A Note on Extension Variances in IR²     

Joël Chaduf  Chris Moran  Michel Goulard 《Mathematical Geology》1998,30(6):575-587

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.  相似文献   

Spatial continuity measures for probabilistic and deterministic geostatistics   总被引：3，自引：0，他引：3  

E. H. Isaaks  R. Mohan Srivastava 《Mathematical Geology》1988,20(4):313-341

Geostatistics has traditionally used a probabilistic framework, one in which expected values or ensemble averages are of primary importance. The less familiar deterministic framework views geostatistical problems in terms of spatial integrals. This paper outlines the two frameworks and examines the issue of which spatial continuity measure, the covarianceC (h) or the variogram (h), is appropriate for each framework. AlthoughC (h) and (h) were defined originally in terms of spatial integrals, the convenience of probabilistic notation made the expected value definitions more common. These now classical expected value definitions entail a linear relationship betweenC (h) and (h); the spatial integral definitions do not. In a probabilistic framework, where available sample information is extrapolated to domains other than the one which was sampled, the expected value definitions are appropriate; furthermore, within a probabilistic framework, reasons exist for preferring the variogram to the covariance function. In a deterministic framework, where available sample information is interpolated within the same domain, the spatial integral definitions are appropriate and no reasons are known for preferring the variogram. A case study on a Wiener-Levy process demonstrates differences between the two frameworks and shows that, for most estimation problems, the deterministic viewpoint is more appropriate. Several case studies on real data sets reveal that the sample covariance function reflects the character of spatial continuity better than the sample variogram. From both theoretical and practical considerations, clearly for most geostatistical problems, direct estimation of the covariance is better than the traditional variogram approach.This paper was presented at MGUS 87 Conference, Redwood City, California, 14 April 1987.  相似文献   

岩土性质的空间信息统计分析   总被引：1，自引：0，他引：1  

邢君  孙洪泉  李维涛 《岩土工程技术》2004,18(1):5-7

运用地质统计学的原理与方法 ,以变差函数为工具 ,在工程实测数据的基础上对静止水位进行了分析 ,得到不同方向上的实验变差函数及理论变差函数模型 ,并提出了一个变异性综合指标 ,实现了对岩土性质空间变异性的定量化分析。  相似文献   

Multidimensional Self-Affine Distribution with Application in Geochemistry   总被引：5，自引：0，他引：5  

Shen Wei  Zhao Pengda 《Mathematical Geology》2002,34(2):109-123

In this paper, we present the conception of the multidimensional self-affine distribution and show that the multidimensional self-affine distribution possesses the fractal property of scale-invariance under truncation, which means that theoretical study of fractals has expanded from univariate cases to multivariate cases. Application of the multidimensional self-affine distribution is illustrated by means of geochemical Au and Ag elements data sets. The fractal dimension is a parameter which can quantitatively explain the variation of geochemical elements data on some orientation. This method is applied to Au data and Ag data, but also suited for other geochemical elements data or geological data. Theory of multivariate fractal can be applied for the study of change courses of fractal system, that is, fractal dynamics.  相似文献   

Characterization and reconstruction of a rock fracture surface by geostatistics   总被引：1，自引：0，他引：1  

A. Marache  J. Riss  S. Gentier  J.‐P. Chils 《国际地质力学数值与分析法杂志》2002,26(9):873-896

It is well understood that, in studying the mechanical and hydromechanical behaviour of rock joints, their morphology must be taken into account. A geostatistical approach has been developed for characterizing the morphology of fracture surfaces at a decimetre scale. This allows the analysis of the spatial variability of elevations, and their first and second derivatives, with the intention of producing a model that gives a numerical three‐dimensional (3D) representation of the lower and upper surfaces of the fracture. Two samples (I and II) located close together were cored across a natural fracture. The experimental data are the elevations recorded along profiles (using recording steps of 0.5 and 0.02 mm, respectively, for the samples I and II). The goal of this study is to model the surface topography of sample I, so getting estimates for elevations at each node of a square grid whose mesh size will be, for mechanical purposes, no larger than the recording step. Since the fracture surface within the sample core is not strictly horizontal, geostatistical methods are applied to residuals of elevations of sample I. Further, since structural information is necessary at very low scale, theoretical models of variograms of elevations, first and second derivatives are fitted using data of both that sample I and sample II. The geostatistical reconstructions are computed using kriging and conditional simulation methods. In order to validate these reconstructions, variograms and distributions of experimental data are compared with variograms and distributions of the fitted data. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

