Kriging with imprecise (fuzzy) variograms. II: Application

The geostatistical analysis of soil liner permeability is based on 20 measurements and imprecise prior information on nugget effect, sill, and range of the unknown variogram. Using this information, membership functions for variogram parameters are assessed and the fuzzy variogram is constructed. Both kriging estimates and estimation variances are calculated as fuzzy numbers from the fuzzy variogram and data points. Contour maps are presented, indicating values of the kriged permeability and the estimation variance corresponding to selected membership values called levels.     

A two-dimensional fuzzy random model of soil pore structure

A new conceptual model for soil poresolid structure is formalized. Soil poresolid structure is proposed to comprise spatially abutting elements each with a value which is its membership to the fuzzy set “pore, ” termed porosity. These values have a range between zero (all solid) and unity (all pore). Images are used to represent structures in which the elements are pixels and the value of each is a porosity. Twodimensional random fields are generated by allocating each pixel a porosity by independently sampling a statistical distribution. These random fields are reorganized into other poresolid structural types by selecting parent points which have a specified local region of influence. Pixels of larger or smaller porosity are aggregated about the parent points and within the region of interest by controlled swapping of pixels in the image. This creates local regions of homogeneity within the random field. This is similar to the process known as simulated annealing. The resulting structures are characterized using one and twodimensional variograms and functions describing their connectivity. A variety of examples of structures created by the model is presented and compared. Extension to three dimensions presents no theoretical difficulties and is currently under development.     

On the estimation of scale of fluctuation in geostatistics

Describing how soil properties vary spatially is of particular importance in stochastic analyses of geotechnical problems, because spatial variability has a significant influence on local material and global geotechnical response. In particular, the scale of fluctuation θ is a key parameter in the correlation model used to represent the spatial variability of a site through a random field. It is, therefore, of fundamental importance to accurately estimate θ in order to best model the actual soil heterogeneity. In this paper, two methodologies are investigated to assess their abilities to estimate the vertical and horizontal scales of fluctuation of a particular site using in situ cone penetration test (CPT) data. The first method belongs to the family of more traditional approaches, which are based on best fitting a theoretical correlation model to available CPT data. The second method involves a new strategy which combines information from conditional random fields with the traditional approach. Both methods are applied to a case study involving the estimation of θ at three two-dimensional sections across a site and the results obtained show general agreement between the two methods, suggesting a similar level of accuracy between the new and traditional approaches. However, in order to further assess the relative accuracy of estimates provided by each method, a second numerical analysis is proposed. The results confirm the general consistency observed in the case study calculations, particularly in the vertical direction where a large amount of data are available. Interestingly, for the horizontal direction, where data are typically scarce, some additional improvement in terms of relative error is obtained with the new approach.     

Kriging with imprecise (fuzzy) variograms. I: Theory

Imprecise variogram parameters are modeled with fuzzy set theory. The fit of a variogram model to experimental variograms is often subjective. The accuracy of the fit is modeled with imprecise variogram parameters. Measurement data often are insufficient to create good experimental variograms. In this case, prior knowledge and experience can contribute to determination of the variogram model parameters. A methodology for kriging with imprecise variogram parameters is developed. Both kriged values and estimation variances are calculated as fuzzy numbers and characterized by their membership functions. Besides estimation variance, the membership functions are used to create another uncertainty measure. This measure depends on both homogeneity and configuration of the data.     

Definition of kriging in terms of fuzzy logic

In this paper, we have basically attempted to solve two problems: (i) the restricted kriging problem as stated by Matheron, and (ii) the defining of Matheron's kriging problem within the framework of fuzzy logic in order to interpret the Lagrange multiplier, which is a function of kriging variance and is a dual variable with respect to which the generalized Lagrange function F(X, ) is minimized.on leave from Department of Geology, Indian Institute of Technology, Kharagphur 721302, West Bengal, India.     

