Geoscience Reference
In-Depth Information
Then (6.101) and (6.102) become
⎛
⎝
sin
j
π
⎞
⎠
i
ν
2
c
Ω
iγ
j
)
w
w
0
2
(1
−
cos
j
π
e
j
(
w
)=
a
j
at
j
=2
k
+1
,
(6.108)
iγ
j
)
w
w
0
2
(1
−
⎛
⎝
cos
j
π
⎞
⎠
i
ν
2
c
Ω
iγ
j
)
w
w
0
−
2
(1
−
sin
j
π
e
j
(
w
)=
a
j
at
j
=2
k.
(6.109)
iγ
j
)
w
w
0
2
(1
−
The coecients
a
j
are determined from the normalization condition (6.107)
and are given by
iΩ
cν
(2
w
0
)
1
/
2
.
a
j
=
(6.110)
Substitution of numerical values of parameters in (6.110) yields
a
j
=
i
1
.
59
n
1
/
e
L
3
(2
w
0
)
1
/
2
.
The coecient
C
0
j
is obtained from (6.97). With normalization condition
(6.107), we have at
p
=6
2
c
2
w
0
Ω
2
dln
ω
j
d
ν
I
1
πL
2
R
E
,
1)
j
+1
m
2
a
j
C
0
j
=(
−
(6.111)
where
π
cos (
j
(1
iγ
j
)
t
1+3
w
0
t
2
/π
2
−
I
1
=
d
t.
0
Then
10
8
m
2
dln
ω
j
d
ν
1)
j
+1
2
×
C
0
j
=(
−
I
1
.
For calculation of the wave field we use lengths in kilometers. After the nor-
malization we have
L C
0
j
=
2
m
2
(
L
1)
1
/
2
1)
j
+1
10
−
4
(
L
1)
1
/
2
dln
ω
j
d
L
−
−
I
1
(km
−
1
)
.
C
0
j
=(
−
R
E
Introduce the coecient of excitation of the
j
-mode as
e
j
=
n
j
e
j
.
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