井震联合建模技术在萨尔图油田B1DD区块的应用及其效果

为解决以往油藏描述工作单孔资料在深度和广度上存在明显局限性的问题,提出了一套井震联合地质建模的方法：首先以地震精细解释的层位数据和断层数据为约束,结合测井资料建立构造模型;然后采用地震反演体的概率面在平面上作为约束,纵向上在测井曲线上分类统计各微相的概率分布曲线,在变差函数分析的基础上,采用序贯指示模拟算法模拟出储层微相的空间展布,建立沉积相模型;最后采用相控技术和地质统计学理论,分析参数区域化变量的特征,建立储层属性模型。在大庆萨尔图油田的B1DD区块进行验证的结果表明,井震资料的联合应用揭示了大量的小断层,使断点组合率提高了15%,大于2 m的砂岩预测符合率达到90%以上,提高了井间断层和砂岩的预测精度,进而提高了地质模型、尤其是井间模型的精度。     

加入多时相纹理的遥感变化检测

基于遥感技术的变化检测是遥感应用的一个重要方面.传统基于遥感的变化检测方法一般是利用光谱信息,较少注意多时相图像间的光谱特征相关关系分析.本文运用地统计学的伪交叉变差函数(Pseudo Cross Variogram)计算多时相图像纹理,定量表达多时相图像间的空间相关关系,并将得到的多时相纹理信息与光谱信息一起用于多时相变化检测.实验结果表明,加入多时相纹理信息可以显著提高变化检测精度,是一种有效的方法.     

北京市近郊区土壤镍的空间结构及分布特征

通过对北京市近郊区349处土壤的取样调查，利用地统计学方法研究了北京市土壤中镍的空问结构和分布特征。结果显示，镍的空间结构性较好，具有明显的可迁性特点，块金效应所占的比例较大；实验变异函数可用指数模型拟合，利用所得模型进行克立格插值得到土壤镍含量的分布图，发现北京市土壤中，镍的含量分布具有明显的西北低而东南高的趋势。与北京市土壤镍含量的背景值进行对比，全市土壤并不存在非常严重的镍污染，其空间分布主要受成土母质制约；但是人类活动、风向、河流等人文和自然条件对镍的空间结构和分布格局也有一定程度的影响。     

A Note on Extension Variances in IR2

Matheron (1971) proposed an approximation of the extension variance in IR. We propose in this note an extension of this formula in IR ² , based on a MacLaurin formula. Its application is shown in an example, the estimation of the maximum depressional storage of a soil surface.     

地质统计学在东天山化探信息提取中的应用

地球化学场和地球物理场都具有一定的空间结构性和空间自相关性,而揭示这种空间相关性的有力工具是变差函数。利用变差函数对东天山的1∶20万区域地球化学数据Cu和Au进行了结构分析。结果表明：两元素在东西方向有着较好的稳定性和连续性,南北方向有较大的变化性并具有一定的线性漂移,总体呈现带状异常,与东天山EW方向大断裂具有很好的一致性。利用泛克里格法对Cu、Au进行了异常信息的提取和评价,泛克里格法提取的剩余异常不仅能突出高异常区,也较清晰地反映了部分低缓异常带,为研究区域化探异常分布特征提供了丰富的信息。     

Use of indicator variograms for an enhanced spatial analysis

Flat variograms often are interpreted as representing a lack of spatial autocorrelation. Recent research in earthquake engineering shows that nearby field noise can substantially mask a prominent spatial autocorrelation and result in what appears to be a purely random spatial process. A careful selection of threshold in assigning an indicator function can yield an indicator variogram which reveals underlying spatial autocorrelation. Although this application involves use of seismic data, the results are relevant to geostatistical applications in general.     

Quantification of Natural Fracture Surfaces Using Fractal Geometry

The purpose of this paper is to present an extensive evaluation of the methods to calculate the fractal dimension of natural fracture surfaces. Three methods; variogram analysis (VA), power spectral density (PSD), and roughness-length method (RMS) are applied to 2-D surface data (PSD) and 1-D profiles (VA and RMS) extracted from the surface data of 54 mm diameter crystallized limestone samples. Surface topography of the samples is quantified through a newly designed fully automated device. Before the application, self-affinity of the surface roughness and the applicability of these methods are validated using synthetically generated fractal surfaces. Fractal dimension values of the profiles are obtained as between 1 and 1.5 with a few exceptions. VA and RMS methods yield consistent fractal dimensions while the PSD values are lower than those of the other two methods. In terms of practical applicability, the VA is found more convenient than other two methods because there still exists shortcomings with the PSD and RMS methods due to difficulties in the mathematical analysis of the plots whose slopes are used in the computation of fractal dimension. However, it is observed that the data of limited size fracture surfaces are convenient for fractal analysis and the results are promising for further applications if the fracture surface size is restricted like cores recovered from deep boreholes.     

General polygonal variogram functions: Evaluation of estimation variance integrals

The application of regionalized variables requires the estimation of the variogram function and the evaluation of its integral. By representing the variogram by a general polygonal function the requisite integrals may be easily computed by a closed form representation of simple integrals. This paper provides the integration formulas for two-dimensional variogram functions whose domain is represented as a finite collection of rectangles. The integration formulas essential for a fully developed polygonal approach to an extensive statistical evaluation of geostatistical quantities are presented.     

Spatial orthogonality of the principal components computed from coregionalized variables

Within the frame of the linear model of coregionalization, this paper sets up equations relating the variogram matrix of the principal components extracted from the variance-covariance matrix to the diagonal variogram matrices of the regionalized factors. The spatial orthogonality of the principal components is investigated in three situations: the intrinsic correlation, two basic structures with independent nugget components, three basic structures with independent nugget components and uncorrelated subsets of variables. Two examples point out that the correlation between the principal components may be nonnegligible at short distances, especially if the correlation structure changes according to the spatial scale considered. For one of the two case studies, an orthogonal varimax rotation of the first principal components is found to greatly reduce the spatial correlation between some of them.     

On Visualization for Assessing Kriging Outcomes

Extant opinion about kriging is that all weights should be positive. Visualizations rendered by converting kriged grids to digital images are presented to show that negative weights may be beneficial to some spatial problems. In particular, variogram models with zero-valued nuggets, already well known to minimize smoothing through kriging, result in a visual resolution substantially superior to that from kriging with a variogram model having a nonzero nugget value in application to satellite acquired data. Negative weights are more likely when using variogram models with zero-valued nuggets, but resultant visualizations often show a smoother transition between extreme data values. This is true even when a variogram model having a nugget value of zero is not optimum with respect to mean square error, as is demonstrated using a nitrate data set. An analogy to digital image processing is used to suggest that the influence of negative weights in kriging is similar to a high-boost kernel.