Geostatistical regionalization of glacial aquitard thickness in northwestern Germany, based on fuzzy kriging

In many instances hydrogeological parameters obtained by conventional methods for selected localities within an aquifer or an aquitard are not sufficient for adequate regionalization at the scale of the entire layer. Here, we demonstrate an application of the fuzzy kriging method in regionalization of hydrogeological data, in which the set of conventional, crisp values is supplemented by imprecise information subjectively estimated by an expert. It is believed that such an approach eventually may reflect the real-world conditions more closely than a traditional crisp-value approach, because the former does not impose exactness artificially on phenomena which are diffuse by their nature. Spatial interpolation was done for the thickness of one of the major aquitards (till and glaciolacustrine clay) in northwestern Germany. The dataset consists of 329 crisp values from boreholes supplemented by 172 imprecise values defined as fuzzy numbers. It is demonstrated that the reliability of regionalization was higher, compared to regionalization performed with the crisp dataset only. Fuzzy kriging was performed with FUZZEKS (Fuzzy Evaluation and Kriging System) developed at the Ecosystem Research Center at the University of Kiel.     

Bias in estimating fractal dimension with the rescaled-range (R/S) technique

Fractal geostatistics are being applied to subsurface geological data as a way of predicting the spatial distribution of hydrocarbon reservoir properties. The fractal dimension is the controlling parameter in stochastic methods to produce random fields of porosity and permeability. Rescaled range (R/S)analysis has become a popular way of estimating the fractal dimension, via determination of the Hurst exponent (H). A systematic investigation has been undertaken of the bias to be expected due to a range of factors commonly inherent in borehole data, particularly downhole wireline logs. The results are integrated with a review of previous work in this area. Small datasets. overlapping samples, drift and nonstationariry of means can produce a very large bias, and convergence of estimates of H around 0.85–0.90 regardless of original fractal dimension. Nonstationarity can also account for H>1, which has been reported in the literature but which is theoretically impossible for fractal time series. These results call into question the validity of fractal stochastic models built using fractal dimensions estimated with the R/Smethod.     

基于地统计学烟区土壤养分及pH值空间异质性分析——以重庆市酉阳县岩溶区为例

调查了解土壤养分及pH值空间异质性特征是制定烟区土壤养分管理与施肥决策的前提。本研究基于经典统计学和地统计学方法,分析了酉阳烟区土壤表层pH值及土壤养分要素的空间异质性特征。结果表明:酉阳烟区土壤有机质含量丰富,有效磷较缺乏;土壤养分指标的变异系数在13.11%～71.46%之间,有效磷的变异系数最大,而有机质、全氮、碱解氮在土壤中比较稳定;土壤有机质和全氮、全磷、碱解氮和有效磷呈极显著的正相关,pH值和有效磷和速效钾呈极显著的负相关;有机质、全氮、全磷及速效钾的变异函数曲线理论模型符合指数模型,而pH值和碱解氮则与球状模型拟合较好;全氮、碱解氮、全磷及有效磷表现出中等空间相关性,而有机质、全钾及速效钾的空间相关性表现较弱;分维数大小表现为:全钾的分维数最大,pH值、速效钾、有机质其次,全氮、碱解氮最少;土壤养分及pH值空间分布在东西和南北方向具有显著性差异,且在东西方向上的变异要高于南北方向。酉阳烟区土壤养分空间相关性不强,说明地形、施肥及耕作等随机性因素能够显著影响烟区土壤养分空间异质性。      

Geotechnical characterization of the upper Pleistocene–Holocene alluvial deposits of Roma (Italy) by means of multivariate geostatistics: Cross-validation results

We are presenting an attempt to evaluate the spatial variability of geotechnical parameters in the upper Pleistocene–Holocene alluvial deposits of Roma (Italy) by means of multivariate geostatistics.The upper Pleistocene–Holocene alluvial deposits of Roma are sensitive to high levels of geohazard. They occupy a sizable and significant part of the city, being the foundation for many monuments, historical neighborhoods, and archaeological areas, and the main host of the present and future subway lines. We have stored information from more than 2000 geotechnical boreholes crossing the alluvial deposits into a relational database. For the present study, only the boreholes with lithologic/textural interpretation and geotechnical information were selected. The set includes 283 boreholes and 719 samples, which have a set of geotechnical information comprising physical properties and mechanical parameters.Techniques of multivariate statistics and geostatistics were combined and compared to evaluate the estimation methods of the mechanical parameters, with special reference to the drained friction angle from direct shear test (φ′). Principal Component Analysis was applied to the dataset to highlight the relationships between the geotechnical parameters. Through cross-validation analysis, multiple linear regression, kriging, and cokriging were tested as estimators of φ′. Cross-validation demonstrates that the cokriging with granulometries as auxiliary variables is the most suitable method to estimate φ′. In addition to proving that cokriging is a good estimator of φ′, cross-validation demonstrates that input data are coherent and this allows us to use them for estimation of geotechnical parameters, although they come from different laboratories and different vintages.Nevertheless, to get the same good results of cross-validation in estimation, it is necessary for granulometries to be available at grid points. Since this information being not available at all grid points, it is expected that, in the future, textural information can be derived in an indirect way, i.e., from lithologic/textural spatial reconstructions.     

