Creation of Histograms for Data in Various Mineral Resource and Engineering Problems: A Review of Existing Methods and a Proposed New Method to Define Bin Number

Histograms are widely used in geosciences for data analysis and visualization. In cases where a distribution is not fitted to data, histograms are often used to address various sampling- and interpolation-related aspects. However, the results of these applications are substantially affected by the histogram’s number of bins as determined by several binning methods. This paper proposes a new binning approach and compares it with various standard approaches to demonstrate the relative performance of the new approach. Cut-off grade optimization for polymetallic deposits, Monte-Carlo modeling, and derivation of conditional distribution, all of which use histograms, are used as case studies. The proposed technique is based on calculating the squared error for each bin in a histogram, and combining the error values to evaluate the total error for each histogram. The new technique then selects the bin number which minimizes the total error. The results showed that the new binning approach is well suited for binning small datasets and can be used in geoscience applications if needed.     

Prediction of categorical spatial data via Bayesian updating

This study introduces a transition probability-based Bayesian updating (BU) approach for spatial classification through expert system. Transition probabilities are interpreted as expert opinions for updating the prior marginal probabilities of categorical response variables. The main objective of this paper is to provide a spatial categorical variable prediction method which has a solid theoretical foundation and yields relatively higher classification accuracy compared with conventional ones. The basic idea is to first build a linear Bayesian updating (LBU) model that corresponds to an application of Bayes’ theorem. Since the linear opinion pool is intrinsically suboptimal and underconfident, the beta-transformed Bayesian updating (BBU) model is proposed to overcome this limitation. Another type of BU approach, conditional independent Bayesian updating (CIBU), is derived based on conditional independent experts. It is shown that traditional Markovian-type categorical prediction (MCP) is equivalent to a particular CIBU model with specific parameters. As three variants of the BU method, these techniques are illustrated in synthetic and real-world case studies, comparison results with both the LBU and MCP favor the BBU model.     

Geostatistical modelling of spatial uncertainty using p -field simulation with conditional probability fields

This paper presents a variant of p-field simulation that allows generation of spatial realizations through sampling of a set of conditional probability distribution functions (ccdf) by sets of probability values, called p-fields. Whereas in the common implementation of the algorithm the p-fields are nonconditional realizations of random functions with uniform marginal distributions, they are here conditional to 0.5 probability values at data locations, which entails a preferential sampling of the central part of the ccdf around these locations. The approach is illustrated using a randomly sampled (200 observations of the NIR channel) SPOT scene of a semi-deciduous tropical forest. Results indicate that the use of conditional probability fields improves the reproduction of statistics such as histogram and semivariogram, while yielding more accurate predictions of reflectance values than the common p-field implementation or the more CPU-intensive sequential indicator simulation. Pixel values are then classified as forest or savannah depending on whether the simulated reflectance value exceeds a given threshold value. In this case study, the proposed approach leads to a more precise and accurate prediction of the size of contiguous areas covered by savannah than the two other simulation algorithms.     

Estimating number and field size distribution in frontier sedimentary basins using a Pareto model

Estimating the number of deposits likely to be found and their size distribution is important in exploration planning. In a frontier basin the geologic information for conducting a resource assessment is mostly limited to the regional level. Some methods, such as the play analysis approach (Crovelli and Balay, 1986) and the conceptual play model (Lee and Wang, 1983), can be used in conceptual plays or frontier basins, but these methods require the knowledge of the number of prospects, pool data characterizing the conditional field size distribution, and information documenting the exploration risk. For unexplored sedimentary basins, such as those in southern Africa, there are neither sufficient data covering reservoir volumetric parameters nor a number of mapped prospects that can be used to conduct such an assessment. In such a case a volumetric method using geologic analogy is applicable, by which a point estimate of hydrocarbon potential can be estimated, but this estimate provides no information on the likely size distribution. As a complement to the volumetric method, we discuss how to use the empirical Pareto law for estimating the number of fields and their size distribution in such a frontier region.     

