Bayesian Maximum Entropy Analysis and Mapping: A Farewell to Kriging Estimators?

The Bayesian Maximum Entropy (BME) method of spatial analysis and mapping provides definite rules for incorporating prior information, hard and soft data into the mapping process. It has certain unique features that make it a loyal guardian of plausible reasoning under conditions of uncertainty. BME is a general approach that does not make any assumptions regarding the linearity of the estimator, the normality of the underlying probability laws, or the homogeneity of the spatial distribution. By capitalizing on various sources of information and data, BME introduces an epistemological framework that produces predictive maps that are more accurate and in many cases computationally more efficient than those derived by traditional techniques. In fact, kriging techniques can be derived as special cases of the BME approach, under restrictive assumptions regarding the prior information and the data available. BME is a more rigorous approach than indicator kriging for incorporating soft data. The BME formulation, in fact, applies in a spatial or a spatiotemporal domain and its extension to the case of block and vector random fields is straightforward. New theoretical results are presented and numerical examples are discussed, which use the BME approach to account for important sources of knowledge in a systematic manner. BME can be useful in practical situations in which prior information can be used to compensate for the limited amount of measurements available (e.g., preliminary or feasibility study levels) or soft data are available that can be combined with hard data to improve mapping significantly. BME may be then viewed as an effort towards the development of a more general framework of spatial/temporal analysis and mapping, which includes traditional geostatistics as its limiting case, and it also provides the means to derive novel results that could not be obtained by traditional geostatistics.     

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.     

Modelling Short‐Scale Variability and Uncertainty During Mineral Resource Estimation Using a Novel Fuzzy Estimation Technique

For mineral resource assessment, techniques based on fuzzy logic are attractive because they are capable of incorporating uncertainty associated with measured variables and can also quantify the uncertainty of the estimated grade, tonnage etc. The fuzzy grade estimation model is independent of the distribution of data, avoiding assumptions and constraints made during advanced geostatistical simulation, e.g., the turning bands method. Initially, fuzzy modelling classifies the data using all the component variables in the data set. We adopt a novel approach by taking into account the spatial irregularity of mineralisation patterns using the Gustafson–Kessel classification algorithm. The uncertainty at the point of estimation was derived through antecedent memberships in the input space (i.e., spatial coordinates) and transformed onto the output space (i.e., grades) through consequent membership at the point of estimation. Rather than probabilistic confidence intervals, this uncertainty was expressed in terms of fuzzy memberships, which indicated the occurrence of mixtures of different mineralogical phases at the point of estimation. Data from different sources (other than grades) could also be utilised during estimation. Application of the proposed technique on a real data set gave results that were comparable to those obtained from a turning bands simulation.     

新疆北部中——大型金、铜矿床的基本成矿特征

通过对新疆北部10多个中－大型金、铜矿床的对比研究，探讨了其含矿建造及其岩石化学成分，将这些中－大型金、铜矿床概括为块状硫化物型铜－多金属－金矿系列、浅成低温热液型金矿系列、铜镍硫化物型矿床系列、与韧性剪切带有关的构造蚀变岩型金矿系列、与夕卡岩有关的铜（钼）矿床系列等5个成矿系列类型、并指出本区金、铜矿床存在“一代，双峰”和“集中成矿，分片富集”的时空分布特点；在探讨有关典型矿床的硫同位素、铅同位素、稀土元素地球化学特征的基础上，阐述了本区中－大型金、铜矿床具有明显的多成矿物质来源和多成矿阶段等基本特性；最后建立了本区中－大型金、铜矿床的区域成矿模式。     

Two Artifacts of Probability Field Simulation

Probability field simulation is being used increasingly to simulate geostatistical realizations. The method can be faster than conventional simulation algorithms and it is well suited to integrate prior soft information in the form of local probability distributions. The theoretical basis of probability field simulation has been established when there are no conditioning data; however, no such basis has been established in presence of conditioning data. Realizations generated by probability field simulation show two severe artifacts near conditioning data. We document these artifacts and show theoretically why they exist. The two artifacts that have been investigated are (1) local conditioning data appear as local minima or maxima of the simulated values, and (2) the variogram model in range of conditioning data is not honored; the simulated values have significantly greater continuity than they are supposed to. These two artifacts are predicted by theory. An example flow simulation study is presented to illustrate that they affect more than the visual appearance of the simulated realizations. Notwithstanding the flexibility of the probability field simulation method, these two artifacts suggest that it be used with caution in presence of conditioning data. Future research may overcome these limitations.     

