Geoscience Reference
In-Depth Information
where
sin
(
k
tanh(
k
))
1
/
2
t
cosh(
k
)(
k
tanh(
k
))
1
/
2
∞
∞
2
cos(
ny
) sin(
nb
)
n
ζ
4
(
x
,
y
,
t
)=
d
m
d
n
2
π
τ
0
0
cos(
mx
)
η
1
cos(
ma
2
)]
η
2
a
2
m
2
[1
×
a
1
m
2
[1
−
cos(
ma
1
)]
−
−
+ sin(
mx
)
η
.
−
η
η
−
η
1
a
1
m
2
sin(
ma
1
)
1
m
2
a
2
m
2
sin(
ma
2
)
2
m
+
(2.115)
Integration over the components
m
and
n
of the wave vector in formula (2.115) was
performed numerically.
Figure 2.37 shows the example of the space structure of waves, excited by a bot-
tom displacement alternating in sign with parameters
a
1
= 7,
a
2
= 3,
b
= 10,
= 1.
The active area (its horizontal projection) exhibits the shape of a rectangle of size
10
τ
20 (along axes 0
x
and 0
y
, respectively). The 'fault' passes along the axis 0
y
,
the elevation and depression areas of the ocean bottom correspond, respectively,
to negative and positive values of the
x
coordinate. From the figure it is seen that
waves of maximum amplitude propagate in a direction, perpendicular to the 'fault'
×
Fig. 2.37 Perturbation of free
surface caused by displace-
ment of bottom alternating
in sign. Calculations are per-
formed for a sequence of
time moments (indicated in
the figure) for
a
1
= 7,
a
2
= 3,
b
= 10,
τ
= 1
