Some Results on the Spatial Breakdown Point of Robust Point Estimates of the Variogram     

R. M. Lark 《Mathematical Geosciences》2008,40(7):729-751

The effect of outliers on estimates of the variogram depends on how they are distributed in space. The ‘spatial breakdown point’ is the largest proportion of observations which can be drawn from some arbitrary contaminating process without destroying a robust variogram estimator, when they are arranged in the most damaging spatial pattern. A numerical method is presented to find the spatial breakdown point for any sample array in two dimensions or more. It is shown by means of some examples that such a numerical approach is needed to determine the spatial breakdown point for two or more dimensions, even on a regular square sample grid, since previous conjectures about the spatial breakdown point in two dimensions do not hold. The ‘average spatial breakdown point’ has been used as a basis for practical guidelines on the intensity of contaminating processes that can be tolerated by robust variogram estimators. It is the largest proportion of contaminating observations in a data set such that the breakdown point of the variance estimator used to obtain point estimates of the variogram is not exceeded by the expected proportion of contaminated pairs of observations over any lag. In this paper the behaviour of the average spatial breakdown point is investigated for cases where the contaminating process is spatially dependent. It is shown that in two dimensions the average spatial breakdown point is 0.25. Finally, the ‘empirical spatial breakdown point’, a tool for the exploratory analysis of spatial data thought to contain outliers, is introduced and demonstrated using data on metal content in the soils of Sheffield, England. The empirical spatial breakdown point of a particular data set can be used to indicate whether the distribution of possible contaminants is likely to undermine a robust variogram estimator.  相似文献   

一种基于双重距离的空间聚类方法   总被引：10，自引：1，他引：9  

李光强  邓敏  程涛  朱建军 《测绘学报》2008,37(4):0-520

传统聚类方法大都是基于空间位置或非空间属性的相似性来进行聚类,分裂了空间要素固有的二重特性,从而导致了许多实际应用中空间聚类结果难以同时满足空间位置毗邻和非空间属性相近。然而,兼顾两者特性的空间聚类方法又存在算法复杂、结果不确定以及不易扩展等问题。为此,本文通过引入直接可达和相连概念,提出了一种基于双重距离的空间聚类方法,并给出了基于双重距离空间聚类的算法,分析了算法的复杂度。通过实验进一步验证了基于双重距离空间聚类算法不仅能发现任意形状的类簇,而且具有很好的抗噪性。  相似文献   

中强地震前后能量分布的自仿射特性     

蒋海昆  王忠民 《地震》1996,16(2):135-143

根据简化的地震波传播理论,“漫化”地震能量在空间的分配,减弱能量空间分布概率的极端情形及消除统计域为“空”的情形,由此构造类似于二维ｆＢｍ的地震能量空间分布概率曲面。与起伏不平的地形相似,由于基在水平方向及垂直方向的变化不是等比例的,因而这一分形曲面可能是统计自仿射的。  相似文献   

Textural segmentation of digital rock images into bedding units using texture energy and cluster labels     

Stefan M. Luthi 《Mathematical Geology》1994,26(2):181-196

The texture of digital rock images, as recorded, for instance, with borehole imaging devices, is shown to reflect different bedding types. Textural segmentation of borehole images, therefore, subdivides the recorded sequence into bedding units. We show that a textural segmentation algorithm based on the concept of texture energy achieves good results when compared with synthetic as well as real data in which petroleum geologists have performed zonations on cores. Texture energy involves filtering of the original image with a set of texture sensitive masks. The filtering is done as a finite convolution over the size of the masks. On the resulting images the variance is computed over a relatively large sliding window, which, in its practical implementation, covers the full width of the image. The resulting nine one-dimensional curves are then clustered hierarchically into a user-determined number of image texture or lithological bedding classes. Principal component analysis previous to clustering can be used to reduce redundancy in the data. A recurring and relatively ill-defined problem in this field are macro-textures, i.e., the cyclic interbedding of two or more bedding types. We show that sliding Fourier transforms and variable mask scale can successfully address the zonation of macro-textures. In general, the method gives best results with mask sizes equivalent to 2–4 centimeters, reflecting the length scale at which the investigated geological bedding seems to have its highest variation.  相似文献   

The deposit size frequency method for estimating undiscovered uranium deposits     

Richard B. McCammon  Warren I. Finch 《Natural Resources Research》1993,2(2):106-112

The deposit size frequency (DSF) method has been developed as a generalization of the method that was used in the National Uranium Resource Evaluation (NURE) program to estimate the uranium endowment of the United States. The DSF method overcomes difficulties encountered during the NURE program when geologists were asked to provide subjective estimates of (1) the endowed fraction of an area judged favorable (factorF) for the occurrence of undiscovered uranium deposits and (2) the tons of endowed rock per unit area (factorT) within the endowed fraction of the favorable area. Because the magnitudes of factorsF andT were unfamiliar to nearly all of the geologists, most geologists responded by estimating the number of undiscovered deposits likely to occur within the favorable area and the average size of these deposits. The DSF method combines factorsF andT into a single factor (F·T) that represents the tons of endowed rock per unit area of the undiscovered deposits within the favorable area. FactorF·T, provided by the geologist, is the estimated number of undiscovered deposits per unit area in each of a number of specified deposit-size classes. The number of deposit-size classes and the size interval of each class are based on the data collected from the deposits in known (control) areas. The DSF method affords greater latitude in making subjective estimates than the NURE method and emphasizes more of the everyday experience of exploration geologists. Using the DSF method, new assessments have been made for the young, organic-rich surficial uranium deposits in Washington and idaho and for the solution-collapse breccia pipe uranium deposits in the Grand Canyon region in Arizona and adjacent Utah.  相似文献   

近几十年我国极端气温变化特征分区方法探讨   总被引：7，自引：0，他引：7  

刘吉峰  李世杰  丁裕国  姚书春 《山地学报》2006,24(3):291-297

采用聚类统计检验分析和旋转主分量分析相结合确定中心站的方法,利用我国多年极端气温资料,对我国最高和最低气温年际变化型态进行区划。结果表明,这两种方法结合可以互相补充,使分区结果更具客观性。中国极端高温和极端低温年际变化分别可划为12和11个不同类型的区域,分别计算了各区域第一主成分的方差贡献率以及各区域之间的两两相关系数,检验证明分区是合理的。  相似文献   

Statistical analysis for the hydrogeological evaluation of the fracture networks in hard rocks     

J. Hofrichter  G. Winkler 《Environmental Geology》2006,49(6):821-827

The hydrogeological effectiveness of fracture sets is determined and evaluated by the fuzzy c-mean and hierarchical clustering. These cluster analyses combine the geological spatial attributes and the hydraulic relevant attributes of fractures. Based on the results of the clustering the fracture set volumes are estimated.  相似文献   

Structural and nutritional heterogeneity of riparian vegetation in Patagonia (Argentina) in relation to seasonal grazing by sheep     

V.R. Utrilla  M.A. Brizuela  A.F. Cibils 《Journal of Arid Environments》2006,67(4):661-670

Riparian meadows of southern Patagonia are temporally and spatially heterogeneous habitats. They are thought to play a key role in regulating the dynamics of arid grazed steppes of the region. We conducted a 2-year study with sheep to determine the influence of two grazing conditions (deferment and spring grazing) on structural and nutritional parameters of three vegetation types apparently associated with a soil moisture gradient in a riparian meadow in southern Santa Cruz (Argentina). Spring deferment allowed forage accumulation in very moist and intermediate vegetation types by the beginning of the summer and had no detrimental impact on forage quality. Deferment had no effect on biomass accumulation of the drier vegetation type at our study site. Structural attributes of the vegetation appeared to affect spatial grazing patterns of sheep. Soil-related patchiness, rather than sheep grazing, appeared to control vegetation structure and nutritional value. The proportion of more mesic plant communities in riparian habitats of Patagonia could determine the outcome of plant–animal interactions in these systems. Practical recommendations of grazing capacity in paddocks, or more theoretical considerations of ecosystem dynamics of the Patagonian steppes need to explicitly consider the internal patchiness of riparian habitats.  相似文献   

Dissolved trace elements in river water: spatial distribution and the influencing factor, a study for the Pearl River Delta Economic Zone, China   总被引：1，自引：0，他引：1  

T. P. Ouyang  Z. Y. Zhu  Y. Q. Kuang  N. S. Huang  J. J. Tan  G. Z. Guo  L. S. Gu  B. Sun 《Environmental Geology》2006,49(5):733-742

Twenty-nine water samples were collected from different river channels of the Pearl River Delta Economic Zone, China. An inductively coupled plasma-mass spectromonitor (ICP-MS) was used to measure concentrations of the trace elements in these samples. The results suggest that the average concentrations of rare earth elements in river water show an increasing trend from the West River, the North River, the rivers of the Pearl River Delta, and the Shenzhen River to the East River. Relatively high concentrations of heavy metals appear in the East River, the rivers of the Pearl River Delta and the Shenzhen River, while the West River and the North River have relatively low heavy metal concentrations. Trace element concentrations in samples collected near urban or industrial areas are much higher than those of samples collected from distant areas, away from urban and industrial areas. After natural conditions, human activities have significant influence on the trace element concentrations in river water. This trace element concentration’s spatial distribution in the river water from the Pearl River Delta Economic Zone is actually an integrated effect of natural conditions and human activity.  相似文献   

Towards models of strategic spatial choice behaviour: theory and application issues   总被引：1，自引：0，他引：1  

Qi Han  Harry Timmermans 《GeoJournal》2006,67(3):195-206

Models of spatial choice behaviour have been around in geography urban planning for decades to assess the feasibility of planning actions or to predict external (competition) effects on existing destinations. Although these models differ in terms of complexity and key concepts, they all have in common that spatial choice behaviour is predicted as a function of the attributes of the choice alternatives and distance or travel time separation only. None of these models do take into account that the attributes of choice alternatives and travel time may be highly non-stationary and that often the utility that people derive from visiting a particular location also depends on the choice behaviour of other individuals. Under these circumstances, individuals may exhibit strategic choice behaviour. That is, they will choose particular choice options taking into account their expected behaviour of others such as to maximize their own utility. The purpose of the proposed paper is to discuss possible models of strategic choice behaviour for these urban planning problems. Theory will be outlined and some critical issues in the application of such models to problems of spatial choice will be discussed.  相似文献