Using a Discrete Fracture Network and Spatial Point Processes to Populate Veins and Model Grade in a Coarse Gold Deposit

Vein-hosted gold deposits are characterized by mineralization, which is spatially restricted to narrow vein structures. Drillholes intersecting a mineralized vein can lead to unreliable and biased assay values compared to selective mining unit scale block grades. In this work, a discrete fracture network is simulated and adapted to model gold mineralization within the veins. Veins are assumed planar and the required inputs are distributions of vein orientation, vein length, and vein intensity (i.e., density). These inputs are collected from drillhole data, geological mapping, and expert knowledge of the deposit. A spatial point process is then applied to model gold grade as discrete events or “nuggets,” which are spatially restricted to the simulated quartz veins for the case of incomplete mineralization of the veins; when the vein is completely mineralized, a vein thickness distribution is required. The methodology is applied to an epithermal gold deposit in northwestern British Columbia, Canada and shows improvement in restricting the influence of the high-grade gold samples without resorting to ad-hoc manipulation of input assays through capping or cutting. The final output of this methodology is a block model of gold grade, which better honors the spatial structure of the veins in the deposit and is suitable for use in mine planning or resource estimation.     

Grade and Tonnage Uncertainty Analysis of an African Copper Deposit Using Multiple-Point Geostatistics and Sequential Gaussian Simulation

Spatial uncertainty analysis is a complex and difficult task for orebody estimation in the mining industry. Conventional models (kriging and its variants) with variogram-based statistics fail to capture the spatial complexity of an orebody. Due to this, the grade and tonnage are incorrectly estimated resulting in inaccurate mine plans, which lead to costly financial decision. Multiple-point geostatistical simulation model can overcome the limitations of the conventional two-point spatial models. In this study, a multiple-point geostatistical method, namely SNESIM, was applied to generate multiple equiprobable orebody models for a copper deposit in Africa, and it helped to analyze the uncertainty of ore tonnage of the deposit. The grade uncertainty was evaluated by sequential Gaussian simulation within each equiprobable orebody models. The results were validated by reproducing the marginal distribution and two- and three-point statistics. The results show that deviations of volume of the simulated orebody models vary from ? 3 to 5% compared to the training image. The grade simulation results demonstrated that the average grades from the different simulation are varied from 3.77 to 4.92% and average grade 4.33%. The results also show that the volume and grade uncertainty model overestimates the orebody volume as compared to the conventional orebody. This study demonstrates that incorporating grade and volume uncertainty leads to significant changes in resource estimates.     

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.     

Geostatistical Algorithm Selection for Mineral Resources Assessment and its Impact on Open-pit Production Planning Considering Metal Grade Boundary Effect

Mine planning is influenced by many sources of uncertainty. Significant sources of geological uncertainty in mine planning include uncertainty in layout of geological domains and uncertainty in metal grades. These two sources of uncertainty cannot be modeled separately because the distribution of the grade is controlled usually by geological domains. Two approaches exist for combining these two sources of uncertainty: the joint simulation approach and the cascade approach. In this paper, these two approaches were compared using a real case study. To this end, uncertainty in iron grade (quantitative variable) and ore zones (qualitative variable) was modeled using both approaches. There were some considerable differences in the results obtained by each approach, which confirm the importance of choosing the most appropriate approach with consideration of the dominate features of a deposit.

     

Support and Information Effect Modeling for Recoverable Reserve Estimation of a Beach Sand Deposit in India

Application of geostatistics in estimating recoverable reserves of beach sand deposit is rare. This paper made an attempt to estimate local recoverable reserves using disjunctive kriging and discrete Gaussian model considering support and information effects for a beach sand deposit located in the eastern part of India. The dependence of different selective mining unit (SMU) sizes and different production sampling strategies on the estimated tonnage, metal quantity, and the ore tonnage versus metal quantity relationships has been examined. The results of the study show that nonlinear geostatistics should be used for more precise assessment of the grade, ore tonnage, and metal quantity and their relationships, which are necessary for recoverable reserve estimation. In selective mining operation, both support and information effects have significant influence on recoverable reserve. Recoverable reserve estimation based on SMU involves estimating grade distributions of mining unit with much bigger support than the available drill core sample data. Information effect comes into picture from the real scenario where the actual grades of the blocks remain unknown even during mining. At the mining stage, discrimination of ore and waste blocks is carried out based on estimated grades of the production samples and it is likely that the blocks might be misclassified as either ore or waste and thus sent to wrong destination. Information effect modeling makes the estimation more reliable by taking care of misclassification.     

