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.     

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。     

露天矿边坡实用型专家系统PESOPS V1.0的设计与应用

结合边坡工程和岩质边坡普遍存在的问题，建造了一个露天矿边坡实用型专家系统ＰＥＳＯＰＳ Ｖ１．０。介绍了滑坡预报子系统的原理和方法，通过应用实例表明该子系统适用性强，预报可靠、使用方便。     

层次分析-多级模糊评判法在贵州普晴锑(金)矿区综合信息成矿预测中的应用

因综合信息成矿预测涉及的控矿因子较多,各度量指标间具有一定的层次性,有些定性指标还具有模糊性特征,高精度和定量化一直是制约其发展的难题。为了实现对研究程度较低的新矿区的成矿预测,并解决上述难题,本文试图将专家的主观判断与精确的数学运算巧妙地融合,将复杂问题及定性指标定量化,使评价过程和评判结果更具客观性,建立一种层次分析-多级模糊评价的成矿预测模型。以贵州大厂锑(金)矿田普晴矿区为例,选取地质、化探和遥感多元致矿信息,基于GIS平台,建立了层次分析-多级模糊评判的综合信息成矿预测模型,最终圈定出锑(金)矿远景区18个,其中Ⅰ、Ⅱ和III级远景区分别有4个、5个和9个。根据勘查验证,预测结果较为客观有效。     

准等时距QGM(1,1)模型分段预测法及其在草炭土路基沉降预测中的应用

利用传统非等时距模型预测草炭土路基沉降时,存在计算繁琐、中短期预报精度低等缺点,尤其是当沉降曲线存在斜率突变点时,采用该模型很难达到预测精度的要求。针对以上不足,对非等时距时间序列进行平均步长换算,得到准等时距序列,利用线性插值法对原始沉降数据进行修正,得到改进后的准等时距QGM(1,1)预测模型,并将沉降曲线在斜率突变点处分成两部分进行分段预测。实例计算表明:采用改进后的准等时距QGM(1,1)模型预测草炭土路基沉降,两段的预测值平均误差分别为2.99%和0.25%,均远远小于传统非等时距模型,且具有很高的中短期预测精度,可以为工程沉降控制提供可靠参考。     

欧洲应用地球物理现状——浅层（特）高分辨（VHRS）地震勘探

介绍了欧洲近几年浅层(特)高分辩地震勘探的发展现状，浅层(特)高分辩地震勘探中存在的主要技术难点与解决途径，其特制的采集设备与经验参数的设置情况，以及浅层高分辩地震勘探在冰川侵蚀古河道、溶洞、管道、表层地层结构的部分应用实例。     

青藏高原土壤水热过程模拟研究(Ⅱ):土壤温度

模拟青藏高原土壤水分和热量迁移过程的连续变化对于全球变化研究具有非常重要的意义, 其准确模拟是提高陆面过程模拟精度的重要条件. 利用大尺度水文模型对沱沱河站点以1 h为步长, 共399 d的土壤温度模拟结果与观测结果的对比表明, 土壤中共11个不同深度的观测点的模拟温度总体的变化趋势与观测值一致, 可以进行长时间的模拟. 对于地表温度, 模拟的日变化幅度比实测的变化幅度大, 但均值一致, 原因在于模型的土壤参数中没有考虑有机质含量, 在计算能量平衡时需要增加该土壤参数. 对于土壤底部的土壤温度的连续模拟表明, 采用常数的土壤下界算法和倾斜的(damping)土壤下界算法均与观测值的变化具有一定的差别, 而常数的下界算法与观测值更为接近.     

Endangering of the Upper Jurassic karst-fissured aquifer in the Krakow Upland (southern Poland)