Spatial interpolation using conditional generative adversarial neural networks

ABSTRACT

Spatial interpolation is a traditional geostatistical operation that aims at predicting the attribute values of unobserved locations given a sample of data defined on point supports. However, the continuity and heterogeneity underlying spatial data are too complex to be approximated by classic statistical models. Deep learning models, especially the idea of conditional generative adversarial networks (CGANs), provide us with a perspective for formalizing spatial interpolation as a conditional generative task. In this article, we design a novel deep learning architecture named conditional encoder-decoder generative adversarial neural networks (CEDGANs) for spatial interpolation, therein combining the encoder-decoder structure with adversarial learning to capture deep representations of sampled spatial data and their interactions with local structural patterns. A case study on elevations in China demonstrates the ability of our model to achieve outstanding interpolation results compared to benchmark methods. Further experiments uncover the learned spatial knowledge in the model’s hidden layers and test the potential to generalize our adversarial interpolation idea across domains. This work is an endeavor to investigate deep spatial knowledge using artificial intelligence. The proposed model can benefit practical scenarios and enlighten future research in various geographical applications related to spatial prediction.     

水资源承载能力评价的熵权模糊物元模型

以模糊物元分析理论为基础,结合熵值法和欧氏贴近度概念,构建用于评价水资源承载能力的熵权模糊物元分析模型。介绍了该模型的计算步骤,应用该模型对淮河流域各分区的水资源承载能力进行了综合评价,并与其他评价方法的评价结果进行了比较。结果表明,该文建立的模型合理且计算简单,可靠性、实用性强,适用于多种综合评价问题。     

基于时间可达性与伽萨法则的大卖场区位探讨——以上海市中心城区为例

目前多数基于GIS的商业区位模型与技术研究,未全面考虑交通网络、道路等级、网点吸引力与竞争因素。针对此局限,借助GIS软件,依托可达性方法与伽萨法则,尝试综合考虑上述因素探讨大卖场可达性与商圈特征。以上海中心城区大卖场为例,采用同心圆法、扇形法与最近邻域法探讨卖场空间特征;利用行进成本分析法计算卖场可达性,并根据伽萨法则叠加了卖场引力因素,得到伽萨法则商圈。结果表明:大卖场集中分布于距市中心4.5~10km范围,各方向扩张不均衡。城区整体可达性较好,浦西优于浦东。外环附近商圈面积大,外环附近与市中心区商圈市场规模大,内环附近商圈面积与市场规模小。伽萨法则商圈市场规模"两极分化"既表明卖场市场竞争激烈地区与网点短缺区并存,也说明网点市场规模与职能存在等级差异。     

基于判别空间条件熵加权的土地覆盖分类方法研究

针对遥感专题类别信息的机理问题,从土地覆盖参考数据的偏差程度对分类精度的影响角度,提出了一种基于判别空间条件熵加权的土地覆盖分类方法。引入判别空间模型概念,基于此模型生成土地覆盖数据类别,并分析了土地覆盖信息类别与数据类别的语义偏差出现的深层次原因;计算信息类别与数据类别的对应关系矩阵,据此得到二者的条件熵,实现对土地覆盖信息类别与数据类别的语义偏差的量化;根据信息类别与数据类别的条件熵计算修正判别变量的权重因子,实现基于判别空间条件熵加权的土地覆盖分类。采用一景SPOT-5影像进行分类实验,并利用同一地区的Landsat 5TM影像进行方法验证。实验表明,条件熵加权修正方法使土地覆盖分类精度有了显著提高,并对不同分辨率的遥感影像具有适用性。     

Geomorphic hazard assessment of landslide dams in South Westland, New Zealand: fundamental problems and approaches

