Matheronian geostatistics—Quo vadis?

Components of geostatistical estimation, developed as a method for ore deposit assessment, are discussed in detail. The assumption that spatial observations can be treated as a stochastic process is judged to be an inappropriate model for natural data. Problems of semivariogram formulation are reviewed, and this method is considered to be inadequate for estimating the function being sought. Characteristics of bivariate interpolation are summarized, highlighting kriging limitations as an interpolation method. Limitations are similar to those of inverse distance weighted observations interpolation. Attention is drawn to the local bias of kriging and misplaced claims that it is an “optimal” interpolation method. The so-called “estimation variance,” interpreted as providing confidence limits for estimation of mining blocks, is shown to be meaningless as an index of local variation. The claim that geostatistics constitutes a “new science” is examined in detail. Such novelties as exist in the method are shown to transgress accepted principles of scientific inference. Stochastic modeling in general is discussed, and purposes of the approach emphasized. For the purpose of detailed quantitative assessment it can provide only prediction qualified by hypothesis at best. Such an approach should play no part in ore deposit assessment where the need is for local detailed inventories; these can only be achieved properly through local deterministic methods, where prediction is purely deductive.     

基于三维地质模型的河南韩梁铝土矿成矿分析及资源量估算

依据河南省鲁山—宝丰韩梁地区铝土矿的地质特征,利用Surpac 6.3矿业软件建立了该矿区的地质数据库及地层、矿体、断层和地表模型,形象表达了矿区的地形地貌和矿体的产状及空间关系。推断出矿床形成的环境和成因,应用块体模型和距离幂次反比法对矿体的品位分布和资源量进行了动态估算,表明块体估算资源量的方法可靠准确,提高了储量估算的效率,为勘查工作提供了可靠的参考和科学依据。     

Comparison between ordinary kriging (OK) and inverse distance weighted (IDW) based on estimation error. Case study: Dardevey iron ore deposit,NE Iran

Estimation of mineral resources and reserves with low values of error is essential in mineral exploration. The aim of this study is to compare inverse distance weighted (IDW) and ordinary kriging (OK) methods based on error estimation in the Dardevey iron ore deposit, NE Iran. Anisotropic ellipsoid and variograms were calculated and generated for estimation of Fe distribution by both methods. Density, continuity of ore and waste, the number of points involved, and the discretization factor in the estimation of ore and waste boundaries were determined and the resource estimated by IDW and OK methods. Estimation errors were classified based on JORC standard, and both methods were compared due to distribution of error estimation. Results obtained by the study indicate that error estimation of OK method is less than IDW method and that the results of OK method are reliable.     

基于3DMine软件的地质统计学在河北羊崖山铁矿床资源量估算中的应用

现有矿业软件的储量估算模块核心方法主要基于地质统计学。文章以河北迁安羊崖山铁矿床为例,通过3DMine软件在数据资料准备、变异函数确定、块体模型构建及储量报告等多方面的应用,规范了矿业软件在资源量估算方面的工作流程。利用普通克里金法和距离幂次反比法分别进行品位插值,完成资源量估算;并与传统储量估算结果进行比较,分析产生误差原因,建立了开采境界模型,计算了矿山开采储量和保有储量;利用赋值参数分析矿体控制程度,指导未来探矿工程重点部位。     

基于Surpac软件的矿床模型构建及矿体资源量估算-以陕西山阳夏家店金钒矿床为例

文章介绍了陕西省山阳县夏家店金钒矿床矿体地质特征,矿体赋存于与寒武系有关的地层及断裂构造中。根据矿床以往地质勘查工程资料,应用Surpac软件建立了矿床数据库,建立了矿区地表模型、矿体模型和品位块体模型,模型形象直观的展现了矿区地形地貌、矿体展布位置及形态。应用普通克立格法建立的矿体品位块体模型,简洁清晰的表达了矿体品位分布位置及高低,并对部分矿体采用不同的基本块体单元估算了资源量,分析认为采用的基本块体单元越小,估算的矿体资源量越精确。将其与勘查报告中采用传统地质块段法估算的资源量进行了对比,表明采用该软件估算的矿体资源量可靠准确,计算过程高效、便捷。     

Influence of the ore block model estimation on the determination of the mining cutoff grade policy for sustainable mine production

