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1

Digitale Medien

Robust kriging—A proposal (1984)

Hawkins, Douglas M. ; Cressie, Noel

Springer

Mathematical geology 16 (1984), S. 3-18

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ISSN: 1573-8868

Schlagwort(e): Geostatistics ; kriging ; robust estimation ; time series

Quelle: Springer Online Journal Archives 1860-2000

Thema: Geologie und Paläontologie , Mathematik

Notizen: Abstract Geological data frequently have a heavy-tailed normal-in-the-middle distribution, which gives rise to grade distributions that appear to be normal except for the occurrence of a few outliers. This same situation also applies to log-transformed data to which lognormal kriging is to be applied. For such data, linear kriging is nonrobust in that (1)kriged estimates tend to infinity as the outliers do, and (2)it is also not minimum mean squared error. The more general nonlinear method of disjunctive kriging is even more nonrobust, computationally more laborious, and in the end need not produce better practical answers. We propose a robust kriging method for such nearly normal data based on linear kriging of an editing of the data. It is little more laborious than conventional linear kriging and, used in conjunction with a robust estimator of the variogram, provides good protection against the effects of data outliers. The method is also applicable to time series analysis.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01036237

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2

Digitale Medien

Smoothing and interpolation by kriging and with splines (1984)

Watson, G. S.

Springer

Mathematical geology 16 (1984), S. 601-615

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ISSN: 1573-8868

Schlagwort(e): kriging ; splines ; interpolation ; smoothing ; prediction ; Green's function

Quelle: Springer Online Journal Archives 1860-2000

Thema: Geologie und Paläontologie , Mathematik

Notizen: Abstract 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.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01029320

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3

Digitale Medien

Cokriging of aquifer transmissivities from field measurements of transmissivity and specific capacity (1984)

Aboufirassi, Mohamed ; Mariño, Miguel A.

Springer

Mathematical geology 16 (1984), S. 19-35

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ISSN: 1573-8868

Schlagwort(e): groundwater ; geostatistics ; cokriging ; kriging ; transmissivity ; specific capacity

Quelle: Springer Online Journal Archives 1860-2000

Thema: Geologie und Paläontologie , Mathematik

Notizen: Abstract This paper presents a new application of the cokriging technique for constructing maps of aquifer transmissivity from field measurements of transmissivity and specific capacity. The technique is illustrated using data from Yolo Basin, California. Cokriging is well-suited for estimating undersampled variables. To improve the accuracy of the estimation, cokriging considers the spatial auto-correlation of the variable to be estimated and the spatial cross-correlation between the variable to be estimated and other, better-sampled variables. Consequently, in regions that lack data of the variable to be estimated, accurate estimation can still be made on the basis of auto- and cross-correlation. In addition, estimation variances can be obtained with a little additional computation effort.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01036238

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4

Digitale Medien

A geostatistically based approach to the identification of aquifer transmissivities in Yolo Basin, California (1984)

Aboufirassi, Mohamed ; Mariño, Miguel A.

Springer

Mathematical geology 16 (1984), S. 125-137

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ISSN: 1573-8868

Schlagwort(e): kriging ; cokriging ; hydrology ; groundwater

Quelle: Springer Online Journal Archives 1860-2000

Thema: Geologie und Paläontologie , Mathematik

Notizen: Abstract A geostatistically based approach is developed for the identification of aquifer transmissivities in Yolo Basin, California. The approach combines weighted least-squares with universal kriging and cokriging techniques in an overall scheme that (1)considers a prioriknown information on aquifer transmissivity and specific capacities of wells, (2)considers uncertainties in water level and transmissivity data, and (3)estimates the reliability of the generated transmissivity values. Minimization of a global least-squares function that incorporates calibration and plausibility criteria leads to a transmissivity map that shows a good agreement with pumping-test results.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01032212

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5

Digitale Medien

Analysis of nonintrinsic spatial variability by residual kriging with application to regional groundwater levels (1984)

Neuman, Shlomo P. ; Jacobson, Elizabeth A.