 A karst-fissured aquifer in the Upper Jurassic carbonate rocks of the Krakow Upland shows a very high yield (safe yield 117 000 m³/day) and belongs to the major groundwater basins (MGBs) of Poland. The uncovered character of the aquifer and its hydraulic structure favor the intensive infiltration and migration of anthropogenic pollutants from the surface. This pollution is caused by agriculture and industry in the proximity of Krakow and the Upper Silesian agglomeration. Progressive degradation of groundwater quality on a regional scale results. Evaluation of the endangering of the aquifer studied is based on the analysis of the time interval of vertical water percolation from the surface, the time interval of groundwater horizontal flow through the aquifer and the duration of water residence in the aquifer derived from tritium data. Quaternary and Cretaceous overburden occur in the Krakow Upland in addition to numerous outcrops of limestones. The time interval of vertical water percolation in highly permeable limestones does not exceed 3 years and in the areas covered by overburden it is from several to 50 years. The mean effective time interval of horizontal groundwater flow through the Upper Jurassic rocks along the flow paths ranges from several months in the areas of direct drainage to over 15 years in the elevated areas of local groundwater divides. The age of water in the rock matrix was determined using tritium data interpreted according to an exponential model and it ranges from 70 years to over 130 years. In karst-fissured systems with a high retardation index (R_p=21) the effective time of water circulation in local drainage basins does not exceed 7 years. The Krakow-Wieluń Upland is the most extensive and uniform karst region in Poland. It is a belt of Upper Jurassic limestone extending from Krakcow in the southeast to Wieluń in the northwest on the northeast slope of the Silesian Upland. Residual hills of Paleogene age separated by infilled karst depressions are the most characteristic features of the Krakow-Wieluń Upland. More than 800 small caves are known in this area, but only two of them reach 1 km of aggregate passage length (Gazek and others 1992). Received: 4 December 1996 · Accepted: 29 April 1997     

Copper(II) humate mobility in kaolinite soil

An investigation of the influence of humate on the mobility of copper(II) ions in a kaolinite soil using leaching tests and electrokinetic experiments is reported. The data are interpreted in terms of humate–copper–clay interactions and humate electrical charge. Humate is mostly immobile below pH8 but is more mobile in alkaline conditions (sorption to kaolinite reduces its mobility in neutral conditions). Copper humate complexes are mobile in both acidic and alkaline conditions, but not in neutral conditions where they are sorbed. The dissolved copper humate complexes that form in acidic conditions are positively charged. The net effect of humate is to increase cupric ion mobility in kaolinite soil, especially in alkaline conditions.     

玉林市岩溶塌陷地理信息系统

GIS技术的发展为地质灾害的资料管理、危险性评价及对策研究等提供了有力的支持工具。玉林市岩溶塌陷地理信息系统是以GIS软件—MapInfo为平台，针对岩溶塌陷的特点，用VB语言进行二次开发的集数据管理、分析统计、输出为一体的综合系统。系统中录入了建国以来，玉林市发生的71次岩溶塌陷灾害事件，共414个塌陷坑的详细资料，及30多个与岩溶塌陷有关的其它专题信息。分别归类为岩溶塌陷信息、市政信息、勘探信息、水文气象信息、玉(林)柴(油厂)塌陷子系统等。此外，系统提供了信息查询、制作专题图、统计分析等功能，方便、快捷地为地质灾害管理、城市规划、勘察设计等部门提供服务。     

GM（1,1）模型在矿井水动态预测中的应用

本文以灰色系统理论为基础，建立了矿井地下水涌出的ＧＭ（１，１）动态预测模型，并用该模型进行了实际预测。     

Numerical study of soil heterogeneity effects on contaminant transport in unsaturated soil (model development and validation)

The movement of chemicals through soil to groundwater is a major cause of degradation of water resources. In many cases, serious human and stock health implications are associated with this form of pollution. The study of the effects of different factors involved in transport phenomena can provide valuable information to find the best remediation approaches. Numerical models are increasingly being used for predicting or analyzing solute transport processes in soils and groundwater. This article presents the development of a stochastic finite element model for the simulation of contaminant transport through soils with the main focus being on the incorporation of the effects of soil heterogeneity in the model. The governing equations of contaminant transport are presented. The mathematical framework and the numerical implementation of the model are described. The comparison of the results obtained from the developed stochastic model with those obtained from a deterministic method and some experimental results shows that the stochastic model is capable of predicting the transport of solutes in unsaturated soil with higher accuracy than deterministic one. The importance of the consideration of the effects of soil heterogeneity on contaminant fate is highlighted through a sensitivity analysis regarding the variance of saturated hydraulic conductivity as an index of soil heterogeneity. Copyright © 2011 John Wiley & Sons, Ltd.     

Power Laws Governing Historical Earthquakes in the Apennine Chain (Southern Italy)

Rank-ordering analysis is applied to the intertimes between seismic events recorded in the Apennine belt between 40–42° N and 14–16° E from the 15th century onwards. It shows a power law capable of governing the intertimes between 1529 and 368 months and another power law which approximates a random simulation, for the intertimes shorter than 368 months. Only the first power law allows the computation of the return period of major events. Earthquakes with the same energy that are aligned according to different power laws imply the presence of two different populations, indicating, in turn, that the physics of seismic phenomena in the region examined is not straightforward, that the stress is probably not unidirectional and that it acts on a non-isotropic medium. The most probable estimated intertime value for the next event is found to be equal to 60 ± 20 years.