Quantitative assessments of landslide hazard usually employ empirical, heuristic, deterministic, or statistical methods to derive estimates of magnitude–frequency distributions of landsliding. The formation and failure of landslide dams are common geomorphic processes in mountain regions throughout the world, causing a series of consequential off-site hazards such as catastrophic outburst floods, debris flows, backwater ponding, up- and downstream aggradation, and channel instability.Conceptual and methodological problems of quantifying geomorphic hazard from landslide dams result from (a) aspects of defining “landslide-dam magnitude”, (b) scaling effects, i.e. the geomorphic long-range and long-term implications of river blockage, and (c) paucity of empirical data. Geomorphic hazard from a landslide dam-break flood on the basis of conditional probabilities is being analysed for the alpine South Westland region of New Zealand, where formation and failure of landslide dams is frequent. Quantification of the annual probability of landsliding and subsequent dam formation in the area is limited by historical and only partially representative empirical data on slope instability. Since landslide-dam stability is a major control governing the potential of catastrophic outburst flooding, the ensuing hazard is best assessed on a recurring basis. GIS-based modelling of virtual landslide dams is a simple and cost-effective approach to approximate site-specific landslide dam and lake dimensions, reservoir infill times, and scaled magnitude of potential outburst floods. Although crude, these order-of-magnitude results provide information critical to natural hazard planning, mitigation, or emergency management decisions.     

Bayesian and multivariate methods applied to favorability quantification in Recôncavo Basin and Ribeira Belt, Brazil

A methology to define favorable areas in petroleum and mineral exploration is applied, which consists in weighting the exploratory variables, in order to characterize their importance as exploration guides. The exploration data are spatially integrated in the selected area to establish the association between variables and deposits, and the relationships among distribution, topology, and indicator pattern of all variables. Two methods of statistical analysis were compared. The first one is the Weights of Evidence Modeling, a conditional probability approach (Agterberg, 1989a), and the second one is the Principal Components Analysis (Pan, 1993). In the conditional method, the favorability estimation is based on the probability of deposit and variable joint occurrence, with the weights being defined as natural logarithms of likelihood ratios. In the multivariate analysis, the cells which contain deposits are selected as control cells and the weights are determined by eigendecomposition, being represented by the coefficients of the eigenvector related to the system’s largest eigenvalue. The two techniques of weighting and complementary procedures were tested on two case studies: 1. Recôncavo Basin, Northeast Brazil (for Petroleum) and 2. Itaiacoca Formation of Ribeira Belt, Southeast Brazil (for Pb-Zn Mississippi Valley Type deposits). The applied methdology proved to be easy to use and of great assistance to predict the favorability in large areas, particularly in the initial phase of exploration programs.     

Studying Resource-Dependent Communities Through a Social-Ecological Lens? Examining Complementarity with Existing Research Traditions in Canada

This article explores the suitability of Ostrom and colleagues' social-ecological systems framework (SESF) for the study of resource-dependent communities in Canada. Through a broad literature about resource-dependent communities in Canada, three main approaches are identified, named staples research, rural development, and sustainability studies. Each of these research traditions is analyzed with regards to a common set of criteria – focus, scale, methods, treatment of institutions, and treatment of environmental dimensions. Research in each category is compared and contrasted with the SESF approach, to identify areas of overlap and divergence. Results indicate that the SESF is unlikely to provide additional benefit in terms of in-depth of social analysis, however, it does provide a unique contribution in terms of its coupled approach to conceiving social and ecological systems and its ability to operationalize these relationships through structured variables.     

Combining spatial transition probabilities for stochastic simulation of categorical fields

Categorical spatial data, such as land use classes and socioeconomic statistics data, are important data sources in geographical information science (GIS). The investigation of spatial patterns implied in these data can benefit many aspects of GIS research, such as classification of spatial data, spatial data mining, and spatial uncertainty modeling. However, the discrete nature of categorical data limits the application of traditional kriging methods widely used in Gaussian random fields. In this article, we present a new probabilistic method for modeling the posterior probability of class occurrence at any target location in space-given known class labels at source data locations within a neighborhood around that prediction location. In the proposed method, transition probabilities rather than indicator covariances or variograms are used as measures of spatial structure and the conditional or posterior (multi-point) probability is approximated by a weighted combination of preposterior (two-point) transition probabilities, while accounting for spatial interdependencies often ignored by existing approaches. In addition, the connections of the proposed method with probabilistic graphical models (Bayesian networks) and weights of evidence method are also discussed. The advantages of this new proposed approach are analyzed and highlighted through a case study involving the generation of spatial patterns via sequential indicator simulation.     

