Graphics Programs Reference
In-Depth Information
variogram models. Common
authorized models
are the spherical, the expo-
nential, and the linear model (more models can be found in the literature).
Spherical model:
Exponential model:
Linear model:
where
c
is the sill,
a
is the range, and
b
is the slope (in the case of the linear
model). The parameters
c
and
a
or
b
have to be modifi ed when a variogram
model is fi tted to the variogram estimator. The so called
nugget effect
is spe-
cial type of variogram model. In practice, when extrapolating the variogram
towards separation distance zero, we often observe a positive intercept on
the ordinate. This is called the nugget effect and it is explained by measure-
ment errors and by small scale fl uctuations (
nuggets
), which are not captured
due to too large sampling intervals. Thus, we sometimes have expectations
about the minimum nugget effect from the variance of repeated measure-
ments in the laboratory or other previous knowledge. More details about the
nugget effect can be found in Cressie (1993) and Kitanidis (1997). If there
is a nugget effect, it can be added to the variogram model. An exponential
model with a nugget effect looks like this:
where
c
0
is the nugget effect.
We can even combine more variogram models, e.g., two spherical models
with different ranges and sills. These combinations are called
nested models
.
During variogram modeling the components of a nested model are regarded
as spatial structures which should be interpreted as the results of geological
