Page 187 - MATLAB Recipes for Earth Sciences

182 7 Spatial Data

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 modified when a variogram

model is fitted 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 is the nugget effect.
0
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