Indicator Kriging without Order Relation Violations

Indicator kriging (IK) is a spatial interpolation technique aimed at estimating the conditional cumulative distribution function (ccdf) of a variable at an unsampled location. Obtained results form a discrete approximation to this ccdf, and its corresponding discrete probability density function (cpdf) should be a vector, where each component gives the probability of an occurrence of a class. Therefore, this vector must have positive components summing up to one, like in a composition in the simplex. This suggests a simplicial approach to IK, based on the algebraic-geometric structure of this sample space: simplicial IK actually works with log-odds. Interpolated log-odds can afterwards be easily re-expressed as the desired cpdf or ccdf. An alternative but equivalent approach may also be based on log-likelihoods. Both versions of the method avoid by construction all conventional IK standard drawbacks: estimates are always within the (0,1) interval and present no order-relation problems (either with kriging or co-kriging). Even the modeling of indicator structural functions is clarified.     

Monotone Regression and Correction for Order Relation Deviations in Indicator Kriging

The indicator kriging (IK) is one of the most efficient nonparametric methods in geo-statistics. The order relation problem in the conditional cumulative distribution values obtained by IK is the most severe drawback of it. The correction of order relation deviations is an essential and important part of IK approach. A monotone regression was proposed as a new correction method which could minimize the deviation from original quintiles value, although, ensuring all order relations.     

Indicator kriging for unit vectors: Rock joint orientations

Indicator kriging (IK) is extended to analyze three-dimensional random unit vectors and evaluate the local probability distribution of rock joint orientations in geological formations. The pole vector representing joint orientations is regionalized and projected on a plane normal to the mean attitude of the joint family and centered at the mean. A two-dimensional cutoff system is developed to define the indicator variable, and corresponding indicator variograms and indicator kriging. The cutoff system defines probability regions similar to those of a bivariate distribution, concentric rings sliced into radial sectors. A case study made on an open pit mine proved positively the efficiency of IK and encourages its applications to localized probabilistic structural modeling for geotechnical or geohydrological analysis and oil and gas reservoir analysis.     

基于地质统计学的NDVI图像估值技术

将疏采样后的NDVI图像作为未受云层影响的已知数据,分别用普通克里格、泛克里格、指示克里格和序贯指示模拟对NDVI图像进行恢复并比较其效果。研究发现,各种克里格法对NDVI图像的估值效果由高到低依次为泛克里格、普通克里格、指示克里格,通常计算方便的普通克里格法就能够满足图像恢复所要求的精度;普通克里格方差和泛克里格方差只能反映数据的构型,不能很好地衡量估值图像的不确定性,指示克里格的条件方差的分布和实际误差的分布基本一致,能够较好地衡量估值图像的不确定性,并且其大小与NDVI影像数据的不确定性大小的分布一致。序贯指示模拟得到的多个等概率实现表现出很大的空间变异性,多个实现的均值图像光滑效应明显,估值精度不高,但是多个实现的方差分布可以很好地表征空间数据的不确定性分布。     

Probabilistic assessment of the water quality of bathing beaches on the Taiwanese coast using indicator-based geostatistics with one-dimensional cyclic coordinates

Because Taiwan is a subtropical island, many pleasure beaches are situated on its coast. However, according to long-term monitoring data, fecal contamination at Taiwanese coastal beaches frequently exceeds the U.S. Environmental Protection Agency (EPA) guidelines. To avoid public health hazards, mapping the spatial extent of this contamination is crucial. This study applied indicator kriging (IK) to probabilistically assess the water quality of bathing beaches on the Taiwanese coast. Moreover, because the discontinuity of the traditional Cartesian coordinate established on an island coastline is difficult for geostatistical estimates, this study proposed a novel kriging estimation approach to deal with this problem. First, a one-dimensional (1-D) cyclic coordinate system of the Taiwanese coast was established using primary and secondary coordinates at each beach site. Escherichia coli (E. coli) and enterococci concentrations at coastal beaches were converted into indicator variables according to the U.S. EPA guidelines. IK was then used to spatially model the occurrence probabilities that exceeded the U.S. EPA guidelines for E. coli and enterococci. Finally, the water quality of bathing beaches on the Taiwanese coast was classified on the basis of the estimated probabilities. The study results indicated that bathing on the central western, northeastern, and southeastern Taiwanese coasts poses a potential threat to human health caused by high levels of fecal contamination. Moreover, primary and secondary coordinates established at beach sites were capable of analyzing the spatial variability and kriging estimates of the 1-D cyclic coordinates along the coastline.     

