does not tend towards zero when 
tends towards zero, although by definition
.
The variability between two
values 
and
taken at two very close points may be quite
high and increases as the size of the discontinuity at the origin of
increases.
This local variability can be compared to the random
phenomenon of white noise known to physicists. As the distance
increases, the variability often becomes more continuous and this is
reflected in the continuity of
for
.
The discontinuity of the variogram at the origin is called a nugget effect and is due both to measurement errors and to micro-variabilities of the mineralization; since the structure of these micro-variabilities is not accessible at the scale at which the data are available, they appear in the form of a white noise.