Robustness of variograms and conditioning of kriging matrices   总被引：1，自引：0，他引：1  

Phil Diamond  Margaret Armstrong 《Mathematical Geology》1984,16(8):809-822

Current ideas of robustness in geostatistics concentrate upon estimation of the experimental variogram. However, predictive algorithms can be very sensitive to small perturbations in data or in the variogram model as well. To quantify this notion of robustness, nearness of variogram models is defined. Closeness of two variogram models is reflected in the sensitivity of their corresponding kriging estimators. The condition number of kriging matrices is shown to play a central role. Various examples are given. The ideas are used to analyze more complex universal kriging systems.Research performed while on leave at Centre de Geóstatistique et de Morphologie Mathématique, Fontainebleau.  相似文献   

Isofactorial models for granulodensimetric data   总被引：1，自引：0，他引：1  

M. Armstrong  G. Matheron 《Mathematical Geology》1986,18(8):743-757

Existing isofactorial models developed for disjunctive kriging using a cutoff grade on one variable are extended to the bivariate case which arises when dealing with granulo-densimetric data, such as are obtained from coal washing or mineral processing.  相似文献   

Integration of mineral resource data for Kasmere Lake area, Northwest Manitoba, with emphasis on uranium   总被引：1，自引：0，他引：1  

G. F. Bonham-Carter  C. F. Chung 《Mathematical Geology》1983,15(1):25-45

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Probabilistic Assessment of Temperature in the Euganean Geothermal Area (Veneto Region, NE Italy)     

P. Fabbri 《Mathematical Geology》2001,33(6):745-760

In the geothermal Euganean area (Veneto region, NE Italy) water temperatures range from 60 to 86°C. The aquifer considered is rocky and the production wells in this study have a depth ranging from 300 to 500 m. For exploitation purposes, it is important to identify zones with a high probability that the temperature is more than 80°C and zones with a high probability that the temperature is less than 70°C. First, variographic analysis was conducted from 186 temperature data of thermal ground waters. This analysis gave results that are consistent with the main regional tectonic structure, the NW-SE trending Schio-Vicenza fault system. Then indicator variograms of the second, fifth, and eighth decile were compared to identify the spatial continuity at different thresholds. The unacceptability of a multigaussian hypothesis of the random function and the necessity to know the cumulative distribution function in any location, suggested the use of a nonparametric geostatistical procedure such as indicator kriging. Thus, indicator variograms at the cutoffs of 65, 70, 73, 75, 78, 80, 82, and 84°C were analyzed, fitted, and used during the indicator kriging procedure. Finally, probability maps were derived from postprocessing indicator kriging results. These maps identified scarcely exploited areas with a high probability of the temperature being higher than 80°C, between 70 and 80°C and areas with high probability of the temperature being below 70°C.  相似文献   

Uncertainty in Coal Property Valuation in West Virginia: A Case Study     

Michael E. Hohn  Ronald R. McDowell 《Mathematical Geology》2001,33(2):191-216

Interpolated grids of coal bed thickness are being considered for use in a proposed method for taxation of coal in the state of West Virginia (United States). To assess the origin and magnitude of possible inaccuracies in calculated coal tonnage, we used conditional simulation to generate equiprobable realizations of net coal thickness for two coals on a 7 min topographic quadrangle, and a third coal in a second quadrangle. Coals differed in average thickness and proportion of original coal that had been removed by erosion; all three coals crop out in the study area. Coal tonnage was calculated for each realization and for each interpolated grid for actual and artificial property parcels, and differences were summarized as graphs of percent difference between tonnage calculated from the grid and average tonnage from simulations. Coal in individual parcels was considered minable for valuation purposes if average thickness in each parcel exceeded 30 inches. Results of this study show that over 75% of the parcels are classified correctly as minable or unminable based on interpolation grids of coal bed thickness. Although between 80 and 90% of the tonnages differ by less than 20% between interpolated values and simulated values, a nonlinear conditional bias might exist in estimation of coal tonnage from interpolated thickness, such that tonnage is underestimated where coal is thin, and overestimated where coal is thick. The largest percent differences occur for parcels that are small in area, although because of the small quantities of coal in question, bias is small on an absolute scale for these parcels. For a given parcel size, maximum apparent overestimation of coal tonnage occurs in parcels with an average coal bed thickness near the minable cutoff of 30 in. Conditional bias in tonnage for parcels having a coal thickness exceeding the cutoff by 10 in. or more is constant for two of the three coals studied, and increases slightly with average thickness for the third coal.  相似文献   

A Combined Three-Dimensional Geological-Geostatistical-Numerical Model of Underground Excavations in Rock   总被引：1，自引：1，他引：1  