北京市近郊区土壤镍的空间结构及分布特征   总被引：30，自引：1，他引：30  

郑袁明  陈同斌  陈煌  吴泓涛  周建利  罗金发  黄泽春 《地理学报》2003,58(3):470-476

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。  相似文献   

在储层建模中利用多点地质统计学整合地质概念模型及其解释(英文)   总被引：1，自引：0，他引：1  

张团峰 《地学前缘》2008,15(1):26-35

基于三维空间中稀疏的观测数据,地质学家和储层建模人员尝试预测井间的地质沉积相的空间非均质性时,地质概念模型和先验认识在其中扮演着重要的角色。这种整合先验模型或解释的过程有时是隐蔽或不易察觉的,正如在手工绘等值线图中的情形;它也能够被显式地运用到某种算法当中,比如数字绘图中的算法。新近兴起的多点地质统计学为地质学家和储层建模人员提供了一种有力工具,它强调使用训练图像把先验模型明确而定量地引入到储层建模当中。先验地质模型包含了被研究的真实储层中确信存在的样式,而训练图像则是该模型的定量化表达。通过再现高阶统计量,多点算法能够从训练图像中捕捉复杂的(非线性)特征样式并把它们锚定到观测的井位数据。文中描述了多点地质统计学原理,以突出训练图像概念重要性为主线,描述了多点地质统计学在建立三维储层模型中的应用。  相似文献   

IDENTIFICATION OF PALEO-EARTHQUAKES OF LUOYUNSHAN PIEDMONT FAULT BY QUANTITATIVE MORPHOLOGY OF LIMESTONE FAULT SURFACES     

ZOU Jun-jie  HE Hong-lin  SHI Feng  WEI Zhan-yu  SU Peng  YAN Xiao-bing 《地震地质》2019,41(2):400-418

The quantitative analysis of morphologic characteristics of bedrock fault surface is a useful approach to study faulting history and identify paleo-earthquake. It is an effective complement to trenching technique, specially to identifying paleo-earthquakes in a bedrock area where the trenching technique cannot be applied. This paper focuses on the Luoyunshan piedmont fault, which is an active normal fault extending along the eastern boundary of the Shanxi Graben, China. There are a lot of fault scarps along the fault zone, which supply plentiful samples to be selected to our research, that is, to study faulting history and identify paleo-earthquakes in bedrock area by the quantitative analysis of morphologic characteristics of fault surfaces. In this paper, we calculate the 2D fractal dimension of two bedrock fault surfaces on the Luoyunshan piedmont fault in the Shanxi Graben, China using the isotropic empirical variance function, which is a popular method in fractal geometry. Results indicate that the fractal dimension varies systematically with height above the base of the fault surface exposures, indicating segmentation of the fault surface morphology. The 2D fractal dimension on a fault surface shows a ‘stair-like’ vertical segmentation, which is consistent with the weathering band and suggests that those fault surfaces are outcropped due to periodic faulting earthquakes. However, compared to the results of gneiss obtained by the former researchers, the characteristic fractal value of limestone shows an opposite evolution trend. 1)The paleo-earthquake study of the bedrock fault surface can be used as a supplementary method to study the activity history of faults in specific geomorphological regions. It can be used to fill the gaps in the exploration of the paleo-earthquake method in the bedrock area, and then broaden the study of active faults in space and scope. The quantitative analysis of bedrock fault surface morphology is an effective method to study faulting history and identify paleo-earthquake. The quantitative feature analysis method of the bedrock fault surface is a cost-effective method for the study of paleo-earthquakes in the bedrock fault surface. The number of weathered bands and band height can be identified by the segment number and segment height of the characteristic fractal dimension, and then the paleoearthquake events and the co-seismic displacement can be determined; 2)The exposure of the fault surface of the Luoyunshan bedrock is affected and controlled by both fault activity and erosion. A strong fault activity(ruptured earthquake)forms a segment of fault surface which is equivalent to the vertical co-seismic displacement of the earthquake. After the segment is cropped out, it suffers from the same effect of weathering and erosion, and thus this segment has approximately the same fractal dimension. Multiple severe fault activities(ruptured earthquake)form multiple fault surface topography. The long-term erosion under weak hydrodynamic conditions at the base of the fault cliff between two adjacent fault activities(intermittent period)will form a gradual slow-connect region where the fractal dimension gradually changes with the height of the fault surface. Based on the segmentation of quantitative morphology of the two fault surfaces on the Luoyunshan piedmont fault, we identified four earthquake events. Two sets of co-seismic displacement of about 3m and 1m on the fault are obtained; 3)The relationship between the fault surface morphology parameters and the time is described as follows:The fractal dimension of the limestone area decreases with the increase of the exposure time, which reflects the gradual smoothing characteristics after exposed. The phenomenon is opposite to the evolution of the geological features of gneiss faults acquired by the predecessors on the Huoshan piedmont fault; 4)Lithology plays an important role in morphology evolution of fault surface and the two opposite evolution trends of the characteristic fractal value on limestone and gneiss show that the weathering mechanism of limestone is different from that of the gneiss.  相似文献   