Strategic mine planning includes different cut-off grade policy depending on economic parameters of mining projects and grade–tonnage distribution of the deposit. Minimizing incorrect classification of ore and waste during grade–tonnage distribution is of critical importance for a mining operation. This article reviews the influence of the ore grade–tonnage distribution over the cut-off grade policy in a given mining operation. In this study, firstly, the interpolation parameters used to characterize the grade–tonnage distribution in the orebody are given. The resulting distribution of ore and waste is used to analyze uncertainty, risk impact, and to justify mine-planning decisions, according to the interpolation technique used and the number of geological settings and sampling scenarios being considered. Then, the working scheme of the cut-off grade policy and economic parameters are compared according to the resulting estimation from the inverse distance and the nearest neighbor methods.     

Application of disjunctive kriging for estimating economic grade distribution in an iron ore deposit: A case study of the Choghart North Anomaly,Iran

Most significant iron ore deposits in Iran are located in Central Iran Zone. These deposits belong to the Bafq mining district. The Bafq mining district is located in the Early Cambrian Kashmar-Kerman volcanic arc of Central Iran. Linear estimation of regionalized variables (for example by inverse distance weighting or ordinary Kriging) results in relatively high estimation variances, i.e. the estimates have very low precision. Assessment of project economics (or other critical decision making) based on linear estimation is therefore risky. Non-linear estimation methods like disjunctive kriging perform better and the lower estimation variance allows less risky economic decision-making. Another advantage of disjunctive kriging is that it allows estimation of functions of the primary variable, which here is the grade (Fe %) of the ore. In particular it permits estimation of indicator functions defined using thresholds on the primary variable. This paper is devoted to application of disjunctive kriging method in Choghart North Anomaly iron ore deposit in Central Iran, Yazd province, Iran. In this study, the Fe concentration of Choghart North Anomaly iron ore deposit was modelled and estimated. The exploration data consists of borehole samples measuring the Fe concentration. A Gaussian isofactorial model is fitted to these data and disjunctive kriging was used to estimate the regionalized variable (Fe %) at unsampled locations and to assess the probabilities that the actual concentrations exceed a threshold value at a given location. Consequently a three dimensional model of probability of exceeding a threshold value and the estimated value are provided by disjunctive kriging to divide the ore into an economic and uneconomic part on the basis of estimation of indicator functions using thresholds grades defined on point support. The tools and concepts are complemented by a set of computer programs that are applied to the case study. The study showed that disjunctive kriging can be applied successfully for modeling the grade of an ore deposit. Results showed that the correlation between the estimated value and real value at locations close to each other is 81.9%.     

Comparison of regression-based and combined versions of Inverse Distance Weighted methods for spatial interpolation of daily mean temperature data

This paper focuses on the performance of two regression-based and one Inverse Distance Weighted (IDW) and two combined versions of IDW methods for interpolation of daily mean temperature at the Black Sea Region of Turkey. Simple linear regression (SLR) and multiple linear regression (MLR) are used as regression-based methods. Combinations of IDW with TLR (temperature lapse rate) and gradient plus inverse distance squared (GIDS) are used as combined versions of IDW. This study targets to compare five spatial interpolation methods based on RMSE (root-mean-square error) statistics of interpolation errors for daily mean temperatures from 1981 to 2012. In order to compare the interpolation errors of the five methods, the leave-one-out cross-validation method was applied over long periods of 32 years on 52 different sites. The algorithms of the five interpolation methods’ codes were written in MATLAB by the authors of the paper.     

3D矿床建模技术在数字矿产勘查中的应用

为弥补现有数字矿床建模技术在地质矿产勘查处理和应用中的不足,从原始勘查数据建库及标准化、多指标单工程矿体自动圈定、基于语义识别的剖面矿体的连接与外推、矿体表面和品位建模、基于剖面矿体线框模型构建矿体表面模型及基于TIN+Octree数据结构和地质统计学理论建立矿体的空间属性模型等5个方面总结提出一套面向地质矿产勘查业务处理的矿床建模流程和总体技术解决方案.提高了地质矿产勘查研究精度,为进一步的矿山开采提供可靠的数据模型.      

