Application of Gaussian Mixture Model and Geostatistical Co-simulation for Resource Modeling of Geometallurgical Variables

Natural Resources Research - This work addresses the practice of resource calculation for geometallurgical variables. Similar to mineral resource modeling, estimation domains for geometallurgical...     

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.     

Assessment of Geochemical Anomaly Uncertainty Through Geostatistical Simulation and Singularity Analysis

Natural Resources Research - Geochemical anomalies are commonly separated into different geochemical anomaly levels based on one or more thresholds. However, this practice may cause some important...     

Reservoir Characterization of McMurray Formation by 2D Geostatistical Modeling

There is a need to estimate reserve uncertainty for large lease areas. Detailed 3D models of heterogeneity are not necessarily required, but there is a need to integrate all available data into an in-situ reserve estimate with uncertainty. A 2D mapping approach is presented to appraise reserves accounting for multiple variables, multiple data sources, and uncertainty. The approach can be considered in three primary steps: (1) Bayesian updating is used to determine local distributions of uncertainty for each primary variable while integrating multiple secondary information, (2) matrix simulation is employed to jointly and simultaneously simulate multiple collocated variables to determine a derived variable such as OOIP, and (3) probability field simulation then is applied to permit joint simulation of multiple locations. This methodology permits local and global uncertainty assessment while integrating multiple sources of information. An application to the McMurray Formation in Alberta, Canada is demonstrated.     

Accounting for Parameter Uncertainty in Reservoir Uncertainty Assessment: The Conditional Finite-Domain Approach

An important aim of modern geostatistical modeling is to quantify uncertainty in geological systems. Geostatistical modeling requires many input parameters. The input univariate distribution or histogram is perhaps the most important. A new method for assessing uncertainty in the histogram, particularly uncertainty in the mean, is presented. This method, referred to as the conditional finite-domain (CFD) approach, accounts for the size of the domain and the local conditioning data. It is a stochastic approach based on a multivariate Gaussian distribution. The CFD approach is shown to be convergent, design independent, and parameterization invariant. The performance of the CFD approach is illustrated in a case study focusing on the impact of the number of data and the range of correlation on the limiting uncertainty in the parameters. The spatial bootstrap method and CFD approach are compared. As the number of data increases, uncertainty in the sample mean decreases in both the spatial bootstrap and the CFD. Contrary to spatial bootstrap, uncertainty in the sample mean in the CFD approach decreases as the range of correlation increases. This is a direct result of the conditioning data being more correlated to unsampled locations in the finite domain. The sensitivity of the limiting uncertainty relative to the variogram and the variable limits are also discussed.     

Implementation of the Iterative Proportion Fitting Algorithm for Geostatistical Facies Modeling

In geostatistics, most stochastic algorithm for simulation of categorical variables such as facies or rock types require a conditional probability distribution. The multivariate probability distribution of all the grouped locations including the unsampled location permits calculation of the conditional probability directly based on its definition. In this article, the iterative proportion fitting (IPF) algorithm is implemented to infer this multivariate probability. Using the IPF algorithm, the multivariate probability is obtained by iterative modification to an initial estimated multivariate probability using lower order bivariate probabilities as constraints. The imposed bivariate marginal probabilities are inferred from profiles along drill holes or wells. In the IPF process, a sparse matrix is used to calculate the marginal probabilities from the multivariate probability, which makes the iterative fitting more tractable and practical. This algorithm can be extended to higher order marginal probability constraints as used in multiple point statistics. The theoretical framework is developed and illustrated with estimation and simulation example.     

Geostatistical Modeling of Ore Grade Distribution from Geomorphic Characterization in a Laterite Nickel Deposit

Due to growing consumption of nickel (Ni) in a range of industries, the demand for Ni has increased rapidly around the world. This trend requires a more precise estimation of available Ni grade deposits and an identification of factors controlling the grade distribution. To achieve these requirements, this study applies geostatistical techniques to spatial modeling of the Ni grade in a laterite Ni deposit, with reference to geomorphic features such as slope gradient and the thickness of limonite and saprolite zones. The Sorowako area in Sulawesi Island, Indonesia, was chosen as a case study area because it has a representative laterite Ni deposit with large reserves. Chemical content data from drillhole cores at 294 points were used for the analysis. The slope gradient was found to have a remarkable correlation with the thickness of the limonite zone, but there was no correlation between the thickness of the limonite and the saprolite zones above the bedrock. One important feature was a general correlation between the thickness of the saprolite zone and the maximum Ni grade in this zone: the grade increases with the thickness of the zone. Co-kriging was adopted to incorporate this correlation into estimating the maximum Ni grade in the saprolite zone. As a result, the maximum Ni grade in the saprolite zone tends to be high mainly in areas of slight slope. The Ni accumulation at this topographic feature probably originates from deep weathering by groundwater infiltrating through well-developed rock fractures.     

