Dispersion as a Function of Block Size

This chapter deals with the effect of the support of a regionalized variable (i.e. its physical shape and volume) on its histogram and its variogram. In an introductory exercise, the histograms and the basic statistics are calculated for two support sizes: 1m x 1m blocks and 2m x 2m blocks. Although the means of the two distributions are identical, the variance of the larger support is much smaller and its histogram isalmost bell shaped whereas the other one is skewed.The formulas for the variance of a point within a block and of one support v inside another V are then given. Krige’s additivity relation is proved. Then we see how the regularized variogram is related to the point support variogram. An exercise illustrates the effect that regularizing has on the variogram.