密云水库周边山区滑坡泥石流易发区预估

滑坡、泥石流等地质灾害的易发度主要是地质灾害自然属性特征的体现,它与孕灾环境的各项因子密切相关。这些因子包括地形地貌、流域水文、构造等内部条件因子以及地震、降雨等外部触发因子。为突出反映滑坡及泥石流主导因子的作用,本文参考了许多研究所采用的评价方法和因子选择,重点选取对该地区滑坡及泥石流发生区域分析评价起一定主导作用的、便于研究区域数据资料与空间资料匹配、关系密切的几个指标,包括地形地貌要素(坡度、坡向、坡形、相对高差、地貌类型)、环境要素(植被指数、河网密度、洪水淹没范围)、构造要素(距断层的距离、断层密度、地质岩性),通过对这些因子的敏感性进行分析,采用专家打分方法确定每种要素及因子的权重,借助因子加权叠加办法得出研究区地质灾害易发程度空间分布,用于表示其可能发生的统计意义上的可能性(概率),该研究对于区域地质灾害预防具有一定的适用价值。     

Lithology-derived structure classification from the joint interpretation of magnetotelluric and seismic models

Magnetotelluric and seismic methods provide complementary information about the resistivity and velocity structure of the subsurface on similar scales and resolutions. No global relation, however, exists between these parameters, and correlations are often valid for only a limited target area. Independently derived inverse models from these methods can be combined using a classification approach to map geologic structure. The method employed is based solely on the statistical correlation of physical properties in a joint parameter space and is independent of theoretical or empirical relations linking electrical and seismic parameters. Regions of high correlation (classes) between resistivity and velocity can in turn be mapped back and re-examined in depth section. The spatial distribution of these classes, and the boundaries between them, provide structural information not evident in the individual models. This method is applied to a 10 km long profile crossing the Dead Sea Transform in Jordan. Several prominent classes are identified with specific lithologies in accordance with local geology. An abrupt change in lithology across the fault, together with vertical uplift of the basement suggest the fault is sub-vertical within the upper crust.     

Bayesian and Neural Network Approaches to Estimate Deep Temperature Distribution for Assessing a Supercritical Geothermal System: Evaluation Using a Numerical Model

The temperature distribution at depth is a key variable when assessing the potential of a supercritical geothermal resource as well as a conventional geothermal resource. Data-driven estimation by a machine-learning approach is a promising way to estimate temperature distributions at depth in geothermal fields. In this study, we developed two methodologies—one based on Bayesian estimation and the other on neural networks—to estimate temperature distributions in geothermal fields. These methodologies can be used to supplement existing temperature logs, by estimating temperature distributions in unexplored regions of the subsurface, based on electrical resistivity data, observed geological/mineralogical boundaries, and microseismic observations. We evaluated the accuracy and characteristics of these methodologies using a numerical model of the Kakkonda geothermal field, Japan, where a temperature above 500 °C was observed below a depth of about 3.7 km. When using geological and geophysical knowledge as prior information for the machine learning methods, the results demonstrate that the approaches can provide subsurface temperature estimates that are consistent with the temperature distribution given by the numerical model. Using a numerical model as a benchmark helps to understand the characteristics of the machine learning approaches and may help to identify ways of improving these methods.

     

Identifying minimal sets of survey techniques for multi-species monitoring across landscapes: an approach utilising species distribution models

