Mathematical Geology

, Volume 26, Issue 3, pp 301–321 | Cite as

The integral of the semivariogram: A powerful method for adjusting the semivariogram in geostatistics

  • Fréderick Delay
  • Ghislain de Marsily


A good fining of the structural junction that describes the variability of a spatial phenomenon is an essential stage in the building of an accurate estimator by kriging. The technique of the integral of the semivariogram (ISV) makes it possible to find this structural function while overcoming the problem of grouping together the pairs of experimental points into classes of distances when the data are not sampled on a regular grid. The ISV is particularly useful when the dispersion of the values of the classical Semivariogram (SV) makes it difficult to fit a model. Since the ISV is composed of a large number of values, it is more continuous than a SV and therefore easier to fit analytically. In fact, when the general shape of the SV is known, the ISV method proves its worth in finding the parameters that best fit a given variogram model. The analytical models of ISV which will be used, are the integral expressions of the traditional analytical SV. In this paper and on the basis of hydrogeological examples, we propose a method to adjust all the parameters of each model. The first derivative of a filled ISV, used in the kriging equations, appears to be systematically the best SV for a cross-validation on the data. This is why we think that the ISV technique should be used when the strong spatial variability of a parameter spreads out the values of the experimental SV.

Key words

intrinsic random function spatial variability dispersion of a semivariogram kriging cross-validation 


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Copyright information

© International Association for Mathematical Geology 1994

Authors and Affiliations

  • Fréderick Delay
    • 1
  • Ghislain de Marsily
    • 1
  1. 1.Laboratoire de Géologie Appliquée, URA CNRS 1367Université P. & M. CurieParis Cedex 05France

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