Os experimentos florestais que estudam os efeitos de espaçamento devem adotar delineamentos distintos daqueles utilizados convencionalmente, por conta da grande demanda de área experimental dos delineamentos convencionais, o delineamento sistemático tipo \"leque\" é a forma mais viável de se executar este tipo de ensaio. Neste delineamento, as árvores são dispostas em diversos círculos concêntricos, de modo que, vários espaçamentos são gerados, porém, sem que haja possibilidade para a casualização. Para este tipo de experimento, convencionalmente são realizadas análises geoestatísticas que modelam o comportamento espacial de dependência entre os elementos, utilizando além da variável observada, as coordenadas das observações. Assim, é modelada uma função denominada semivariograma que explica esta dependência espacial, possibilitando a criação de um mapa de tendências denominado krigagem. Neste trabalho, são tratadas as variáveis de altura, diâmetro do fuste, diâmetro da copa, área da copa e volume cilíndrico de árvores de Canafístula, aos seis meses para altura e aos 13, 25 e 37 meses para todas as variáveis, após o plantio de mudas de Canafístula (Peltophorum dubium) em um experimento conduzido em Mato Grosso do Sul. Além da análise geoestatística, também é realizada a análise multivariada objetivando relacionar as variáveis por meio de medidas de correlação, efetuar a análise de componentes principais, de agrupamentos e discriminante. Além disso, é realizada a análise de medidas repetidas, objetivando avaliar o comportamento dessas variáveis ao longo dos períodos. Por fim, algumas formas combinadas de avaliar e interpretar os resultados são apresentadas, de modo a relacionar as análises já realizadas, calculando novos componentes principais para as variáveis, por período, efetuando a análise geoestatística dos componentes principais e avaliando o comportamento desses componentes ao longo do tempo. / Forest experiments which study the spacing effects should adopt different delineations from those conventionally used, due to the great demand for experimental area of conventional delineations, the systematic fan design is the most viable way to perform this type of test. In this design, the trees are arranged in several concentric circles, so that various spacings are generated, however, with no possibility for randomization. For this type of experiment, statistical analyses modeling the spatial behavior of dependence between the elements are conventionally performed using, in addition to the variable observed, the coordinates of the observations. Thus, a function called semivariogram that explains the spatial dependence is modeled, enabling the creation of a map of trends called kriging. In this paper, the variables of height, bole diameter, treetop diameter, area and its cylindrical volume of trees Canafistula, are treated at six months for height and at 13, 25 and 37 months for all variables after planting canafístula seedlings (Peltophorum dubium) in an experiment carried out in Mato Grosso do Sul. In addition to the geostatistical analysis, a multivariate analysis is also performed, aiming to relate the variables by correlation measures and performing the analysis of the main, grouping and discriminating components. Furthermore, the repeated measures analysis is performed aiming to evaluate the behavior of these variables over the periods. Finally, some combined ways to assess and interpret the results are presented in order to relate the previous analyses, calculating new key components for the variables, by period, performing the geostatistical analysis of the main components and evaluating the behavior of these components over time.

O solo é um importante sumidouro de carbono (C) atmosférico, uma vez que concentrações de CO2 da atmosfera podem ser atenuadas através de mecanismos de sequestro de C no solo. Nesse contexto, solos sob clima semi-árido estão sendo atualmente avaliados como potenciais sequestradores de C, sobretudo no processo de recuperação de áreas degradadas. No entanto, ainda há carência de informações referentes aos mecanismos envolvidos no sequestro de C. Adicionalmente, há incertezas nas estimativas dos estoques de C pela falta de conhecimento sobre sua variabilidade espacial devido à complexidade dos processos físicos, químicos e biológicos que influenciam o ciclo do referido elemento. As variações espaciais do C no solo estão relacionadas a fatores naturais e induzidos pelo homem e essas variações apresentam-se em diferentes escalas espaciais. Por tais motivos a presente pesquisa teve como objetivo avaliar a variabilidade espacial do C e de outros atributos físicos, químicos e biológicos do solo numa área de 100 ha destinada ao reflorestamento na região semi-árida do Rio Grande do Norte. Para tanto, foi estabelecida uma grade regular de 644 pontos amostrais espaçados de 40 m numa área localizada no município de Angicos (RN), pertencente à Universidade Federal Rural do SemiÁrido. Foram coletadas 1932 amostras de solo nas profundidades 0-0,1; 0,1-0,2; e 0,2-0,3 m para determinações de C, areia, silte, argila, pH, Na, P, Ca, Mg e K. Para determinar