Spatial Prediction of Lateral Variability of a Laterite-Type Bauxite Horizon Using Ancillary Ground-Penetrating Radar Data

Tropical laterite-type bauxite deposits often pose a unique challenge for resource modelling and mine planning due to the extreme lateral variability at the base of the bauxite ore unit within the regolith profile. An economically viable drilling grid is often rather sparse for traditional prediction techniques to precisely account for the lateral variability in the lower contact of a bauxite ore unit. However, ground-penetrating radar (GPR) offers an inexpensive and rapid method for delineating laterite profiles by acquiring fine-scale data from the ground. These numerous data (secondary variable) can be merged with sparsely spaced borehole data (primary variable) through various statistical and geostatistical techniques, provided that there is a linear relation between the primary and secondary variables. Four prediction techniques, including standard linear regression, simple kriging with varying local means, co-located cokriging and kriging with an external drift, were used in this study to incorporate exhaustive GPR data in predictive estimation the base of a bauxite ore unit within a lateritic bauxite deposit in Australia. Cross-validation was used to assess the performance of each technique. The most robust estimates are produced using ordinary co-located cokriging in accordance with the cross-validation analysis. Comparison of the estimates against the actual mine floor indicates that the inclusion of ancillary GPR data substantially improves the quality of the estimates representing the bauxite base surface.     

Economic Filters Applied to Quantitative Mineral Resource Simulations

The U.S. Geological Survey has developed a technique that allows mineral resource experts to apply economic filters to estimates of undiscovered mineral resources. This technique builds on previous work that developed quantitative methods for mineral resource assessments. A Monte-Carlo calculation uses mineral deposit models to estimate commodity grades and tonnages of undiscovered deposits. The results then are analyzed using simple estimates of capital expenditures and daily operating costs for a mine and associated mill. The daily operating costs and the value of the ore are used to calculate the net present value of the deposit, which is compared to the capital expenditures to determine whether the deposit is economic. Repetition of these calculations for many deposits produces a table that can be interpreted in terms of the probability of there being deposits that have anet present value exceeding some specified amount. Sample calculations indicate that applying economic filters to simulated mineral resources might change the perception of the results compared to presenting the calculations in terms of the expected mean gross-in-place value of the minerals.     

Large-scale mineral potential estimation for blind precious metal ore bodies

Conventional evaluation of quantitative mineral potential has focused on target selection at small scales. Mapping at small scales usually results in large-area targets, which may be suitable for grass-roots exploration or regional evaluation of potential. Unfortunately, the estimates in small-scale exploration are commonly associated with large uncertainties. Large-scale estimation is used for optimal in-fill drilling design and step-out drilling target selection. In-fill drilling helps to confirm ore-grade continuities and translate a portion of geological resources into minable reserves, whereas step-out target estimation is useful for finding new orebodies in the vicinity of known ore deposits. Both of these processes are necessary for mine development and production planning. A comprehensive methodology is proposed here, particularly for large-scale mineral exploration. The central information synthesizer is canonical or indicator favorability analysis. A case study is presented to demonstrate the methodology for large-scale target selection. The study involves a gold-mining district where step-out drilling targets are being sought to expand the resource base. Several drilling targets were delineated in the study region. Two of them were tested through surface sampling with positive results.     