http://www.sciencedirect.com/science/article/pii/S1674987111001411

正Three-dimensional geological modeling(3DGM) assists geologists to quantitatively study in three-dimensional(3D) space structures that define temporal and spatial relationships between geological objects.The 3D property model can also be used to infer or deduce causes of geological objects.3DGM technology provides technical support for extraction of diverse geoscience information,3D modeling,and quantitative calculation of mineral resources.Based on metallogenic concepts and an ore deposit model, 3DGM technology is applied to analyze geological characteristics of the Tongshan Cu deposit in order to define a metallogenic model and develop a virtual borehole technology;a BP neural network and a 3D interpolation technique were combined to integrate multiple geoscience information in a 3D environment. The results indicate:(1) on basis of the concept of magmatic-hydrothermal Cu polymetallic mineralization and a porphyry Cu deposit model,a spatial relational database of multiple geoscience information for mineralization in the study area(geology,geophysics,geochemistry,borehole,and cross-section data) was established,and 3D metallogenic geological objects including mineralization stratum,granodiorite, alteration rock,and magnetic anomaly were constructed;(2) on basis of the 3D ore deposit model,23,800 effective surveys from 94 boreholes and 21 sections were applied to establish 3D orebody models with a kriging interpolation method;(3) combined 23,800 surveys involving 21 sections,using VC++ and OpenGL platform,virtual borehole and virtual section with BP network,and an improved inverse distance interpolation(IDW) method were used to predict and delineate mineralization potential targets (Cu-grade of cell not less than 0.1%);(4) comparison of 3D ore bodies,metallogenic geological objects of mineralization,and potential targets of mineralization models in the study area,delineated the 3D spatial and temporal relationship and causal processes among the ore bodies,alteration rock,metallogenic stratum,intrusive rock,and the Tongshan Fault.This study provides important technical support and a scientific basis for assessment of the Tongshan Cu deposit and surrounding exploration and mineral resources.     

敦煌金滩子金矿床地质特征及找矿前景分析

敦煌金滩子金矿床系20世纪70年代初,在区调工作中检查古代采矿遗迹时发现,80年代开展过普查,经2014~2015年详查提交的一处中型金矿床。矿区由梭子山、八卦图和金滩子3个矿段组成。金矿化受断裂破碎带控制,加里东晚期石英闪长岩为八卦图和金滩子矿段石英脉型金矿的赋矿岩石,华力西中期二长花岗岩为梭子山矿段蚀变岩型金矿的赋矿岩石。目前控制主矿体长151~320 m、斜深155~350 m、矿体平均品位7.61×10~(-6)~17.94×10~(-6),矿体延伸较稳定,金品位较高。黄铁矿、褐铁矿、石英、方解石为主要载体矿物。据对金滩子金矿各矿段深部矿化特点及走向上控矿因素的分析,认为该矿床具有较好的找矿前景。     

矿床三维地质建模及储量估算——以丰村铅锌矿径口矿段为例

钦杭成矿带是我国最重要的成矿带之一,丰村铅锌矿位于钦杭成矿带南段庞西垌地区,是区内典型的沉积热液改造型矿床。依据现代成矿预测理论,结合已有的地形地质图、勘探线剖面图、钻孔数据等资料,运用三维地质建模技术建立了丰村铅锌矿径口矿段的地表模型、断裂模型、地层实体模型、矿体模型。在此基础上分别应用地质块段法和块体模型统计法进行了矿体的资源储量估算,并将两种估算结果进行了对比分析。结果表明,块体模型统计法比地质块段法应用范围更广,效果更精准,可以清晰表达矿体品位值变化特征,进而加深对矿体、矿床的空间分布规律的认识。同时,利用多元信息进行三维地质建模,可靠性高,可视化效果好。将传统的二维地质拓展到三维空间进行定位与定量化,有助于分析矿区地质构造特点与矿床成因,是现代寻找矿床的一种有效手段。     

河南栾川西沟铅锌银金矿床三维地质建模与深部找矿预测评价

随着矿区浅部矿的日益减少,深部找矿越来越受到重视,三维地质建模技术在成矿预测、资源定量评价等方面得到了广泛的应用。本文利用三维地质建模平台GOCAD中的三维建模技术及地质统计学等方法,基于收集测试得到的地质图、钻孔和采样点的地层、岩性、构造、品位等数据,构建了西沟铅锌银金矿区的三维地质模型,包括断裂构造模型、矿体模型及地层模型等,并且通过离散光滑插值及克里金插值等方法建立了西沟铅锌银金矿区的三维属性模型,完成了矿区3处找矿预测靶区的圈定与评价。基于地质认识及建立的矿区三维地质模型的研究认为:(1)该矿床的找矿有利标志主要为地层、构造、辉长岩以及品位指示等4个方面;(2)基于三维地质建模技术的找矿预测方法科学有效;(3)S139矿体的中部及东南部深部仍有找矿潜力。本文能够为将来的深部找矿突破提供一定的参考依据。     