o C da biomassa microbiana (Cmic) foram utilizadas 156 amostras referentes à camada 0-0,1m. Com relação à densidade do solo (Ds) foram coletadas 246 amostras nas três profundidades mencionadas anteriormente. Adicionalmente, foram efetuados os seguintes cálculos: estoques de C, saturação por bases (V %), CTC (CTC(T)), saturação por Al (m) e soma de bases (SB). Os resultados foram submetidos à análise estatística descritiva clássica, seguida de análise geoestatística. O solo da área apresenta predominância de textura muito arenosa, baixa CTC e teores de C e Cmic; altos valores de Ds, acidez elevada e médios teores P e bases disponíveis. Estes resultados são comuns em solos de região semi-árida sob Caatinga em decorrência das condições climáticas desfavoráveis. Na análise descritiva a maioria dos atributos avaliados apresentou normalidade na sua distribuição. Os coeficientes de variação (CV) foram classificados como médios para a maioria dos atributos, a dependência espacial foi moderada com média geral dos alcances de 135 m. A maioria dos atributos ajustou-se ao modelo esférico. Na avaliação da eficiência dos modelos ajustados, tanto a validação interna como a externa apresentaram comportamentos semelhantes. A modelagem aplicada permitiu estimar o alcance e a magnitude das dependências espaciais. Por meio da krigagem foi efetuada a interpolação dos dados e gerados os mapas de variabilidade espacial para os atributos físicos, químicos e biológicos estudados. Os resultados obtidos nesta pesquisa ressaltam a importância do entendimento da variabilidade espacial do C e outras propriedades do solo, informações que servem como ponto de referência inicial (linha de base) e tem implicações importantes para futuras avaliações do impacto no sequestro de C e do potencial produtivo de Jatrofa na região semi-árida do Nordeste Brasileiro. / Soil is an important carbon (C) sink, since atmospheric CO2 concentrations can be attenuated by soil C sequestration. In this context, soils under semi-arid conditions are being evaluated as potential soil C sinks, mainly considering the process of rehabilitation of degraded areas. However, little information is available on the mechanisms associated with soil C sequestration. Moreover, there are uncertainties on soil C stocks estimates because of the lack of knowledge about its spatial variability due to the complexity of physical, chemical and biological processes that directly influence soil C cycle. Soil C spatial variability is associated with a series of natural and human-induced factors and those variations can be expressed in different spatial scales. Therefore, the main objective of the present study was to evaluate the spatial variability of C and soil physical, chemical and biological attributes in a 100 ha area destined to reforestation in the semi-arid region of Rio Grande do Norte (RN), Brazil. In order to do that, a regular grid (40 x 40 m) of 644 sampling points was defined in an area located in the city of Angicos (RN) that belongs to the Universidade Federal Rural do Semi-Árido. Samples from the 0-0,1; 0,1-0,2; e 0,2- 0,3 m soil layers were collected in each sampling point totalizing 1932 soil cores that were used for the following analyses: C, sand, silt, clay, pH, Na, P, Ca, Mg and K. For microbial biomass C, 156 samples were used from the 0-0,1 m soil depth. Samples for soil bulk density (total of 246 samples) were collected in the three mentioned soil layers. Additionally, the following calculations were performed: soil C stocks, base saturations, cation exchange capacity and aluminum saturation. The results were analyzed using classical descriptive statistics and geostatistics. The soil at the studied area is very sandy and presented low values of cation exchange capacity, C content and microbial biomass; high values of bulk density and soil acidity and medium values of P content and available bases. Those results are typical for soils under native vegetation at the semi-arid region due to unfavorable climatic conditions. From the descriptive analyses, the majority of the studied attributes presented normal distribution. The coefficients of variation (CV) for the majority of the studied attributes presented medium values; the spatial dependence was moderated with mean range value of 135 m. The majority of the attributes were fitted by the spherical model. Assessment of model adjustment efficiency was performed through internal and external validations and both presented similar trends. The application of modeling technique provides estimations of the range and the spatial dependence magnitude of the evaluated soil attributes. Using kriging techniques, analytical results were interpolated and maps were generated to show the spatial variability of the soil physical, chemical and biological properties. The results from the present study stressed the importance of adequately understand C and other soil properties spatial variability. Such information has important implications for future assessments of soil C sequestration and is useful for potential production of Jatropha in the semi-arid condition of the Brazilian northeast region.

