共查询到20条相似文献，搜索用时 31 毫秒
1.
I. C. Lemmer 《Mathematical Geology》1986,18(7):589-604
For any distribution of grades, a particular cutoff grade is shown here to exist at which the indicator covariance is proportional to the grade covariance to a very high degree of accuracy. The name mononodal cutoff is chosen to denote this grade. Its importance for robust grade variography in the presence of a large coefficient of variation—typical of precious metals—derives from the fact that the mononodal indicator variogram is then linearly related to the grade variogram yet is immune to outlier data and is found to be particularly robust under data information reduction. Thus, it is an excellent substitute to model in lieu of a difficult grade variogram. A theoretical expression for the indicator covariance is given as a double series of orthogonal polynomials that have the grade density function as weight function. Leading terms of this series suggest that indicator and grade covariances are first-order proportional, with cutoff grade dependence being carried by the proportionality factor. Kriging equations associated with this indicator covariance lead to cutoff-free kriging weights that are identical to grade kriging weights. This circumstance simplifies indicator kriging used to estimate local point-grade histograms, while at the same time obviating order relations problems.This paper is based in part on a PhD thesis submitted to the Department of Applied Earth Sciences, Stanford University, Stanford, California 94305, in 1984 (unpublished). 相似文献
2.
3.
Kriging without negative weights 总被引：1，自引：0，他引：1
Under a constant drift, the linear kriging estimator is considered as a weighted average ofn available sample values. Kriging weights are determined such that the estimator is unbiased and optimal. To meet these requirements, negative kriging weights are sometimes found. Use of negative weights can produce negative block grades, which makes no practical sense. In some applications, all kriging weights may be required to be nonnegative. In this paper, a derivation of a set of nonlinear equations with the nonnegative constraint is presented. A numerical algorithm also is developed for the solution of the new set of kriging equations. 相似文献
4.
一种考虑权值非负约束的克立格算法 总被引：2，自引：0，他引：2
基于线性规划方法提出了一种考虑权值非负约束的克立格算法,该算法既利用了线性规划求解简便、快捷的优点,又克服了其它正克立格法计算工作量大以及受主观因素影响的缺点。 相似文献
5.
I. C. Lemmer 《Mathematical Geosciences》1986,18(7):589-604
For any distribution of grades, a particular cutoff grade is shown here to exist at which the indicator covariance is proportional to the grade covariance to a very high degree of accuracy. The name “mononodal cutoff” is chosen to denote this grade. Its importance for robust grade variography in the presence of a large coefficient of variation—typical of precious metals—derives from the fact that the mononodal indicator variogram is then linearly related to the grade variogram yet is immune to outlier data and is found to be particularly robust under data information reduction. Thus, it is an excellent substitute to model in lieu of a difficult grade variogram. A theoretical expression for the indicator covariance is given as a double series of orthogonal polynomials that have the grade density function as weight function. Leading terms of this series suggest that indicator and grade covariances are first-order proportional, with cutoff grade dependence being carried by the proportionality factor. Kriging equations associated with this indicator covariance lead to cutoff-free kriging weights that are identical to grade kriging weights. This circumstance simplifies indicator kriging used to estimate local point-grade histograms, while at the same time obviating order relations problems. 相似文献
6.
Smoothing and interpolation by kriging and with splines 总被引：1，自引：0，他引：1
G. S. Watson 《Mathematical Geology》1984,16(6):601-615
Let scalar measurements at distinct points x1, , xn
be y1, , yn.We may look for a smooth function f(x)that goes through or near the points (xi, yi).Kriging assumes f(x)is a random function with known (possibly estimable) covariance function (in the simplest case). Splines assume a definition of the smoothness of a nonrandom function f(x).An elementary explanation is given of the fact that spline approximations are special cases of the solution of a kriging problem. 相似文献
7.
Conditioning of the stationary kriging matrices for some well-known covariance models 总被引：1，自引：0，他引：1
D. Posa 《Mathematical Geology》1989,21(7):755-765
In this paper, the condition number of the stationary kriging matrix is studied for some well-known covariance models. Indeed, the robustness of the kriging weights is strongly affected by this measure. Such an analysis can justify the choice of a covariance function among other admissible models which could fit a given experimental covariance equally well. 相似文献
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9.
