Geoscience Reference
In-Depth Information
Z
1
¼
1
k¼
1
e
x
x
m
dx ¼ u
m=
2
e
u
=
2
J
k
ð
c
Þ
z
k
exp
ð
1
½
=
z
z
Þ
c
=
2
;
W
m=
2
;ð
1
mÞ=
2
ð
u
Þ;
u
Finally, the following algorithm is considered to evaluate the distribution
function W
c
(x):
w
c
ðÞ
¼A
0
u
0
ðÞþ
A
1
u
1
ð Þþþ
A
m
u
m
ð Þþ;
where
Z
1
i
A
i
¼
ð
1
Þ
w
c
ð
z
Þ
R
i
ð
z
Þ
dz
i
!
1
1)
i
and R
i
(z) is the Chebyshev-Hermite polynomial approximation: R
i
(z)=(
−
ˆ
i
(z)/
)
−
1
exp(
t
2
/2),
ˆ
i
(z)=d
i
ˆ
0
(z)/dz
i
,(i =1,2,
ˆ
0
(z), where
ˆ
0
(z)=(2
ˀ
−
…
).
Additionally, the normalization requirement should be satis
ed:
Z
1
0
;
i
6
¼ j
;
u
0
ð
z
Þ
R
i
ð
z
Þ
R
j
ð
z
Þ
dz ¼
1
;
i ¼ j
1
Thus, the sequential analysis distribution should be written in the form:
þ
1
p
ð
x
1
Þ
p
ð
x
1
Þ
k
c
k
=
2
ð
2k
þ
1
Þ!!
W
c
ð
x
Þ
¼
u
0
k¼1
ð
1
Þ
ð
k
þ
2
Þ!
u
k
þ
1
As mentioned above, the sequential method helps to tackle some unsolved
problems related to minimizing the detection delay time, and to detect a point where
safe environmental process becomes dangerous. As seen from Eq. (
3.12
) and
Figs.
3.3
and
3.8
, there are environmental processes, for which parameter c tends to
large values. In these cases, the approximations of function W
c
(x) given above can
help to overcome this situation.
3.5 Processing the Multichannel Information
3.5.1 Introduction
The schematic diagram of a monitoring system for detecting anomalies on the
Earth
'
s surface involves many levels. The search organization structure may contain
a more profound hierarchy including processing of information from satellites,
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