Movido pelo crescimento populacional, a visão de sistemas sustentáveis tem despertado a atenção de diversos setores. Sendo um dos principais domínios economicamente ativo do país, a agropecuária vem buscando meios para se adequar a essa realidade. Nesse contexto, surgem as Boas Práticas Agropecuárias, das quais pode-se citar a Agricultura de Precisão, o pastejo rotacionado e o manejo ambiental, os quais se implementados em conjunto proporcionam um melhor gerenciamento da área de interesse. Assim, objetivou-se, aplicar conceitos de geoestatística e geoprocessamento para a obtenção de zonas de manejo de uma área de pastagem de capim Tanzânia, em São Carlos - SP, e delimitação de unidades de manejo para aplicação de calagem e adubação, com base no melhor método de interpolação. Com os resultados de análise de solo foram realizadas análises geoestatísticas para avaliação da dependência espacial dos atributos químicos, e a Validação Cruzada dos modelos adotados. Os mapas foram obtidos pelo método de interpolação por Krigagem Ordinária e a definição das zonas de manejo foi realizada por meio de lógica fuzzy. A partir dos mapas dos parâmetros químicos do solo gerou-se o mapa de zonas de manejo resultando em cinco zonas sendo: 0,02 ha (1,2% da área total) considerada como \"muito baixa\" fertilidade; 0,3 ha (18%) \"baixa\" fertilidade; 0,75 ha (44%) como \"média\" fertilidade; 0,55 ha (32%) como \"alta\" fertilidade e, 0,08 ha (4,8%) como \"muita alta\" fertilidade. A comparação dos métodos de interpolação demonstrou que a Krigagem Ordinária foi a melhor metodologia para o estudo. A geoestatística e o geoprocessamento demonstraram ser técnicas que auxiliam nas decisões estratégicas e complexas em relação ao gerenciamento do sistema de produção agrícola. / Movin by population growth, the vision of sustainable systems has attracted the attention of various sectors. Being one of the main areas economically active of the country, agriculture has been seeking ways to adapt to this reality. In this context, emerge the Good Farming Practices, which among them we can mention the Agriculture of Precision, the rotate pasture and environmental management, which if implemented together will provide a better management of the area of interest. The present study aimed to apply the concepts of geostatistics and gis to obtain areas of management of an area of pasture grass, Tanzania, São Carlos – SP, and delimitation of management units for the application of liming and fertilization, based on the best interpolation method. With the analysis results of the soil analyses were performed geo-statistical for evaluation of the dependence on the spatial attributes of chemicals. The maps were obtained by the method of interpolation by Kriging Ordinary and the definition of zones for the management was performed by fuzzy logic. From the maps of chemical parameters of the soil has resulted from the management zone map, resulting in five areas being: 0.02 ha (1.2% of total area) regarded as \"very low\" fertility; and 0.3 ha (18%) \"low\" fertility; 0.75 ha (44%) as \"average\" fertility; 0.55 ha (32%) as \"high\" fertility and, 0.08 ha (4.8%) as \"very high\" fertility. The comparison of the interpolation methods showed that Kriging Ordinary was the best methodology for the study. The geostatistics and gis have proved to be techniques that help with strategic and complex decisions in relation to the management of the agricultural production system.