基于模糊逻辑法的冀西北地区铅锌银多金属矿定位预测

模糊逻辑空间决策模型在变量取值上不是采用二态法将研究区分为成矿有利区和成矿不利区两部分,而是根据地质数据的规律取连续变化的隶属度赋值,有效避免了有用地质信息的丢失。笔者在GIS平台上利用Arc-SDM模块对冀西北地区的地质、地球化学、地球物理等资料进行了处理,利用证据权法进行了线缓冲形成的证据层与矿床（点）之间的亲近度分析,在此基础上采用列表法对原始地质变量进行了直观模糊隶属度赋值。模糊逻辑的预测结果表明,在圈出的仅占研究区面积13.2%的靶区范围内有85%的已知矿床（点）出现,与已知矿床（点）吻合程度高,预测效果理想,其结果可用于指导下一步找矿工作。     

混合模糊证据权模型在河北承德煤炭资源预测中的应用

应用模糊逻辑法、加权证据权法相结合的混合模糊证据权模型和GeoDASGIS技术开展了承德煤炭资源预测研究。采用模糊逻辑法对与煤炭矿床有关的证据层进行了系统的处理和分析,并在此基础上采用加权证据权方法编制了成矿后验概率图,最终划分出5个主要的找矿远景区。研究结果不仅对进一步开展预测区优选评价具有重要的参考意义,而且为混合知识驱动与数据驱动的混合预测模型提供了一种可借鉴的有效方法。     

模糊证据权方法在纳米比亚白岗岩型铀矿预测中的应用

纳米比亚埃龙戈地区位于达马拉构造带中部, 是全球重要的铀成矿带, 但纳米比亚第四系覆盖较重, 严重影响了铀矿找矿效果。为摸清纳米比亚铀资源现状, 开展铀资源潜力评价工作, 充分利用和深度挖掘现有资料, 圈定了预测靶区, 为中国矿业企业在海外投资提供支撑。在对纳米比亚埃龙戈地区白岗岩型铀矿床控矿因素系统总结的基础上, 建立了综合信息找矿模型; 在GeoDAS GIS平台上, 利用非线性理论、奇异性理论及分形滤波技术, 实现了对该区隐伏构造、航放铀异常等弱缓信息的提取; 基于模糊证据权方法开展综合信息矿产预测, 圈定铀找矿远景区7个。通过模型检验, 验证了本次预测工作的有效性。认为Ⅰ级远景区内第四系覆盖区还存在巨大的找矿潜力, Ⅱ级远景区也具有较好的成矿条件, 但工作程度较低, 有望实现找矿突破。     

模糊神经网络在矿震预测中的应用

矿震同天然地震一样会给矿山生产及人身安全等带来重大灾难。也是目前尚不能准确预测的矿山灾害现象之一。根据现有的研究成果可知，矿震是一个多输入、多干扰、单输出的复杂系统。由于干扰项的存在，使利用建模、神经网络等手段对系统进行预测时会导致很大误差。模糊神经网络系统在建立对象输入、输出关系时与传统数学方法不同。即可以建立在无模型基础上，并利用其较强的学习训练特性，自动获取对象的输入、输出关系表达；可以将专家的评价语言作为系统的干扰项引入。这在一定程度上缓解了人为因素对预测结果的影响，且平滑了观测数据的随机性。文章利用改进的模糊神经网络及抚顺老虎台矿的矿震资料，对矿震最大震级的预测方法进行了探索。‘初步探讨了改进的模糊神经网络在矿震预测中的应用。得出在运用模糊神经网络进行预测时，为减小预测误差，应综合多种因素并提高专家评判语言的精确度的结论。指出在建立矿震系统预测模型时，利用干扰项将人为因素引入系统是必需的。通过实际应用证明其可行性。     

