Geoscience Reference
In-Depth Information
ρ
s
= 1
.
816 g/cm
3
,
respectively. Besides, like in the previous case, account was taken of the range of
variations of the speed of sound in water and of the ocean depths at the points,
where the sensors were established.
In Fig. 3.16 the frequency ranges, calculated with account of the sedimentary
layer, are shown by thick horizontal lines. Like it was to be expected, the ranges
have become wider and shifted towards low frequencies. From the figure it is seen
that with account of the sedimentary layer the positions of the main maxima are in
good agreement with theoretical notions.
Note that quite a significant part of the energy of the spectra, depicted in
Fig. 3.16, is to be attributed to frequencies, lying below the principal maxima.
This effect cannot be explained within the framework of the absolutely-rigid-ocean-
bottom model. The point is that the formation of low frequencies takes place at large
depths, and owing to the existence of a cut-off frequency they cannot reach the sen-
sors. But, in reality, the rock of the ocean bottom is not absolutely rigid. Therefore,
from our point of view, low-frequency oscillations reach the sensors like seismic
waves. We note that the low-frequency limits of the spectra
waves and the density were set equal to
c
s
= 1
.
74 km/s and
ν
min
∼
0
.
05 Hz comply
well with the maximum depth of the ocean in the region dealt with,
ν
min
∼
c
/
4
H
max
7
,
500 m).
As to the high-frequency limits of the spectra (0.3-0.4 Hz), in this case it is not
correct to relate them to any minimum depths. The point is that the deformation area
also embraces part of the the island of Hokkaido, consequently, the ocean depth can
decrease down to zero, and the minimum normal frequency can increase indefinitely.
In such a situation one must turn to the possibility of the source (ocean bottom
displacement) to cause perturbations of high frequencies. It is seen that the lower
estimate, obtained above for the duration of the ocean bottom deformation,
≈
(
H
max
τ
PGi
,
complies quite well with the right-hand limit of the spectrum,
ν
max
∼
1
/
τ
PGi
ν
max
, permits to make
one more interesting conclusion. The boundary, separating the two regions of
the tsunami source, goes along the isobath
H
0
∼
Knowledge of the high-frequency limit of the spectrum,
1
,
000 m. In the first of
these two regions, where
H
<
H
0
, the ocean behaves like an incompressible liquid.
In the second region, which is deeper, the water compressibility effects play an im-
portant role.
Analysis of direct measurements of the near-bottom pressure at the source of
the Tokachi-Oki, 2003 tsunami (taken advantage of as an example) results in the rev-
elation of general-physics regularities determining the behaviour of water as a com-
pressible liquid:
•
c
/
4
ν
max
≈
Low-frequency elastic oscillations of the water column have been revealed.
These oscillations were shown to be one of the main dynamic processes at
the tsunami source.
•
Estimation has been performed of the velocity, amplitude and duration of
the ocean bottom deformation at the tsunami source.
•
The relationship has been established between the low-frequency limit of
the spectrum of near-bottom pressure variations and the ocean depth in
the tsunami source area. The high-frequency limit of the spectrum has been
shown to depend upon the minimal duration of the ocean bottom deformation.