Change of Support for Estimating Local Block Grade Distributions

An important aspect in mineral resource evaluation is the reduction of variance when post-processing the grade distributions defined on the support (volume) of the available data into distributions defined on the support of the proposed selective mining units. Although the volume-variance relationship is well understood for the estimation of global grade distributions, it is still an unsolved issue for local estimation studies based on non-parametric geostatistical methods, such as indicator kriging, for which the support correction is not inherent to the method. To clarify this relationship, the local change of support problem is examined in the scope of two parametric models (multi-Gaussian and discrete Gaussian models). It is shown that the variance reduction factor between point and block-support local distributions depends on the block being considered and is less than the global variance reduction factor. As a consequence, post-processing the local point-support grade distributions on the basis of the latter systematically understates the importance of the change of support at the local scale and makes selective mining appear more economically attractive than it really is. In the light of these results, a methodology is proposed to post-process the local point-support distributions obtained via non-parametric (indicator) methods into block-support distributions. An application to simulated data indicates that this methodology provides an accurate estimation at the block support when dealing with diffusion-type random fields.     

降雨资料Kriging与IDW插值对比分析—以漓江流域为例

降水空间化信息在很多领域都具有重要意义,而进行空间插值方法形成降水空间化信息是当代较为常用的方式。面对众多的插值方法其插值精度成为我们是否采用的关键,就kirging插值法与IDW(Inverse Distance Weighting)插值进行研究以探讨其插值效果,为此类科学研究提供依据。研究以漓江流域内各气象站点降水统计资料为基础分别采用上述两种方法进行插值处理,通过与预留实测站点比较评判方法的插值效果的优劣。结果表明,多年月平均降水量作为时间步长时,降水丰沛的月份使用kriging插值法较优于IDW插值法,而枯水月份则使用IDW插值法较优于kriging插值法。     

A Comparative Study for 3D Surface Modeling of Coal Deposit by Spatial Interpolation Approaches

The planning stages of mining require comprehensive and detailed analyses. The proper determination of the orebody boundary is one of the most important points to provide optimum model structure and projections. The limits can be determined by different methods based on the site geology. Although some three dimensional (3D) models were proposed for providing detailed information concerning a mine deposit, developing a solid model via a 3D approach is novelty. In other words, surface modeling should be performed for creating a solid model and determining limits of the deposit. In this way, sensible generation of the surface model can be achieved. This study investigated the estimation capability of the polynomial approach, which is a novel spatial interpolation method, for modeling a coal deposit surface. The performance of the proposed model was compared with some conventional methods in the literature. The results showed that the polynomial interpolation method is an effective method to employ for surface modeling of a mine deposit.     

局域地应力场获取的插值平衡方法

针对由整体地应场插值计算局域地应力场的问题计算量大、受地质结构的影响大、不过分追求高精度等特点,改进了反距离加权插值法,考虑了单元体积的影响,提高了该方法在此问题中的适用性。基于此,提出了平面问题、三维地面和地下工程局域地应力场的求取策略,建议了边界全平动约束和法向约束两种边界条件,并验证了其合理性和适用场合。最后,在大型水电工程深切河谷坝肩边坡分析中进行了应用分析。结果表明：该插值方法简单实用,能够满足工程分析的精度要求;局域地应力场的求取策略计算效率高,计算精度能够满足工程分析的要求。     

MICROMINE IDW方法在福安堡钼矿储量估算中的应用

床位于舒兰市开原镇薛家村福安堡屯西火石顶子附近。矿区位于舒兰市91°方向26 km。该矿床属斑岩型钼矿床,矿石类型主要为蚀变似斑状二长花岗岩型,主要矿物为辉钼矿。资源储量估算是利用澳大利亚Micromine公司开发的MICROMINE 11.03来完成的,资源储量估算方法用IDW。文中详细地介绍了利用该软件进行储量估算的过程和方法。