Estimating Freshwater Acidification Critical Load Exceedance Data for Great Britain Using Space-Varying Relationship Models

In this study, two distinct sets of analyses are conducted on a freshwater acidification critical load dataset, with the objective of assessing the quality of various models in estimating critical load exceedance data. Relationships between contextual catchment and critical load data are known to vary across space; as such, we cater for this in our model choice. Firstly, ordinary kriging (OK), multiple linear regression (MLR), geographically weighted regression (GWR), simple kriging with GWR-derived local means (SKlm-GWR), and kriging with an external drift (KED) are used to predict critical loads (and exceedances). Here, models that cater for space-varying relationships (GWR; SKlm-GWR; KED using local neighbourhoods) make more accurate predictions than those that do not (MLR; KED using a global neighbourhood), as well as in comparison to OK. Secondly, as the chosen predictors are not suited to providing useable estimates of critical load exceedance risk, they are replaced with indicator kriging (IK) models. Here, an IK model that is newly adapted to cater for space-varying relationships performs better than those that are not adapted in this way. However, when site misclassification rates are found using either exceedance predictions or estimates of exceedance risk, rates are intolerably high, reflecting much underlying noise in the data.     

Geographical Information Systems and Geostatistics for Modelling Radioactively Contaminated Land Areas

The Chernobyl plume contaminated vast lands of Europe with radiocaesium (¹37Cs) in 1986 because of the deposition of radionuclides on the ground by wet and dry deposition processes. Nevertheless, in a nuclear emergency, contamination data may be very sparse and there is need to make rapid and scientifically supported decisions. Here we analyze the rainfall field, an important precursor of the wet deposition, during the passage of the plume. Thus, estimating rainfall spatial variability can help to identify possible contaminated areas and associated risks when rainfall exceeded a given threshold. In this paper, we show that the conditional probabilities of exceeding threshold rainfall values could be spatially assessed using the mutual benefits of linking geostatistical and geographical information system (GIS) to quantify the evaluation of the risk involved in decision making. In particular, the non-parametric geostatistic technique, termed Indicator Kriging (IK), enables one to efficiently estimate the probability that the true value exceeds the threshold values by means of the indicator coding transform. Afterward, GIS has been used to find the areas probably affected by wash-out (probability >0.5 that rainfall is above a certain threshold). The experimental study has been focused on a test site in Beneventan agroecosystem (Southern Italy) to model the spatial uncertainty over a continuous area from sparse rainfall data. This enabled to generate probability maps delineating area potentially affected by to contamination to be monitored after wet deposition of Chernobyl releases.     

弹性地基上水工结构各向异性Mindlin底板计算分析的无单元法（EFGM）

无单元法（element free galerkin method）是一种基于滑动最小二乘法构造插值函数的无网格数值方法。以该方法中插值函数及其导函数为基础,从变分原理出发,建立了弹性地基上正交各向异性Mindlin板的无单元法求解控制方程,其中弹性地基采用Winkler地基模型。对该理论方法进行了相应的程序实现,最后通过算例分析表明了提出方法用于水工结构中弹性地基板问题分析的可行性和有效性。     

区域地下水功能及可持续利用性评价理论与方法

本文针对我国北方地下水评价中偏重资源而对地下水的生态功能和地质环境功能重视不足的问题，立足流域尺度地下水循环系统，从地下水的自然属性切入，突出协调综合发挥地下水的资源功能、生态功能和地质环境功能的目标，应用系统论和层次分析方法，建立了地下水功能的基本理念、评价标准和方法及评价指标体系，并以华北滹沱河流域作为示范区应用，结果表明具有实用性。     

Theoretical Study on Stochastic Modeling of Combined Gravity-Magnetic-Electric-Seismic Inversion and Its Application