Orientador: César Gustavo da Rocha Lima / Resumo: A água exerce influência direta no desenvolvimento de sociedades. Por sua vez, as águas subterrâneas apresentam um papel fundamental para o abastecimento humano por constituírem aproximadamente dois terços da fonte de água doce no mundo. A Companhia Ambiental do Estado de São Paulo (CETESB) controla e monitora atividades que possam ser fontes de poluição e avalia periodicamente os parâmetros de qualidade das águas. Sua rede conta com 75 pontos de monitoramento até 2012, dificultando um panorama amplo da qualidade das águas no Sistema Aquífero Bauru. O objetivo do trabalho foi estudar a variabilidade espacial e temporal dos parâmetros de qualidade das águas subterrâneas do SAB no Estado de São Paulo. Foram avaliados os parâmetros: Alcalinidade Bicarbonato, Bário, Cálcio, Condutividade Elétrica, Dureza, Magnésio, Nitrato, Potássio, pH, Sódio, Sólidos Totais Dissolvidos e Temperatura. Para tanto foi realizada a análise descritiva, de correlação e a análise geoestatística por meio do cálculo de variogramas experimentais para avaliação da dependência espacial e interpolações por krigagem ordinária. Os resultados indicaram que à exceção do pH e da Temperatura, todos os parâmetros possuíam elevada variabilidade dos dados, com Coeficientes de Variação (CV) elevados, em sua maior parte. As correlações significativas do ponto de vista prático de determinação laboratorial foram de Sólido Total Dissolvido com Cálcio (r = 0,770) e com Magnésio (r = 0,700), além da Dureza com Cálcio (r = 0... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Water is essential for the life maintenance. It influences directly the society development over the centuries. Currently, groundwater resources have a crucial role for supply. These resources constitute around two thirds of the global freshwater sources. The Sao Paulo Environmental Company (CETESB) is responsible for manage activities which can be source of contamination and periodically assess water parameters. However, the CETESB system had 75 monitoring points until 2012, hindering area overview. This study aims evaluate variability and temporal-spatial dependency of water parameters for groundwater quality in the Bauru Aquifer System (BAS), in the State of Sao Paulo, using geostatistical techniques. The parameters were: Bicarbonate Alkalinity, Barium, Hardness, Calcium, Magnesium, Nitrate, Potassium, pH, Sodium, Total Dissolved Solids and Temperature. It has been done at first descriptive analysis and then spatial dependency for which parameter by semivariogram analyzes. The results showed that the parameters have a high variability, except by pH and Temperature, the coefficient variation were very high for the parameters. The significant correlations were Total Dissolved Solids with Calcium (r = 0.770) and Magnesium (r = 0.700) on a laboratorial practice. Besides Hardness and Calcium with r = 0.910. All parameters showed spatial dependency with appreciable semivariographic adjustments and kriging maps defined. The pH values were allowed for human consumption, except by ... (Complete abstract click electronic access below) / Mestre

Irrigation needs to be applied to soils in relatively humid regions such as western Kentucky to supply water for crop uptake to optimize and stabilize yields. Characterization of soil and crop variability at the field scale is needed to apply site specific management and to optimize water application. The objective of this work is to propose a characterization and modeling of soil and crop processes to improve irrigation management. Through an analysis of spatial and temporal behavior of soil and crop variables the variability in the field was identified. Integrative analysis of soil, crop, proximal and remote sensing data was utilized. A set of direct and indirect measurements that included soil texture, electrical conductivity (EC), soil chemical properties (pH, organic matter, N, P, K, Ca, Mg and Zn), NDVI, topographic variables, were measured in a silty loam soil near Princeton, Kentucky. Maps of measured properties were developed using kriging, and cokriging. Different approaches and two cluster methods (FANNY and CLARA) with selected variables were applied to identify management zones. Optimal scenarios were achieved with dividing the entire field into 2 or 3 areas. Spatial variability in the field is strongly influenced by topography and clay content. Using Root Zone Water Quality Model 2.0 (RZWQM), soil water tension was modeled and predicted at different zones based on the previous delineated zones. Soil water tension was measured at three depths (20, 40 and 60 cm) during different seasons (20016 and 2017) under wheat and corn. Temporal variations in soil water were driven mainly by precipitation but the behavior is different among management zones. The zone with higher clay content tends to dry out faster between rainfall events and reveals higher fluctuations in water tension even at greater depth. The other zones are more stable at the lower depth and share more similarities in their cyclic patterns. The model predictions were satisfactory in the surface layer but the accuracy decreased in deeper layers. A study of clay mineralogy was performed to explore field spatial differences based on the map classification. kaolinite, vermiculite, HIV and smectite are among the identified minerals. The clayey area presents higher quantity of some of the clay minerals. All these results show the ability to identify and characterize the field spatial variability, combining easily obtainable data under realistic farm conditions. This information can be utilized to manage resources more effectively through site specific application.

