Graphics Programs Reference
In-Depth Information
in a one or multidimensional space. While usually we do not know the true
variogram of the spatial process we have to estimate it from observations.
This procedure is called variography. Variography starts with calculating
the
experimental variogram
from the raw data. In the next step, the experi-
mental variogram is summarized by the variogram estimator. Variography
fi nishes with fi tting a variogram model to the
variogram estimator
. The
ex-
perimental variogram
is calculated as the difference between pairs of the
observed values depending on the
separation vector h
(Fig. 7.11). The clas-
sical experimental variogram is given by the
semivariance
,
where
z
x
is he observed value at location
x
and
z
x+h
is he observed value at
another point within a distance
h
. The length of the separation vector
h
is
called
lag distance
or simply
lag
. The correct term for
(
h
) is
semivariogram
(or
semivariance
), where
semi
refers to the fact that it is half of the variance
of the difference between
z
x
and
z
x+h
. It is, nevertheless, the variance per
point when points are considered as in pairs (Webster and Oliver, 2001).
Conventionally,
γ
(
h
) is termed
variogram
instead of semivariogram and so
we do at the end of this chapter. To calculate the experimental variogram we
fi rst have to build pairs of observations. This is done by typing
γ
[X1,X2] = meshgrid(x);
[Y1,Y2] = meshgrid(y);
[Z1,Z2] = meshgrid(z);
The matrix of separation distances
D
between the observation points is
D = sqrt((X1 - X2).^2 + (Y1 - Y2).^2);
x = x + h
j
i
h
x
i
Fig. 7.11
Separation vector
h
between two points.
