Traveltime delay relative to the maximum energy of the wave train for dispersive tsunamis propagating across the Pacific Ocean: the case of 2010 and 2015 Chilean Tsunamis

This paper evaluates the importance of frequency dispersion in the propagation of recent trans-Pacific tsunamis. Frequency dispersion induces a time delay for the most energetic waves, which increases for long propagation distances and short source dimensions. To calculate this time delay, propagation of tsunamis is simulated and analysed from spectrograms of time-series at specific gauges in the Pacific Ocean. 1-D and 2-D simulations are performed by solving either shallow-water (SW) or Boussinesq equations and by considering realistic seismic sources. 1-D sensitivity tests are first performed in a constant-depth channel to study the influence of the source width. 2-D tests are then performed in a simulated Pacific Ocean with a 4000-m constant depth and by considering tectonic sources of 2010 and 2015 Chilean earthquakes. For these sources, both the azimuth and the distance play a major role in the frequency dispersion of tsunamis. Finally, simulations are performed considering the real bathymetry of the Pacific Ocean. Multiple reflections, refractions as well as shoaling of waves result in much more complex time-series for which the effects of the frequency dispersion are hardly discernible. The main point of this study is to evaluate frequency dispersion in terms of traveltime delays by calculating spectrograms for a time window of 6 hr after the arrival of the first wave. Results of the spectral analysis show that the wave packets recorded by pressure and tide sensors in the Pacific Ocean seem to be better reproduced by the Boussinesq model than the SW model and approximately follow the theoretical dispersion relationship linking wave arrival times and frequencies. Additionally, a traveltime delay is determined above which effects of frequency dispersion are considered to be significant in terms of maximum surface elevations.