Geoscience Reference
In-Depth Information
where
∞
∞
)
2
'
X
' =
(
η
0
ω
X
i
(
k
1
)
X
i
(
k
2
)
k
2
cosh(
k
1
) cosh(
k
2
)
d
k
1
d
k
2
2
H
4
π
0
0
(
k
1
+
k
2
)
(
k
1
−
×
k
2
)
cos ((
k
1
+
k
2
)
x
) sinh ((
k
1
−
k
2
))
k
2
)
x
) sinh ((
k
1
+
k
2
))
,
(
k
1
k
2
)
(
k
1
+
k
2
)
cos ((
k
1
−
−
−
(3.70)
∞
∞
)
2
'
Z
' =
(
η
0
ω
X
i
(
k
1
)
X
i
(
k
2
)
k
2
cosh(
k
1
) cosh(
k
2
)
d
k
1
d
k
2
2
H
4
π
0
0
(
k
1
−
k
2
)
2
(
k
1
+
k
2
)
2
cos ((
k
1
×
−
k
2
)
x
)((
k
1
+
k
2
)
−
sinh (
k
1
+
k
2
))
.
(
k
1
+
k
2
)
2
(
k
1
−
−
k
2
)
2
cos ((
k
1
+
k
2
)
x
)
{
(
k
1
−
k
2
)
−
sinh (
k
1
−
k
2
)
}
(3.71)
The quantity
X
(
x
) determines the contribution of the horizontal component of
the force field to the formation of long gravitational (tsunami) waves, and the quan-
tity
Z
(
x
) determines the contribution of the vertical component.
Figure 3.20 presents functions
Q
(
x
),
X
(
x
) and
Z
(
x
), which were calculated in
accordance with formulae (3.69)-(3.71) for the space distribution of the ocean
Fig. 3.20 Characteristic form of function
Q
(
x
) and of its components
X
(
x
) and
Z
(
x
). The calcula-
tion is performed for the space distribution of the ocean bottom oscillation amplitude
η
1
for
a
= 1,
3and5