Monitoring for species occupancy is often carried out at local scales, reflecting specific targets, available logistics, and funding. Problematically, conservation planning and management operate at broader scales and use information inventories with good scale coverage. Translating information between local and landscape scales is commonly treated in an ad hoc manner, but conservation decision-making can benefit from quantifying spatial-knowledge relationships. Fauna occupancy monitoring, in particular, suffers from this issue of scale, as there are many different survey methods employed for different purposes. Rather than ignoring how informative these methods are when predicting regional distributions, we describe a statistical approach that identifies survey combinations that provide the greatest additive value in mammal detection across different scales. We identified minimal sets of survey methods for 53 terrestrial mammal species across a large area in Australia (New South Wales (NSW), 800,000 km²) and for each of the 18 bioregions it encompasses. Utility of survey methods varied considerably at a landscape scale. Unplanned opportunistic sightings were the single largest source of species information (35%). The utility of other survey methods varied spatially; some were retained in minimal sets for many bioregions, while others were spatially restricted or unimportant. Predator scats, Elliot and pitfall trapping, spotlighting, and diurnal herpetofauna surveys were the most frequently included survey methods at a landscape scale. Use of our approach can guide identification of efficient combinations of survey methods, maximising detection and returns for monitoring. Findings and methodologies are easily transferable and are globally applicable across any taxa. They provide guidelines for managing scarce resources for regional ?monitoring programs, and improving regional strategic ?conservation planning.     

A case study of model selection and parameter inference by maximum likelihood with application to uncertainty analysis

One of the uses of geostatistical conditional simulation is as a tool in assessing the spatial uncertainty of inputs to the Monte Carlo method of system uncertainty analysis. Because the number of experimental data in practical applications is limited, the geostatistical parameters used in the simulation are themselves uncertain. The inference of these parameters by maximum likelihood allows for an easy assessment of this estimation uncertainty which, in turn, may be included in the conditional simulation procedure. A case study based on transmissivity data is presented to show the methodology whereby both model selection and parameter inference are solved by maximum likelihood.     

GIS技术支持下的招远市金矿区崩塌遥感调查

在总结前人研究成果的基础上,全面系统地分析了诱发招远市金矿区崩塌的自然和人为因数,然后运用遥感技术对金矿区遥感图像进行处理,提取诱发崩塌的条件因子,聘请有经验的专家对各项诱发因子进行诊断分析,以此作为判断条件,在G IS技术的支持下对诱发崩塌的条件因子进行空间分析,预测出招远金矿区发生崩塌的危害程度,为防治崩塌提供科学依据。预测结果表明,招远金矿区崩塌有进一步发展的可能,其中,高危险区有36820 m2,中易发区有50 610 m2,低易发区有67 200 m2,需要采取有效措施加以防治。     

Issues of Spatial and Temporal Variability in Climate Impact Studies

The accuracy of impact estimates relating climate change to regional-scale agricultural production is constrained by the temporal and spatial resolution of climate change projections. Several techniques have been used to compensate for these limitations in order to provide reasonable estimates of the impact of climate change on crop yield. One approach assumes that variability over time can substitute for spatial variability, thereby reducing the need to estimate the impacts at a spatially dense network of stations—an assumption that has not been generally tested. This study evaluates this assumption using methods similar to those employed in the climate impact literature. The findings suggest that current practices are generally defensible if the goal is to provide a range of possible crop responses to climate change. However, the results also show that the assumption is highly sensitive to specific interactions at the soil-plant-atmosphere interface and, consequently, does not hold under certain circumstances.     

Geostatistical Simulation with a Trend Using Gaussian Mixture Models

Geostatistics applies statistics to quantitatively describe geological sites and assess the uncertainty due to incomplete sampling. Strong assumptions are required regarding the location independence of statistical parameters to construct numerical models with geostatistical tools. Most geological data exhibit large-scale deterministic trends together with short-scale variations. Such location dependence violates the common geostatistical assumption of stationarity. The trend-like deterministic features should be modeled prior to conventional geostatistical prediction and accounted for in subsequent geostatistical calculations. The challenge of using a trend in geostatistical simulation algorithms for the continuous variable is the subject of this paper. A stepwise conditional transformation with a Gaussian mixture model is considered to provide a stable and artifact-free numerical model. The complex features of the regionalized variable in the presence of a trend are removed in the forward transformation and restored in the back transformation. The Gaussian mixture model provides a seamless bin-free approach to transformation. Data from a copper deposit were used as an example. These data show an apparent trend unsuitable for conventional geostatistical algorithms. The result shows that the proposed algorithm leads to improved geostatistical models.