As gravity field,magnetic field,electric field and seismic wave field are all physical fields,their object function,reverse function and compound function are certainly infinite contiuously differentiable func-tions which can be expanded into Taylor (Fourier) series within domain of definition and be further reduced in-to solving stochastic distribution function of series and statistic inference of optimal approximation,This is the basis of combined gravity-magnetic-electric-seismic inversion built on the basis of separation of field and source gravity-magnetic difference-value(D-value)trend surface,taking distribution-independent fault sys-tem as its unit,depths of seismic and electric interfaces of interests as its corresponding bivariate compound re-verse function of gravity-magnetic anomalies and using high order polynomial(high order trigonometric func-tion)approximating to its series distribution,The difference from current dominant inversion techniques is that,first,it does not respectively create gravity-seismic,magnetic-seismic deterministic inversion model from theoretical model,but combines gravity-magnetic-electric-seismic stochastic inversion model from stochastic model;second,after the concept of equivalent geological body being introduced,using feature of independent variable of gravity-magnetic field functions,taking density and susceptibility related to gravity-magnetic func-tion as default parameters of model,the deterministic model is established owing to better solution to the con-tradictioc of difficulty in identifying strata and less test analytical data for density and susceptibility in newly explored area;third,under assumption of independent parent distribution,a real modeling by strata,the prob-lem of difficult plane closure arising in profile modeling is avoided,This technology has richer and more detailed fault and strata information than sparse pattern seismic data in newly explored area,successfully inverses and plots structural map of Indosinian discontinuty in Hefei basin with combined gravity-magnetic-electric-seismic inversion,With development of high precision gravity-magnetic and overall geophysical technology,it is certain for introducing new methods of stochastic modeling and computational intelligence and promoting the develop-ment of combined gravity-magnetic-electric-seismic inversion to open a new substantial and promoting the develop-ment of combined gravity-magnetic-electric-seismic inversion to open a new substantial path.     

地下水硝酸盐污染的同位素研究进展

土壤原生氮、无机化肥和动物粪便等氮源中15N富集程度存在差异,使得利用稳定同位素N(δ15N/14N)能有效识别地下水中NO3-的来源。但N不是一个稳定的示踪剂,地下水中NO3-的δ15N是N源的初始δ15N值、后期进入含水层的迁移路径中和地下水流运动途径中不同形态的N之间相互转化过程,如矿化、吸附、硝化和反硝化作用,发生的同位素分馏作用后的综合反映。利用地下水中NO3-的δ15N确定其来源必须首先确定分馏作用是否发生及其反应程度。本文重点探讨了判断分馏作用是否发生及其反应程度的方法,总结了N同位素判别地下水NO3-污染源方法的发展历程,并指出未来研究工作应该以硝酸盐在包气带中的迁移转化规律为重点。     

多孔介质渗透率的分形描述

针对土壤、岩石等多孔介质结构的复杂性,从其结构形成的物理机制和达西定律出发,利用分形几何理论,将土壤等作为在统计意义上具有分形特征的多孔介质来研究其水力参数与结构之间的关系,建立了饱和多孔介质渗透率与其分维数之间的定量化的函数式。试验应用扫描电镜法研究了多孔介质断面微结构并算出分维数。试验结果表明:利用该模型预测的多孔介质渗透率与实测值基本吻合,能够比较精确地预测多孔介质水力参数。     

WA联合ELM与OS-ELM的滑坡位移预测模型

滑坡累积位移监测曲线往往呈现出复杂的非线性增长特性,对此建立了不少相关的预测模型,而以往的预测模型存在着许多不足。本文基于小波函数（Wavelet Analysis,WA）,ELM与OS-ELM,提出一种名为WA联合ELM、OS-ELM的预测方法。首先,该方法基于小波函数,将滑坡累积位移分解成受内部地质条件影响的趋势项和受外部影响因子影响的周期项;然后,基于ELM与OS-ELM分别对趋势项和周期项进行预测;最后将趋势项和周期项的预测值叠加得到累积位移的预测值。结果表明,小波函数得到的趋势项展现出良好的趋势性,而周期项也展现出良好的周期性;以Sigmoid方程为核函数,隐含层神经元个数为33的ELM模型能准确高效对趋势项进行预测,而以RBF方程为核函数,隐含层神经元个数为100的OS-ELM模型能准确高效对周期项进行预测;累积位移预测数据的RMSE分别为0.1423和0.1315,预测结果相对较好,能够在滑坡位移预测领域发挥一定的作用。     

基于紧支径向基函数的点插值无网格方法

紧支径向基函数能使支配方程中的刚度矩阵具有稀疏性,很适合应用于无网格方法中,其缺点是在插值计算时精度不高.点插值方法的插值函数具有Delta函数性质,可以很方便的施加本质边界条件,但在计算插值函数时矩阵易出现奇异.为了提高计算精度并避免点插值法的局限性,首先对紧支径向基函数进行完备性修正,然后用完备性修正的紧支径向基函数代替多项式来形成插值函数,建立了紧支径向基函数点插值方法.由于该方法中的形函数满足Delta函数性质,因此本质边界条件可以像传统的有限元方法一样很容易施加.然后将该方法用于二维弹性静力问题的求解,导出了其相应的离散方程.最后将该方法应用于一个悬臂梁的分析中,初步验证了该方法的有效性与合理性.     