Improving agricultural water management is important for conserving water during dry seasons, using limited water resources in the most efficient way, and minimizing environmental risks (e.g., leaching, surface runoff). The understanding of water movement in different zones of agricultural production fields is crucial to developing an effective irrigation strategy. This work centered on optimizing field water management by characterizing the spatial patterns of soil hydraulic properties. Soil hydraulic conductivity was measured across different zones in a farmer’s field, and its spatial variability was investigated by using geostatistical techniques. Since direct measurement of hydraulic conductivity is time-consuming and arduous, pedo-transfer functions (PTFs) have been developed to estimate hydraulic conductivity indirectly through more easily measurable soil properties. Due to ignoring soil structural information and spatial covariance between soil variables, PTFs often perform unsatisfactorily when field-scale estimations of hydraulic conductivity are needed. The performance of PTFs in estimating hydraulic conductivity in the field was therefore critically evaluated. Due to the presence of structural macro-pores, saturated hydraulic conductivity (Ks) showed high spatial heterogeneity, and this variability was not captured by texture-dominated PTF estimates. However, the general spatial pattern of near-saturated hydraulic conductivity can still be reasonably generated by PTF estimates. Therefore, the hydraulic conductivity maps based on PTF estimates should be evaluated carefully and handled with caution. Recognizing the significant contribution of macro-pores to saturated water flow, PTFs were further improved by including soil macro-porosity and were proven to perform much better in estimating Ks compared with established PTFs tested in this study. Additionally, the spatial relationship between hydraulic conductivity and its potential influencing factors were further quantified by the state-space approach. State-space models outperformed current PTFs and effectively described the spatial characteristics of hydraulic conductivity in the studied field. These findings provided a basis for modeling water/solute transport in the vadose zone, and sitespecific water management.

This thesis concerns the development, estimation and investigation of a general anisotropic spatial correlation function, within model-based geostatistics, expressed as a Gaussian linear mixed model, and estimated using residual maximum likelihood (REML). The Matern correlation function is attractive because of its parameter which controls smoothness of the spatial process, and which can be estimated from the data. This function is combined with geometric anisotropy, with an extension permitting different distance metrics, forming a flexible spatial covariance model which incorporates as special cases many infinite- range spatial covariance functions in common use. Derivatives of the residual log-likelihood with respect to the four correlation-model parameters are derived, and the REML algorithm coded in Splus for testing and refinement as a precursor to its implementation into the software ASReml, with additional generality of linear mixed models. Suggestions are given regarding initial values for the estimation. A residual likelihood ratio test for anisotropy is also developed and investigated. Application to three soil-based examples reveals that anisotropy does occur in practice, and that this technique is able to fit covariance models previously unavailable or inaccessible. Simulations of isotropic and anisotropic data with and without a nugget effect reveal the following principal points. Inclusion of some closely-spaced locations greatly improves estimation, particularly of the Matern smoothness parameter, and of the nugget variance when present. The presence of geometric anisotropy does not adversely affect parameter estimation. Presence of a nugget effect introduces greater uncertainty into the parameter estimates, most dramatically for the smoothness parameter, and also increases the chance of non-convergence and decreases the power of the test for anisotropy. Estimation is more difficult with very “unsmooth" processes (Matern smoothness parameter 0.1 or 0.25) | non- convergence is more likely and estimates are less precise and/or more biased. However it is still often possible to fit the full model including both anisotropy and nugget effect using REML with as few as 100 observations. Additional simulations involving model misspecification reveal that ignoring anisotropy when it is present can substantially increase the mean squared error of prediction, but overfitting by attempting to model anisotropy when it is absent is less damaging. Further, plug-in estimates of prediction error variance are reasonable estimates of the actual mean squared error of prediction, regardless of the model fitted, weakening the argument requiring Bayesian approaches to properly allow for uncertainty in the parameter estimates when estimating prediction error variance. The most valuable outcome of this research is the implementation of an anisotropic Matern correlation function in ASReml, including the full generality of Gaussian linear mixed models which permits additional fixed and random effects, making publicly available the facility to fit, via REML estimation, a much wider range of variance models than has previously been readily accessible. This greatly increases the probability and ease with which a well-fitting covariance model can be found for a spatial data set, thus contributing to improved geostatistical spatial analysis. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1297562 / Thesis (Ph.D.) -- University of Adelaide, School of Agriculture, Food and Wine, 2007

