Characteristics of leading tsunami waves generated in three recent tsunami events

In this paper, the time series of ocean water surface elevation, recorded by Deep-ocean Assessment and Recording of Tsunamis (DART) sensors in the Pacific Ocean, during three recent tsunami events - 2010 Chile tsunami, 2011 Tohoku tsunami, and 2012 Haida Gwaii tsunami - are analyzed. The characteristics of leading tsunami waves are examined in terms of their propagation speed, wave period and wave amplitude so as to determine the importance of wave nonlinearity and frequency dispersion. Using the estimated arrival time of leading waves at each DART station and the distance from each station to the epicenter of the corresponding earthquake, the averaged propagation speed of leading waves for each event is calculated. It is found that the wave propagation speed for 2010 Chile tsunami is roughly 190 m/s, and is slightly slower than that of 2011 Tohoku and 2012 Haida Gwaii tsunamis, 210 m/s for both events. Two time scales associated with the leading waves are introduced: the duration of leading wave crest and the leading wave period obtained from a wavelet analysis. The results show that the leading wave crest duration is roughly 15-20 min and the wave period is roughly 25-30 min at most of DART stations for all the three events. The wave nonlinearity and frequency dispersion parameters, being defined as the wave amplitude to water depth ratio and the square of water depth to wavelength ratio, respectively, are calculated for the leading waves. The parameter for wave nonlinearity is found to be smaller than 4.0 × 10^-4, while the parameter for frequency dispersion is smaller than 0.02 at all stations for all the three events. Finally, the cumulative effects of nonlinearity and frequency dispersion for the leading waves are investigated. It is found that the distances between the epicenter and all DART stations in each event are much smaller than those required for the nonlinearity and/or frequency dispersive effects to become significant.