DEM提取黄土高原地面坡度的不确定性

选择陕北黄土高原6个典型地貌类型区为试验样区,采用野外实测及高精度的1:1万比例尺DEM为基准数据,研究栅格分辨率及地形粗糙度对DEM所提取地面平均坡度精度的影响。结果显示,对于1:1万比例尺DEM,5 m是保证该地区地形描述精度的理想分辨率尺度;多要素逐步回归模拟的方法进一步揭示了DEM所提取的地面平均坡度误差E与栅格分辨率X以及地形起伏的代表性因子-沟壑密度S之间存在的量化关系为E = (0.0015S2+0.031S-0.0325)X-0.0045S2-0.155S+0.1625,该结果也为确定适用的DEM分辨率提供了理论依据。     

Nonparametric Geostatistical Simulation of Subsurface Facies: Tools for Validating the Reproduction of,and Uncertainty in,Facies Geometry

Delineation of facies in the subsurface and quantification of uncertainty in their boundaries are significant steps in mineral resource evaluation and reservoir modeling, which impact downstream analyses of a mining or petroleum project. This paper investigates the ability of nonparametric geostatistical simulation algorithms (sequential indicator, single normal equation and filter-based simulation) to construct realizations that reproduce some expected statistical and spatial features, namely facies proportions, boundary regularity, contact relationships and spatial correlation structure, as well as the expected fluctuations of these features across the realizations. The investigation is held through a synthetic case study and a real case study, in which a pluri-Gaussian model is considered as the reference for comparing the simulation results. Sequential indicator simulation and single normal equation simulation based on over-restricted neighborhood implementations yield the poorest results, followed by filter-based simulation, whereas single normal equation simulation with a large neighborhood implementation provides results that are closest to the reference pluri-Gaussian model. However, some biases and inaccurate fluctuations in the realization statistics (facies proportions, indicator direct and cross-variograms) still arise, which can be explained by the use of a single finite-size training image to construct the realizations.

     

大尺度水循环模拟系统不确定性研究进展

水循环过程受众多自然因素和人为因素影响,决定了水循环系统的变化性和复杂性。水循环系统模型作为研究流域水文循环过程及演变规律的重要工具,必然也存在较大的不确定性,特别是对于大尺度陆-气耦合下的水循环模拟系统,其不确定性来源包括输入和参数不确定性、结构不确定性、方法不确定性以及初始和边界条件不确定性。本文在分析不确定性量化方法和传统水文模型不确定性研究基础上,重点评述当前大尺度水循环系统模拟的不确定性研究进展和存在的瓶颈问题,并介绍一种针对大型复杂动力系统的不确定性量化解决方案和工具系统-PSUADE,基于此讨论PSUADE在大尺度水循环模拟系统不确定性量化过程中的优势。     

新疆流域水资源分配模拟系统设计

通过对有关项目研究成果的分析，总结了新疆流域水资源分配模拟系统设计的基本原理与方法。其中对模拟模型的建立、模拟系统的结构与各子模块的功能及寻求合理分水方案的方法进行了详细分析与说明。     

Developments in Quantitative Assessment and Modeling of Mineral Resource Potential: An Overview

Natural Resources Research - The special issue entitled “Developments in Quantitative Assessment and Modeling of Mineral Resource Potential” is composed of 17 papers that cover a...     

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.     

Multivariate Statistical Analysis and Geochemical Modeling to Characterize the Surface Water of Oued Chemora Basin,Algeria

Multivariate statistical methods and inverse geochemical modeling were jointly used to deduce the genetic origin of chemical parameters of surface water in the Oued Chemora Basin. The analysis of variance indicates that variations of all parameters at the three stations are significant except for pH and T (p > 0.05). R-mode cluster analysis reveals two distinct groups at each station and led to the conclusion that the major ion chemistry in the three stations is derived from organic and artificial fertilizers due to agricultural activities in the area and water–rock interaction. Mineral saturation indices, calculated from major ions, indicate that the surface water is generally super-saturated with carbonate phases, and all the water samples are under-saturated with respect to gypsum, halite, and CO_2(g). In a broad sense, the reactions responsible for the hydrochemical evolution in the Basin fall into three categories: (1) dissolution of evaporite minerals; (2) precipitation of carbonate minerals; and (3) ion exchange.     

