A Chart for Judging Optimal Sample Spacing for Ore Grade Estimation

Mineral deposit grades are usually estimated using data from samples of rock cores extracted from drill holes. Commonly, mineral deposit grade estimates are required for each block to be mined. Every estimated grade has always a corresponding error when compared against real grades of blocks. The error depends on various factors, among which the most important is the number of correlated samples used for estimation. Samples may be collected on a regular sampling grid and, as the spacing between samples decreases, the error of grade estimated from the data generally decreases. Sampling can be expensive. The maximum distance between samples that provides an acceptable error of grade estimate is useful for deciding how many samples are adequate. The error also depends on the geometry of a block, as lower errors would be expected when estimating the grade of large-volume blocks, and on the variability of the data within the region of the blocks. Local variability is measured in this study using the coefficient of variation (CV). We show charts analyzing error in block grade estimates as a function of sampling grid (obtained by geostatistical simulation), for various block dimensions (volumes) and for a given CV interval. These charts show results for two different attributes (Au and Ni) of two different deposits. The results show that similar errors were found for the two deposits, although they share similar features: sampling grid, block volume, CV, and continuity model. Consequently, the error for other attributes with similar features could be obtained from a single chart.     

Radial Basis Function Network for Ore Grade Estimation

This paper highlights the performance of a radial basis function (RBF) network for ore grade estimation in an offshore placer gold deposit. Several pertinent issues including RBF model construction, data division for model training, calibration and validation, and efficacy of the RBF network over the kriging and the multilayer perceptron models have been addressed in this study. For the construction of the RBF model, an orthogonal least-square algorithm (OLS) was used. The efficacy of this algorithm was testified against the random selection algorithm. It was found that OLS algorithm performed substantially better than the random selection algorithm. The model was trained using training data set, calibrated using calibration data set, and finally validated on the validation data set. However, for accurate performance measurement of the model, these three data sets should have similar statistical properties. To achieve the statistical similarity properties, an approach utilizing data segmentation and genetic algorithm was applied. A comparative evaluation of the RBF model against the kriging and the multilayer perceptron was then performed. It was seen that the RBF model produced estimates with the R ² (coefficient of determination) value of 0.39 as against of 0.19 for the kriging and of 0.18 for the multilayer perceptron.     

Spatial Pair-Copula Modeling of Grade in Ore Bodies: A Case Study

A real-world mining application of pair-copulas is presented to model the spatial distribution of metal grade in an ore body. Inaccurate estimation of metal grade in an ore reserve can lead to failure of a mining project. Conventional kriged models are the most commonly used models for estimating grade and other spatial variables. However, kriged models use the variogram or covariance function, which produces a single average value to represent the spatial dependence for a given distance. Kriged models also assume linear spatial dependence. In the application, spatial pair-copulas are used to appropriately model the non-linear spatial dependence present in the data. The spatial pair-copula model is adopted over other copula-based spatial models since it is better able to capture complex spatial dependence structures. The performance of the pair-copula model is shown to be favorable compared to a conventional lognormal kriged model.     

Selection of Optimal Thresholds for Estimation and Simulation Based on Indicator Values of Highly Skewed Distributions of Ore Data

This study strives to outline a geostatistics model for estimation and simulation of the Qolqoleh gold ore deposit located in Saqqez, NW of Iran. Considering that this gold deposit contains high-grade values, accurate evaluation of such values is of high importance, and therefore different methods based on indicator values, such as full indicator kriging (FIK) and sequential indicator simulation (SIS), have been employed to improve the accuracy of estimation and simulation of high-grade values. FIK and SIS cover the full range of grades based on several thresholds on the indicator data. The cumulative distribution function (CDF) is typically used for selection of threshold values. Given the highly skewed distribution of gold grade and its intense fluctuations, the number of thresholds is increased using CDF, which in turn results in a whole lot of calculations. To reduce the volume of calculations, the number–size (N–S) fractal model has been used to select thresholds. From such a model, all optimal thresholds are chosen with respect to geology and the unnecessary thresholds are excluded from selection. Thus, a study of the selection of optimal thresholds for estimation and simulation of a gold ore resource by means of FIK and SIS, respectively, based on thresholds selected using the N–S fractal model is presented. Finally, it is proved that results of these geostatistical methods based on thresholds selection from the N–S model appear to be better-positioned to explain ore grade variability compared to thresholds selected from the CDF and threshold selection from the N–S model is more effective for reducing the volume of required calculations.     

