RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 8, ES4004, doi:10.2205/2006ES000214, 2006
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Figure 2 |
[5] Wavelet analysis of the observed wave elevations (Figure 2b)
reveals that the high frequency components of the 2004 Indian Ocean
tsunami were markedly dispersive. The leading edge of the wave
components with 10-km wavelength were significantly delayed in
comparison with the main wavefront components with about 1000 km
wavelengths. It is also worth noting that oscillations for all
frequencies (and wavenumbers) were abruptly dampened northward of
8o N (delineated by the vertical dashed line in the figure). The
latter zone consists of short tsunami waves with wavelengths
L = T(gH)1/2 1400 km, where
T =2 hours is the time of wave
propagation,
g is gravity, and
H
4000 m is the ocean
depth. Based on this calculation, it is possible to state that the
"boundary of the high-frequency wave generation zone" was located
at between 7-8o N, in the region of the red line in Figure 1.
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Figure 3 |
[7] The time step in Figure 3 gives the time scale for estimating the main periods of the tsunami waves recorded at a fixed location in the open ocean, for example at an island tide gauge. According to this figure, most of the energy was associated with a wave period of about 50-60 min. Although the satellite trace does not coincide with the wave ray trace, we assume that this period (50-60 min) is the fundamental period for the Sumatra tsunami waves. This assumption is in good agreement with spectral analyses of the tide gauge tsunami records (Alexander Rabinovich, pers. comm.). The bottom panel presents results from frequency band-pass analysis of the tsunami signal and clearly indicates the spatial shift (time delay) of the short wave components compared to the leading wavefront.
[8] The effect of tsunami wave dispersion in the open ocean has been previously reported by González and Kulikov [1993] and Kulikov and González [1996]. Small tsunami waves (of about 2 cm amplitude) arising from the earthquake 6 March, 1988 in the Alaska Bight have been recorded by precise bottom pressure gauges located in about 1000 km from the source area. The seismic source was of small horizontal extent and, accordingly, generated relatively short, highly dispersive tsunami waves. The amplitude and frequency modulation of the observed tsunami bottom pressure records has been shown to be due to the dispersion predicted by the linear wave theory.
[9] González and Kulikov [1993] compared the observed dispersion with a theoretical estimate of the wave dispersion derived from the group velocity of the waves. From the generalized dispersion relation for water waves [LeBlond and Mysak, 1978],
![]() | (1) |
where w is the angular frequency, k is the wavenumber, and H is the local water depth. The phase speed for these waves is
![]() | (2) |
and the group speed (which characterizes the wave dispersion) is
![]() | (3) |
[10] Wavelet analysis used in [Kulikov and González, 1996] clearly revealed this effect of delaying high frequency wave components with the time-delay t = L/cg (w), where L is a wave travel distance and group velocity cg (w) is given by (3). A simple wave model developed for comparison with the data was consistent with the sea floor displacement estimated from a seismic fault plane deformation model (western-subsidence-uplift dipole).
[11] Okal et al. [1999], who appear to have been the first to detect fluctuations in the sea surface due to a tsunami wave field (associated with the 1992 Nicaragua tsunami), also found evidence of tsunami wave dispersion; specifically 9% dispersion for wave periods of 850 s and 350 s, which is close to the value of 7.7% measured by González and Kulikov [1993]. The high resolution altimeter data from Jason-1 enables us to examine this effect more precisely for a much stronger and much larger-scale earthquake and associated tsunami events.
[12] A similar analysis for "spatial dispersion" has been undertaken in the wavenumber domain for the tsunami profile derived from the Jason-1 altimetry. The track line crosses the calculated wavefront at an angle of about 30o-40o to the tsunami rays. Numerical modeling of the Sumatra wave event by Titov (2005), which is based on an extensive source area (about 1100 km in length), presents several patterns of the wavefront (these model results are available now in graphic form on the NOAA website http://www.pmel.noaa.gov/tsunami/indo_1204.html). The orientation of the satellite track relative to the tsunami wavefronts is assumed to be close to normal (taken as the direction to the middle of aftershock area). The dispersion curve in Figure 2 indicates the wavefronts for different spectral components. To the right (north) of the wave-affected area of the figure is located an empty wave zone separated from the other area by a vertical dashed line. This feature may have arisen as a result of the strong directivity of this specific tsunami source. There were no highly frequency waves propagating in the northward direction, a feature which is probably related to the high directional character of the source. Most of the energy was apparently directed in a southwestward direction, in good agreement with the numerical simulations of Titov, PMEL (http://www.pmel.noaa.gov/tsunami/indo_1204.html).
Citation: 2006), Dispersion of the Sumatra Tsunami waves in the Indian Ocean detected by satellite altimetry, Russ. J. Earth Sci., 8, ES4004, doi:10.2205/2006ES000214.
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