Quantifying the uncertainty in the spatial layout of rock type domains in an iron ore deposit

This work addresses the problem of delineating the spatial layout of ten rock type domains in an iron ore body and of assessing the uncertainty in the domain boundaries. A stochastic approach is proposed to this end, based on truncated Gaussian simulation, which consists in defining successive partitions of the space that comply with the desired spatial continuity and contact relationships between rock type domains. The sequencing of these domains is driven by their position (surficial vs. underlying rocks), granulometry (compact vs. friable rocks), and grades (rich vs. poor) of iron, alumina, manganese and loss on ignition. A total of 100 realizations are produced, conditioned to available drill hole data, and used to quantify the uncertainty in the occurrence of each rock type domain, at both global and local scales.     

Risk quantification with combined use of lithological and grade simulations: Application to a porphyry copper deposit

The uncertainty in the recoverable tonnages and grades in a mineral deposit is a key factor in the decision-making process of a mining project. Currently, the most prevalent approach to model the uncertainty in the spatial distribution of mineral grades is to divide the deposit into domains based on geological interpretation and to predict the grades within each domain separately. This approach defines just one interpretation of the geological domain layout and does not offer any measure of the uncertainty in the position of the domain boundaries and in the mineral grades. This uncertainty can be evaluated by use of geostatistical simulation methods. The aim of this study is to evaluate how the simulation of rock type domains and grades affects the resources model of Sungun porphyry copper deposit, northwestern Iran. Specifically, three main rock type domains (porphyry, skarn and late-injected dykes) that control the copper grade distribution are simulated over the region of interest using the plurigaussian model. The copper grades are then simulated in cascade, generating one grade realization for each rock type realization. The simulated grades are finally compared to those obtained using traditional approaches against production data.     

Geological modeling of rock type domains in the Balya (Turkey) lead-zinc deposit using plurigaussian simulation

Mineral resource evaluation requires defining geological rock-type domains. The traditional simulation methods have serious limitations for applications to large numbers of domains, which have complex contact relations. Plurigaussian simulation is an effective method which can be applied, in a simple way, to any number of domains, using both local and global geological information to infer the distributions of rock types. This work not only presents the application of the plurigaussian simulation method to the Balya lead-zinc deposit, but also assesses the spatially varying rock type proportions, and accounts for uncertainties between them. These parameters are extremely important for mining deposits, since the mineralizations of interest generally occur only in certain rock types. Furthermore, being able to model the different geological rock types is vital to good mine operations, production planning, and management. The results indicate that the plurigaussian method correctly reproduces the different orientations of the individual rock types, as seen in drill holes, and the proportion of each rock type, even if this varies in space.     

A probabilistic parametrization for geological uncertainty estimation using the ensemble Kalman filter (EnKF)

In the past years, many applications of history-matching methods in general and ensemble Kalman filter in particular have been proposed, especially in order to estimate fields that provide uncertainty in the stochastic process defined by the dynamical system of hydrocarbon recovery. Such fields can be permeability fields or porosity fields, but can also fields defined by the rock type (facies fields). The estimation of the boundaries of the geologic facies with ensemble Kalman filter (EnKF) was made, in different papers, with the aid of Gaussian random fields, which were truncated using various schemes and introduced in a history-matching process. In this paper, we estimate, in the frame of the EnKF process, the locations of three facies types that occur into a reservoir domain, with the property that each two could have a contact. The geological simulation model is a form of the general truncated plurigaussian method. The difference with other approaches consists in how the truncation scheme is introduced and in the observation operator of the facies types at the well locations. The projection from the continuous space of the Gaussian fields into the discrete space of the facies fields is realized through in an intermediary space (space with probabilities). This space connects the observation operator of the facies types at the well locations with the geological simulation model. We will test the model using a 2D reservoir which is connected with the EnKF method as a data assimilation technique. We will use different geostatistical properties for the Gaussian fields and different levels of the uncertainty introduced in the model parameters and also in the construction of the Gaussian fields.     