Uncertainty Estimate in Resources Assessment: A Geostatistical Contribution

For many decades the mining industry regarded resources/reserves estimation and classification as a mere calculation requiring basic mathematical and geological knowledge. Most methods were based on geometrical procedures and spatial data distribution. Therefore, uncertainty associated with tonnages and grades either were ignored or mishandled, although various mining codes require a measure of confidence in the values reported. Traditional methods fail in reporting the level of confidence in the quantities and grades. Conversely, kriging is known to provide the best estimate and its associated variance. Among kriging methods, Ordinary Kriging (OK) probably is the most widely used one for mineral resource/reserve estimation, mainly because of its robustness and its facility in uncertainty assessment by using the kriging variance. It also is known that OK variance is unable to recognize local data variability, an important issue when heterogeneous mineral deposits with higher and poorer grade zones are being evaluated. Altenatively, stochastic simulation are used to build local or global uncertainty about a geological attribute respecting its statistical moments. This study investigates methods capable of incorporating uncertainty to the estimates of resources and reserves via OK and sequential gaussian and sequential indicator simulation The results showed that for the type of mineralization studied all methods classified the tonnages similarly. The methods are illustrated using an exploration drill hole data sets from a large Brazilian coal deposit.     

Computer Monte Carlo simulation in quantitative resource estimation

The method of making quantitative assessments of mineral resources sufficiently detailed for economic analysis is outlined in three steps. The steps are (1) determination of types of deposits that may be present in an area, (2) estimation of the numbers of deposits of the permissible deposit types, and (3) combination by Monte Carlo simulation of the estimated numbers of deposits with the historical grades and tonnages of these deposits to produce a probability distribution of the quantities of contained metal.Two examples of the estimation of the number of deposits (step 2) are given. The first example is for mercury deposits in southwestern Alaska and the second is for lode tin deposits in the Seward Peninsula.The flow of the Monte Carlo simulation program is presented with particular attention to the dependencies between grades and tonnages of deposits and between grades of different metals in the same deposit.     

重力测量在老挝万象盆地固体钾盐矿勘查中的有效性分析

老挝万象盆地钾盐矿赋矿地层为古近系古新统塔贡组下岩段,为隐伏矿层,分布面积广,厚度大,品位高。由于受钾盐矿层沉积基底地形差异及矿层的后期改造,钾盐矿层局部缺失。在钻探揭露控制矿层前预测矿体的赋存位置,可有效节约探矿成本。根据万象盆地古近系古新统塔贡组石盐岩、钾镁岩矿与泥岩之间存在密度差,认为重力测量能够有效区分盐类矿层的埋深、厚度,而钾盐矿层往往赋存于古近系古新统塔贡组巨厚层石盐矿层上部,重力负异常与钾盐矿层的对应性好,是钻探验证首选区域和万象盆地钾盐矿勘查较为有效的物探方法。     

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.     

马关都龙曼家寨锡锌多金属矿床经济评价研究

在对马关都龙曼家寨锡锌多金属矿床地质特征进行分析、研究的基础上,应用地质统计学的理论和方法,运用大型矿业专用软件Surpac建立了该矿体的原始资料数据库和三维数学模型.根据不同边界品位多方案圈定矿体,分别计算矿体的盈亏平衡品位、平均品位和综合品位.通过对比以平衡品位和综合品位圈定的矿体块体模型,对该矿床进行技术经济评价研究,得出了有利于矿产资源综合利用、减少资源浪费的以综合品位圈定矿体的结论.     

Exploring Spatially Non-stationary Relationships in the Determinants of Mineralization in 3D Geological Space

