用协同—指示克立格预测储层物性参数：以胜利油田罗家砂四上砾岩为例

指示克立格是一种非参数统计方法,它能在不舍弃特异值的条件下进行有效的空间估计,协同克立格以协同区域化变量的研究对象,充分考虑了变量空间相关性和变量间的统计相关性,有着单变量克立格法可可比拟的优点,因而,本文提出协同－指示克立格法这一方法,在指示克立格中考虑多变量的空间相关性和变量间的统计相关性,使指示克拉立格与协同克立格相互补充,模拟现实,提高预测精度,并以胜利油田罗家砂四上砾岩为例进行参数预测,     

析取克立格方法分析

非线性空间信息统计学主要包括对数正态克立格、指示克立格、析取克立格、条件期望等理论方法。通过源代码和运行结果对各种克立格方法在数据特点、时间复杂度等方面进行了比较。DK估计较普通克立格更有效。首先，DK考虑到了Z(x)的二维概率分布，充分应用有效信息，克服了线性克立格的前提条件太少，导致数值离散性大时，估计不够准确的缺点；其次，DK利用区域化变量的非线性组合估计，所以可以方便地得到变量的任意函数的估计结果，在局部可回采储量等方面比线性方法更容易、结果更准确。     

时空多元协同克立格的理论研究

本文结合地质统计学的最新成果,在空间协同区域化理论的基础上,对时空域中多元信息的协同克立格（ＳＴＣＯＫ）理论进行了较为详细的研究。主要研究内容有：（１）ＳＴＣＯＫ中的互变异函数与互协方差函数;（２）ＳＴＣＯＫ方程组及求解估值权因子的三种方法：①传统普通协同克立格法（ＳＴＴＯＣＯＫ）,②标准普通协同克立格法（ＳＴＳＯＣＯＫ）,③简单协同克立格法（ＳＴＳＣＯＫ）;（３）排列协同克立格（ＳＴＣＯＬＣＯＫ）;（４）指示协同克立格（ＳＴＩＫＣＯＫ）。     

时空域中的指示克立格理论研究

对时空域内的指示克立格进行了较全面的研究,主要研究内容有：（１） 时空域内的指示克立格（ＳＴＩＫ） 变换;（２） 指示二阶距;（３）单元指示克立格（ＳＴＩＫ）：①简单指示克立格（ＳＴＳＩＫ） ,②普通指示克立格（ＳＴＯＩＫ） ,③中值指示克立格（ＳＴＭＩＫ）;（４）多元指示克立格：①指示协同克立格（ＳＴＣＯＩＫ）,②主分量指示克立格（ＳＴＰＣＩＫ）     

克立格方法在区域化探数据处理中的应用

针对克立格方法能表征变量空间结构特征 ,以团结沟金矿研究区的化探数据处理为例 ,讨论了一般多元统计方法、协同克立格方法和普通克立格方法在化探元素间的相关分析结果。协同克立格方法对原始数据进行估值得到的绝对误差的均值要比用其它方法得到的绝对误差的均值低 ,标准差也明显降低。相比之下 ,协同克立格方法在一定程度上较为优越 ,它提高了地质统计学的预测精度 ,缺点是计算工作量较大。     

纯时间域多元信息地质统计学

随着人们动态地认识客观世界的要求日益增加,时空域中的多元信息地质统计学技术研究受到重视。本文在时间域内对几种纯时间域克立格技术进行了研究,重点对纯时间域中的普通克立格（ＴＯＫ）、简单克立格（ＴＳＫ）及泛克立格（ＴＵＫ）进行了论述,也对纯时间域中的协同克立格（ＴＣＯＫ）和指示克立格（ＴＩＫ）作了简要的概括。     

岩溶水区域化变量特异值识别与处理方法研究

在岩溶水区域化变量克立格估计中,特异值的存在将对区域化变量局部估计精度产生重要影响。本文针对岩溶发育的极不均匀性,分析了特异值产生的客观物理背景,并结合实际探讨了影响岩溶水区域化变量克立格估计精度的特异值的识别与处理方法。      

农田土壤水分和盐分空间分布的指示克立格分析评价

运用非参数地质统计学的多元指示克立格法,结合单元指示克立格法,对黄河河套灌区55hm2的盐渍化土地上两个比较关键时期的土壤水分和盐分进行空间分布的分析,给出了同一时期土壤水盐和不同时期土壤盐分满足一定标准的综合概率图,并借助该案例详细介绍了多元指示克立格的原理、步骤及应用范围。指示克立格方法为不同尺度(从农田到区域)上水土资源质量的评价提供了新的方法,能为水土资源的现代决策管理提供指导。     

归来庄金矿床化探信息金异常的协同克立格法研究

根据收集到的归来庄金矿床的化探资料,选取与Au相关系数较大的W、As、Sb等区域化探元素作为变量,对该区金异常空间分布进行协同克立格法研究.在对4个区域化变量进行空间结构分析的基础上,建立空间结构模型并进行估计.综合化探金异常的协同克立格法研究结果表明,该区有多处金异常存在,具有较好的找矿前景.     