基于模糊逻辑的中甸岛弧斑岩型铜矿定位预测

文章选择中甸岛弧地区中比例尺地表填图所圈定的侵入岩及火山岩、航磁解译构造格架及汇水盆地沉积物多元素异常作为斑岩型铜矿定位预测的主要方法,总结提出了该区斑岩型铜矿的定位预测准则,并根据该准则在GIS平台上基于模糊逻辑模型进行了模糊成员权重赋值和模糊推理网络构建。通过模糊推理计算得到该区不同高度、不同方向航磁解译构造的交汇部位以及不同元素的组合异常特征,最终确定了该区可以发现斑岩型铜矿的模糊概率分布图。该区主要矿床如普朗、红山和雪鸡坪等均处于高模糊概率分布区,经野外检查验证发现普上和地苏嘎两处斑岩铜矿矿化新区。     

基于模糊证据权法的广西典型金矿矿产定量预测

多信息融合的矿产资源定量预测是当前资源潜力预测的前缘课题,不同地质背景信息与地球化学数据的深度挖掘是当前该领域急需解决的关键问题。文章通过总结广西各构造单元地质背景和成矿控制要素,在ArcGIS、GeoDAS等软件平台基础上,分析了广西全区60767个地球化学样品中Au、Ag、Mn、Cu、Pb、Zn、Sn、Sb等主要成矿及伴生元素的空间分布特征。基于GeoDAS平台,通过IDW插值、S-A异常分解、主成分分析等技术,选取地球化学组合元素异常、重磁异常以及岩浆岩与断层交点缓冲区数据,通过模糊证据权模型,重点选取卡林型金矿和破碎带蚀变金矿2种典型矿产类型,编制了成矿后验概率图,圈定了金成矿有利地段。该研究对应用新的成矿理论和评价技术方法在广西开展矿产资源潜力评价以及区划工作具有重要的参考意义。     

陆相页岩气资源评价中人工智能算法的探索——以苏北盆地溱潼凹陷为例

将下扬子区苏北盆地溱潼凹陷作为示范区,探讨了人工智能该如何进行页岩气资源评价的问题.给出了可采用的运算方法的组合设计,针对工区陆相页岩气资源评价参数进行了全过程的示范操作:用变形结构分区的方法在平面上将溱潼凹陷分成14个样品区,用模糊数学的方法对定性参数进行定量、半定量取值打分,用因子分析方法对平面上14个样品区进行了单层评价;以平面上14个样品区单层评价为基础,给出了14个样品区5个页岩气目的层在垂向上的叠合评价.为了解决叠合评价时样品区各单层数据的等价性,引入全零值和分级值进行评价、排优.这种针对页岩气资源评价的定性、定量和多层混合问题进行定量综合评价的组合运算方法,可以被开发页岩气资源人工智能评价系统所借鉴.     

甘肃敦煌地块基于岩浆岩(氧化物)信息的金找矿靶区定量优选

借用计算机强大的计算处理能力,以判别分析方法构建起甘肃敦煌地块基于化探资料的金找矿定量预测模型和基于岩浆岩(氧化物)信息的金找矿靶区定量优选模型,鉴别出18个与现有金矿床(点)相关关系高度密切的侵入岩体和123个由化探资料确定的金找矿靶区。优选出分布在上述18个岩体5km范围内的金找矿靶区,与化探资料确定的金矿找矿靶区进行综合优选,共选出27个金找矿靶区并分为三级,Ⅰ级靶区5个(其中3个靶区有已知金矿分布,见矿率58.2%),Ⅱ级靶区9个(见矿率33.3%),Ⅲ级靶区13个(见矿率14.8%)。综合信息定量优选的找矿靶区有极高的见矿率,为进一步地质找矿工作提供依据。     

地测空间信息系统功能在地质勘探报告中的应用简介

地测空间信息系统(CGIS)在地质勘探部门、矿山地测部门实现了自动化处理地测图形,即钻孔柱状图、煤层结构综合柱状、煤岩层对比图、封孔结构图、地质实测剖面图、地质剖面图及各类等值线图等图件,并可自动形成各类报告、生产报表,改变以往手工绘制图件,可节省大量的人力、物力、财力。