Transition probability-based indicator geostatistics 总被引：30，自引：0，他引：30
Traditionally, spatial continuity models for indicator variables are developed by empirical curvefitting to the sample indicator (cross-) variogram. However, geologic data may be too sparse to permit a purely empirical approach, particularly in application to the subsurface. Techniques for model synthesis that integrate hard data and conceptual models therefore are needed. Interpretability is crucial. Compared with the indicator (cross-) variogram or indicator (cross-) covariance, the transition probability is more interpretable. Information on proportion, mean length, and juxtapositioning directly relates to the transition probability: asymmetry can be considered. Furthermore, the transition probability elucidates order relation conditions and readily formulates the indicator (co)kriging equations. 相似文献
10.
On the condition number of covariance matrices in kriging, estimation, and simulation of random fields 总被引：1，自引：0，他引：1
The numerical stability of linear systems arising in kriging, estimation, and simulation of random fields, is studied analytically and numerically. In the state-space formulation of kriging, as developed here, the stability of the kriging system depends on the condition number of the prior, stationary covariance matrix. The same is true for conditional random field generation by the superposition method, which is based on kriging, and the multivariate Gaussian method, which requires factoring a covariance matrix. A large condition number corresponds to an ill-conditioned, numerically unstable system. In the case of stationary covariance matrices and uniform grids, as occurs in kriging of uniformly sampled data, the degree of ill-conditioning generally increases indefinitely with sampling density and, to a limit, with domain size. The precise behavior is, however, highly sensitive to the underlying covariance model. Detailed analytical and numerical results are given for five one-dimensional covariance models: (1) hole-exponential, (2) exponential, (3) linear-exponential, (4) hole-Gaussian, and (5) Gaussian. This list reflects an approximate ranking of the models, from best to worst conditioned. The methods developed in this work can be used to analyze other covariance models. Examples of such representative analyses, conducted in this work, include the spherical and periodic hole-effect (hole-sinusoidal) covariance models. The effect of small-scale variability (nugget) is addressed and extensions to irregular sampling schemes and higher dimensional spaces are discussed. 相似文献
11.
建立盆地三维构造-地层格架是进行三维盆地模拟的关键技术之一.为了使一系列二维地震解释剖面转化为盆地的三维构造-地层格架, 必须选择有效的内插外推方法, 而插值方法的选择和空间分析的实现依赖于空间拓扑结构.在探讨基于BRep模型的盆地三维空间拓扑结构表示法及图形编码准则的基础上, 引进了适合于构建盆地三维构造-地层格架的几种形态插值方法, 并提出了一种新的方法———相似变形插值法.这些方法曾成功地应用于珠三盆地三维构造-地层格架的模拟, 能够很好地支持包括矢量剪切在内的各种空间分析 相似文献
12.
Geostatistical estimations of the hydraulic conductivity field (K) in the Carrizo aquifer, Texas, are performed over three regional domains of increasing extent: 1) the domain corresponding
to a three-dimensional groundwater flow model previously built (model domain); 2) the area corresponding to the 10 counties
encompassing the model domain (County domain), and; 3) the full extension of the Carrizo aquifer within Texas (Texas domain).
Two different approaches are used: 1) an indirect approach where transmissivity (T) is estimated first and K is retrieved through division of the T estimate by the screen length of the wells, and; 2) a direct approach where K data are kriged directly. Due to preferential well screen emplacement, and scarcity of sampling in the deeper portions of
the formation (> 1 km), the available data set is biased toward high values of hydraulic conductivities. Kriging combined
with linear regression, simple kriging with varying local means, kriging with an external drift, and cokriging allow the incorporation
of specific capacity as secondary information. Prediction performances (assessed through cross-validation) differ according
to the chosen approach, the considered variable (log-transformed or back-transformed), and the scale of interest. For the
indirect approach, kriging of log T with varying local means yields the best estimates for both log-transformed and back-transformed variables in the model domain.
For larger regional scales (County and Texas domains), cokriging performs generally better than other kriging procedures when
estimating both (log T)∗ and T∗. Among procedures using the direct approach, the best prediction performances are obtained using kriging of log K with an external drift. Overall, geostatistical estimation of the hydraulic conductivity field at regional scales is rendered
difficult by both preferential well location and preferential emplacement of well screens in the most productive portions
of the aquifer. Such bias creates unrealistic hydraulic conductivity values, in particular, in sparsely sampled areas. 相似文献
13.