Simulation of mineral grades and classification of mineral resources by using hard and soft conditioning data: application to Sungun porphyry copper deposit

The presence of geological units with different grade characteristics mostly leads to problems during the grade modeling process. In special cases, if the area under study has units with small thickness and low grade with respect to the dominant unit of the area, it is difficult to reproduce different grade contents in these units in the simulated grade models because of the low thickness and lack of data in these units. In this study, the local moment constraints method, based on the definition of soft conditioning data reflecting geological knowledge, is investigated for improving simulated grade models under the mentioned conditions. This method is applied for grade simulation at the 1,750 m level of Sungun porphyry copper mine. The studied area is divided into two rock type domains: Sungun porphyry and Dyke. The Sungun porphyry unit is the dominant rock type in the considered area and has, on average, a higher copper grade, while dykes discontinue Sungun porphyry rock units sporadically and most of them are barren of mineralization. It is demonstrated that the use of soft conditioning data makes the simulated grade model closer to reality and improves the reproduction of grade contents considering the rock type units in the area. In the next step, the results obtained from conditional simulation are used for mineral resources classification. To this end, the conditional coefficient of variation is chosen as a criterion for measuring uncertainty and for defining the resources classes. Then, it is shown that uncertainty can be considerably reduced in the prepared models if soft data are considered; as a result, an increase in measured resource classification is observed.     

新疆西天山新发现新源县卡特巴阿苏大型金铜矿床

乌兹别克斯坦-吉尔吉斯斯坦中天山不乏世界级金铜矿床,新疆西部中天山及其南北缘是值得高度关注的金铜找矿方向。最近,新疆地质矿产勘查开发局第一区域地质调查大队在新疆西天山新发现新源县卡特巴阿苏大型金铜矿床。矿床位于新源县城南东直线距离30km处,产在新疆西部中天山北缘,矿体主体形成于石炭纪二长花岗岩热液蚀变体内,呈板状和透镜状,长度几米到几千米,厚度几米到几十米,上部以金矿体为主,下部铜矿体增多。矿石中黄铁矿和黄铜矿可能是主要的载金矿物,矿石平均品位金 3.84g/t、铜 0.65%。金铜成矿作用受控于二长花岗岩等岩体侵入期后热液蚀变过程。矿床的发现具有重要的经济价值,同时证实新疆西部中天山及其南北缘具备金、铜矿的巨大潜力;是地质调查先行、引导商业勘探、实现找矿突破的典范。     

Effects of intrusions on grades and contents of gold and other metals in volcanogenic massive sulfide deposits

The reason some VMS deposits contain more gold or other metals than others might be due to the influence of intrusions. A new approach examining this possibility is based on examining the information about many VMS deposits to test statistically if those with associated intrusions have significantly different grades or amounts of metals. A set of 632 VMS deposits with reported grades, tonnages, and information about the observed presence or absence of subvolcanic or plutonic intrusive bodies emplaced at or after VMS mineralization is statistically analyzed.Deposits with syn-mineralization or post-mineralization intrusions nearby have higher tonnages than deposits without reported intrusions, but the differences are not statistically significant. When both kinds of intrusions are reported, VMS deposit sizes are significantly higher than in the deposits without any intrusions. Gold, silver, zinc, lead, and copper average grades are not significantly different in the VMS deposits with nearby intrusions compared to deposits without regardless of relative age of intrusive. Only zinc and copper contents are significantly higher in VMS deposits with both kinds of intrusive reported. These differences in overall metal content are due to significantly larger deposit sizes of VMS deposits where both intrusive kinds are observed and reported, rather than any difference in metal grades.     

