A Modified Weights-of-Evidence Method for Regional Mineral Resource Estimation

Weights-of-evidence (WofE) modeling and weighted logistic regression (WLR) are two methods of regional mineral resource estimation, which are closely related: For example, if all the map layers selected for further analysis are binary and conditionally independent of the mineral occurrences, expected WofE contrast parameters are equal to WLR coefficients except for the constant term that depends on unit area size. Although a good WofE strategy is supposed to achieve approximate conditional independence, a common problem is that the final estimated probabilities are biased. If there are N deposits in a study area and the sum of all estimated probabilities is written as S, then WofE generally results in S > N. The difference S − N can be tested for statistical significance. Although WLR yields S = N, WLR coefficients generally have relatively large variances. Recently, several methods have been developed to obtain WofE weights that either result in S = N, or become approximately unbiased. A method that has not been applied before consists of first performing WofE modeling and following this by WLR applied to the weights. This method results in modified weights with unbiased probabilities satisfying S = N. An additional advantage of this approach is that it automatically copes with missing data on some layers because weights of unit areas with missing data can be set equal to zero as is generally practiced in WofE applications. Some practical examples of application are provided.     

Assessment of Exploration Bias in Data-Driven Predictive Models and the Estimation of Undiscovered Resources

The spatial distribution of discovered resources may not fully mimic the distribution of all such resources, discovered and undiscovered, because the process of discovery is biased by accessibility factors (e.g., outcrops, roads, and lakes) and by exploration criteria. In data-driven predictive models, the use of training sites (resource occurrences) biased by exploration criteria and accessibility does not necessarily translate to a biased predictive map. However, problems occur when evidence layers correlate with these same exploration factors. These biases then can produce a data-driven model that predicts known occurrences well, but poorly predicts undiscovered resources. Statistical assessment of correlation between evidence layers and map-based exploration factors is difficult because it is difficult to quantify the “degree of exploration.” However, if such a degree-of-exploration map can be produced, the benefits can be enormous. Not only does it become possible to assess this correlation, but it becomes possible to predict undiscovered, instead of discovered, resources. Using geothermal systems in Nevada, USA, as an example, a degree-of-exploration model is created, which then is resolved into purely explored and unexplored equivalents, each occurring within coextensive study areas. A weights-of-evidence (WofE) model is built first without regard to the degree of exploration, and then a revised WofE model is calculated for the “explored fraction” only. Differences in the weights between the two models provide a correlation measure between the evidence and the degree of exploration. The data used to build the geothermal evidence layers are perceived to be independent of degree of exploration. Nevertheless, the evidence layers correlate with exploration because exploration has preferred the same favorable areas identified by the evidence patterns. In this circumstance, however, the weights for the “explored” WofE model minimize this bias. Using these revised weights, posterior probability is extrapolated into unexplored areas to estimate undiscovered deposits.     

A Modified Weights-of-Evidence Method for Mineral Potential Prediction Based on Structural Equation Modeling

Structural equation modeling (SEM) was applied here to modify the ordinary weights-of-evidence (WofE) method for calculating posterior probability to improve conditional independence (CI) in the application of this method mineral potential prediction. The new method attempts to reduce the effect of CI by defining new binary patterns with an optimum combination of cutoff values of patterns. The solution is calculated through SEM, and the goodness of fit between evidence and mineral deposit occurrences is evaluated by a specified target function. The main difference between the new WofE and ordinary WofE is that evidence in the new method maintains a balance between the significance for mineral potential prediction and CI, rather than the significance for mineral prediction only as in ordinary WofE. A case study of prediction of potential for hydrothermal Au mineral deposits in Nova Scotia, Canada, is discussed here. The results indicate that the new method performs better than the ordinary WofE.

     

Sediment yield and spurious correlation—toward a better portrayal of the annual suspendend-sediment load of rivers

Bivariate relations between annual sediment yield (tons per year per unit drainage area) and drainage-basin area are spurious because drainage-basin area is common to both axes. Two alternative methods for portraying the annual suspended-sediment load of a river are suggested. One method consists of plotting suspended-sediment load (tons per year) against distance downstream. Such plots indicate that annual suspended-sediment load does not necessarily have a linear relationship with distance. The second method consists of plotting annual suspended-sediment load against drainage-basin area. Both methods more accurately portray fundamental relations between annual sediment load and drainage-basin characteristics than does the yield-area relation because spurious correlation is avoided. Plots were made of annual suspended-sediment load versus time for several stations along each of eight rivers for the 10–15 years of available data. The plots are in-phase with respect to relative magnitude of annual sediment loads.     