This thesis primarily addresses the problem of automatic measurement of ore textures by image analysis in a way that is relevant to mineral processing. Specifically, it addresses the following major hypotheses: • Automatic logging of drill core by image analysis provides a feasible alternative to manual logging by geologists. • Image analysis can quantify process mineralogy by physically meaningful parameters. • Multi-scale image analysis, over a wide range of size scales, provides potential benefits to process mineralogy that are additional to those available from small-scale analysis alone, and also better retains the information content of manual logging. • Image analysis can provide physically meaningful, ore-texture-related, additive regionalised variables that can be input to geostatistical models and the definition of domains. The central focus of the thesis is the development of an automatic, multi-scale method to identify and measure objects in an image, using a specially-developed skeleton termed the morphological CWT skeleton. This skeleton is a multi-scale extension of the morphological skeleton commonly used in image analysis, and is derived from the continuous wavelet transform (CWT). Objects take the form of hierarchical segments from image segmentation based on the CWT. Only the Mexican hat, also known as the Laplacian-of-Gaussian, wavelet is used, although other wavelet shapes are possible. The natural scale of each object is defined to be the size scale at which its CWT signal (the contrast between the interior and exterior of the object) is strongest. In addition to the natural scale, the analysis automatically records the mineral composition of both the interior and exterior of each object, and shape descriptors of the object. The measurements of natural scale, mineral composition and shape are designed to relate to: • The size to which ore must be broken in order to liberate objects. • Minerals that need to be separated by physical or chemical means once objects have been liberated. • Capability to distinguish qualitatively different ore-texture types that may have different geological origins and for which different processing regimes may provide an economic benefit. Measurements are taken over size scales from three pixels to hundreds of pixels. For the major case study the pixel size is about 50 µm, but the methodology is equally applicable to photomicrographs in which the pixel size is about 4 µm. The methodology for identifying objects in images contributes to the field of scale-space image segmentation, and has advantages in performing the following actions automatically: • Finding optimal size scales in hierarchical image segmentation (natural scale). • Merging segments that are similar and spatially close together (although not necessarily touching), using the structure of the morphological CWT skeleton, thus aiding recognition of complex structures in an image. • Defining the contrast between each segment and its surrounding segments appropriately for the size scale of the segment, in a way that extends well beyond the segment boundary. For process mineralogy this contrast quantifies mineral associations at different size scales. The notion of natural scale defined in this thesis may have applications to other fields of image processing, such as mammography and cell measurements in biological microscopy. The objects identified in images are input to cluster analysis, using a finite mixture model to group the objects into object populations according to their size, composition and shape descriptors. Each image is then characterised by the abundances of different object populations that occur in it. These abundances form additive, regionalised variables that can be input into geostatistical block models. The images are themselves input to higher-level cluster analysis based on a hidden Markov model. A collection of images is divided into different ore texture types, based on differences in the abundances of the textural object populations. The ore texture types help to define geostatistical domains in an ore body. Input images for the methodology take the form of mineral maps, in which a particular mineral has been assigned to each pixel in the image prior to analysis. A method of analysing unmapped, raw colour images of ore is also outlined, as is a new model for fracture of ore. The major case study in the thesis is an analysis of approximately 1000 metres of continuously-imaged drill core from four drill holes in the Ernest Henry iron-oxide-copper-gold ore deposit (Queensland, Australia). Thirty-one texture-related variables are used to summarise the individual half-metres of drill core, and ten major ore texture types are identified. Good agreement is obtained between locations of major changes in ore type found by automatic image analysis, and those identified from manual core logging carried out by geologists. The texture-related variables are found to explain a significant amount of the variation in comminution hardness of ore within the deposit, over and above that explained by changes in abundances of the component minerals. The thesis also contributes new algorithms with wide applicability in image processing: • A fast algorithm for computing the continuous wavelet transform of a signal or image: The new algorithm is simpler in form and several times faster than the best previously-published algorithms. It consists of a single finite impulse response (FIR) filter. • A fast algorithm for computing Euclidean geodesic distance. This algorithm runs in O(1) arithmetic operations per pixel processed, which has not been achieved by any previously published algorithm. Geodesic distance is widely used in image processing, for segmentation and shape characterisation.

