Application of kriging with external drift to estimate hydraulic conductivity from electrical-resistivity data in unconsolidated deposits near Montalto Uffugo, Italy   总被引：2，自引：0，他引：2  

S. Troisi  C. Fallico  S. Straface  E. Migliari 《Hydrogeology Journal》2000,8(4):356-367

In the framework of various studies to characterize the aquifer at the groundwater experimental field near Montalto Uffugo, Italy, the present work estimates the spatial distribution of hydraulic conductivity of the unconsolidated deposits that underlie the area, by applying the geostatistical technique of kriging with external drift to electrical-resistivity and hydraulic-conductivity data. The reliability of the estimation method was tested by implementing a model, based on the method of cells, that simulates groundwater flow, with the estimated values of hydraulic conductivity. The results obtained indicate that the estimation method used has an acceptable degree of reliability.  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   

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   

Efficiency of kriging estimation for square, triangular, and hexagonal grids   总被引：8，自引：0，他引：8  

Evangelos A. Yfantis  George T. Flatman  Joseph V. Behar 《Mathematical Geology》1987,19(3):183-205

Although several researchers have pointed out some advantages and disadvantages of various soil sampling designs in the presence of spatial autocorrelation, a more detailed study is presented herein which examines the geometrical relationship of three sampling designs, namely the square, the equilateral triangle, and the regular hexagon. Both advantages and disadvantages exist in the use of these designs with respect to estimation of the semivariogram and their effect on the mean square error or variance of error. This research could be used to design optimal sampling strategies; it is based on the theory of regionalized variables, in which the intrinsic hypothesis is satisfied. Among alternative designs, an equilateral triangle design gives the most reliable estimate of the semivariogram. It also gives the minimum maximum mean square error of point estimation of the concentration over the other two designs for the same number of measurements when the nugget effect is small relative to the variance. If the nugget effect is large (.90 ² or more), and the linear sampling density is >0.85r where r is the range, the hexagonal design is best. This study computes and compares the maximum mean square error for each of these designs.  相似文献   

Geographical Information Systems and Geostatistics for Modelling Radioactively Contaminated Land Areas   总被引：2，自引：0，他引：2  

NAZZARENO?DIODATOEmail author  MICHELE?CECCARELLI 《Natural Hazards》2005,35(2):229-242

The Chernobyl plume contaminated vast lands of Europe with radiocaesium (¹37Cs) in 1986 because of the deposition of radionuclides on the ground by wet and dry deposition processes. Nevertheless, in a nuclear emergency, contamination data may be very sparse and there is need to make rapid and scientifically supported decisions. Here we analyze the rainfall field, an important precursor of the wet deposition, during the passage of the plume. Thus, estimating rainfall spatial variability can help to identify possible contaminated areas and associated risks when rainfall exceeded a given threshold. In this paper, we show that the conditional probabilities of exceeding threshold rainfall values could be spatially assessed using the mutual benefits of linking geostatistical and geographical information system (GIS) to quantify the evaluation of the risk involved in decision making. In particular, the non-parametric geostatistic technique, termed Indicator Kriging (IK), enables one to efficiently estimate the probability that the true value exceeds the threshold values by means of the indicator coding transform. Afterward, GIS has been used to find the areas probably affected by wash-out (probability >0.5 that rainfall is above a certain threshold). The experimental study has been focused on a test site in Beneventan agroecosystem (Southern Italy) to model the spatial uncertainty over a continuous area from sparse rainfall data. This enabled to generate probability maps delineating area potentially affected by to contamination to be monitored after wet deposition of Chernobyl releases.  相似文献   

An Improved Perturbation Mechanism for Simulated Annealing Simulation     

C. V. Deutsch  X. H. Wen 《Mathematical Geology》1998,30(7):801-816

Simulated annealing (SA) is being increasingly used for the generation of stochastic models of spatial phenomena because of its flexibility to integrate data of diverse types and scales. The major shortcoming of SA is the extensive CPU requirements. We present a perturbation mechanism that significantly improves the CPU speed. Two conventional perturbation mechanisms are to (1) randomly select two locations and swap their attribute values, or (2) visit a randomly selected location and draw a new value from the global histogram. The proposed perturbation mechanism is a modification of option 2: each candidate value is drawn from a local conditional distribution built with a template of kriging weights rather than from the global distribution. This results in accepting more perturbations and in perturbations that improve the variogram reproduction for short scale lags. We document the new method, the increased convergence speed, and the improved variogram reproduction. Implementation details of the method such as the size of the local neighborhood are considered.  相似文献   