The gold content of volcanogenic massive sulfide deposits

Volcanogenic massive sulfide deposits contain variable amounts of gold, both in terms of average grade and total gold content, with some VMS deposits hosting world-class gold mines with more than 100?t Au. Previous studies have identified gold-rich VMS as having an average gold grade, expressed in g/t, exceeding the total abundance of base metals, expressed in wt.%. However, statistically meaningful criteria for the identification of truly anomalous deposits have not been established. This paper presents a more extensive analysis of gold grades and tonnages of 513 VMS deposits worldwide, revealing a number of important features in the distribution of the data. A large proportion of deposits are characterized by a relatively low gold grade (<2?g/t), with a gradual decrease in frequency towards maximum gold grades, defining a log-normal distribution. In the analysis presented in this paper, the geometric mean and geometric standard deviation appear to be the simplest metric for identifying subclasses of VMS deposits based on gold grade, especially when comparing deposits within individual belts and districts. The geometric mean gold grade of 513 VMS deposits worldwide is 0.76?g/t; the geometric standard deviation is +2.70?g/t Au. In this analysis, deposits with more than 3.46?g/t Au (geometric mean plus one geometric standard deviation) are considered auriferous. The geometric mean gold content is 4.7?t Au, with a geometric standard deviation of +26.3?t Au. Deposits containing 31?t Au or more (geometric mean plus one geometric standard deviation) are also considered to be anomalous in terms of gold content, irrespective of the gold grade. Deposits with more than 3.46?g/t Au and 31?t Au are considered gold-rich VMS. A large proportion of the total gold hosted in VMS worldwide is found in a relatively small number of such deposits. The identification of these truly anomalous systems helps shed light on the geological parameters that control unusual enrichment of gold in VMS. At the district scale, the gold-rich deposits occupy a stratigraphic position and volcanic setting that commonly differs from other deposits of the district possibly due to a step change in the geodynamic and magmatic evolution of local volcanic complexes. The gold-rich VMS are commonly associated with transitional to calc-alkaline intermediate to felsic volcanic rocks, which may reflect a particularly fertile geodynamic setting and/or timing (e.g., early arc rifting or rifting front). At the deposit scale, uncommon alteration assemblages (e.g., advanced argillic, aluminous, strongly siliceous, or potassium feldspar alteration) and trace element signatures may be recognized (e.g., Au?CAg?CAs?CSb ± Bi?CHg?CTe), suggesting a direct magmatic input in some systems.     

Controls on pit lake water quality at sixteen open-pit mines in Nevada

Thirty-five mines in Nevada currently have, or will likely have, a pit lake. The large bulk mineable deposits in Nevada mined below the water table are of several types, including Carlin-type Au, quartz-adularia precious metal, quartz-alunite precious metal and porphyry-Cu (-Mo) deposits. Of the 16 past or existing pit lakes at 12 different Nevada mines, most had near neutral pH and low metal concentrations, yet most had at least one constituent (e.g., SO₄) which exceeded drinking water standards for at least one sampling event. Water quality data indicate that, in general, poor water quality will not develop in Carlin-type Au deposits. Wall rocks in the geologic environment typical of these deposits, and in the specific pits sampled, contain substantial amounts of carbonate, which buffers the pH at slightly basic conditions and thereby limits the solubility of most metals. Similarly, the quartz-adularia precious metal deposits generally have geologic conditions that buffer pH and naturally prevent the development of poor water quality. In both of these deposit types, certain elements such as As and Se that are mobile in neutral to basic waters may accumulate to levels near or exceeding drinking water standards. Pit lakes forming in quartz-alunite precious metal deposits hosted in volcanic rocks or in porphyry-Cu (-Mo) deposits in plutonic rocks are of greatest environmental concern in Nevada, as both deposit types have relatively high acid-generating potential and low buffering capacity. However, the sampled Nevada pits in these deposit types indicate that the water may not be of poor quality. In addition, water quality in some pits may actually improve with time due to the increased water-rock ratio as the pit fills with water, as suggested by pit waters at one mine in a Carlin-type deposit (Getchell) that improved between 1968 and 1982. Although water quality in pits in each deposit type is generally good, local, site specific conditions (e.g., surface water inflow) and variations (e.g., evaporation rates) result in some pit lakes (e.g., Boss) in the quartz-adularia deposit type being of substantially poorer water quality than other lakes (e.g., Tuscarora) in the same deposit type. Despite underlying geologic controls based on deposit type, site specific variations in hydrogeologic conditions and surface geologic features can result in differing water quality in pit lakes in the same deposit types, and these factors may, in some cases, provide an overriding control on the geochemical evolution of specific pit lakes.     

