Variogram

Like correlograms, semi-variograms (called variograms for simplicity) decompose the spatial (or temporal) variability of observed variables among distance classes. The structure function plotted as the ordinate, called semi-variance, is the numerator of eq. 13.2:

or, for symmetric distance and weight matrices, n - 1 n d) =h X X whi(yh - yi)2 (13-10)

Y(d) is thus a non-standardized form of Geary's c coefficient. y may be seen as a measure of the error mean square of the estimate of yi using a value yh distant from it by d. The two forms lead to the same numerical value in the case of symmetric distance and weight matrices. The calculation is repeated for different values of d. This provides the sample variogram, which is a plot of the empirical values of variance y(d) as a function of distance d.

The equations usually found in the geostatistical literature look a bit different, but they correspond to the same calculations:

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