地壳平均丰度最小值法——成矿省成矿元素区域背景值的简易计算方法     

易建斌  单业华  解庆林 《地球学报》1998,19(2):221-224

本文在Ａｇｔｅｒｂｅｒｇ和Ｄｉｖｉ（１９７８）的地壳丰度地质统计模型（ＣｒｕｓｔａｌＡｂｕｎｄａｎｃｅＧｅｏｓｔａｓｔｉｃｓ,简称ＣＡＧ）的基础上,提出了一种成矿省成矿元素区域背景值下限的简易计算方法。在区域背景值未知的情况下,根据成矿省某成矿元素的截切品位和金属量,可由此法计算出其地壳平均丰度最小值,以此作为成矿省中该元素区域背景值。将这一方法运用于华南Ｓｂ成矿省所得Ｓｂ元素区域背景值与通过区域地球化学方法得到的华南地区Ｓｂ的地壳平均丰度值相近,这充分说明这种地壳平均丰度最小值法的可靠性。  相似文献   

Depth of the base of the Jackson aquifer, based on geophysical exploration, southern Jackson Hole, Wyoming, USA     

Bernard T. Nolan  David L. Campbell  Robert M. Senterfit 《Hydrogeology Journal》1998,6(3):374-382

 A geophysical survey was conducted to determine the depth of the base of the water-table aquifer in the southern part of Jackson Hole, Wyoming, USA. Audio-magnetotellurics (AMT) measurements at 77 sites in the study area yielded electrical-resistivity logs of the subsurface, and these were used to infer lithologic changes with depth. A 100–600 ohm-m geoelectric layer, designated the Jackson aquifer, was used to represent surficial saturated, unconsolidated deposits of Quaternary age. The median depth of the base of the Jackson aquifer is estimated to be 200 ft (61 m), based on 62 sites that had sufficient resistivity data. AMT-measured values were kriged to predict the depth to the base of the aquifer throughout the southern part of Jackson Hole. Contour maps of the kriging predictions indicate that the depth of the base of the Jackson aquifer is shallow in the central part of the study area near the East and West Gros Ventre Buttes, deeper in the west near the Teton fault system, and shallow at the southern edge of Jackson Hole. Predicted, contoured depths range from 100 ft (30 m) in the south, near the confluences of Spring Creek and Flat Creek with the Snake River, to 700 ft (210 m) in the west, near the town of Wilson, Wyoming. Received, May 1997 · Revised, February 1998 · Accepted, April 1998  相似文献   

Hierarchical decomposition of variance with applications in environmental mapping based on satellite images     

Ferenc Csillag  Sándor Kabos 《Mathematical Geology》1996,28(4):385-405

A quadtree-based image segmentation procedure (HQ) is presented to map complex environmental conditions. It applies a hierarchical nested analysis of variance within the framework of multiresolution wavelet approximation. The procedure leads to an optimal solution for determining mapping units based on spatial variability with constraints on the arrangement and shape of the units. Linkages to geostatisiics are pointed out, but the HQ decomposition algorithm does not require any homogeneity criteria. The computer implementation can be parameterized by either the number of required mapping units or the maximum within-unit variance, or it can provide a spectrum of significances of nested ANOVA. The detailed mathematical background and methodology is illustrated by a salt-affected grassland mapping study (Hortobágy, Hungary), where heterogeneous environmental characteristics have been sampled and predicted based on remotely sensed images using these principles.  相似文献   

Efficient generation of conditional simulations by chebyshev matrix polynomial approximations to the symmetric square root of the covariance matrix     

C. R. Dietrich  G. N. Newsam 《Mathematical Geology》1995,27(2):207-228

Consider the problem of generating a realization y₁ of a Gaussian random field on a dense grid of points ₁ conditioned on field observations y₂ collected on a sparse grid of points ₂. An approach to this is to generate first an unconditional realization y over the grid =_{1 2}, and then to produce y₁ by conditioning y on the data y₂. As standard methods for generating y, such as the turning bands, spectral or Cholesky approaches can have various limitations, it has been proposed by M. W. Davis to generate realizations from a matrix polynomial approximations to the square root of the covariance matrix. In this paper we describe how to generate a direct approximation to the conditional realization y₁, on ₁ using a variant of Davis' approach based on approximation by Chebyshev polynomials. The resulting algorithm is simple to implement, numerically stable, and bounds on the approximation error are readily available. Furthermore we show that the conditional realization y₁ can be generated directly with a lower order polynomial than the unconditional realization y, and that further reductions can be achieved by exploiting a nugget effect if one is present. A pseudocode version of the algorithm is provided that can be implemented using the fast Fourier transform if the field is stationary and the grid ₁ is rectangular. Finally, numerical illustrations are given of the algorithm's performance in generating various 2-D realizations of conditional processes on large sampling grids.  相似文献