Geoscience Reference
In-Depth Information
[
]
2
G
[
G
]
{
G
}
G
G
G
G
⎩
⎨
⎧
2
⎭
⎬
⎫
2
γ
(
h
)
=
E
R
(
x
,
ω
)
−
R
(
x
+
h
,
ω
)
−
E
R
(
x
,
ω
)
−
R
(
x
+
h
,
ω
)
k
k
k
k
D
D
G
[
G
]
G
G
⎩
⎨
⎧
2
⎭
⎬
⎫
2
γ
(
h
)
=
E
R
(
x
,
ω
)
−
R
(
x
+
h
,
ω
)
−
0
k
k
D
{
}
{
G
G
[
G
]
⎭
⎬
⎫
}
G
G
G
G
2
⎩
⎨
⎧
[
]
2
2
γ
(
h
)
=
E
R
(
x
,
ω
)
−
2
E
R
(
x
+
h
,
ω
)
R
(
x
,
ω
)
+
E
R
(
x
+
h
,
ω
)
k
k
k
k
D
D
D
However:
{
}
[
G
]
G
G
⎩
⎨
⎧
2
⎭
⎬
⎫
[
]
2
2
2
E
R
(
x
,
ω
)
−
m
=
E
R
(
x
+
h
,
ω
)
−
m
=
C
(
)
k
k
D
D
{
}
G
G
G
G
G
G
G
2
2
E
R
(
x
+
h
,
ω
)
R
(
x
,
ω
)
−
2
m
=
2
C
(
x
,
x
+
h
)
=
2
C
(
h
)
k
k
D
Therefore:
{
}
G
{
G
}
G
G
G
[
]
2
2
2
γ
(
h
)
=
E
R
(
x
,
ω
)
−
m
−
2
E
R
(
x
+
h
,
ω
)
R
(
x
,
ω
)
...
D
k
D
k
k
G
[
]
G
⎩
⎨
⎧
2
⎭
⎬
⎫
2
2
...
+
2
m
+
E
R
(
x
+
h
,
ω
)
−
m
D
k
G
G
γ
(
h
)
=
C
(
−
C
(
h
)
The initial system can therefore be transformed into:
n
n
n
∗
G
G
G
G
G
G
∑
∑
∑
R
(
x
,
ω
)
=
λ
R
(
x
,
ω
)
with
λ
(
x
,
x
)
−
μ
=
γ
(
x
,
x
)
et
λ
=
1
o
i
i
j
j
i
0
i
i
=
1
j
=
1
i
=
1
and can also be represented as a matrix:
G
G
G
G
G
G
G
G
G
G
γ
(
x
,
x
)
γ
(
x
,
x
)
...
γ
(
x
,
x
)
...
γ
(
x
,
x
)
1
γ
(
x
,
x
)
1
1
1
2
1
j
1
n
1
0
G
G
G
G
G
G
G
G
G
G
λ
1
γ
(
x
,
x
)
γ
(
x
,
x
)
...
γ
(
x
,
x
)
...
γ
(
x
,
x
)
1
γ
(
x
,
x
)
2
1
2
2
2
j
2
n
2
0
2
...
...
...
...
...
...
...
...
...
G
G
G
G
G
G
G
G
G
G
=
γ
(
x
,
x
)
γ
(
x
,
x
)
...
γ
(
x
,
x
)
...
γ
(
x
,
x
)
1
λ
γ
(
x
,
x
)
i
1
i
2
i
j
i
n
i
i
0
...
...
...
...
...
...
...
...
...
G
G
G
G
G
G
G
G
G
G
λ
γ
(
x
,
x
)
γ
(
x
,
x
)
...
γ
(
x
,
x
)
...
γ
(
x
,
x
)
n
γ
(
x
,
x
)
n
1
n
2
n
j
n
n
n
0
1
1
...
1
...
1
0
1
So that the variogram can be used in practice, an experimental variogram needs
to be developed:
G
[
G
]
⎭
⎬
⎫
G
G
2
⎩
⎨
⎧
2
γ
(
h
)
=
E
R
(
x
,
ω
)
−
R
(
x
+
h
,
ω
)
D
k
k
This equation is created by evaluating the distance
Δ
(in the case of an
anisotropic function phases of azimuth are used instead). The couplets of
i
x
G
G
(
,
)
are
j
represented as follows:
G
−
G
Δ
h
x
x
=
h
±
i
j
2
