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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
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