Exploring the spatial relationships between various geological features and mineralization is not only conducive to understanding the genesis of ore deposits but can also help to guide mineral exploration by providing predictive mineral maps. However, most current methods assume spatially constant determinants of mineralization and therefore have limited applicability to detecting possible spatially non-stationary relationships between the geological features and the mineralization. In this paper, the spatial variation between the distribution of mineralization and its determining factors is described for a case study in the Dingjiashan Pb–Zn deposit, China. A local regression modeling technique, geological weighted regression (GWR), was leveraged to study the spatial non-stationarity in the 3D geological space. First, ordinary least-squares (OLS) regression was applied, the redundancy and significance of the controlling factors were tested, and the spatial dependency in Zn and Pb ore grade measurements was confirmed. Second, GWR models with different kernel functions in 3D space were applied, and their results were compared to the OLS model. The results show a superior performance of GWR compared with OLS and a significant spatial non-stationarity in the determinants of ore grade. Third, a non-stationarity test was performed. The stationarity index and the Monte Carlo stationarity test demonstrate the non-stationarity of all the variables throughout the area. Finally, the influences of the degree of non-stationary of all controlling factors on mineralization are discussed. The existence of significant non-stationarity of mineral ore determinants in 3D space opens up an exciting avenue for research into the prediction of underground ore bodies.

     

On a proposed plutonic porphyry gold deposit model

A plutonic porphyry gold deposit model is proposed that is imilar to the plutonic porphyry copper deposit model. However, unlike the plutonic porphyry copper deposit model, the proposed model is deficient in copper and contains less than 1 percent total sulfides. In the proposed model, gold is accompanied by scheelite, molybdenite, arsenopyrite, a variety of bismuth sulfides, tellurides, and native bismuth. The host rock varies from granite to granodiorite stock. Most of the ore is in the pluton. Deposits cited as examples of the proposed model are the Mokrsko deposit in Czechoslovakia, the Fort Knox deposit in the United States, and the Dublin Gulch deposit in Canada. In each of these deposits, pervasive potassic or phyllic alteration zones accompany the gold ore, which is disseminated in quartz-rich stockworks, veinlet swarms, and veins. Tonnages of gold-bearing material are large, but grades are low in the cited deposits. The proposed model is distinct from other gold deposit models because of the low Cu to Au ratio and the association of Au, Bi, W, and Mo.     

Typing Mineral Deposits Using Their Grades and Tonnages in an Artificial Neural Network

A test of the ability of a probabilistic neural network to classify deposits into types on the basis of deposit tonnage and average Cu, Mo, Ag, Au, Zn, and Pb grades is conducted. The purpose is to examine whether this type of system might serve as a basis for integrating geoscience information available in large mineral databases to classify sites by deposit type. Benefits of proper classification of many sites in large regions are relatively rapid identification of terranes permissive for deposit types and recognition of specific sites perhaps worthy of exploring further.Total tonnages and average grades of 1,137 well-explored deposits identified in published grade and tonnage models representing 13 deposit types were used to train and test the network. Tonnages were transformed by logarithms and grades by square roots to reduce effects of skewness. All values were scaled by subtracting the variable's mean and dividing by its standard deviation. Half of the deposits were selected randomly to be used in training the probabilistic neural network and the other half were used for independent testing. Tests were performed with a probabilistic neural network employing a Gaussian kernel and separate sigma weights for each class (type) and each variable (grade or tonnage).Deposit types were selected to challenge the neural network. For many types, tonnages or average grades are significantly different from other types, but individual deposits may plot in the grade and tonnage space of more than one type. Porphyry Cu, porphyry Cu-Au, and porphyry Cu-Mo types have similar tonnages and relatively small differences in grades. Redbed Cu deposits typically have tonnages that could be confused with porphyry Cu deposits, also contain Cu and, in some situations, Ag. Cyprus and kuroko massive sulfide types have about the same tonnages. Cu, Zn, Ag, and Au grades. Polymetallic vein, sedimentary exhalative Zn-Pb, and Zn-Pb skarn types contain many of the same metals. Sediment-hosted Au, Comstock Au-Ag, and low-sulfide Au-quartz vein types are principally Au deposits with differing amounts of Ag.Given the intent to test the neural network under the most difficult conditions, an overall 75% agreement between the experts and the neural network is considered excellent. Among the largestclassification errors are skarn Zn-Pb and Cyprus massive sulfide deposits classed by the neuralnetwork as kuroko massive sulfides—24 and 63% error respectively. Other large errors are the classification of 92% of porphyry Cu-Mo as porphyry Cu deposits. Most of the larger classification errors involve 25 or fewer training deposits, suggesting that some errors might be the result of small sample size. About 91% of the gold deposit types were classed properly and 98% of porphyry Cu deposits were classes as some type of porphyry Cu deposit. An experienced economic geologist would not make many of the classification errors that were made by the neural network because the geologic settings of deposits would be used to reduce errors. In a separate test, the probabilistic neural network correctly classed 93% of 336 deposits in eight deposit types when trained with presence or absence of 58 minerals and six generalized rock types. The overall success rate of the probabilistic neural network when trained on tonnage and average grades would probably be more than 90% with additional information on the presence of a few rock types.     