Application of plurigaussian simulation to delineate the layout of alteration domains in Sungun copper deposit

An accurate estimation of mineral grades in ore deposits with heterogeneous spatial variations requires defining geological domains that differentiate the types of mineralogy, alteration and lithology. Deterministic models define the layout of the domains based on the interpretation of the drill holes and do not take into account the uncertainty in areas with fewer data. Plurigaussian simulation (PGS) can be an alternative to generate multiple numerical models of the ore body, with the aim of assessing the uncertainty in the domain boundaries and improving the geological controls in the characterization of quantitative attributes. This study addresses the application of PGS to Sungun porphyry copper deposit (Iran), in order to simulate the layout of four hypogene alteration zones: potassic, phyllic, propylitic and argillic. The aim of this study is to construct numerical models in which the alteration structures reflect the evolution observed in the geology.     

Data Assimilation in Truncated Plurigaussian Models: Impact of the Truncation Map

Assimilation of production data into reservoir models for which the distribution of porosity and permeability is largely controlled by facies has become increasingly common. When the locations of the facies bodies must be conditioned to observations, the truncated plurigaussian model has been often shown to be a useful method for modeling as it allows gaussian variables to be updated instead of facies types. Previous experience has also shown that ensemble Kalman filter-like methods are particularly effective for assimilation of data into truncated plurigaussian models. In this paper, some limitations are shown of the ensemble-based or gradient-based methods when applied to truncated plurigaussian models of a certain type that is likely to occur for modeling channel facies. It is also shown that it is possible to improve the data match and increase the ensemble spread by modifying the updating step using an approximate derivative of the truncation map.     

Local and Spatial Joint Frequency Uncertainty and its Application to Rock Mass Characterisation

Stability is a key issue in any mining or tunnelling activity. Joint frequency constitutes an important input into stability analyses. Three techniques are used herein to quantify the local and spatial joint frequency uncertainty, or possible joint frequencies given joint frequency data, at unsampled locations. Rock quality designation is estimated from the predicted joint frequencies. The first method is based on kriging with subsequent Poisson sampling. The second method transforms the data to near-Gaussian variables and uses the turning band method to generate a range of possible joint frequencies. The third method assumes that the data are Poisson distributed and models the log-intensity of these data with a spatially smooth Gaussian prior distribution. Intensities are obtained and Poisson variables are generated to examine the expected joint frequency and associated variability. The joint frequency data is from an iron ore in the northern part of Norway. The methods are tested at unsampled locations and validated at sampled locations. All three methods perform quite well when predicting sampled points. The probability that the joint frequency exceeds 5 joints per metre is also estimated to illustrate a more realistic utilisation. The obtained probability map highlights zones in the ore where stability problems have occurred. It is therefore concluded that the methods work and that more emphasis should have been placed on these kinds of analyses when the mine was planned. By using simulation instead of estimation, it is possible to obtain a clear picture of possible joint frequency values or ranges, i.e. the uncertainty.     

高放废物地质处置阿拉善预选区巴彦诺日公地段目标深度岩体质量预测

高放废物地质处置阿拉善预选区巴彦诺日公地段位于阿拉善地块东部,主要由二叠纪侵入的花岗岩构成,地壳次稳定。通过踏勘,确定了2个钻孔,布置了若干条物探剖面。以这2个钻孔为中心,在17km×17km范围内进行了工程地质测绘,获得了地表结构面分布特征。地表岩体质量以III级岩体为主,地表以下3m~4m处多为I级和II级岩体。根据钻孔岩芯编录和力学试验数据,对岩芯质量进行评价,岩芯整体质量较好,以Ⅰ级和Ⅱ级岩体为主。对比岩体质量和测井数据,发现岩体质量与岩体的物理参数具有明显的相关性。通过和CSAMT剖面上对应位置的对比,建立了岩体质量与电阻率的关系。结合地表岩体质量、钻孔岩芯质量和物探剖面,对目标深度岩体进行了预测：目标深度（600m深左右）岩体质量以Ⅰ级岩体为主,局部有Ⅱ级岩体和Ⅲ岩体。     

江西银山矿田伴生金银综合回收利用研究

叙述了银山铜铅锌多金属矿田铅锌成矿系列和铜硫成矿系列６个成矿带中伴生金银的赋存状态、富集特征和成矿规律，并进行伴生金银相关性分析。认为伴生金银是以独立矿物存在为主，主要载体矿物有黄铜矿，含砷铜矿物、黄铁矿、方铅矿和闪锌矿。Ａｕ、Ａｇ与Ｐｂ、Ｚｎ、Ｃｕ、Ｓ密切相关。同时分析了金银生产中存在的具体问题，提出综合回收金银的措施和建议。     