Classification of Soil Groups Using Weights-of-Evidence-Method and RBFLN-Neural Nets

Weights-of-Evidence (WofE) and Radial Basis Function Link Net (RBFLN) were applied to soil group mapping in eastern Finland. The data consisted of low altitude airborne geophysical measurements, Landsat 5 TM-satellite image, and digital elevation model (DEM) and slope information derived from it. Probability maps were constructed for each soil group one by one and combined into a prediction map of soil groups using maximum posterior probability (WofE) or pattern membership (RBFLN). Self-Organizing Map (SOM) and Sammon’s Mapping were applied for selecting the data sets for modeling and visualizing the data. The soil types belonging to each soil group used in the Arc-SDM modeling were defined by clusters revealed by the SOM and Sammon’s Mapping algorithms. The soil types with similar characters were collected in the same cluster. Numerical evaluation of the models’ performance was performed using the confusion matrix. The Ratio of Correct Classifications (RCC) for the best WofE model was 0.64 in the training area and 0.61 in the testing area. The RCC for the best RBFLN model was 0.62. Modeling of soil groups using Arc-SDM is time consuming because models need to be constructed for each soil group before combining them into a final prediction map. In this study a simple method was tested for combining the maps. In the future, more attention should be paid to combining the posterior probability models and also to selecting data sets used for modeling.     

Rapid zonation of abrupt mass movement hazard: Part I. General principles

Hazards caused by mass movement cost many human lives and cause severe damage to property. Accurate zonation of such hazards provides an important tool for preventive measures. Previous approaches for mass movement hazard zonation are costly because they require large amounts of data, time and labor, and are only applicable to specific local areas. In this paper, a Rapid Zonation of Abrupt Mass-movement Hazard (RZAMH), applicable to large regions, is proposed. It involves the selection of appropriate zonation principles, routes, units, and indexes that can be used for the classification of reference groups, identification of matching groups of test sites, evaluation of blank test sites, and coalescence of sub-regions into specified zonation areas. The K-means clustering method is used in the classification processes. The applicability of the RZAMH approach to a large area implies that the number of reference sites required to build the reference groups is not of primary importance as long as the reference sites are representative. Therefore, for large areas, the RZAMH approach would be more economical than other conventional methods. The RZAMH approach is probably applicable to all abrupt mass movement hazards including rock falls, landslides, and debris flows.     

Interactive discovery of sequential patterns in time series of wind data

Wind speed and direction vary over space and time due to the interactions between different pressures and temperature gradients within the atmospheric layers. Near the earth’s surface, these interactions are modulated by topography and artificial structures. Hence, characterizing wind behaviour over large areas and long periods is a complex but essential task for various energy-related applications. In this study, we present a novel approach to discover wind patterns by integrating sequential pattern mining and interactive visualization techniques. The approach relies on the use of the Linear time Closed pattern Miner sequence algorithm in conjunction with a time sliding window that allows the discovery of all sequential patterns present in the data. These patterns are then visualized using integrated 2D and 3D coordinated multiple views and visually explored to gain insight into the characteristics of the wind from a spatial, temporal and attribute (type of wind pattern) point of view. This proposed approach is used to analyse 10 years of hourly wind speed and direction data for 29 weather stations in the Netherlands. The results show that there are 15 main sequential patterns in the data. The spatial task shows that weather stations located in the same region do not necessarily experience similar wind pattern. For within the selected time interval, similar wind patterns can be observed in different stations and in the same station at different times of occurrence. The attribute task discovered that the repetitive occurrences of chosen pattern indicate as regular wind behaviour at different weather stations that persisted continuously over time. The results of these tasks show that the proposed interactive discovery facilitates the understanding of wind dynamics in space and time.     