An Analysis of the Published Mineral Resource Estimates of the Haji-Gak Iron Deposit,Afghanistan

The Haji-Gak iron deposit of eastern Bamyan Province, eastern Afghanistan, was studied extensively and resource calculations were made in the 1960s by Afghan and Russian geologists. Recalculation of the resource estimates verifies the original estimates for categories A (in-place resources known in detail), B (in-place resources known in moderate detail), and C₁ (in-place resources estimated on sparse data), totaling 110.8 Mt, or about 6% of the resources as being supportable for the methods used in the 1960s. C₂ (based on a loose exploration grid with little data) resources are based on one ore grade from one drill hole, and P₂ (prognosis) resources are based on field observations, field measurements, and an ore grade derived from averaging grades from three better sampled ore bodies. C₂ and P₂ resources are 1,659.1 Mt or about 94% of the total resources in the deposit. The vast P₂ resources have not been drilled or sampled to confirm their extent or quality. The purpose of this article is to independently evaluate the resources of the Haji-Gak iron deposit by using the available geologic and mineral resource information including geologic maps and cross sections, sampling data, and the analog-estimating techniques of the 1960s to determine the size and tenor of the deposit.     

Categorization of Mineral Resources Based on Different Geostatistical Simulation Algorithms: A Case Study from an Iron Ore Deposit

Mineral resource classification plays an important role in the downstream activities of a mining project. Spatial modeling of the grade variability in a deposit directly impacts the evaluation of recovery functions, such as the tonnage, metal quantity and mean grade above cutoffs. The use of geostatistical simulations for this purpose is becoming popular among practitioners because they produce statistical parameters of the sample dataset in cases of global distribution (e.g., histograms) and local distribution (e.g., variograms). Conditional simulations can also be assessed to quantify the uncertainty within the blocks. In this sense, mineral resource classification based on obtained realizations leads to the likely computation of reliable recovery functions, showing the worst and best scenarios. However, applying the proper geostatistical (co)-simulation algorithms is critical in the case of modeling variables with strong cross-correlation structures. In this context, enhanced approaches such as projection pursuit multivariate transforms (PPMTs) are highly desirable. In this paper, the mineral resources in an iron ore deposit are computed and categorized employing the PPMT method, and then, the outputs are compared with conventional (co)-simulation methods for the reproduction of statistical parameters and for the calculation of tonnage at different levels of cutoff grades. The results show that the PPMT outperforms conventional (co)-simulation approaches not only in terms of local and global cross-correlation reproductions between two underlying grades (Fe and Al₂O₃) in this iron deposit but also in terms of mineral resource categories according to the Joint Ore Reserves Committee standard.

     

Basic concepts in three-part quantitative assessments of undiscovered mineral resources

Since 1975, mineral resource assessments have been made for over 27 areas covering 5×10⁶ km² at various scales using what is now called the three-part form of quantitative assessment. In these assessments, (1) areas are delineated according to the types of deposits permitted by the geology,(2) the amount of metal and some ore characteristics are estimated using grade and tonnage models, and (3) the number of undiscovered deposits of each type is estimated.Permissive boundaries are drawn for one or more deposit types such that the probability of a deposit lying outside the boundary is negligible, that is, less than 1 in 100,000 to 1,000,000.