Radio magnetotellurics (RMT), crosshole ground penetrating radar (GPR), and crosshole electrical resistance tomography (ERT) were applied in a range of hydrogeological applications where geophysical data could improve hydrogeological characterization. A profile of RMT data collected over highly resistive granite was used to map subhorizontal fracture zones below 300m depth, as well as a steeply dipping fracture zone, which was also observed on a coinciding seismic reflection profile. One-dimensional inverse modelling and 3D forward modelling with displacement currents included were necessary to test the reliability of features found in the 2D models, where the forward models did not include displacement currents and only lower frequencies were considered. An inversion code for RMT data was developed and applied to RMT data with azimuthal electrical anisotropy signature collected over a limestone formation. The results indicated that RMT is a faster and more reliable technique for studying electrical anisotropy than are azimuthal resistivity surveys. A new sequential inversion method to estimate hydraulic conductivity fields using crosshole GPR and tracer test data was applied to 2D synthetic examples. Given careful surveying, the results indicated that regularization of hydrogeological inverse problems using geophysical tomograms might improve models of hydraulic conductivity. A method to regularize geophysical inverse problems using geostatistical models was developed and applied to crosshole ERT and GPR data collected in unsaturated sandstone. The resulting models were geologically more reasonable than models where the regularization was based on traditional smoothness constraints. Electromagnetic geophysical techniques provide an inexpensive data source in estimating qualitative hydrogeological models, but hydrogeological data must be incorporated to make quantitative estimation of hydrogeological systems feasible.

Soil is extremely important for providing food, biomass and raw materials, water and nutrient storage; supporting biodiversity and providing foundations for man-made structures. However, its health is threatened by human activities, which can greatly affect the potential of soils to fulfil their functions and, consequently, result in environmental, economic and social damage. These issues require the characterisation of the impact and spatial extent of the problems. This can be achieved through the creation of detailed and comprehensive soil maps that describe both the spatial and vertical variability of key soil properties. Detailed three-dimensional (3D) digital soil maps can be readily used and embedded into environmental models. Three-dimensional soil mapping is not a new concept. However, only with the recent development of more powerful computers has it become feasible to undertake such data processing. Common techniques to estimate soil properties in the three-dimensional space include geostatistical interpolation, or a combination of depth functions and geostatistics. However, these two methods are both partially flawed. Geostatistical interpolation and kriging in particular, estimate soil properties in unsampled locations using a weighted average of the nearby observations. In order to produce the best possible estimate, this form of interpolation minimises the variance of each weighted average, thus decreasing the standard deviation of the estimates, compared to the soil observations. This appears as a smoothing effect on the data and, as a consequence, kriging interpolation is not reliable when the dataset is not sampled with a sampling designs optimised for geostatistics. Depth function approaches, as they are generally applied in literature, implement a spline regression of the soil profile data that aims to better describe the changes of the soil properties with depth. Subsequently, the spline is resampled at determined depths and, for each of these depths, a bi-dimensional (2D) geostatistical interpolation is performed. Consequently, the 3D soil model is a combination of a series of bi-dimensional slices. This approach can effectively decrease or eliminate any smoothing issues, but the way in which the model is created, by combining several 2D horizontal slices, can potentially lead to erroneous estimations. The fact that the geostatistical interpolation is performed in 2D implies that an unsampled location is estimated only by considering values at the same depth, thus excluding the vertical variability from the mapping, and potentially undermining the accuracy of the method. For these reasons, the literature review identified a clear need for developing, a new method for accurately estimating soil properties in 3D – the target of this research, The method studied in this thesis explores the concept of soil specific depth functions, which are simple mathematical equations, chosen for their ability to describe the general profile pattern of a soil dataset. This way, fitting the depth function to a particular sample becomes a diagnostic tool. If the pattern shown in a particular soil profile is dissimilar to the average pattern described by the depth function, it means that in that region there are localised changes in the soil profiles, and these can be identified from the goodness of fit of the function. This way, areas where soil properties have a homogeneous profile pattern can be easily identified and the depth function can be changed accordingly. The application of this new mapping technique is based on the geostatistical interpolation of the depth function coefficients across the study area. Subsequently, the equation is solved for each interpolated location to create a 3D lattice of soil properties estimations. For this way of mapping, this new methodology was denoted as top-down mapping method. The methodology was assessed through three case studies, where the top-down mapping method was developed, tested, and validated. Three datasets of diverse soil properties and at different spatial extents were selected. The results were validated primarily using cross-validation and, when possible, by comparing the estimates with independently sampled datasets (independent validation). In addition, the results were compared with estimates obtained using established literature methods, such as 3D kriging interpolation and the spline approach, in order to define some basic rule of application. The results indicate that the top-down mapping method can be used in circumstances where the soil profiles present a pattern that can be described by a function with maximum three coefficients. If this condition is met, as it was with key soil properties during the research, the top-down mapping method can be used for obtaining reliable estimates at different spatial extents.