基于Windows克立格算法的可视化编程与应用

随着信息社会的发展,克立格法已被广泛应用于矿产储量计算,物探、化探、遥感地质数据处理,环境科学、水文地质、农林科学和农田水利等诸多方面.文章综合分析克立格各种计算方法,对克立格复杂计算过程进行模块分解,基于Windows编写了克立格算法流程图并在Visual C 6.0平台上实现可视化编程,并对二维普通克立格算法的优化进行了有益的探索.     

Indicator principal component kriging

An alternative to multiple indicator kriging is proposed which approximates the full coindicator kriging system by kriging the principal components of the original indicator variables. This transformation is studied in detail for the biGaussian model. It is shown that the cross-correlations between principal components are either insignificant or exactly zero. This result allows derivation of the conditional cumulative density function (cdf) by kriging principal components and then applying a linear back transform. A performance comparison based on a real data set (Walker Lake) is presented which suggests that the proposed method achieves approximation of the conditional cdf equivalent to indicator cokriging but with substantially less variogram modeling effort and at smaller computational cost.     

Application of geostatistics to identify gold-rich areas in the Finisterre-Fervenza region,NW Spain

Three univariate geostatistical methods of estimation are applied to a geochemical data set. The studied methods are: ordinary kriging (cross-validation), factorial kriging, and indicator kriging. These techniques use the probabilistic and spatial behaviour of geochemical variables, giving a tool for identifying potential anomalous areas to locate mineralization. Ordinary kriging is easy to apply and to interpret the results. It has the advantage of using the same experimental grid points for its estimates, and no additional grid points are needed. Factorial kriging decomposes the raw variable into as many components as there are identified structures in the variogram. This, however, is a complex method and its application is more difficult than that of ordinary or indicator kriging. The main advantages of indicator kriging are that data are used by their rank order, being more robust about outlier values, and that the presentation of results is simple. Nevertheless, indicator kriging is incapable of separating anomalous values and the high values from the background, which have a behaviour different to the anomaly. In this work, the results of the application of these 3 kriging methods to a set of mineral exploration data obtained from a geochemical survey carried out in NW Spain are presented. This area is characterised by the presence of Au mineral occurrences. The kriging methods were applied to As, considered as a pathfinder of Au in this area. Numerical treatment of Au is not applicable, because it presents most values equal to the detection limit, and a series of extreme values. The results of the application of ordinary kriging, factorial kriging and indicator kriging to As make possible the location of a series of rich values, sited along a N–S shear zone, considered a structure related to the presence of Au.     

Geostatistical method to delineate anomalies of multi-scale spatial variation in hydrogeological changes due to the ChiChi earthquake in the ChouShui River alluvial fan in Taiwan

This study uses Ordinary Kriging (OK), Sequential Gaussian Simulation (SGS) and Simulated Annealing Simulation (SAS) to relocate the completely heterotopic dataset from the locations of the Standardized Satellite Oriented Control Point System (SSOCPS) stations to the Groundwater Monitoring Networks (GMNS) stations and factorial kriging to analyze and map relationships among seven variables, including the hydraulic conductivities of three aquifers, the vertical displacements of the ground and groundwater level changes in the wells of three aquifers, and also to delineate the anomalies of multi-scale spatial variation of hydrogeological properties associated with the ChiChi earthquake, measuring 7.3 on the Richter scale, in the ChouShui River alluvial fan in Taiwan. In this study, the anomalies of spatial variation of hydrogeological properties associated with the earthquake are illustrated at micro, local and regional scales of 9, 12 and 36 km, respectively. In the study area, regionalization components associated with variation at local and regional scales are obtained and mapped by factorial kriging. Factorial Kriging Analysis (FKA) also demonstrated that the main effects of the ChiChi earthquake on the spatial variations of groundwater hydrological changes include porous media compression at micro scale, hydrogeological heterogeneousness of the sediments within the aquifer at local scale and the cyclic loading of deviatoric stress at regional scale. Finally, maps of spatial variations of regional components fully depicted all of the anomalies of spatial variation of hydrogeological changes due to the ChiChi earthquake and can be used to identify, confirm and monitor the hydrogeological properties in this study area.     

Six factors which affect the condition number of matrices associated with kriging

Determining kriging weights to estimate some variable of interest at a given point in the field involves solving a system of linear equations. The matrix of this linear system is subject to numerical instability, and this instability is measured by the matrix condition number. Six parameters in the kriging process have been identified which directly affect this condition number. Analysis of a series of 648 experiments gives some insight on these parameters, and how the condition number relates to kriging variance.     