Cost Implications of Uncertainty in CO<Subscript>2</Subscript> Storage Resource Estimates: A Review

Carbon capture from stationary sources and geologic storage of carbon dioxide (CO₂) is an important option to include in strategies to mitigate greenhouse gas emissions. However, the potential costs of commercial-scale CO₂ storage are not well constrained, stemming from the inherent uncertainty in storage resource estimates coupled with a lack of detailed estimates of the infrastructure needed to access those resources. Storage resource estimates are highly dependent on storage efficiency values or storage coefficients, which are calculated based on ranges of uncertain geological and physical reservoir parameters. If dynamic factors (such as variability in storage efficiencies, pressure interference, and acceptable injection rates over time), reservoir pressure limitations, boundaries on migration of CO₂, consideration of closed or semi-closed saline reservoir systems, and other possible constraints on the technically accessible CO₂ storage resource (TASR) are accounted for, it is likely that only a fraction of the TASR could be available without incurring significant additional costs. Although storage resource estimates typically assume that any issues with pressure buildup due to CO₂ injection will be mitigated by reservoir pressure management, estimates of the costs of CO₂ storage generally do not include the costs of active pressure management. Production of saline waters (brines) could be essential to increasing the dynamic storage capacity of most reservoirs, but including the costs of this critical method of reservoir pressure management could increase current estimates of the costs of CO₂ storage by two times, or more. Even without considering the implications for reservoir pressure management, geologic uncertainty can significantly impact CO₂ storage capacities and costs, and contribute to uncertainty in carbon capture and storage (CCS) systems. Given the current state of available information and the scarcity of (data from) long-term commercial-scale CO₂ storage projects, decision makers may experience considerable difficulty in ascertaining the realistic potential, the likely costs, and the most beneficial pattern of deployment of CCS as an option to reduce CO₂ concentrations in the atmosphere.     

Some Aspects of Resource Uncertainty and Their Economic Consequences in Assessment of the 1002 Area of the Arctic National Wildlife Refuge

Natural Resources Research - Exploration ventures in frontier areas have high risks. Before committing to them, firms prepare regional resource assessments to evaluate the potential payoffs. With...     

Geostatistical Simulation of Hydrofacies Heterogeneity of the West Thessaly Aquifer Systems in Greece

Integrating geological properties, such as relative positions and proportions of different hydrofacies, is of highest importance in order to render realistic geological patterns. Sequential indicator simulation (SIS) and Plurigaussian simulation (PS) are alternative methods for conceptual and deterministic modeling for the characterization of hydrofacies distribution. In this work, we studied the spatial differentiation of hydrofacies in the alluvial aquifer system of West Thessaly basin in Greece. For this, we applied both SIS and PS techniques to an extensive set of borehole data from that basin. Histograms of model versus experimental hydrofacies proportions and indicative cross sections were plotted in order to validate the results. The PS technique was shown to be more effective in reproducing the spatial characteristics of the different hydrofacies and their distribution across the study area. In addition, the permeability differentiations reflected in the PS model are in accordance to known heterogeneities of the aquifer capacity.     

Modeling the Uncertainty in the Layout of Geological Units by Implicit Boundary Simulation Accounting for a Preexisting Interpretive Geological Model

Natural Resources Research - An implicit simulation algorithm that uses signed distance functions is proposed to represent subsurface geological configuration while accounting for two sources of...     

基于地统计学的北运河下游土壤养分空间分布

通过对北运河下游土壤的取样,采用地统计的方法分析北运河流域农田土壤pH、碱解氮、有效磷、速效钾和有机质五种养分的空间分布规律,结合武清区土壤类型和其他的相关资料的数据进行分析,结果表明:土壤类型对土壤pH、有效磷分布有影响,对土壤pH影响尤为明显;北运河流域的水系对碱解氮、有机质空间分布影响较大,水系发达的区域含量明显高于水系不发达的区域;速效钾多是由其他因素引起。     

利用 GIS地理统计模块预测海南岛植被指数季节性变化趋势

虽然采用遥感图像提取的植被指数在空间上能较好的反映作物的状况,但其不能预测植被指数在空间上的变化范围,如果能从整体上了解不同市县在不同季节的平均植被指数值,就可以对该区域整体植被状态进行量化分析,也就可以从大范围内进行植被指数的预测分析.利用地理信息系统(GIS)和地统计学相结合的地理统计分析模块(ArcGIS Geostatistical Analyst),根据MODIS遥感数据提取的每季度不同市县平均NDVI植被指数,采用Kriging插值的方法分析了海南岛归一化植被指数(NDVI)季节性变化趋势,并