Geostatistical regionalization of glacial aquitard thickness in northwestern Germany, based on fuzzy kriging   总被引：1，自引：0，他引：1  

J. A. Piotrowski  F. Bartels  A. Salski  G. Schmidt 《Mathematical Geology》1996,28(4):437-452

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.  相似文献   

Foliation fields and 3D cartography in geology: Principles of a method based on potential interpolation   总被引：4，自引：0，他引：4  

Christian Lajaunie  Gabriel Courrioux  Laurent Manuel 《Mathematical Geology》1997,29(4):571-584

A modeling method that takes into account known points on a geological interface and plane orientation data such as stratification or foliation planes is described and tested. The orientations data do not necessarily belong to one of the interfaces but are assumed to sample the main anisotropy of a geological formation as in current geological situations. The problem is to determine the surfaces which pass through the known points on interfaces and which are compatible with the orientation data. The method is based on the interpolation of a scalar field defined in the space the gradient in which is orthogonal to the orientations, given that some points have the same but unknown scalar value (points of the same interface), and that scalar gradient is known on the other points (foliations). The modeled interfaces are represented as isovalues of the interpolated field. Preliminary two-dimensional tests carried-out with different covariance models demonstrate the validity of the method, which is easily transposable in three dimensions.  相似文献   

Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging     

Nils-Otto Kitterrød  Lars Gottschalk 《Stochastic Environmental Research and Risk Assessment (SERRA)》1997,11(6):459-482

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.  相似文献   

Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging     

Nils-Otto Kitterr?d  Lars Gottschalk 《Stochastic Hydrology and Hydraulics》1997,11(6):459-482

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.  相似文献   

中国地质统计学（空间信息统计学）发展的回顾与前景   总被引：23，自引：0，他引：23  

侯景儒 《地质与勘探》1997,33(1):53-58

讨论了地质统计学（空间信息统计学）发展的若干问题，其内容包括４部分：１．地质统计学的理论及方法；２．关于软件系统的现状；３．关于实际应用；４．地质统计学发展前景的若干看法。  相似文献   

普通克里格法在矿产储量计算中的应用   总被引：9，自引：1，他引：9  

邢红星  琚太忠 《地质与勘探》1997,33(4):46-51

普通克里格法能充分利用样品信息，有效地提高块段平均品位及矿产储量精度。以刁泉银铜矿为实例，介绍了该方法的理论和方法应用以及储量计算流程图。  相似文献   

Correcting the Smoothing Effect of Ordinary Kriging Estimates   总被引：2，自引：0，他引：2  

Jorge Kazuo Yamamoto 《Mathematical Geology》2005,37(1):69-94

The smoothing effect of ordinary kriging is a well-known dangerous effect associated with this estimation technique. Consequently kriging estimates do not reproduce both histogram and semivariogram model of sample data. A four-step procedure for correcting the smoothing effect of ordinary kriging estimates is shown to be efficient for the reproduction of histogram and semivariogram without loss of local accuracy. Furthermore, this procedure provides a unique map sharing both local and global accuracies. Ordinary kriging with a proper correction for smoothing effect can be revitalized as a reliable estimation method that allows a better use of the available information.  相似文献   

Statistical identification of orographic effects in the regional analysis of extreme rainfall          下载免费PDF全文

Pierluigi Furcolo  Anna Pelosi  Fabio Rossi 《水文研究》2016,30(9):1342-1353

Regional models of extreme rainfall must address the spatial variability induced by orographic obstacles. However, the proper detection of orographic effects often depends on the availability of a well‐designed rain gauge network. The aim of this study is to investigate a new method for identifying and characterizing the effects of orography on the spatial structure of extreme rainfall at the regional scale, including where rainfall data are lacking or fail to describe rainfall features thoroughly. We analyse the annual maxima of daily rainfall data in the Campania region, an orographically complex region in Southern Italy, and introduce a statistical procedure to identify spatial outliers in a low order statistic (namely the mean). The locations of these outliers are then compared with a pattern of orographic objects that has been a priori identified through the application of an automatic geomorphological procedure. The results show a direct and clear link between a particular set of orographic objects and a local increase in the spatial variability of extreme rainfall. This analysis allowed us to objectively identify areas where orography produces enhanced variability in extreme rainfall. It has direct implications for rain gauge network design criteria and has led to promising developments in the regional analysis of extreme rainfall. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

Data analysis of a revisited exploration geochemical dataset of quartz porphyrites from SW Jordan using GIS techniques     

《Chemie der Erde / Geochemistry》2016,76(4):519-527

The spatial distribution of Cu and its pathfinder elements in quartz porphyrites along Wadi Araba was studied in order to gain an insight about the geologic framework of Cu mineralization in the area. A geochemical exploration data set of 242 samples was revisited. Multivariate statistical and geostatistical analysis were performed on the data set. The objectives of the study were to define Cu relationships with its possible pathfinder elements and to figure out whether geostatistical treatment of exploration data would help telescoping already existing Cu mineralization in Wadi Araba, SW Jordan. Factor analysis and hierarchical cluster analysis were performed on the data set. The results of which indicate that seven elements, namely, Ba, Cr, Mn, Ni, Sc, Sr and V can be considered as pathfinder elements for Cu. Significant correlations do exist between Cu and these elements. The encountered experimental semivariograms of the defined pathfinders were fit to exponential models with varying nugget effects with the exception of Mn which was fit to the spherical model. Ordinary kriging was found to be most appropriate to generate geochemical exploration maps. The applied methods succeeded in deriving valuable information and visualizing the already existing Cu mineralization in Wadi Abu Khusheiba area.  相似文献   

Improving kriging of groundwater level data using nonlinear normalizing transformations—a field application     

E.A. Varouchakis  G.P. Karatzas 《水文科学杂志》2013,58(7):1404-1419

Abstract

The present research study investigates the application of nonlinear normalizing data transformations in conjunction with ordinary kriging (OK) for the accurate prediction of groundwater level spatial variability in a sparsely-gauged basin. We investigate three established normalizing methods, Gaussian anamorphosis, trans-Gaussian kriging and the Box-Cox method to improve the estimation accuracy. The first two are applied for the first time to groundwater level data. All three methods improve the mean absolute prediction error compared to the application of OK to the non-transformed data. In addition, a modified Box-Cox transformation is proposed and applied to normalize the hydraulic heads. The modified Box-Cox transformation in conjunction with OK is found to be the optimal spatial model based on leave-one-out cross-validation. The recently established Spartan semivariogram family provides the optimal model fit to the transformed data. Finally, we present maps of the groundwater level and the kriging variance based on the optimal spatial model.

Editor D. Koutsoyiannis; Associate editor A. Montanari

Citation Varouchakis, E.A., Hristopoulos, D.T., and Karatzas, G.P., 2012. Improving kriging of groundwater level data using nonlinear normalizing transformations—a field application. Hydrological Sciences Journal, 57 (7), 1404–1419.  相似文献