Graphics Programs Reference
In-Depth Information
(Fig. 7.15). At a closer look we can see that the linear model fi ts reason-
ably well over the fi rst three lags. This can be suffi cient when we use the
variogram model only for kriging, because in kriging the nearby points are
the most important for the estimate (see discussion of kriging below). Thus,
different variogram models with similar fi ts near the origin will yield simi-
lar kriging results when sampling points are regularly distributed. If you
are interested in describing the spatial structures it is another case. Then it
is important to fi nd a suitable model over all lags and to determine the sill
and the range accurately. A collection of geologic case studies in Rendu
and Readdy (1982) show how process knowledge and variography can be
linked. Good guidelines to variogram modeling are given by Gringarten and
Deutsch (2001) and Webster and Oliver (2001).
We will now briefl y discuss some more aspects of variography.
1.
Sample size
- As in any statistical procedure you need as large a sample
as possible to get a reliable estimate. For variography it is recommended
to have more than 100 to 150 samples (Webster and Oliver, 2001). If you
Linear model
0.8
Population
variance
0.7
Exponential model
0.6
0.5
0.4
0.3
Spherical model
0.2
0.1
0
0
20
40
60
80
100
120
140
Distance between observations
Fig. 7.15
Variogram estimator (gray circles), population variance (dashed line), spherical,
exponential, and linear models (solid lines).