Trend removal in spatially correlated datasets

Typically, datasets originated from mining exploration sites, industrially polluted and hazardous waste sites are correlated spatially over the region under investigation. Ordinary kriging (OK) is a well-established geostatistical tool used for predicting variables, such as precious metal contents, biomass, species counts, and environmental pollutants at unsampled spatial locations based on data collected from the neighboring sampled locations at these sites. One of the assumptions required to perform OK is that the mean of the characteristic of concern is constant for the entire region under consideration (e.g., there is no spatial trend present in the contaminant distribution across the site). This assumption may be violated by dalasets obtained from environmental applications. The occurrence of spatial trend in a dataset collected from a polluted site is an indication of the presence of two or more statistical populations (strata) with significantly different mean concentrations. Use of OK in these situations can result in inaccurate kriging estimates with higher SDs which, in turn, can lead to incorrect decisions regarding all subsequent environmental monitoring and remediation activities. A univariate and a multivariate approach have been described to identify spatial trend that may be present at the site. The trend then is removed by subtracting the respective means from the corresponding populations. The results of OK before and after trend removal are being compared. Using a real dataset, it is shown that standard deviations (SDs) of the kriging estimates obtained after trend removal are uniformly smaller than the corresponding SDs of the estimates obtained without the trend removal.     

Ordinary kriging and indicator kriging in the cartography of trace elements contamination in São Domingos mining site (Alentejo, Portugal)

The abandoned pyrite mine of São Domingos, in the southeast Portugal is still an acid mine drainage generator and a source for trace elements pollution. This study aims to evaluate and map the soils and sediments chemical pollution. With this purpose three test sites located in the vicinities of the mine were sampled for soils, sediments and mining waste materials. The samples were analysed for pH, organic carbon, iron oxides and total content of As, Cu, Cr, Hg, Pb, Sb, U, Zn, Mn, S, Fe Al, Ca, K, Mg and P. The hyperspectral image of the test sites was acquired using the aero transported sensor HymapTM. Chemical analysis and hyperspectral images data were processed to estimate the contamination maps by multivariate data analysis, ordinary kriging, cokriging and indicator kriging methodologies.The test sites located downstream the mine open pit, are highly contaminated mainly in As, Hg, Pb and Sb, but no contamination was found in the third test site, upstream the mining site. The acid mining drainage seems to be the main spreading agent of chemical contaminants mostly originating from the mine waste materials. Factorial analysis and the geostatistical methodologies allowed several approaches for the contamination cartography of mining areas.     

Robust kriging—A proposal

Geological data frequently have a heavy-tailed normal-in-the-middle distribution, which gives rise to grade distributions that appear to be normal except for the occurrence of a few outliers. This same situation also applies to log-transformed data to which lognormal kriging is to be applied. For such data, linear kriging is nonrobust in that (1)kriged estimates tend to infinity as the outliers do, and (2)it is also not minimum mean squared error. The more general nonlinear method of disjunctive kriging is even more nonrobust, computationally more laborious, and in the end need not produce better practical answers. We propose a robust kriging method for such nearly normal data based on linear kriging of an editing of the data. It is little more laborious than conventional linear kriging and, used in conjunction with a robust estimator of the variogram, provides good protection against the effects of data outliers. The method is also applicable to time series analysis.     

克里格法在整理放射性水化学区调资料中的应用

本文对东北地区5706km~2范围内的放射件水化学详细区调资料用克里格法进行了电算处理,编制了1:20万铀水文地球化学图件。用克里格法对水中铀含量进行变异结构分析、确定异常结构(方向,大小),然后,再进行克里格估值。编图效果显著。     

Image Filtering by Factorial Kriging—Sensitivity analysis and application to Gloria side-scan sonar images

Factorial Kriging (FK) is a data- dependent spatial filtering method that can be used to remove both independent and correlated noise on geological images as well as to enhance lineaments for subsequent geological interpretation. The spatial variability of signal, noise, and lineaments, characterized by a variogram model, have been used explicitly in calculating FK filter coefficients that are equivalent to the kriging weighting coefficients. This is in contrast to the conventional spatial filtering method by predefined, data-independent filters, such as Gaussian and Sobel filters. The geostatistically optimal FK filter coefficients, however, do not guarantee an optimal filtering effect, if filter geometry (size and shape) are not properly selected. The selection of filter geometry has been investigated by examining the sensitivity of the FK filter coefficients to changes in filter size as well as variogram characteristics, such as nugget effect, type, range of influence, and anisotropy. The efficiency of data-dependent FK filtering relative to data-independent spatial filters has been evaluated through simulated stochastic images by two examples. In the first example, both FK and data-independent filters are used to remove white noise in simulated images. FK filtering results in a less blurring effect than the data-independent fillers, even for a filter size as large as 9 × 9. In the second example, FK and data-independent filters are compared relative to the extraction of lineaments and components showing anisotropic variability. It was determined that square windows of the filter mask are effective only for removing Isotropie components or white noise. A nonsquare windows must be used if anisotropic components are to be filtered out. FK filtering for lineament enhancement is shown to be resistant to image noise, whereas data-independent filters are sensitive to the presence of noise. We also have applied the FK filtering to the GLORIA side-scan sonar image from the Gulf of Mexico, illustrating that FK is superior to the data-independent filters in removing noise and enhancing lineaments. The case study also demonstrate that variogram analysis and FK filtering can be used for large images if a spectral analysis and optimal filter design in the frequency domain is prohibitive because of a large memory requirement.