Geoscience Reference
In-Depth Information
Fig. 2.4 Timescales of a tsunami source as
functions of the earthquake magnitude.
T
TS
is
the tsunami period,
T
hd
is the duration of the pro-
cess at the earthquake source (the “half duration”),
T
S
is the propagation time of the hydroacoustic
wave along the tsunami source,
T
0
is the maximal
period of normal elastic oscillations of the water
layer,
0
is the time scale for gravitational waves.
The ranges correspond to the interval of oceanic
depths, 10
2
-10
4
m
τ
From Fig. 2.4 it can be seen that, as a rule, the duration of processes at the earth-
quake source,
T
hd
, is significantly inferior to the period of the tsunami wave,
T
TS
,
that lies within the range 10
2
-10
4
s. Therefore, the generation of waves is generally
a relatively rapid process. The quantity
τ
0
(within the considered range of mag-
nitudes) is always smaller than the period of the tsunami wave,
T
TS
, however, in
a number of cases this difference may turn out to be not so significant. In this con-
nection, a tsunami can be considered a long wave, but with certain restrictions: in
the case of small-size sources phase dispersion is certain to be manifested. Let us,
now, turn to the quantity
T
S
, which always lies between the quantities
T
TS
and
T
hd
.
This reflects the fact that the speed of hydroacoustic waves is always superior to
the speed of long waves, but inferior to the speed, with which the fault opens up at
the earthquake source. We further turn to elastic oscillations of the water layer. It is
readily noted that the quantities
T
0
and
T
hd
have very close values, so that effective
excitation of elastic oscillations of the water layer is possible at the tsunami source.
From the figure it is also seen that the maximal period
T
0
of elastic eigen oscillations
of the water layer is always smaller than the tsunami period
T
TS
, i.e. elastic oscil-
lations and tsunami waves exist in ranges that do not intersect. This, however, does
not mean that elastic oscillations cannot at all contribute to the energy of tsunami
waves. Such a contribution can be realized by means of non-linear effects.
2.1.2 Secondary Effects
In setting boundary conditions on hard surfaces in hydrodynamic problems one con-
ventionally distinguishes between the normal and tangential components of the flow
velocity of the liquid. In the problem of tsunami generation such a hard surface is
represented by the ocean bottom, which in the case of an earthquake can undergo
motion both in its own plane, and in a perpendicular direction. We will term such
displacements as tangential and normal. Actually, the surface of the ocean bottom
has a complex structure, therefore the normal is conventionally constructed in a
