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.     

Additional Samples: Where They Should Be Located

Information for mine planning requires to be close spaced, if compared to the grid used for exploration and resource assessment. The additional samples collected during quasimining usually are located in the same pattern of the original diamond drillholes net but closer spaced. This procedure is not the best in mathematical sense for selecting a location. The impact of an additional information to reduce the uncertainty about the parameter been modeled is not the same everywhere within the deposit. Some locations are more sensitive in reducing the local and global uncertainty than others. This study introduces a methodology to select additional sample locations based on stochastic simulation. The procedure takes into account data variability and their spatial location. Multiple equally probable models representing a geological attribute are generated via geostatistical simulation. These models share basically the same histogram and the same variogram obtained from the original data set. At each block belonging to the model a value is obtained from the n simulations and their combination allows one to access local variability. Variability is measured using an uncertainty index proposed. This index was used to map zones of high variability. A value extracted from a given simulation is added to the original data set from a zone identified as erratic in the previous maps. The process of adding samples and simulation is repeated and the benefit of the additional sample is evaluated. The benefit in terms of uncertainty reduction is measure locally and globally. The procedure showed to be robust and theoretically sound, mapping zones where the additional information is most beneficial. A case study in a coal mine using coal seam thickness illustrates the method.     

Using PETRIMES to estimate mercury deposits in California

In this article, we examine the use of an unconventional procedure, PETRIMES, to estimate mineral resources of mercury deposits in California. The study, which is based on the nonparametric discovery process model and Q-Q plots, suggests that a lognormal distribution is appropriate for the mercury deposits in California. The results of the assessment are summarized as follows: (1) the total number of mercury deposits in the population is approximately 165; (2) the median value of the largest undiscovered deposit size is 487 flasks; (3) the mean of the remaining mercury potential is 2,500 flasks; and (4) the population resource ranges from 1,040,000 to 4,300,000 flasks (at a 0.9 probability level).     

Map Scale Effects on Estimating the Number of Undiscovered Mineral Deposits

Estimates of numbers of undiscovered mineral deposits, fundamental to assessing mineral resources, are affected by map scale. Where consistently defined deposits of a particular type are estimated, spatial and frequency distributions of deposits are linked in that some frequency distributions can be generated by processes randomly in space whereas others are generated by processes suggesting clustering in space. Possible spatial distributions of mineral deposits and their related frequency distributions are affected by map scale and associated inclusions of non-permissive or covered geological settings. More generalized map scales are more likely to cause inclusion of geologic settings that are not really permissive for the deposit type, or that include unreported cover over permissive areas, resulting in the appearance of deposit clustering. Thus, overly generalized map scales can cause deposits to appear clustered. We propose a model that captures the effects of map scale and the related inclusion of non-permissive geologic settings on numbers of deposits estimates, the zero-inflated Poisson distribution. Effects of map scale as represented by the zero-inflated Poisson distribution suggest that the appearance of deposit clustering should diminish as mapping becomes more detailed because the number of inflated zeros would decrease with more detailed maps. Based on observed worldwide relationships between map scale and areas permissive for deposit types, mapping at a scale with twice the detail should cut permissive area size of a porphyry copper tract to 29% and a volcanic-hosted massive sulfide tract to 50% of their original sizes. Thus some direct benefits of mapping an area at a more detailed scale are indicated by significant reductions in areas permissive for deposit types, increased deposit density and, as a consequence, reduced uncertainty in the estimate of number of undiscovered deposits. Exploration enterprises benefit from reduced areas requiring detailed and expensive exploration, and land-use planners benefit from reduced areas of concern.     

Uncertainty and sensitivity analysis: tools for GIS-based model implementation

A novel procedure to analyse the uncertainty associated to the output of GIS-based models is presented. The procedure can handle models of any degree of complexity that accept any kind of input data. Two important aspects of spatial modelling are addressed: the propagation of uncertainty from model inputs and model parameters up to the model output (uncertainty analysis); and the assessment of the relative importance of the sources of uncertainty in the output uncertainty (sensitivity analysis). Two main applications are proposed. The procedure allows implementation of a GIS-based model whose output can reliably support the decision process with an optimized allocation of resources for spatial data acquisition. This is possible in low cost strategy, based on numerical simulations on a small prototype of the GIS-based model. Furthermore, the procedure provides an effective model building tool to choose, from a group of alternative models, the best one in terms of cost-benefit analysis. A comprehensive case study is described. It concerns the implementation of a new GIS-based hydrologic model, whose goal is providing near real-time flood forecasting.     

