Geography Reference
In-Depth Information
It is not possible to use this experimental variogram in the estimation
purpose due to its inconsistent nature. Therefore, the curve of the experimental
variogram is approximated by another theoretical curve with a defined
mathematical expression. This smooth curve fitted to the experimental
variogram is known as ‗theoretical variogram' as shown in Figure 4.
This fitting or modeling is performed in several ways mostly visual or
using some form of difference between the two variograms but on a trial and
error basis. Sometimes an automatic modeling is proposed but is not proved to
be very useful. The commonly used variogram models are: spherical, circular,
Gaussian, and exponential (Issaks and Srivastava, 1989; Kitanidis, 1997). The
mathematical expressions for these theoretical variogram models are given
below.
(i) Spherical Model:
3
h
3
h
h
)
C
C
0
3
2
a
2
a
, for 0 < h ≤ a
(10)
(
h
)
C
C
0
, for
h
>
a
(11)
(ii) Circular Model:
2
2
h
2
(
h
)
C
C
1
arc
cos
h
a
1
h
a
0
a
, for 0<
h
≤
a
(12)
(
h
)
C
C
0
, for
h
>
a
(13)
(iii) Gaussian Model:
2
h
a
(
h
)
C
C
1
e
0
(14)
(iv) Exponential Model:
