Semivariance is an autocorrelation statistic defined as
Semivariance is evaluated in GS+ by calculating g(h) for all possible pairs of points in the data set and assigning each pair to a lag or distance interval class h. For uniform interval classes, GS+ makes interval class assignments for any given pair of points using the following formula:
class = INT(D/DI)+1
where
D = distance separating the pair
DI = lag class distance interval
INT = Integer function
Where the first lag is offset by ½ interval in order to better resolve values close to the origin, the formula is:
class = INT([D/DI]+0.5)+1
This option is available by checking a box in the Preferences – Analyses dialog. It can provide better resolved variograms when there are sufficient pairs of points at shorter separation distances. The disadvantage is that if there are few pairs of points for the shortest distance classes when the first lag is not offset (a common problem), there will be even fewer pairs available with the first lag offset. If this is the case, there will be little if any improvement to the variogram.
For individually-specified lag class intervals, pairs of points are assigned to interval lag classes based on values in the Define Lag Class Intervals window.
GS+ calculates a semivariance statistic for each interval class; the graph of all h's vs. all semivariances for each interval class in the analysis constitutes the variogram (sometimes called the semivariogram).
Various options for defining interval classes and summary variograms appear in the Autocorrelation window.
For co-kriging, semivariance analysis must be performed for the primary variate (Z), for the covariate (Z2), and for the cross (Z x Z2) situation.