Springer

Mathematical geology 16 (1984), S. 499-521

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ISSN: 1573-8868

Schlagwort(e): Spatial variability ; nonintrinsic ; nonstationary ; drift ; kriging ; residuals ; groundwater levels

Quelle: Springer Online Journal Archives 1860-2000

Thema: Geologie und Paläontologie , Mathematik

Notizen: Abstract A method for obtaining pointwise or spatially averaged estimates of a nonintrinsic function is introduced based on residual kriging. The method relies on a stepwise iterative regression process for simultaneously estimating the global drift and residual semivariogram. Estimates of the function are then obtained by solving a modified set of simple kriging equations written for the residuals. The modification consists of replacing the true variogram in the kriging equations by the variogram of the residual estimates as obtained from the iterative regression process. The method is illustrated by considering groundwater levels in an Arizona aquifer. The results are compared with those obtained for the aquifer by the generalized covariance package BLUEPACK-3D.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01886329

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6

Digitale Medien

Kriging in a global neighborhood (1984)

Davis, Michael W. ; Grivet, Cyril

Springer

Mathematical geology 16 (1984), S. 249-265

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ISSN: 1573-8868

Schlagwort(e): kriging ; moving neighborhood ; global neighborhood ; geostatistics ; automatic contouring

Quelle: Springer Online Journal Archives 1860-2000

Thema: Geologie und Paläontologie , Mathematik

Notizen: Abstract The kriging estimator is usually computed in a moving neighborhood; only the data near the point to be estimated are used. This moving neighborhood approach creates discontinuities in mapping applications. An alternative approach is presented here, whereby all points are estimated using all the available data. To solve the resulting large linear system the kriging estimator is expressed in terms of the inverse of the covariance matrix. The covariance matrix has the advantage of being positive definite and the size of system which can be solved without encountering numerical instability is substantially increased. Because the kriging matrix does not change, the estimator can be written in terms of scalar products, thus avoiding the more time-consuming matrix multiplications of the standard approach. In the particular case of a covariance which is zero for distances greater than a fixed value (the range), the resulting banded structure of the covariance matrix is shown to lead to substantial computational savings in both run time and storage space. In this case the calculation time for the kriging variance is also substantially reduced. The present method is extended to the nonstationary case.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01032690

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7

Digitale Medien

Application of fuzzy clustering and fuzzy classification to evaluate the provenance of glacial till (1984)

Granath, Göran

Springer

Mathematical geology 16 (1984), S. 283-301

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ISSN: 1573-8868

Schlagwort(e): Bayesian classifiers ; classification ; cluster analysis ; cluster validity ; fuzzyc means ; fuzzyc varieties ; fuzzy covariances ; geochemical prospecting ; glacial till ; kriging

Quelle: Springer Online Journal Archives 1860-2000

Thema: Geologie und Paläontologie , Mathematik

Notizen: Abstract To evaluate the provenance of glacial till, the trace element content of magnetite was used. Magnetite was present in all known rock types and all till samples in the area investigated. By using fuzzy-set theory it was possible to group samples of magnetite taken from bedrock into relatively homogeneous and geologically meaningful groups and also, by fuzzy classification, to relate the till samples to the rocks in such a way that the relative contribution of each rock type to the till is estimated. Each rock and till sample is assigned a membership value between 0 and 1 for each rock type. The membership values, for a certain rock type in the till, are then interpolated by kriging onto maps. Magnetites from skarns associated with sulfide ores especially are rather distinct, and so a map of such membership values for till unveils all known ore deposits some 1–5 km “downstream”in the general direction of the ice flow. Other anomalies show up which cannot be related to hitherto known ores or mineralizations.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01032692

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8

Digitale Medien

Robustness of variograms and conditioning of kriging matrices (1984)

Diamond, Phil ; Armstrong, Margaret

Springer

Mathematical geology 16 (1984), S. 809-822

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ISSN: 1573-8868

Schlagwort(e): variogram ; robustness ; kriging ; conditioning number

Quelle: Springer Online Journal Archives 1860-2000

Thema: Geologie und Paläontologie , Mathematik

Notizen: Abstract 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.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01036706

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