As far as the second-order moments of the random function
are concerned, these
nested structures can be conveniently represented as the sum of a number
of variograms (or covariances), each one characterizing the variability at a
particular scale.
For example,
may be a transition model (spherical or exponential)
which very rapidly reaches its sill value
for distances
that are only
slightly larger than the data support. This model thus combines all the
micro-variabilities (e.g., measurement errors and petrographic differentiations).
may be another transition model with a larger range (e.g.,
) characterizing the lenticular beds and
may be a third transition model with a range (
)
representing the alternation of
strata or the extent of homogeneous mineralized zones.
At smaller distances (), the observed total variability depends
on
, cf. Figure 4.1,
while for large distances it will depend on all the
.