Geoscience Reference
In-Depth Information
average due to that the Kriging method of interpolation considers both criterions
of distance and the changing of points' elevation. It is the best unbiased linear
Vary-gram of weights with the minimal estimation of variance. This means that
the difference between actual and estimated values is minimal. In the Kriging
method, there are numerous techniques for valuing the height values, which nor-
mally are divided into two different ways; ordinary Kriging and general Kriging.
The ordinary Kriging is calculated based on the following equation:
n
z
(
x
,
y
) =
i
z
(
x
i
,
y
i
)
i
=
1
where z(x, y) is the height estimated at unknown point, z(x
i
, y
i
) is the height of
sample point i and
λ
i
is the weight of point i.
For the estimation of the weight, various Vary-grams are used, such as; linear,
exponential, Gaussian and spherical. General Kriging method is also the combina-
tion of ordinary Kriging with local process. The local process can be defined in
two ways; linear trend and quadratic.
4.4 Nearest Neighbour Method
In the nearest neighbour method, the nearest point to the unknown neighbour is
selected and its height is assumed based on the height of the unknown point. This
method is an appropriate way if the data is taken based on a regular network and
matching with the grid lines.
4.5 Natural Neighbour Method
Natural neighbour method was developed in 1980 by Sibson (
1980
). This method
is based on Voronoi Pattern for a set of separated points. Voronoi Pattern is a dia-
gram, which is dividing space into a number of regions. This method has more
advantage compared with the nearest neighbour's method such as its ability to cre-
ate a surface that is relatively smooth. This method is based on the following func-
tion (Sibson and Barnett
1981
):
n
z
(
x
,
y
) =
i
z
(
x
i
,
y
i
)
i
=
1
where z (x, y) is the estimated height at unknown point, z (x
i
, y
i
) is height of sam-
ple point i and
λ
i
is weight of sample i followed by the area enclosed by any parts
of the unknown sample point.