Weights of Evidence Modeling of Mineral Potential: A Case Study Using Small Number of Prospects,Abra, Philippines

Weights of evidence (WofE) modeling usually is applied to map mineral potential in areas with large number of deposits/prospects. In this paper, WofE modeling is applied to a case study area measuring about 920 km² with 12 known porphyry copper prospects. A pixel size of 100 m × 100 m was used in the spatial data analyses to represent in a raster-based GIS lateral extents of prospects and of geological features considered as spatial evidence. Predictor maps were created based on (a) estimates of studentized values of positive spatial association between prospects and spatial evidence; (b) proportion of number of prospects in zones where spatial evidence is present; and (c) geological interpretations of positive spatial association between prospects and spatial evidence. Uncertainty because of missing geochemical evidence is shown to have an influence on tests of assumption of conditional independence (CI) among predictor maps with respect to prospects. For the final predictive model, assumption of CI is rejected based on omnibus test but is accepted based on a new omnibus test. The final predictive model, which delineates 30% of study area as zones with potential for porphyry copper, has 83% success rate and 73% prediction rate. The results demonstrate plausibility of WofE modeling of mineral potential in large areas with small number of mineral prospects.     

黄土高原典型流域LCM模型集总、半分布和分布式构建对比分析

暴雨中心的空间分布是影响小流域暴雨洪水过程模拟精度的关键要素。不同模型构建方式对降雨空间异质性的响应差异很大,选择恰当的水文模型构建方式对提高模型计算效率,减少降雨空间异质性对模型的影响从而提高预测精度具有重要意义。为此,本文基于刘昌明提出的适用于黄土高原超渗产流机制的LCM （Liu Changming Model）模型,分别构建了集总式、半分布式和全分布式的暴雨—径流模型,旨在比较分析不同模型构建方式对于降雨空间异质性的响应及其对模拟精度和计算效率的影响。结果表明：分布式构建模拟精度最高,纳什效率系数达到0.81,相关系数达到0.82;集总式构建计算时间最短;相比较而言,半分布式构建方法纳什效率系数达到0.78,主峰值模拟精度分别达到76.1%和65.8%。总体上,全分布式构建方法模拟精度最高,集总式计算耗时最短效率最高,半分布式在保持较高模拟精度的同时也具有较高的计算效率。     

Modeling the spatial patterns of human wildfire ignition in Yunnan province,China

Despite wildfire being an important regulator of dryland ecosystems, uncontrolled wildfire can be harmful to both forest ecosystems and human society, and wildfire prevention and control continue to raise worldwide concern. Wildfire management depends on knowledge of wildfire ignitions, both for cause and location. The regimes and factors influencing wildfire ignition have been studied at length. Humans have a profound effect on fire regimes and human activity is responsible for igniting the largest number of fires in our study area. Understanding the spatial patterns of ignitions is foremost to achieving efficiency in wildfire prevention. Previous studies mainly concentrate on overall wildfire risk integrating numerous factors simultaneously, yet the importance of human factors on ignition has not received much attention. In this study, we mapped human accessibility to explore the influence of human activity on wildfire ignition in a simple and straightforward way. A Bayesian weights-of-evidence (WofE) method was developed based on fire hotspots in China's Yunnan province extracted from satellite images and verified as known wildfires for the period 2007–2013. We considered a set of factors that impact fire ignition as associated with human accessibility: the locations of settlements, roads, water and farmland susceptible to human wildfire ignition. Known points of likely wildfire ignition were selected as training samples and all suspected thematic maps of the factors were taken as explanatory layers. Next, the weights of each layer in terms of its explanatory power were computed and used to generate evidence based on a threshold to pass a statistical test. The conditional independence (CI) of each layer was checked with the Agterberg-Cheng test. Finally, the posterior probability was calculated and its precision validated using samples of both presence and absence by withheld validation data. A comparison of WofE models was made to test the predictability. Results show proximity to villages, roads and farmland are strongly associated with human wildfire ignition and that wildfire more often occurs at an intermediate distance from high-density human activity. The WofE method proved more powerful than logistic regression, improving predictive accuracy by 10% and was more straightforward in presenting the association of dependence and independence. In addition, WofE with 1000 m buffer bands is more robust in predicting human wildfire ignition risk than binary or 100 m buffers for the ecoregion studied. Our results are significant for advising practical wildfire management and resource allocation, evaluation of human ignition control and also provides a foundation for future efforts toward integrated wildfire prediction.     