Application of a Modular Feedforward Neural Network for Grade Estimation

This article presents new neural network (NN) architecture to improve its ability for grade estimation. The main aim of this study is to use a specific NN which has a simpler architecture and consequently achieve a better solution. Most of the commonly used NNs have a fully established connection among their nodes, which necessitates a multivariable objective function to be optimized. Therefore, the more the number of variables in the objective function, the more the complexity of the NN. This leads the NN to trap in local minima. In this study, a new NN, in which the connections based on the final performance are eliminated, is used. Toward this aim, several network architectures were tested, and finally a network which yielded the minimum error was selected. This selected network has low complexity and connection among nodes which help the learning algorithm to converge rapidly and more accurately. Furthermore, this network has this ability to deal with the small number of data sets. For testing and evaluating this new method, a case study of an iron deposit was performed. Also, to compare the obtained results, some common techniques for grade estimation, e.g., geostatistics and multilayer perceptron (MLP) were used. According to the obtained results, this new NN architecture shows a better performance for grade estimation.     

A New Use for the Geography Chart

Abstract

Geography occupies a prominent position in the high school curriculum in China. The syllabus for geography, as for other subjects, has been centrally prescribed since the early 1900s but during the last 40 years it has undergone major changes. The current syllabus, which covers both human and physical aspects of the subject, also embraces people-environment and resource issues. Obstacles to the further development of the subject include a lack of qualified staff, wide variations in educational standards, and the fact that geography, although a “required” subject in some years, is not yet a compulsory subject in the University Entrance Examination. Gradually these problems are being addressed and there are grounds to be optimistic about the future of the discipline at this level in China.     

Systematic Geography for Grade 4: A Spatial Systems Approach

Abstract

Various social and geographical strategies that have been used to assign children to schools in the United States are examined in order to: 1) support the contention that social space and geographic space are rarely considered in concert in the context of community problem solving, 2) point out the need for the consideration of various socio-spatial concepts such as action space, territoriality, and neighborhood in social scientific research addressing itself to the understanding of social issues, and 3) urge consideration of the fundamental changes overtaking American society, particularly the processes of time-space convergence which underlie the socio-geographical reorganization of earth space.     

Economic-Geological Estimation of Gold and Ore Deposits Using Information-Analytical System for the Selection of Analogues

The computer system is developed for evaluation of gold deposits over the world using data collected by experts in the field of gold deposit geology. With the system in use, gold object of interest can be described on the basis of selected groups of tags. The similarity of the considered object to an object from the database is estimated by designed algorithms on the basis of available information characterizing the considered object. These algorithms allow to apply mathematical methods for analysis of the problem what improves quality and reliability of the results. By the method of analogue determination, user can always evaluate unknown properties of the considered object, as for example, ore formation type, economic geological estimate of the deposit on the basis of known properties of the determined analogue.The software equipped by an intuitive graphical interface is developed with use of GIS technologies and modern methods of object-oriented programming.     

The Spatial Distribution of Rapid Geomagnetic Fluctuations: Part II

i
A detailed examination has been made of some examples of rapid irregular magnetic field changes which occurred during a typical geomagnetic storm, selected from 180mm/h recordings. The following points were noted:
1. At a number of different times of day, the rapid irregular changes at a given observing station were extremely various. They varied widely in form, and loops ranged in shape from nearly linear ones to crude circles.
2. During a chosen interval, the rapid irregular changes at neighbouring stations were very similar, and between mid-latitude stations 1200 km apart there was still a strong relationship between the changes occurring during defined time intervals.
3. Phase differences between stations, during the chosen interval, were very small. The average phase gradient North to South was less than 0.5 ∼ 10–⁷ s/cm. There was a suggestion of an average phase gradient East to West of the order of 10–⁷ s/cm.
4. Vector diagrams of increments between selected times indicated large scale patterns in which the horizontal vectors tended to converge, the points of convergence being variable in position. To this extent, the changes examined cannot be distinguished either from micropulsations or from slow irregular variations.
5. Some of the evidence suggested a type of current circulation which either travelled eastwards as a whole, or spread in extent, while pulsating in amplitude.
6. The average phase gradient East to West and the suggestion of an eastward moving current circulation, both referring to daylight hemisphere changes, are reminiscent of a deduction by Dungey concerning propagation of waves on the Chapman-Ferraro surface.     