缓倾坡外软硬互层型高斜坡演化及失稳机理研究

基于对贵州省德江县香树坪斜坡工程地质条件分析及斜坡变形破坏特征分析,建立了缓倾坡外软硬互层型高斜坡演化概念模型,分析了斜坡演化机制,将斜坡形成及变形破坏过程分为河谷形成过程中的时效变形、滑移-逐级拉裂、滑移-弯曲-剪断3个阶段。并通过数值分析,再现了斜坡失稳机理及发生过程。基于软硬互层特性在斜坡演化过程中的作用量化分析表明,由于硬岩层限制软岩层的变形,导致坡体不易发生整体失稳。但软岩持续蠕变导致硬岩内能量积累增大,局部变形扩大,最终发生失稳破坏。     

西藏班公湖-怒江成矿带及邻区铋矿化带的发现与意义

铋是一种稀有金属, 在世界分布很不均匀, 全世界铋资源绝大部分赋存在中国, 我国的铋资源主要集中在湖南的柿竹园。本文通过系统的野外调查与样品采集、室内ICP-MS与扫描电镜及电镜能谱方法分析, 确定班公湖-怒江成矿带12个矿床(点)单件样品铋含量达到边界品位的要求, 9个矿床(点)单件样品达到工业品位的要求, 最高达到9575×10?6。铋含量高的地质体东西向呈带状展布, 为一铋的成矿带。确定材玛矽卡岩型铁矿、尕尔穷矽卡岩型铜矿、舍索矽卡岩型铜铅锌多金属矿-社样多金属矿-更乃矽卡岩型铜铁矿、拉屋矽卡岩型铜矿-尤卡浪脉状铅矿共4个铋矿找矿远景区。铋矿物种类为硫铜铋矿、自然铋、硫铋铜铅矿、硫铋银矿共4种。铋含量较高的样品主要分布于矽卡岩型矿床中, 斑岩型矿床的铋含量较低。班公湖-怒江成矿带铋的矿化时代应为燕山期,为班公湖-怒江向南(即冈底斯地块)俯冲使之闭合后碰撞阶段所形成的。拉屋多金属矿床正在开采, 其矿石含有较高的铋含量, 由于铋的单位价值远远大于正在开采的铜与铅锌等资源, 因此, 该矿床开采时需加强铋资源的评价, 以提高其资源的综合利用价值。     

新疆卡拉先格尔铜矿韧脆性剪切变形与铜矿化的关系

卡拉先格尔铜矿位于阿尔泰成矿带南缘东段, 通过对阿尔泰南缘卡拉先格尔铜矿发育的构造变形的分析, 认为矿区内发育的脆韧性剪切带对矿化、围岩蚀变的形成和空间展布具有一定的控制作用。今后在矿区内找矿不仅要重视岩性对矿化的控制, 还要重视韧性剪切变形带对矿化的制约, 尤其是位于剪切带的斑岩岩体与围岩的接触带附近, 岩体微裂隙发育, 易形成矿体的富集。      

湖北某地金的区域地球化学特征与找矿效果

本区以往是以铁铜矿产为重点。已知矿床中虽有伴生金,但找金工作,未被重视。区域化探(水系沉积物测显)样品采用痕量测金技术(化学光讲法,检出限0 ．3ppb),圈出作为找金远景的毛村—丙山—戊县和甲镇两个金的高值(Au＞2ppb)区和22处局部金异常。除已知伴生金矿床外,推测10处有找金远景。其中两处,经查证,发现一处中型金矿床和两处有远景的金矿点。金的区域地球化学资料,正使这个地区的地质工作重点,发生着转移。金量区域地球化学分布,呈相互复合的北东(西北部)、北西(东西部)向带状分布,高、低值带相间排布,强度自北而南增强。反映了受北东、北西向两组构造制约的特点。金的局部异常,即位于此两组构造的结点上,呈棋盘格状分布。本文指出甲镇、两山南部,是本区今后找金最有远景的两个地区。本文还对与铁铜成矿作用有关的燕山期中酸性侵入体,作出了含金性的评价,指出以往一直认为不成矿的F岩体,有找金前景,并找到已村、庚村两处金矿点。     

Co-simulating Total and Soluble Copper Grades in an Oxide Ore Deposit

In oxide copper deposits, the acid soluble copper represents the fraction of total copper recoverable by heap leaching. Two difficulties often complicate the joint modeling and simulation of total and soluble copper grades: the inequality constraint linking both grade variables and the sampling design for soluble copper grade, which may be preferential and cause biases in sample statistics. A methodology is presented in order to accurately estimate the total and soluble copper grade bivariate distribution, based on an explicit modeling of the conditional distributions of soluble copper grade. Co-simulation is then realized by converting the copper grades into Gaussian random fields, through stepwise conditional transformation, and by fitting a coregionalization model while accounting for the preferential sampling design. The proposed approach is illustrated through an application to an ore deposit located in northern Chile.     