Combination of GIS and mathematical modeling to predict floods in semiarid areas: case of Rheraya watershed (Western High Atlas,Morocco)

The Tinitine sub-watershed of Rheraya is renowned for its semiarid climate, irregular supply of water flow, and its historical floods; for these reasons, it is classified as vulnerable areas during a rainfall event. We conducted this study to propose flood prediction models adapted to this risky zone. For this, a hydrological method of flood forecasting rainfall-runoff used to determine a model conforms to the semiarid basin. This model is based on the articulation of the series production and transfer function. The goal of the production function is to determine the portion of the rainfall runoff, which is performed by two approaches that differ in their structures: (1) the first approach is based on the mathematical model of Horton; (2) the second approach is based on the determination of the part of the rain contributes to runoff and obtained by a spatial map of runoff coefficient (GIS). The transfer function is based on the two models of Clark and Nash, rainy efficient routes to the catchment outlet from a unit hydrograph. The characteristic parameters of these models are obtained through the application of mathematical optimization methods such as genetic algorithms. Thereby, the coupling function producing Horton (identified by the parameters: initial infiltration?=?15.03, final infiltration?=?0.3, and phi?=?0.45) and Clark transfer function (identified by the parameters C_A?=?0.21 and C_B?=?0.79) was given very satisfying results, mainly the low difference between observed and simulated hydrograph and Nash coefficient which is about 85%. This shows the interest of this coupling model in flood forecasting.     

浅论真振幅权函数的数值计算

真振幅权函数是Kirchhoff 偏移的核函数,数值计算方案与其表达形式有关。为探讨Kirchhoff 型真振幅加权函数的最优计算方案,对出现在文献中典型的3 种表达形式的权函数的数值实现流程进行了对比分析。结果表明: 基于格林函数振幅的计算方案需要进行动力学射线追踪,最为耗时; 基于旅行时和基于坐标与慢度的计算方案仅需运动学射线追踪; 基于旅行时的计算方案把权函数完全表述成旅行时导数的形式,方便易行,但算法的稳定性对旅行时的依赖度很高; 而基于坐标与慢度的计算方案对复杂模型有很好地适应性。此外,文中还特别讨论了2. 5D 介质下基于旅行时的权函数数值计算方案并进行了实现。     

一种新的半变异函数拟合方法——积分面积法

半变异函数是描述矿床某些区域化变量 (如矿石品位、矿体厚度等 )特征的有效数学模型。用积分面积法进行半变异函数拟合的基本思路是 :使实验函数与拟合的理论模型所包含的面积全等 ;传统的近似线性回归拟合是使围绕理论模型 (曲线 )的散点误差最小。从理论上讲无论积分或求导都不影响原函数的性质。     

基于GIS的海水入侵可视化数值模拟系统

将变密度三维海水入侵模型(SUTRA模型)与地理信息系统(GIS)进行有机集成开发出可视化海水入侵数值模拟系统.该系统充分利用了GIS的空间分析和数据管理功能及其可视化功能,实现了SUTRA模型的可视化构建1、含水层空间和模拟时间的可视化离散、各种参数的可视化赋值、模型的可视化模拟及其模拟结果的可视化表达等功能,为海水入侵研究提供了有效的模拟和分析手段.     

九龙县汤古乡黄牛厂泉水调查及评价研究

汤古乡黄牛厂泉因其独特的医药功能而著称。分析讨论温泉的天然特征,通过对泉点所处位置的地层岩性、地质构造、水文地质条件调查及对泉水水样进行饮用天然矿泉水水质检验。结果表明,该泉属于流量相对稳定的接触带泉;泉水中Li、Sr等多项指标符合界限指标要求,但锰及硼酸盐超过饮用矿泉水限量标准;泉水有一定的理疗功效,具有较高的开发价值。