Computation of a Variogram

Let ${/boma h}$ be a vector of modulus $r = /vert{/boma h}/vert$ and direction ${/boma /alpha}$ (which may be two-dimensional). If there are $n$ pairs of data separated by the vector ${/boma h}$, then the experimental semi-variogram in the direction ${/boma /alpha}$ and for the distance ${/boma h}$ is expressed as

for a regionalization, and

for a coregionalization.

Although these expressions are unique and clear, the methods used in constructing variograms depend on the spatial configuration of the available data. Various cases can be distinguished according to whether or not the data are aligned and to whether or not they are regularly spaced along these alignments.