基于多源数据约束的成矿动力学模拟——以宁芜盆地钟姑矿田典型矿床为例

数据驱动是大数据分析的特点之一。成矿过程的数值模拟即采用数据驱动方式,在基本的物理化学方程及地质模型基础上,通过定量的手段,模拟不同阶段、不同条件下成矿系统的演化过程,从而能够更深入、直观的讨论各种地质要素对成矿系统的影响,验证已有的成矿理论,获得新的认识。姑山铁矿床和杨庄铁矿床是宁芜火山岩盆地钟姑矿田内的典型矿床。前人研究显示,杨庄铁矿床为典型的充填-接触交代型热液矿床,而姑山铁矿床目前在成因上仍存在争议,存在岩浆成因和热液成因等多种观点。为了更好的对比和了解姑山铁矿床和杨庄铁矿床的成因及成矿过程,本文基于多源数据的综合解译剖面,采用力-热耦合数值模拟方法对与热液矿床密切相关的扩容空间的形成机制和特点开展研究。模拟结果显示,姑山铁矿床和杨庄铁矿床可能分属不同的成因类型;随着岩体的逐渐冷却,杨庄铁矿床内岩体和地层接触带会出现明显的扩容空间,可为成矿流体的汇聚及矿质的沉淀提供良好的条件,有利于热液矿床的形成;而姑山铁矿床内岩体和地层接触带只有局部区域出现扩容空间,同时体应变数值较小且形态变化大,并不利于大规模的流体汇聚及矿质的沉淀,姑山铁矿床可能主要为岩浆成因,并受少量热液的叠加改造。     

Two Ordinary Kriging Approaches to Predicting Block Grade Distributions

Multigaussian kriging aims at estimating the local distributions of regionalized variables and functions of these variables (transfer or recovery functions) at unsampled locations. In this paper, we focus on the evaluation of the recoverable reserves in an ore deposit accounting for a change of support and information effect caused by ore/waste misclassifications. Two approaches are proposed: the multigaussian model with Monte Carlo integration and the discrete Gaussian model. The latter is simpler to use but requires stronger hypotheses than the former. In each model, ordinary multigaussian kriging gives unbiased estimates of the recoverable reserves that do not utilize the mean value of the normal score data. The concepts are illustrated through a case study on a copper deposit which shows that local estimates of the metal content based on ordinary multigaussian kriging are close to the optimal conditional expectation when the data are abundant and are not dominated by the global mean when the data are scarce. The two proposed approaches (Monte Carlo integration and discrete Gaussian model) lead to similar results when compared to two other geostatistical methods: service variables and ordinary indicator kriging, which show strong deviations from conditional expectation.     

资源定量评价发展方向展望

未来的资源定量评价希望能够评估未发现矿产资源的量、价值并对其进行定位预测, 以能够表达矿产资源的经济潜力和不确定性.近年来金属价格的长期下跌提出了对更大型的矿床的需求.敏感度分析表明了减少评价中不确定性和风险的最有效途径是降低有关吨位估计因素的不确定性.到目前为止, 在评价中所有可能造成误差的因素中, 那些与吨位估计误差有关的因素是最重要的.鉴于吨位模型的绝对重要地位以及矿床模型是吨位最有效的预测手段, 正确地选择矿床模型是控制误差最重要的途径.地表大部分地区被大面积裸露的岩石和沉积物所覆盖.由于很多出露地表的矿床已经被发现, 人们开始把注意力转向盖层下面岩石可能显露的矿化信息上.这些区域的资源评价必需依靠对其周边地区的外推、地下覆盖岩石新的地质填图或者通过在其他成功勘探区获得的经验进行类推.盖层对评价的不确定性以及评价的方法与程序都具有深远的影响, 因为地下地质现象的不可见性和地球物理方法所获得的是一种被削弱了的信息.许多早期的评价方法都是基于从那些出露地表的矿床中总结出的地球化学和地球物理变量之间的关系而进行的, 而现在我们同样需要研究基于地下隐伏矿床的勘探经验.矿床模型在资源定量评价中的重要地位基于以下两个原因: (1) 大多数矿床类型具有明显不同的品位和吨位分布; (2) 不同的矿床类型出现在不同的地质背景中, 而这种背景可从地质图中进行区分.在综合利用地质、矿产、地球物理和地球化学等地学信息进行资源评价及矿床勘探中, 矿床模型起着至关重要的作用.品位和吨位模型以及定量描述、经济和矿床密度模型的发展将有利于减少这些新的评价的不确定性.      

