Geology Reference
In-Depth Information
)
))
=
(( , ( )
Zx Zx
where
0
i
i
j
i
j
i
j
Answer
'
We know that
Cov(( ,( )
Zx Zx
C
(0)
(( ,( )
Zx Zx
i
j
i
j
))
Hence
VZ
(*( )
x
[(0)
C
(( ,( ]
Zx Zx
i
j
i
j
i
j
))
))
=
C
(0)
(
Z x
(
),
Z x
(
))
i
j
i
j
i
j
i
j
i
j
) )
2
=
C
(0)(
(
)
(
Z x
(
),
Z x
(
))
i
i
j
i
j
i
j
)
But
by the hypothesis.
0
i
)
))
Therefore:
If
0
VZ
(*( )
x
(( ,( )
Zx Zx
i
i
j
i
j
i
j
3. Standard Models
Spherical Model
4
3
a
3
h
1
h
when
h
<
C
..
:
6
:
2
a
2
/0
3
a
()
h
when
h
a
C
8
Question 3.1
Trace the curve of
(
h
) when sill
c
= 2 and range
a
= 100 m.
Answer
The expression for (
h
) when sill
c
= 2 and range
a
= 100 m will be
when
h
<
100
4
:
6
:
3
h
h
3
.
100
/
0
3
100
()
h
when
h
100
2
8
The slope at the origin is equal to (
h
) when
h
= 0 which is equal to
3/100.
2
dh
()
3
3
h
'( )
h
3
dh
100
100
We will calculate (
h
) when
h
takes values 0, 20, 40, 60, 80, 100, 120.
Elaborate calculations are shown for two cases. Rest can be calculated
in similar manner.