M. Stavropoulou  G. Exadaktylos  G. Saratsis 《Rock Mechanics and Rock Engineering》2007,40(3):213-243

Summary. This paper exploits geological and borehole geotechnical data obtained in the exploratory phase of a tunneling project to investigate in a first place if the kriging interpolation scheme may effectively reproduce the spatial variability of rock mass quality (Rock Mass Rating, RMR) in the vicinity of tunnels. For this purpose a quick solver in Fortran has been developed that performs variography analysis of 3D spatial data, fast kriging estimations of RMR between borehole sampling locations at the centroids of the elements of the numerical model, and model validation. For the purpose of an integrated underground excavation design, a step further is made by incorporating into the 3D mechanical numerical model of the rock mass, the three-dimensional (3D) solid geological model, thus coupling the geology with the ground (geotechnical) model (i.e. each element of the numerical model is assigned a geological material). The mechanical properties of each finite difference cell (or Representative Elementary Volume) of the ground model were then prescribed according to its geological type, the spatial heterogeneity of the rock mass expressed quantitatively with the kriging model, and the upscaling calculations of the mechanical properties of the intact rocks determined in the laboratory, based on the size-effect (strength dependence on size) and Damage Theory. Furthermore, a preliminary numerical simulation of the advance of unsupported tunnels in the model of the heterogeneous rock mass was performed for illustration purposes.  相似文献   

Hybrid Estimation of Semivariogram Parameters   总被引：1，自引：0，他引：1  

Hao Zhang  Dale L. Zimmerman 《Mathematical Geology》2007,39(2):247-260

Two widely used methods of semivariogram estimation are weighted least squares estimation and maximum likelihood estimation. The former have certain computational advantages, whereas the latter are more statistically efficient. We introduce and study a “hybrid” semivariogram estimation procedure that combines weighted least squares estimation of the range parameter with maximum likelihood estimation of the sill (and nugget) assuming known range, in such a way that the sill-to-range ratio in an exponential semivariogram is estimated consistently under an infill asymptotic regime. We show empirically that such a procedure is nearly as efficient computationally, and more efficient statistically for some parameters, than weighted least squares estimation of all of the semivariogram’s parameters. Furthermore, we demonstrate that standard plug-in (or empirical) spatial predictors and prediction error variances, obtained by replacing the unknown semivariogram parameters with estimates in expressions for the ordinary kriging predictor and kriging variance, respectively, perform better when hybrid estimates are plugged in than when weighted least squares estimates are plugged in. In view of these results and the simplicity of computing the hybrid estimates from weighted least squares estimates, we suggest that software that currently estimates the semivariogram by weighted least squares methods be amended to include hybrid estimation as an option.  相似文献   

河西走廊风能时空特征   总被引：3，自引：0，他引：3  

王毅荣 《干旱区地理》2007,30(3):43-350

利用河西走廊地区1970-2004年风速气候资料和2004年9月-2005年8月周年风塔精细资料,采用气候订正和即时风速订正,得到接近自然的风速,依此研究了该区域近地面70 m层内风能分布。结果表明:河西走廊区域风速变幅较小、气候变化趋势较稳定;有效风速(≥3 m/s)时数在6 000 h/a,10 m高度风能大多在150 w/m2以上,风能随高度线形增长(在70 m高度层内),平均每升高10 m风能增加28 w/m2;10~70 m层内总风能年储量相当丰富,普遍在1.5×1016kWh/m2(千瓦时/平方米)以上,潜在年产值达千万亿元。河西走廊风能存在明显周日和月季变化,风能和有效风速时数存在空间差异,其时空差异与河西走廊独特的戈壁下垫面关系密切。  相似文献   

Geostatistical incorporation of spatial coordinates into supervised classification of hyperspectral data   总被引：1，自引：0，他引：1  

P. Goovaerts 《Journal of Geographical Systems》2002,4(1):99-111

 This paper presents a methodology to incorporate both hyperspectral properties and spatial coordinates of pixels in maximum likelihood classification. Indicator kriging of ground data is used to estimate, for each pixel, the prior probabilities of occurrence of classes which are then combined with spectral-based probabilities within a Bayesian framework. In the case study (mapping of in-stream habitats), accounting for spatial coordinates increases the overall producer's accuracy from 85.8% to 93.8%, while the Kappa statistic rises from 0.74 to 0.88. Best results are obtained using only indicator kriging-based probabilities, with a stunning overall accuracy of 97.2%. Significant improvements are observed for environmentally important units, such as pools (Kappa: 0.17 to 0.74) and eddy drop zones (Kappa: 0.65 to 0.87). The lack of benefit of using hyperspectral information in the present study can be explained by the dense network of ground observations and the high spatial continuity of field classification which might be spurious. Received: 12 April 2001 / Accepted: 7 September 2001  相似文献   

Building Temporal Topology in a GIS Database to Study the Land‐Use Changes in a Rural‐Urban Environment     

Danielle J. Marceau  Luc Guindon  Mireille Bruel  Claude Marois 《The Professional geographer》2001,53(4):546-558

This article addresses the issue of linking temporal and spatial information into a GIS database structure to investigate the land‐use changes in a rural‐urban region over a thirty‐five‐year period. More specifically, it describes the application of a programming package developed to build temporal topology in an historical land‐use GIS database to efficiently perform spatiotemporal queries. The program was created within the MapInfo environment using MapBasic language. Different types of information, such as the rate of change, the relationship between the change of land use and zoning regulations, and land‐use succession were extracted from the database. A user‐friendly interface was also developed to easily address spatiotemporal queries to the database. This approach represents a flexible and performing tool for scientists and planners who need to efficiently capture essential spatiotemporal information required for geographical inquiry and decision‐making.  相似文献