Abstract
The cumulative semivariogram approach is proposed for modeling regionalized variables in the geological sciences. This semivariogram is defined as the successive summation of half-squared differences which are ranked according to the ascending order of distances extracted from all possible pairs of sample locations within a region. This procedure is useful especially when sampling points are irregularly distributed within the study area. Cumulative semivariograms possess all of the objective properties of classical semivariograms. Classical semivariogram models are evaluated on the basis of the cumulative semivariogram methodology. Model parameter estimation procedures are simplified with the use of arithmetic, semilogarithmic, or double-logarithmic papers. Plots of cumulative semivariogram values vs. corresponding distances may scatter along a straight line on one of these papers, which facilitates model identification as well as parameter estimation. Straight lines are fitted to the cumulative semivariogram scatter diagram by classical linear regression analysis. Finally, applications of the methodology are presented for some groundwater data recorded in the sedimentary basins of the Kingdom of Saudi Arabia.
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Sen, Z. Cumulative semivariogram models of regionalized variables. Math Geol 21, 891–903 (1989). https://doi.org/10.1007/BF00894454
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DOI: https://doi.org/10.1007/BF00894454