Geology Reference
In-Depth Information
Comparison
The Gaussian scheme presents a parabolic behaviour near the origin
with a horizontal tangent. Hence it rises very slowly at the beginning,
in comparison to either Exponential or Spherical Schemes. The Gaussian
scheme also shows a concavity whereas the other two schemes are
convex. Lastly, for the values of
h
nearer to the range, the Spherical and
Gaussian schemes appear same.
Question 3.9
Show that the behaviour of the variogram is parabolic near the origin.
Model in |
h
|
hh
()
0
$<
2
Answer
The behaviour of the variogram is parabolic near the origin.
Behaviour of
e
x
at the origin is:
2
n
x
x
x
e
1
x
.................
(for
x
D
0)
2!
n
!
2
4
2
h
h
h
Hence
D
( )
hc
(1
(1
.........))
D
c
(for
h
0) :
This is
2
4
2
a
2!
a
a
because as
h
0, the higher powers of
h
can be neglected. This represents
the equation of a parabola of axis (0,
y
).
Hence the variogram has a parabolic behaviour near the origin. A few
clarifications below:
Origin =
h
= 0 Behaviour near the origin means
.
h
D
0
Model in
h
Question 3.10
Trace the curves for different values of
(for example
= ½, 1, 3/2).
Answer
The curves for different values of
(for example
= ½, 1, 3/2).
= 0.5
h
0
1
2
3
5
10
15
20
25
(
h
)
0
1
1.41
1.73
2.24
3.16
3.87
4.47
5
= 1
h
0
1
2
3
5
10
15
20
25
(
h
)
0
1
2
3
5
10
15
20
25
= 1.5
h
0
1
2
3
5
10
15
20
25
(
h
)
0
1
2.83
5.2
11.18
31.62
58.1
89.4
125