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.

     

Geologic Coal Assessment: The Interface with Economics

Geologic resource assessments describe the location, general characteristics, and estimated volumes of resources, whether in situ or technically recoverable. Such compilations are only an initial step in economic resource evaluation. This paper identifies, by examples from the Illinois and Appalachian basins, the salient features of a geologic assessment that assure its usefulness to downstream economic analysis. Assessments should be in sufficient detail to allocate resources to production units (mines or wells). Coal assessments should include the spatial distribution of coal bed characteristics and the ability to allocate parts of the resource to specific mining technologies. For coal bed gas assessment, the production well recoveries and well deliverability characteristics must be preserved and the risk structure should be specified so dryholes and noncommercial well costs are recovered by commercially successful wells.     

Geostatistical Simulation of Acoustic Log Data for Seismic Depth Conversion

Seismic reflection methods measure the time a seismic wave takes to travel through the ground, from the user defined source to a series of signal monitoring sensors known as geophones. The measured times need to be depth converted to allow for integration with other geological data. In order to convert from time to depth, an estimate of the rock volume velocity field must be made. The velocity field estimate can be made by assignment of velocity estimates to a geological model independent of the seismic processing. This article presents the results of using the acoustic geophysical log data extrapolated via sequential Gaussian simulation to derive the velocity field. The uncertainties associated with the velocity estimates were significant and provided the means to assess confidence limits for the actual depth determination. The technique is assessed by application to a major coal deposit, approximately 2.1 m thick and 210 m deep. Considering only the uncertainty associated with estimating the velocity field, half of the confidence interval values showed approximately 1 m of uncertainty in depth. The application of sequential Gaussian simulation to model the 3D distribution of acoustic velocity can be extended to other geophysical log parameters or derived estimates.     

A Framework for Quantitative Assessment of Impacts Related to Energy and Mineral Resource Development

Natural resource planning at all scales demands methods for assessing the impacts of resource development and use, and in particular it requires standardized methods that yield robust and unbiased results. Building from existing probabilistic methods for assessing the volumes of energy and mineral resources, we provide an algorithm for consistent, reproducible, quantitative assessment of resource development impacts. The approach combines probabilistic input data with Monte Carlo statistical methods to determine probabilistic outputs that convey the uncertainties inherent in the data. For example, one can utilize our algorithm to combine data from a natural gas resource assessment with maps of sage grouse leks and piñon-juniper woodlands in the same area to estimate possible future habitat impacts due to possible future gas development. As another example: one could combine geochemical data and maps of lynx habitat with data from a mineral deposit assessment in the same area to determine possible future mining impacts on water resources and lynx habitat. The approach can be applied to a broad range of positive and negative resource development impacts, such as water quantity or quality, economic benefits, or air quality, limited only by the availability of necessary input data and quantified relationships among geologic resources, development alternatives, and impacts. The framework enables quantitative evaluation of the trade-offs inherent in resource management decision-making, including cumulative impacts, to address societal concerns and policy aspects of resource development.     

Annotated bibliography of methodology for assessment of undiscovered oil and gas resources

An annotated bibliography of methodology of assessment of undiscovered oil and gas resources is presented as a useful reference for those engaged in resource assessment. The articles that are included deal only with quantitative assessment of undiscovered or inferred resources. the articles in this bibliography are classified largely according to the major assessment method that was applied in each situation. Major assessment methods include areal and volumetric yield methods, field size distributions, historical extrapolation, deposit modeling, organic geochemical mass balance methods, and direct expert assessment. Other categories include mathematical tools, reserve growth/confirmation, quantitative characterization of undiscovered resources, and general topics. For the purpose of future updates, we solicit contributions of articles that may have been missed in the preparation of this bibliography.     

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.     

Choosing Between Two Kind of Sampling Patterns Using Geostatistical Simulation: Regularly Spaced or at High Uncertainty Locations?

Data from a mineral deposit are commonly obtained by core drilling. This kind of sampling involves high costs, limiting the number of drill holes. Additional holes should be located to bring the maximum benefit. The benefit can be evaluated by various ways and must take into account the goals of sampling. This article presents a case study where the deposit has been sampled and the new drillings must be added to reduce the uncertainty about a transfer function, Net Present Value (NPV) of the mining project. There are basically two ways to choose locations where new drillings should be placed for cases where the aim of sampling is to reduce uncertainty about a global function: the addition of new drillings outlining a quasi regular grid with previously collected drillings or the addition of new drillings on the locations of high uncertainty about the attribute of interest (or the attribute that is considered most influential in the transfer function). The performances of these patterns on reducing the uncertainty measured by the function selected are compared. The results point out that the most efficient pattern relates to the distribution (histogram) of the uncertainty about the attribute of interest. Thus, the choice of which sampling pattern should be adopted varies depending on data distribution and its influence on the transfer function.     

两种不确定性来源对干旱指数SPEI及干旱评估的影响

全球气候变暖背景下,干旱问题更加频繁、持久,影响范围也逐步扩大。采用干旱指数进行干旱评估与研究时,受多种因素影响,干旱评估结果往往存在一定的不确定性。以黑河流域为研究区,分析概率分布模型和参数估计误差这两种不确定性来源对标准化降水蒸散指数（Standardized precipitation evapotranspiration index,SPEI）和干旱特征变量（干旱强度、干旱峰值和干旱历时）的影响。结果表明：这两种来源均会对SPEI和干旱特征变量产生影响,且SPEI越极端,其影响越大,二者对于极端和严重干旱的影响程度远大于对轻度和中度干旱的影响;对于极端和严重干旱,概率分布模型导致的干旱强度和干旱峰值的不确定性更大,参数估计误差导致的干旱历时的不确定性更大。研究结果可为干旱的准确评估提供支撑,在防旱减灾工作中为制定更加准确有效的抗旱决策提供理论支持,以避免可能造成的减灾能力不足或抗旱资源的浪费。     

Development of an Improved Methodology to Assess Potential Unconventional Gas Resources

Considering the important role played today by unconventional gas resources in North America and their enormous potential for the future around the world, it is vital to both policy makers and industry that the volumes of these resources and the impact of technology on these resources be assessed. To provide for optimal decision making regarding energy policy, research funding, and resource development, it is necessary to reliably quantify the uncertainty in these resource assessments. Since the 1970s, studies to assess potential unconventional gas resources have been conducted by various private and governmental agencies, the most rigorous of which was by the United States Geological Survey (USGS). The USGS employed a cell-based, probabilistic methodology which used analytical equations to calculate distributions of the resources assessed. USGS assessments have generally produced distributions for potential unconventional gas resources that, in our judgment, are unrealistically narrow for what are essentially undiscovered, untested resources. In this article, we present an improved methodology to assess potential unconventional gas resources. Our methodology is a stochastic approach that includes Monte Carlo simulation and correlation between input variables. Application of the improved methodology to the Uinta–Piceance province of Utah and Colorado with USGS data validates the means and standard deviations of resource distributions produced by the USGS methodology, but reveals that these distributions are not right skewed, as expected for a natural resource. Our investigation indicates that the unrealistic shape and width of the gas resource distributions are caused by the use of narrow triangular input parameter distributions. The stochastic methodology proposed here is more versatile and robust than the USGS analytic methodology. Adoption of the methodology, along with a careful examination and revision of input distributions, should allow a more realistic assessment of the uncertainty surrounding potential unconventional gas resources.     

