Geoscience Reference
In-Depth Information
Fig. 2.26 Dependence of
the quantity
ω
2
P
, determin-
ing the amplitude of a gravi-
tational wave upon the cyclic
frequency of oscillations of
the basin bottom
Fig. 2.27 Amplitude of progressive wave excited by oscillating area of ocean bottom versus
the frequency of bottom oscillations for different sizes of the source,
a
But the amplitude of emitted waves,
A
, does not depend only on the frequency of
basin bottom oscillations, but on the horizontal extension of the oscillating area of
the bottom also. In accordance with formula (2.96) we can write
2sin(
k
0
a
) cosh(
k
0
)
k
0
[
k
0
+ sinh(
k
0
) cosh(
k
0
)]
,
2
A
(
ω
)=
η
0
ω
(2.102)
2
=
k
0
tanh(
k
0
). The dependence of the absolute value of the amplitude
upon the dimensionless oscillation frequency of the ocean bottom (
where
ω
(
H
/
g
)
1
/
2
) is
presented in Fig. 2.27. Calculations were performed for three different values of
parameter
a
. Surface manifestation of the oscillations of a part of the ocean bot-
tom with linear dimensions, smaller than the depth of the layer of liquid, will be
relatively weak. The existence of a set of frequencies, at which the amplitude of
the emitted wave turns to zero, is related to the interference of waves forming at
points
x
=
ν
a
. The automatic locking of the source is a consequence of the rectan-
gular space distribution of the amplitude of bottom oscillations. Actually, manifes-
tation of the automatic locking effect is extremely improbable.
The dependence (2.102) permits to reveal parameters determining the limits of
the tsunami frequency spectrum,
±
ν
min
and
ν
max
. We shall find the limit frequencies
from the solution of equation
A
(
ν
)=
η
0
/
10. From Fig. 2.27 it is not difficult to
conclude that
ν
max
∼
0
.
3, while the quantity
ν
max
does not depend on the size of
the generation area,
a
.