Computational power poses heavy limitations to the achievable problem size for Kriging. In separate research lines, Kriging algorithms based on FFT, the separability of certain covariance functions, and low-rank representations of covariance functions have been investigated, all three leading to drastic speedup factors. The current study combines these ideas, and so combines the individual speedup factors of all ideas. This way, we reduce the mathematics behind Kriging to a computational complexity of only $\mathcal{O}(dL^{*} \log L^{*})$ , where L ? is the number of points along the longest edge of the involved lattice of estimation points, and d is the physical dimensionality of the lattice. For separable (factorized) covariance functions, the results are exact, and nonseparable covariance functions can be approximated well through sums of separable components. Only outputting the final estimate as an explicit map causes computational costs of $\mathcal{O}(n)$ , where n is the number of estimation points. In illustrative numerical test cases, we achieve speedup factors up to 108 (eight orders of magnitude), and we can treat problem sizes of up to 15 trillion and two quadrillion estimation points for Kriging and spatial design, respectively, within seconds on a contemporary desktop computer. The current study assumes second-order stationarity and simple Kriging on a regular, equispaced lattice, without working with restricted neighborhoods. Extensions to many other cases are straightforward. 相似文献
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15.
Ana F. Militino 《Mathematical Geology》1997,29(2):221-229
Kriging as an interpolation method, uses as predictor a linear function of the observations, minimizing the mean squared prediction
error or estimation variance. Under multivariate normality assumptions, the given predictor is the best unbiased predictor,
and will be vulnerable to outliers. To overcome this problem, a robust weighted estimator of the drift model coefficients
is proposed, where unequally spaced data may be weighted through the tile areas of the Dirichlet tessellation. 相似文献
16.
J. R. Carr 《Geotechnical and Geological Engineering》1990,8(4):393-399
Summary A crucial concern when implementing computer algorithms for geostatistical analyses on microcomputers is speed of execution. Kriging, in particular, typically relies on a Gauss elimination algorithm to solve for weights. Because such an alogrithm is required for each estimate, the solution for weights can result in very slow program execution speed on a microcomputer. One approach to enhancing the efficiency of Gauss elimination is demonstrated herein. The upper triangle plus diagonal of the intersample covariance matrix is used in a modified banded Gauss elimination algorithm. Results show that such an algorithm yields approximately a two-fold reduction in execution time for kriging when the number of nearest neighbours used for estimation is large. 相似文献
17.
Block-sample covariances may be calculated by discretizing a block into regularly spaced grid points, computing punctual covariance between each grid point and the sample, then averaging. Gauss quadrature is a better, more accurate method for calculating block-sample covariance as has been demonstrated in the past by other authors (the history of which is reviewed herein). This prior research is expanded upon to provide considerably more detail on Gauss quadrature for approximating the areal or volumetric integral for block-sample covariance. A 4 × 4 Gauss point rule is shown to be optimal for this procedure. Moreover, pseudo-computer algorithms are presented to show how to implement Gauss quadrature in existing computer programs which perform block kriging. 相似文献
18.
Comparison of kriging techniques in a space-time context 总被引：1，自引：0，他引：1
Patrick Bogaert 《Mathematical Geology》1996,28(1):73-86
Space-time processes constitute a particular class, requiring suitable tools in order to predict values in time and space, such as a space-time variogram or covariance function. The space-time co-variance function is defined and linked to the Linear Model of Coregionalization under second-order space-time stationarity. Simple and ordinary space-time kriging systems are compared to simple and ordinary cokriging and their differences for unbiasedness conditions are underlined. The ordinary space-time kriging estimation then is applied to simulated data. Prediction variances and prediction errors are compared with those for ordinary kriging and cokriging under different unbiasedness conditions using a cross-validation. The results show that space-time kriging tend to produce lower prediction variances and prediction errors that kriging and cokriging. 相似文献
19.
Geostatistical regionalization of glacial aquitard thickness in northwestern Germany, based on fuzzy kriging 总被引：1，自引：0，他引：1
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
20.
For earthquake ground motion studies, the actual ground motion distribution should be reproduced as accurately as possible. For optimal estimation of ground motion, kriging has been shown to provide accurate estimates. Although kriging is accurate for this application, some estimates it provides are underestimates. This has dire consequences for subsequent design for earthquake resistance. Kriging does not provide enough information to allow an analysis of each estimate for underestimation. For such an application, disjunctive kriging is better applied. This advanced technique quantifies the probability that an estimate equals or exceeds particular levels of ground motion. Furthermore, disjunctive kriging can provide improved estimation accuracy when applied for local estimation of ground motion. 相似文献