云南大红山矿区梳状断裂构造系及其控矿作用

大红山铜（铁）矿床的形成与分布受控于康滇地轴早元古代裂陷海槽背景下发育的梳状断裂构造系;梳状断裂构造系通过控制沉积盆地、曼岗河组沉积作用、火山活动等间接控制了铜（铁）矿空间展布和定位.大红山矿区外围找矿首先应沿着同沉积断裂寻找古海底洼地.在康滇地轴基底大红山群及同时代含矿火山-沉积建造普遍被中生界覆盖的情况下,同沉积断裂相对于其他标志可能更易于识别,因而可作为区内勘查大红山式铜（铁）矿的重要准则.     

Prospectivity mapping for “Zhuxi-type” copper-tungsten polymetallic deposits in the Jingdezhen region of Jiangxi Province,South China

The Zhuxi deposit is the largest copper-tungsten polymetallic deposit in the world and is in Jiangxi Province in South China. The ore body is characterized by hydrothermal-vein deposits of copper, lead, and zinc minerals at shallow levels, skarn deposits of tungsten and copper minerals at middle levels, and altered-granite-hosted copper and tungsten minerals at depth. Such metallogenic systems are typically intrusion-related. The intrusive granites related to the Zhuxi polymetallic deposit have been dated at 152.9 Ma to 146.9 Ma. The intrusions provided the thermal energy and the source material for the ore mineralization. Skarns mineralization, the main type of ore mineralization, developed in the contact zone of Carboniferous-Permian formations with the granites. Nappe structures changed the dip of the ore bodies from steep in the top part to gentle in the bottom. NE-trending faults provided the fluid pathways and controlled the geological framework and distribution of ore deposits on a regional scale. In this study, recognition exploration criteria were analyzed based on a mineral deposit model and the geological setting. Extraction of favorable geological information and GIS-based data-integration methods were used for mineral-prospectivity mapping of Zhuxi-type polymetallic deposits. Buffering analysis was employed to extract structural information (e.g. faults) and lithologic or stratigraphic information (e.g. granites or geologic units). The singularity method and spatially weighted principal component analysis were used to enhance and delineate geochemical anomalies. The derivative norm was utilized to extract magnetic-gradient anomalies associated with intrusive granites. Student t-test of weights-of-evidence (WofE) proved to be an effective way to optimize threshold values for binarization of variables as evidence layers by evaluating the spatial correlation between known deposits and geological variables. The posterior probabilities of WofE gave a relative estimation of mineralization potential. Areas delineated by high posterior probability had much higher potentiality for the discovery of new deposits where had none had been found yet.     

Application of geostatistical hierarchical clustering for geochemical population identification in Bondar Hanza copper porphyry deposit

Several machine learning approaches have been developed for the identification of geochemical populations. In these approaches, the geochemical elements are usually the sole quantitative variables used as inputs for geochemical population recognition. This means that the presence of other qualitative variables, such as geological information, is overlooked in the analysis. Hierarchical clustering, as an unsupervised machine learning method, is a common approach for dimensional reduction in the analysis of geochemical data. In this study, an alternative to this technique, known as geostatistical hierarchical clustering (GHC), is applied to identify geochemical populations in 3D in the Bondar Hanza copper porphyry deposit, Iran. In this paradigm, the qualitative geological variables can also be incorporated for geochemical population identification, in addition to qualitative geochemical elements. In this study, an innovative solution is presented to tune the weighting parameters of each variable in GHC, based on the associations that the clusters (i.e., geochemical populations) should have with the geological information. The results are compared with k-means and number–size fractal/multifractal (N–S) methods. As a result, GHC showed better agreement with alterations, rock types, and mineralization zones in this deposit. Finally, some important instructions are provided for further mineral exploration.     

Two-dimensional Conditional Simulations Based on the Wavelet Decomposition of Training Images

Scale dependency is a critical topic when modeling spatial phenomena of complex geological patterns that interact at different spatial scales. A two-dimensional conditional simulation based on wavelet decomposition is proposed for simulating geological patterns at different scales. The method utilizes the wavelet transform of a training image to decompose it into wavelet coefficients at different scales, and then quantifies their spatial dependence. Joint simulation of the wavelet coefficients is used together with available hard and or soft conditioning data. The conditionally co-simulated wavelet coefficients are back-transformed generating a realization of the attribute under study. Realizations generated using the proposed method reproduce the conditioning data, the wavelet coefficients and their spatial dependence. Two examples using geological images as training images elucidate the different aspects of the method, including hard and soft conditioning, the ability to reproduce some non-linear features and scale dependencies of the training images.