Geoscience Reference
In-Depth Information
its own depth and set of normal frequencies, corresponding to this depth. Thus, at
a certain fixed point of the source there, first, takes place formation of elastic oscil-
lations with normal frequencies, determined by the ocean depth at this point. Then,
the spectrum of elastic oscillations can be enriched by high frequencies at the cost
of waves arriving from neighbouring shallow-water regions. In Sect. 3.1.5 it was
shown that owing to the existence of a cut-off frequency low-frequency oscillations,
formed in adjacent deep-water regions do not propagate up the slope.
Note two features peculiar to compressibility effects, that explain why they have
been studied weakly. First, elastic low-frequency oscillations of a water column can
be revealed only at sufficiently large depths (in the open ocean), which hinders their
direct registration. Second, the compressibility effects were not quite within the line
of research of tsunamis, since, owing to the significant difference in frequency
ranges, elastic oscillations were not considered capable of giving any contribution
to a tsunami wave. Actually, such an assertion is erroneous, and the contribution of
elastic oscillations to a tsunami wave can be provided for by non-linear mechanisms
(Sect. 3.2).
Till recently the existence of elastic low-frequency oscillations of the water
column at a tsunami source had not been confirmed by measurements in natural
waters, and, therefore, the effect remained only theoretically predicted. To avoid
confusion, the difference must be stressed between such a well-known phenomenon
as the T-phase and the effects dealt with here. Not only the T-phase is related to
a range of higher frequencies (1-100 Hz), but it is also registered at significant dis-
tances from the source.
Figure 3.13 shows the epicentre location of the 25.09.2003 earthquake and
the circular region (dotted line) giving an idea of the size of the tsunami source.
The radius of the source,
R
TS
(
km
), was estimated by the empirical formula (2.3).
In the case considered
R
TS
≈
112 km. At the tsunami source there happened to be
two sensors of ocean bottom pressure, PG1 (41
◦
42.076
N, 144
◦
26.486
E) and PG2
(42
◦
14.030
N, 144
◦
51.149
E). The distances of the sensors from the earthquake
epicentre were
R
PG
1
≈
96 km.
Figures 3.14a and 3.15a present the change in time of the pressure near the ocean
bottom, registered by sensors PG1 and PG2, respectively. The range of pressure
variations, calculated as
p
max
−
49 km and
R
PG
2
≈
p
min
, amounted to
≈
398 kP at sensor PG1 and
≈
348 kP at sensor PG2. If pressure variations are considered manifestations of elas-
tic oscillations of the water column, resulting from a displacement, then it is possible
to estimate the upper limit of the velocity of vertical motion of the bottom (strictly
speaking, in the direction normal to the ocean bottom),
p
max
−
p
min
U
∼
,
ρ
c
= 1
,
000 kg/m
3
is the density of water and
c
= 1
,
500 m/s is the velocity
of sound in water. Estimation yields quite reasonable values:
U
PG
1
∼
where
ρ
0
.
27 m/s,
U
PG
2
∼
0
.
23 m/s. Experience of numerical simulation of the process of tsunami
generation in a compressible ocean (Sect. 3.1.5) permits to assert that the range
