2 and other properties using the SSG. The study was conducted on an regular sampling grid with 141 points, with spacing ranging from 0.50 to 10 m, installed in a sugarcane area. In this place were evaluated FCO2, soil temperature, AFPS, were based on the average of 07 days of evaluation, OM and BD. All variables showed spatial dependence structure, and models adjusted Gaussian, spherical and exponential. The configuration of the sampling grid and the presence of intense layer of crop residues in the soil influenced the structure of spatial variability of FCO2, temperature, and OM. The FCO2 showed positive correlations with OM (r = 0.25, p <0.05) and AFPS (r = 0.27, p <0.01) and negatively with Ds (r = - 0.41, p <0.01). However, when the estimated spatially values are considered, the AFPS becomes the main variable responsible for the spatial characteristics of FCO2, showing correlation of 0.26 (p <0.01). The individual simulations led to all variables, better reproduction of the cumulative distribution functions (cdf), and variograms compared to OK and E-type estimate. The analysis results show strong similarities between the E-type estimates to those generated by the procedure of OK. The major uncertainties in predicting FCO2 were associated with areas with the highest... (Complete abstract click electronic access below)