Cokriging for enhanced spatial interpolation of rainfall in two Australian catchments   总被引：1，自引：0，他引：1       下载免费PDF全文

Sajal Kumar Adhikary  Nitin Muttil  Abdullah Gokhan Yilmaz 《水文研究》2017,31(12):2143-2161

Rainfall data in continuous space provide an essential input for most hydrological and water resources planning studies. Spatial distribution of rainfall is usually estimated using ground‐based point rainfall data from sparsely positioned rain‐gauge stations in a rain‐gauge network. Kriging has become a widely used interpolation method to estimate the spatial distribution of climate variables including rainfall. The objective of this study is to evaluate three geostatistical (ordinary kriging [OK], ordinary cokriging [OCK], kriging with an external drift [KED]), and two deterministic (inverse distance weighting, radial basis function) interpolation methods for enhanced spatial interpolation of monthly rainfall in the Middle Yarra River catchment and the Ovens River catchment in Victoria, Australia. Historical rainfall records from existing rain‐gauge stations of the catchments during 1980–2012 period are used for the analysis. A digital elevation model of each catchment is used as the supplementary information in addition to rainfall for the OCK and kriging with an external drift methods. The prediction performance of the adopted interpolation methods is assessed through cross‐validation. Results indicate that the geostatistical methods outperform the deterministic methods for spatial interpolation of rainfall. Results also indicate that among the geostatistical methods, the OCK method is found to be the best interpolator for estimating spatial rainfall distribution in both the catchments with the lowest prediction error between the observed and estimated monthly rainfall. Thus, this study demonstrates that the use of elevation as an auxiliary variable in addition to rainfall data in the geostatistical framework can significantly enhance the estimation of rainfall over a catchment.  相似文献   

Spatial considerations when monitoring reef fishes     

D Parker  H Winker  ATF Bernard  MKS Smith  A Götz 《African Journal of Marine Science》2019,41(1):93-101

Spatial dependence can obscure relationships between response and explanatory variables because of structuring within the residuals reducing variance and biasing coefficient estimates. Here, we highlight the influence of the spatial component, in the presence of spatial dependence, on abundance trends. This is illustrated using abundance data for a Critically Endangered reef fish, dageraad Chrysoblephus cristiceps, which were obtained from a long-term monitoring programme in the Tsitsikamma National Park marine protected area, South Africa. Correlograms illustrate distinct spatial structuring in the abundance data, and spatial variables were determined as more important than temporal variables when ranked according to predictive power using a random forest analysis. A generalised additive model (GAM) that did not account for spatial dependencies was compared to a generalised additive mixed model (GAMM) that incorporated a spatial residual correlation structure. Results derived from the spatially explicit GAMM differed considerably from the GAM lacking a spatial component, with the latter deemed to produce over-precise and partially biased abundance trends. The study emphasises the importance of space in accurately modelling abundance estimates, particularly temporal trends, and provides an introduction to the minimal statistical requirements necessary to address the violations associated with spatial autocorrelation.  相似文献