Some Suggested Future Directions ofQuantitative Resource Assessments

Like most journeys, success depends critically on wherewe are going to be in the end. Thus, if we are to have someideas about future directions of quantitative assessments ofmineral resources, we need some basic understanding of whatthe assessments will be used for. What will be expected ofquantitative resource assessments in the future? It would behelpful to identify who will use these future assessments, howthe assessments will be used, and what are acceptable forms ofproducts. The purpose o…     

Comparing sequential Gaussian and turning bands algorithms for cosimulating grades in multi-element deposits

Stochastic simulation is increasingly used to map the spatial variability in the grades of elements of interest and to assess the uncertainty in the mineral resources and ore reserves. The practical implementation requires specifying a stochastic model, which describes the spatial distribution of the grades, and an algorithm to construct realizations of these grades, viewed as different possible outcomes or scenarios. In the case of the Gaussian random field model, a variety of algorithms have been proposed in the past decades, but their ability to reproduce the model statistics is often unequal. In this paper, we compare two such algorithms, namely the turning bands and the sequential algorithms. The comparison is hold through a synthetic case study and a real case study in a porphyry copper deposit located in southeastern Iran, in which it is of interest to jointly simulate the copper, molybdenum, silver, lead and zinc grades. Statistical testing and graphical validations are realized to check whether or not the realizations reproduce the features of the true grades, in particular their direct and cross variograms. Sequential simulation based on collocated cokriging turns out to poorly reproduce the cross variograms, while turning bands proves to be accurate in all the analyzed cases.     

Joint High-Order Simulation of Spatially Correlated Variables Using High-Order Spatial Statistics

Joint geostatistical simulation techniques are used to quantify uncertainty for spatially correlated attributes, including mineral deposits, petroleum reservoirs, hydrogeological horizons, environmental contaminants. Existing joint simulation methods consider only second-order spatial statistics and Gaussian processes. Motivated by the presence of relatively large datasets for multiple correlated variables that typically are available from mineral deposits and the effects of complex spatial connectivity between grades on the subsequent use of simulated realizations, this paper presents a new approach for the joint high-order simulation of spatially correlated random fields. First, a vector random function is orthogonalized with a new decorrelation algorithm into independent factors using the so-termed diagonal domination condition of high-order cumulants. Each of the factors is then simulated independently using a high-order univariate simulation method on the basis of high-order spatial cumulants and Legendre polynomials. Finally, attributes of interest are reconstructed through the back-transformation of the simulated factors. In contrast to state-of-the-art methods, the decorrelation step of the proposed approach not only considers the covariance matrix, but also high-order statistics to obtain independent non-Gaussian factors. The intricacies of the application of the proposed method are shown with a dataset from a multi-element iron ore deposit. The application shows the reproduction of high-order spatial statistics of available data by the jointly simulated attributes.     

工程水文地质学及其在水电工程中的应用概述

工程水文地质问题产生于人类工程活动与地质环境中岩土体和地下水之间的相互制约和相互作用过程中,由于问题本身的复杂性,目前对这类问题的研究尚处于相对分散的单一研究状态,缺乏系统的从地质机制分析到地质模型抽象,进而由模拟再现到发展趋势预测以及治理措施论证的全过程研究。本文在系统分析、总结水电工程中水 -岩和水 -工程建筑的作用类型及特征基础上,认为可能出现的工程水文地质问题主要是;水库诱发地震、岩溶渗漏、库岸及高边坡的稳定、坝基、坝肩抗滑稳定、枢纽区深层承压水问题等。     

Simulation of Geological Contacts from Interpreted Geological Model Using Multiple-Point Statistics

