There is no reason to expect that the mineralization will
exhibit the same behavior in every direction, i.e., that the
mineralization
will be isotropic. In the three-dimensional space, x represents the
coordinates
and 
represents a vector of modulus
and direction
. Thus, in condensed form,
represents
the set of semi-variograms
for each direction
.
By studying
in various directions
, it
would be possible to determine any possible anisotropies, such as the
variability of the range
with the direction
.
In the example of Figure 1.3, the semi-variogram for the vertical
direction
reveals a short range 
corresponding to the mean vertical width of the
mineralized lenses, while the semi-variogram for the horizontal direction
has a larger range 
corresponding to the mean horizontal dimensions of
the same lenses. The directional graph of ranges
thus represents the
average morphology of the mineralized lenses.