THE INTEGRAL OF THE SEMIVARIOGRAM - A POWERFUL METHOD FOR ADJUSTING THE SEMIVARIOGRAM IN GEOSTATISTICS

A good fitting of the structural function that describes the variabili ty of a spatial phenomenon is an essential stage in the building of an accurate estimator by kriging. The technique of the integral of the s emivariogram (ISV) makes it possible to find this structural function while overcoming the problem of grouping together the pairs of experim ental points into classes of distances when the data are not sampled o n a regular grid. The ISV is particularly useful when the dispersion o f 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, i t is more continuous than a SV and therefore easier to fit analyticall y. 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 vario gram model. The analytical models of ISV which will be used, are the i ntegral expressions of the traditional analytical SV. In this paper an d on the basis of hydrogeological examples, we propose a method to adj ust all the parameters of each model. The first derivative of a fitted 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 o f a parameter spreads out the values of the experimental SV.