Sparse Data Division Using Data Segmentation and Kohonen Network for Neural Network and Geostatistical Ore Grade Modeling in Nome Offshore Placer Deposit

In this paper, sparse data problem in neural network and geostatistical modeling for ore-grade estimation was addressed in the Nome offshore placer gold deposit. The problem of sparse data arises because of the random data division into training, validation, and test subsets during ore-grade modeling. In this regard, the possibility of generating statistically dissimilar data subsets by random data division was also explored through a simulation exercise. A combined approach of data segmentation and application of a Kohonen network then was used to solve the data division problem. Two neural networks and five kriging models were applied for grade modeling. The neural network was trained using an early stopping method. Performance evaluation of the models was carried out on the test data set. The study results indicated that all the models that were investigated in this study performed almost equally. It was also revealed that by using the secondary variable watertable depth the neural network and the kriging models slightly improved their prediction precision. Further, the overall R ² of the models was poor as a result of high nugget (noisy) component in ore-grade variation.     

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.     

A prototype graphic landscape analysis system: Part 2. A bioeconomic analysis model for grazingland development

A linkage was developed between a spatial graphic landscape system and a bioeconomic analysis model for grazingland. User interactive models were described. The first model evaluated potential water sites based on potential grazing land harvest.The second modelevaluated potential water sites by comparing the annualized net present values of two different water facility developments. The third identified optimal areas of a landscape for woody brush treatment using a linear optimizing procedure. Example analyses are described and recommendations for improvements to future models made.     

最优城市规模理论的发展：文献评述（英文）

伴随着大量人口在城市的集聚,经济、社会和环境遭受了前所未有的压力,最优城市规模问题逐渐引起了广泛的重视,国内外广大学者对此进行了研究,取得了丰硕的成果,因此有必要对最优城市规模的研究进行系统的梳理与总结。本文根据国际上历年来相关理论研究与实证研究,通过运用对比分析与归纳分析两种分析方法,本文详细梳理了最优城市规模的概念与理论进展,介绍了最优城市规模研究的两种经典范式,即Henry George定理与新古典分析方法,同时对各种理论与方法的优点和不足进行了比较与评述。在此基础上,本文引入了供给导向的动态模型(SOUDY模型),提出了基于可持续发展与一般均衡分析的城市最优规模模型。结果表明:(1)单纯的最优城市规模理论来自主流经济学的成本效益分析,不能克服由于生产函数相同、城市最优规模相同的缺陷;(2)作为最优城市规模的经典分析范式之一,亨利·乔治定理近年来被越来越多地用于研究最优税收和公共产品问题,并逐渐失去了与最优城市规模的理论联系;(3)新古典主义的最优城市规模分析主要包括影响最优城市规模的外部性、城市规模的均衡和最优模型、最优城镇、产品多样化和城市规模分布等三种,这类研究仍处于城市最优规模研究的主流。并且与单一的最优城市规模相比,城市规模的最优分布问题受到了更多的关注;(4)以供给为导向的动态模型能够将空间维度融入到最优城市规模的经济研究中,并且放松了城市职能与城市规模之间的约束,对现实问题的解释更有说服力。同时,一般均衡分析作为一种重要的经济研究方法,为研究最优城市规模提供了新的视角。因此,供给导向的动态模型和一般均衡分析这两种新的研究范式,在最优城市规模的分析中更值得关注。     

Multiple Random Walk Simulation: A Fast Method to Map Grade Uncertainty with Large Datasets

Multiple Random Walk Simulation consists of a methodology adapted to run fast simulations if close-spaced data are abundant (e.g., short-term mining models). Combining kriging with the simulation of random walks attempts to approximate traditional simulation algorithm results but at a computationally faster way when there is a large amount of conditioning samples. This paper presents this new algorithm illustrating the situations where the method can be used properly. A synthetic study case is presented in order to illustrate the Multiple Random Walk Simulation and to analyze the speed and goodness of its results against the ones from using Turning Bands Simulation and Sequential Gaussian Simulation.