Descriptive and Predictive Growth Curves in Energy System Analysis

This study reviews a variety of growth curve models and the theoretical frameworks that lay behind them. In many systems, growth patterns are, or must, ultimately be subjected to some form of limitation. A number of curve models have been developed to describe and predict such behaviours. Symmetric growth curves have frequently been used for forecasting fossil fuel production, but others have expressed a need for more flexible and asymmetric models. A number of examples show differences and applications of various growth curve models. It is concluded that these growth curve models can be utilised as forecasting tools, but they do not necessarily provide better predictions than any other method. Consequently, growth curve models and other forecasting methods should be used together to provide a triangulated forecast. Furthermore, the growth curve methodology offers a simple tool for resource management to determine what might happen to future production if resource availability poses a problem. In the light of peak oil and the awareness of natural resources being considered as a basis for the continued well-being of the society and the mankind, resource management should be treated as an important factor in future social planning.     

A Comparative Analysis of Weights of Evidence,Evidential Belief Functions,and Fuzzy Logic for Mineral Potential Mapping Using Incomplete Data at the Scale of Investigation

Large amounts of digital data must be analyzed and integrated to generate mineral potential maps, which can be used for exploration targeting. The quality of the mineral potential maps is dependent on the quality of the data used as inputs, with higher quality inputs producing higher quality outputs. In mineral exploration, particularly in regions with little to no exploration history, datasets are often incomplete at the scale of investigation with data missing due to incomplete mapping or the unavailability of data over certain areas. It is not always clear that datasets are incomplete, and this study examines how mineral potential mapping results may differ in this context. Different methods of mineral potential mapping provide different ways of dealing with analyzing and integrating incomplete data. This study examines the weights of evidence (WofE), evidential belief function and fuzzy logic methods of mineral potential mapping using incomplete data from the Carajás mineral province, Brazil to target for orogenic gold mineralization. Results demonstrate that WofE is the best one able to predict the location of known mineralization within the study area when either complete or unacknowledged incomplete data are used. It is suggested that this is due to the use of Bayes’ rule, which can account for “missing data.” The results indicate the effectiveness of WofE for mineral potential mapping with incomplete data.     

A hybrid calculation technique of the Indirect Boundary Element Method and the analytical solutions for three-dimensional problems of topography

We present a new approach of the Indirect Boundary Element Method (IBEM) for 3-D topographic problems which can be used to deal with an infinitely spread free surface owing to the introduction of a reference solution, that is the analytical solution for the half-space with a flat free surface. This approach is an efficient countermeasure for the non-physical waves owing to the domain truncation which contaminates the computed results in the ordinary approach. Theoretical consideration shows that this newly proposed approach is a higher-grade approximation than some existing ones and achieves a higher efficacy and accuracy than those of existing ones. The discretization of the resulting boundary integral equation for this formulation is carried out with triangular elements. Their contributions to the solution are calculated by Gaussian numerical integration except in the case where the wavefield is evaluated on the source element itself. For this case, we present an analytical formula based on the reasonable assumption that the elements are much smaller than the wavelengths appearing in the calculation. Several numerical examples used for validation show acceptably precise results.     

老年人移动构成的时空——老龄化地理学中非表征理论的引入①

本文主要介绍了非表征理论及其在老龄化地理学研究中的运用。该理论的引入将使老龄化地理学成为一个重新焕发活力的研究领域。该领域涉及老年人生活中广泛而多样的空间移动与体验,涵盖移动的参与者、时效性和感知等维度,从而更好地表达和反映空间移动的本质特征。     

A procedure for landslide susceptibility zonation by the conditional analysis method

