Geoscience Reference
In-Depth Information
the calculated time for the position of the wave front. This resulted in determination
of the position of the intersection point of the satellite's route and the tsunami front.
The position of the wave front is to a certain extent conventional. Calcula-
tions are
per
formed assuming the maximum of the wave propagation velocity to
be
c
=
√
g
H
, where
c
is the wave propagation velocity, g is the acceleration of
gravity and
H
is
the ocean de
pth. In reality, the wave velocity also depends on
its length,
c
=
gtanh(
kH
)
/
k
, where
k
= 2
is the wavelength. The shorter
the wavelength, the slower it propagates. Owing to this dispersion effect, the real
front, as a rule, lags behind this theoretical estimate. The longer the propagation
path, the stronger is the dispersion effect. The wave front can be distorted even
stronger in shallow water and during tides. Nevert
hele
ss, the estimate of the tsunami
wave front position, calculated by formula
c
=
√
g
H
, is quite accurate and its error
does not exceed the size of the tsunami source
π
/
λ
,
λ
50-100 km.
The evolution of a wave packet is due to the dependence of the group velocity on
the frequency:
∼
1 +
,
c
g
=
d
d
k
=
2
k
2
kH
sinh(2
kH
)
(6.1)
where
ω
is the angular wave frequency,
k
is the wave number and
H
is the ocean
depth.
A detailed analysis of altimetry data has been performed in [Zaichenko et al.
(2004)] for six strongest tsunamis: the Shikotan tsunami of 1994, the 1996 tsunami
near the island Irian Jaya, the Okushiri tsunami of 1993, the 1998 tsunami near
the coast of Papua New Guinea, the tsunamis near Island Java (1994) and the coast
of Peru (2001). In the first four cases it turned out to be possible to reveal specific
perturbations of the ocean level, which appear in the records within the time range
close to the moment, when the calculated tsunami front passes. Such perturbations
were most strikingly revealed in the records obtained on July 17, 1998 (Papua New
Guinea). In the last two cases, searches for traces of tsunamis in the records were
not met with success.
Figures 6.12 and 6.13 present a map of the investigated region of the Pacific
Ocean with isolines of tsunami arrival times and oceanic-level profiles at the coast
of Papua New Guinea, on which the perturbation, supposedly corresponding to
the 1998 tsunami passage time, is indicated.
Extremely interesting results were obtained from the analysis of radioaltimetry
observations of the catastrophic tsunami of December 26, 2004, in the Indian Ocean
[Kulikov et al. (2005)]. All available altimetry data from TOPEX/POSEIDON,
ENVISAT and JASON-1 were analysed for the period immediately after the seis-
mic shock. Individual routes revealed anomalous-level variations, probably related
to the passage of tsunami waves. The best-quality record JASON-1 (cycle 109, cir-
cuit 129) was chosen for further calculations.
Figure 6.14 presents the map of the north-eastern part of the Indian Ocean with
epicentres of the main earthquake (the black square) and the main aftershocks
(circles). The isochrones, showing the calculated position of the tsunami front, are
constructed with an interval of 0.5 an hour. The figure also shows the route of
the satellite JASON-1 (cycle 109, circuit 129) and the respective profile of the ocean
