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  • Articles  (8)
  • Articles: DFG German National Licenses  (8)
  • variogram  (8)
  • 2010-2014
  • 1980-1984  (8)
  • Geosciences  (8)
  • History
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  • Articles  (8)
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  • Articles: DFG German National Licenses  (8)
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  • 1
    Electronic Resource
    Electronic Resource
    Variogram models for regional groundwater geochemical data (1982)
    Springer
    Mathematical geology 14 (1982), S. 629-644 
    Details
    ISSN: 1573-8868
    Keywords: variogram ; kriging ; interpolation ; contouring ; inverse distance weighting ; geochemical gradient
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Four variogram models for regional groundwater geochemical data are presented. These models were developed from an empirical study of the sample variograms for more than 10 elements in groundwaters from two geologic regions in the Plainview quandrangle, Texas. A procedure is given for the estimation of the variogram in the isotropic and anisotropic case. The variograms were found useful for quantifying the differences in spatial variability for elements within a geologic unit and for elements in different geologic units. Additionally, the variogram analysis enables assessment of the assumption of statistical independence of regional samples which is commonly used in many statistical procedures. The estimated variograms are used in computation of kriged estimates for the Plainview quadrangle data. The results indicate that an inverse distance weighting model was superior for prediction than simple kriging with the particular variograms used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01033884
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  • 2
    Electronic Resource
    Electronic Resource
    General polygonal variogram functions: Evaluation of estimation variance integrals (1982)
    Springer
    Mathematical geology 14 (1982), S. 77-85 
    Details
    ISSN: 1573-8868
    Keywords: Geostatistics ; variogram ; polygonal function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The application of regionalized variables requires the estimation of the variogram function and the evaluation of its integral. By representing the variogram by a general polygonal function the requisite integrals may be easily computed by a closed form representation of simple integrals. This paper provides the integration formulas for two-dimensional variogram functions whose domain is represented as a finite collection of rectangles. The integration formulas essential for a fully developed polygonal approach to an extensive statistical evaluation of geostatistical quantities are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01037449
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A simple sufficient condition for a variogram model to yield positive variances under restrictions (1983)
    Springer
    Mathematical geology 15 (1983), S. 553-564 
    Details
    ISSN: 1573-8868
    Keywords: variogram ; estimation ; conditionally positive semidefinite
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Estimation of linear combinations is accomplished by using the observed (available) data. Accordingly, to require the negative of a modeled variogram function to be positive definite for all possible data combinations is unnecessary when only the observed data are used in estimation. The requirement that the negative of a variogram model be conditionally positive semidefinite is then relaxed to apply at the observed spatial locations only. In this setting a simple, yet crude, sufficient condition is developed to ensure that a variogram model will yield nonnegative variances for the available data. It is seen that the condition is independent of the dimensionality of the data and applies to both isotropic and anisotropic models. An example of the application of the condition is also presented. The condition is harder to satisfy as the amount of data increases and must be adjusted as the variogram changes to accommodate new data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01031177
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  • 4
    Electronic Resource
    Electronic Resource
    Robust estimation of the variogram: I (1980)
    Springer
    Mathematical geology 12 (1980), S. 115-125 
    Details
    ISSN: 1573-8868
    Keywords: Geostatistics ; kriging ; robust estimation ; variogram
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract It is a matter of common experience that ore values often do not follow the normal (or lognormal) distributions assumed for them, but, instead, follow some other heavier-tailed distribution. In this paper we discuss the robust estimation of the variogram when the distribution is normal-like in the central region but heavier than normal in the tails. It is shown that the use of a fourth-root transformation with or without the use of M-estimation yields stable robust estimates of the variogram.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01035243
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  • 5
    Electronic Resource
    Electronic Resource
    Exact formulas for approximating variogram function integrals (1980)
    Springer
    Mathematical geology 12 (1980), S. 577-588 
    Details
    ISSN: 1573-8868
    Keywords: variogram ; geostatistics ; estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The application of regionalized variables requires the estimation of the variogram function and the evaluation of its integral. By representing the variogram by a polygonal function the integral may be easily approximated by closed form representations of polygonal integrals. This approach provides a basis for more extensive statistical evaluation not evident in existing approximation methods. This paper provides the closed form representations for two-dimensional variogram functions whose domain is represented by a finite collection of rectangles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01034745
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  • 6
    Electronic Resource
    Electronic Resource
    Studies of the effects of outliers and data transformation on variogram estimates for a base metal and a gold ore body (1982)
    Springer
    Mathematical geology 14 (1982), S. 557-564 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; variogram ; outliers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Variograms for gold and lead values from the Loraine and Prieska mines, respectively, indicate that data outliers can seriously distort and/or mask the real variogram patterns. Studies show that this problem is best overcome for these mines by logarithmic transformation of the data, and/or a suitable screening out of such outliers, and/or more robust variogram estimation procedures; the benefits are particularly significant when the basic data is limited.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01033879
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  • 7
    Electronic Resource
    Electronic Resource
    Robustness of variograms and conditioning of kriging matrices (1984)
    Springer
    Mathematical geology 16 (1984), S. 809-822 
    Details
    ISSN: 1573-8868
    Keywords: variogram ; robustness ; kriging ; conditioning number
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01036706
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  • 8
    Electronic Resource
    Electronic Resource
    Testing variograms for positive-definiteness (1984)
    Springer
    Mathematical geology 16 (1984), S. 407-421 
    Details
    ISSN: 1573-8868
    Keywords: variogram ; geostatistics ; positive-definite ; Bochner's theorem ; Hankel transforms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A method based on Bochner's theorem is described for demonstrating the positive-definiteness of variogram models and for generating classes of valid variogram functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01029889
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