Numerous methods have been proposed for landslide probability zonation of the landscape by means of a Geographic Information System (GIS). Among the multivariate methods, i.e. those methods which simultaneously take into account all the factors contributing to instability, the Conditional Analysis method applied to a subdivision of the territory into Unique Condition Units is particularly straightforward from a conceptual point of view and particularly suited to the use of a GIS. In fact, working on the principle that future landslides are more likely to occur under those conditions which led to past instability, landslide susceptibility is defined by computing the landslide density in correspondence with different combinations of instability factors. The conceptual simplicity of this method, however, does not necessarily imply that it is simple to implement, especially as it requires rather complex operations and a high number of GIS commands. Moreover, there is the possibility that, in order to achieve satisfactory results, the procedure has to be repeated a few times changing the factors or modifying the class subdivision. To solve this problem, we created a shell program which, by combining the shell commands, the GIS Geographical Research Analysis Support System (GRASS) commands and the gawk language commands, carries out the whole procedure automatically. This makes the construction of a Landslide Susceptibility Map easy and fast for large areas too, and even when a high spatial resolution is adopted, as shown by application of the procedure to the Parma River basin, in the Italian Northern Apennines.     

A two-stage estimation method with bootstrap inference for semi-parametric geographically weighted generalized linear models

Semi-parametric geographically weighted generalized linear models (S-GWGLMs) are a useful tool in modeling a regression relationship where the impact of certain explanatory variables on a non-Gaussian distributed response variable is global while that of others is spatially varying. In this article, we propose for S-GWGLMs a new estimation method, called two-stage geographically weighted maximum likelihood estimation, and further develop a likelihood ratio statistic-based bootstrap test to determine constant coefficients in the models. The performance of the estimation and test methods is then evaluated by simulations. The results show that the proposed estimation method performs as well as the existing method in estimating both constant and spatially varying coefficients but it is more efficient in terms of computation time; the bootstrap test is of accurate size under the null hypothesis and satisfactory power in identifying spatially varying coefficients. A real-world data set is finally analyzed to demonstrate the application of the proposed estimation and test methods.     

Moment tensor inversions and source models

Summary. The use of a moment tensor formulation in source mechanism inversions is becoming more widespread. However, this method does not yield results that correspond to a double-couple source, which is still the preferred source model. This is because the double couple is characterized by extra constraints on the general symmetric moment tensor. A method is presented of imposing these non-linear constraints while retaining the linear nature of the inversion. An application of this result shows (1) that the double-couple model fits the body-wave data as well as more general models if one explicitly considers the fewer number of free parameters in the double couple and (2) that the principal axes of the moment tensor of the unconstrained model do not necessarily correspond to the P and T axes of the double couple.     

分布式水文模型的并行计算研究进展

大流域、高分辨率、多过程耦合的分布式水文模拟计算量巨大,传统串行计算技术不能满足其对计算能力的需求,因此需要借助于并行计算的支持。本文首先从空间、时间和子过程三个角度对分布式水文模型的可并行性进行了分析,指出空间分解的方式是分布式水文模型并行计算的首选方式,并从空间分解的角度对水文子过程计算方法和分布式水文模型进行了分类。然后对分布式水文模型的并行计算研究现状进行了总结。其中,在空间分解方式的并行计算方面,现有研究大多以子流域作为并行计算的基本调度单元;在时间角度的并行计算方面,有学者对时空域双重离散的并行计算方法进行了初步研究。最后,从并行算法设计、流域系统综合模拟的并行计算框架和支持并行计算的高性能数据读写方法3个方面讨论了当前存在的关键问题和未来的发展方向。     

Discrete displacement analysis for geographic linear features and the application to glacier termini

The extent of glacier terminus displacement is instrumental in investigations of natural or artificial geographic changes. Its importance to earth science and engineering is reflected in the considerable efforts that have been devoted to the development of several boundary displacement analysis methods. Among the methods, the buffering-based approach compares favorably with other approaches in objectivity and robustness. However, it does not consider the relative positions of boundaries, because its buffering operation cannot determine features' relative directions. This limitation incurs inaccurate calculation results – underestimation of mean shifts and overestimation of shape variations, especially when the two compared boundaries intersect. Discrete displacement analysis (DDA), an alternative method that considers given geographic objects as a set of a finite number of points, is proposed here. In a series of tests carried out, including Jakobshavn glacier's calving front, DDA was found to correctly calculate mean shift and shape variation even in cases where the conventional buffering-based method failed. Moreover, this approach is independent of the dimension of space in which it is implemented, and thus is expected to be utilized for analysis of 3D geographic object displacement.