Geoscience Reference
In-Depth Information
t
t
G
G
G
−
G
1
1
≈
∑
=
=
∑
=1
2
with
C
(
h
'
)
(
R
(
x
,
ω
)
R
(
x
,
ω
)
−
m
h
'
x
x
j
t
t
i
k
j
k
i
l
1
l
In order to obtain one of the points of the covariance function all that needs to be
*
done is to adapt the values of
to a theoretical model
and to fill the [C
i,j
]
C
(
h
'
)
C
(
h
'
)
*
and [C
o,i
] matrices with the corresponding
values.
C
(
h
)
What has just been introduced is the process of simple kriging, which can be
∗
G
, which has a zero average and for which the
variance of δ
2
(the difference) is minimal. This minimal value can be represented by
the following equation:
G
R
(
x
0
ω
,
)
R
(
x
o
ω
,
)
used to recreate
-
G
G
n
G
G
2
=
δ
=
C
(
x
,
x
)
+
μ
−
λ
C
(
x
,
x
)
0
0
i
i
o
i
1
Such a case is very rarely dealt with in practice, and as a result the spatial
estimation of m can sometimes be biased. Conversely, it is not strictly true that the
variance of
σ
is finite.
7.2.2.4.
Kriging under intrinsic hypotheses
It is often necessary for an additional hypothesis to be created. This hypothesis is
known as an intrinsic hypothesis, and in this hypothesis assumptions are made in
relation to the increase in the values of
G
G
G
(which are stationary
R
(
x
,
ω
)
−
R
(
x
+
h
,
ω
)
k
k
of order 2) for a given distance
h
G
.
{
G
G
G
}
G
G
G
E
R
(
x
,
ω
)
−
R
(
x
+
h
,
ω
)
=
m
(
x
)
−
m
(
x
+
h
)
=
C
=
0
D
k
k
te
G
The increased values have a zero average, and the value of
R
(
x
,
ω
)
tends to be
k
stationary.
G
can be written as follows:
The constant variance for a distance
h
{
}
G
G
G
G
Var
R
(
x
,
ω
)
−
R
(
x
+
h
,
ω
)
=
2
γ
(
h
)
k
k
D
The intrinsic hypothesis can be summarized as follows: the values of the spatial
increases are zero, and the variance of these increased values depends only on the
vector
h
G
or on its module h.
γ
is referred to as a variogram. Regarding the intrinsic hypothesis, the
variogram is associated with covariances and can be represented as follows:
{
2
(
h
)
}
G
G
G
G
2
γ
(
h
)
=
Var
R
(
x
,
ω
)
−
R
(
x
+
h
,
ω
)
k
k
D
