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extends onto the land). The horizontal size of the tsunami source usually amounts
to tens and even hundreds of kilometres. The empirical dependence that relates
the mean radius
R
TS
[km] of the tsunami source and the earthquake magnitude
M
is
known as
lg
R
TS
=(0
.
50
±
0
.
07)
M
−
(2
.
1
±
0
.
6)
.
(2.3)
Note that real tsunami sources, naturally, do not exhibit a circular, but instead
a more complex, as a rule, elongated shape. At any rate, the boundary of a tsunami
source is a concept that is essentially conventional. The source of a tsunami of seis-
mic origin can be defined as the area, within which an earthquake has resulted in
noticeable residual deformations of the sea-floor or within which significant seismic
oscillations have occurred. From records of waves made by the method of inverse
isochrones it is possible to reconstruct the tsunami source region. It is interesting that
a source reconstructed in this manner usually exhibits a reasonable correspondence
to the area of aftershock manifestations. It must also be stressed that, as a rule, resid-
ual deformations are bipolar, i.e. elevation of the sea-floor takes place in one part of
the source and it is subsided in another part. Figure 2.2, adapted from [Satake, Ima-
mura (1995)], presents the example of the reconstruction of the Tokachi-Oki 1968
tsunami source.
Figure 2.3 shows the areas of the fault surface at the earthquake source (solid
line) and of the tsunami source (dotted line) as functions of the earthquake seismic
moment (magnitude). The area of the tsunami source was calculated as the area of
a circle with a radius determined by formula (2.3). The area of the tsunami source
can be seen to be several times larger than the area of the fault at the earthquake
source, which is quite reasonable from a physical point of view. It is interesting to
note that the said dependencies are practically parallel.
Another essential parameter characterizing tsunami generation by an earthquake
is the displacement amplitude
ξ
0
[
m
] of the oceanic surface at the source. This quan-
tity approximately follows the vertical residual deformations of the ocean bottom.
The corresponding regression estimate exhibits the following form:
lg
ξ
0
=(0
.
8
±
0
.
1)
M
−
(5
.
6
±
1
.
0)
.
(2.4)
Formulae (2.3) and (2.4) were derived in [Dotsenko, Soloviev (1990)] for magni-
tudes within the range of 6
.
7
<
M
<
8
.
5 by analysis of the wave field at the source,
reconstructed from measurements at the coast. The estimates for intervals corre-
spond to an 80% probability. Note that formula (2.4) seems to yield overestimated
values of residual displacements in the case of large magnitudes. The catastrophic
tsunamigenic earthquake that occcurred on December 26, 2004, and the magnitude
of which was
M
w
= 9
.
3 exhibited maximal vertical residual displacements of 8.6 m
for the elevation area and of 3.8 m for the depression area [Grilli et al. (2007)].
The duration of processes at the tsunami source also represents an important
parameter of the problem. Here, one must distinguish among several characteris-
tic quantities. Earlier, we already introduced the timescale
0
=(
H
/
g
)
1
/
2
peculiar
to problems involving surface gravitational waves. Besides, there also exists the
propagation time of a long gravitational wave over a distance, equal to the horizontal
τ