Estimates of Number of Undiscovered Deposits of Gold,Silver, Copper,Lead, and Zinc in the United States

Estimates of the number of undiscovered deposits offer a unique perspective on the nation's undiscovered mineral resources. As part of the 1998 assessment of undiscovered deposits of gold, silver, copper, lead, and zinc, estimates of the number of deposits were made for 305 of the 447 permissive tracts delineated in 19 assessment regions of the country. By aggregating number of undiscovered deposits by deposit type and by assessment region, a picture of the nation's undiscovered resources has emerged. For the nation as a whole, the mean estimate for the number of undiscovered deposits is 950. There is a 90% chance there are at least 747 undiscovered deposits and a 10% chance there are as many as 1,160 undiscovered deposits. For Alaska, the mean estimate for the number of undiscovered deposits is 281. There is a 90% chance there are at least 168 undiscovered deposits and a 10% chance there are as many as 402 undiscovered deposits. Assuming that the majority of deposits used to create the grade and tonnage models that formed the basis for estimating the number of undiscovered deposits are significant deposits, there remain about as many undiscovered deposits as have already been discovered. Consideration of the number of undiscovered deposits as part of national assessments carried out on a recurring basis serves as a leading indicator of the nation's total mineral resources.     

A Framework for Expert Judgment to Assess Oil and Gas Resources

In frontier areas, where well data are sparse, many organizations have used expert judgment to estimate undiscovered resources. In this process, several important issues arise. How should the knowledge be elicited? At what level of aggregation (geologic process model, play, petroleum system, country, etc.) should the assessment be performed? How and at what stage of the assessment process should feedback be given to assessors? Is independent replication of estimates possible? How are issues of dependency treated? When and how should uncertainty be specified? The context for this presentation will be the methodology used in the US Geological Survey's 1998 1002-Arctic National Wildlife Refuge assessment of oil and gas resources.

     

19562000年中国潜在蒸散量变化趋势

利用1956²000年全国580个气象站的逐月气候资料,采用FAO推荐的彭曼-孟蒂斯公式计算潜在蒸散量,对中国及十大流域这45年的潜在蒸散量时空分布特征和变化趋势进行了分析,并采用偏相关分析方法,对造成潜在蒸散量变化的主要气候影响因子进行了探讨。结果表明:45年中除松花江流域外,全国绝大多数流域的年和四季的潜在蒸散量均呈现减少趋势,南方各流域（西南诸河流域除外）年和夏季潜在蒸散量减少趋势尤其明显。1980²000年和1956¹979年两时段多年平均年潜在蒸散量差值表明,我国大部地区1980²000年时段较前一时段减少,山东半岛、黄河和长江源区、西南诸河的中西部以及宁夏等地则增多。分析还表明,全国及大多数流域的年和四季潜在蒸散量与日照时数、风速、相对湿度等要素关系密切,但这45年日照时数和/或风速的明显减少可能是导致大多数地区潜在蒸散量减少的主要原因。     

Public attitudes and policies toward mineral resources on the brink of the 21st century

In this issue, we feature an article by W. David Menzie, a research geologist with the U.S. Geological Survey, Reston, Virginia. Dr. Menzie is a leading expert on quantitative mineral-resource assessment. He has made significant contributions to quantitative assessment methodologies through the development of spatial mineral deposit density models, grade and tonnage models, and the design of metrics for describing mineral deposit occurrences. He has also studied the geology and mineral resources of the Circle quadrangle, Alaska. Dr. Menzie earned a B.S. degree in geology from Dickinson College, an M.S. in geology, an M.A. in statistics, and a Ph.D. in Geology from the Pennsylvania State University.     

河流水质风险评价的灰色-随机风险率方法

提出了量化影响河流水质的随机不确定性与灰色不确定性的水质超标灰色－随机风险率概念，建立了水质超标灰色－随机风险率评价模型。在水质单项参数评价模型中，将河流污染物浓度变量的分布处理成灰色概率分布，将污染物浓度超过水质类别标准值的风险率处理成灰色概率，即水质超标灰色－随机风险率。在水质综合评价模型中，河流水环境系统被考虑为担任某一使用可能的可靠性系统，而任意一种水质参数超标意味着河流水体使用功能不能得到应有的保证，也即表明水体综合评价超标，最后借鉴系统可靠性分析的理论和方法计算水质综合超标率。该方法应用于黄河花园口断面重金属污染风险评价。