Applications of multiple-point statistics (mps) algorithms to large non-repetitive geological objects such as those found in mining deposits are difficult because most mps algorithms rely on pattern repetition for simulation. In many cases, an interpreted geological model built from a computer-aided design system is readily available but suffers as a training image due to the lack of patterns repetitiveness. Porphyry copper deposits and iron ore formations are good examples of such mining deposits with non-repetitive patterns. This paper presents an algorithm called contactsim that focuses on reproducing the patterns of the contacts between geological types. The algorithm learns the shapes of the lithotype contacts as interpreted by the geologist, and simulates their patterns at a later stage. Defining a zone of uncertainty around the lithological contact is a critical step in contactsim, because it defines both the zones where the simulation is performed and where the algorithm should focus to learn the transitional patterns between lithotypes. A larger zone of uncertainty results in greater variation between realizations. The definition of the uncertainty zone must take into consideration the geological understanding of the deposit, and the reliability of the contact zones. The contactsim algorithm is demonstrated on an iron ore formation.     

宁波市地下空间开发利用地质环境适宜性评价

随着城市化建设快速推进,地下空间资源开发是解决城市土地资源紧张的合理途径,而地质环境适宜性评价对地下空间的开发利用具有至关重要的作用。本文分析了城市地下空间开发利用地质环境适宜性评价的影响因素,运用层次分析法确定岩土体特征、水文地质条件、环境地质问题、技术经济等指标因素的权重,建立模糊综合评价模型,定量评价宁波东部新城浅层(-15~0m)和中层(-30~-15m)的地下空间开发利用地质环境适宜程度。评价结果显示,东部新城地下空间开发地质环境适宜性等级分为Ⅱ级较适宜和Ⅲ级较不适宜,并根据不同的适宜等级提出了地下空间开发利用方式,为宁波东部新城的地下空间开发利用提供依据。     

Simulation of mineral grades with hard and soft conditioning data: application to a porphyry copper deposit

This work deals with the geostatistical simulation of mineral grades whose distribution exhibits spatial trends within the ore deposit. It is suggested that these trends can be reproduced by using a stationary random field model and by conditioning the realizations to data that incorporate the available information on the local grade distribution. These can be hard data (e.g., assays on samples) or soft data (e.g., rock-type information) that account for expert geological knowledge and supply the lack of hard data in scarcely sampled areas. Two algorithms are proposed, depending on the kind of soft data under consideration: interval constraints or local moment constraints. An application to a porphyry copper deposit is presented, in which it is shown that the incorporation of soft conditioning data associated with the prevailing rock type improves the modeling of the uncertainty in the actual copper grades.     

Assessing the impact of conceptual mineral systems uncertainty on prospectivity predictions

The past two decades have seen a rapid adoption of artificial intelligence methods applied to mineral exploration. More recently, the easier acquisition of some types of data has inspired a broad literature that has examined many machine learning and modelling techniques that combine exploration criteria, or ‘features’, to generate predictions for mineral prospectivity. Central to the design of prospectivity models is a ‘mineral system’, a conceptual model describing the key geological elements that control the timing and location of economic mineralisation. The mineral systems model defines what constitutes a training set, which features represent geological evidence of mineralisation, how features are engineered and what modelling methods are used. Mineral systems are knowledge-driven conceptual models, thus all parameter choices are subject to human biases and opinion so alternative models are possible. However, the effect of alternative mineral systems models on prospectivity is rarely compared despite the potential to heavily influence final predictions. In this study, we focus on the effect of conceptual uncertainty on Fe ore prospectivity models in the Hamersley region, Western Australia. Four important considerations are tested. (1) Five different supergene and hypogene conceptual mineral systems models guide the inputs for five forest-based classification prospectivity models model. (2) To represent conceptual uncertainty, the predictions are then combined for prospectivity model comparison. (3) Representation of three-dimensional objects as two-dimensional features are tested to address commonly ignored thickness of geological units. (4) The training dataset is composed of known economic mineralisation sites (deposits) as ‘positive’ examples, and exploration drilling data providing ‘negative’ sampling locations. Each of the spatial predictions are assessed using independent performance metrics common to AI-based classification methods and subjected to geological plausibility testing. We find that different conceptual mineral systems produce significantly different spatial predictions, thus conceptual uncertainty must be recognised. A benefit to recognising and modelling different conceptual models is that robust and geologically plausible predictions can be made that may guide mineral discovery.