On the role of frequency dispersion on the trans-pacific tsunamis: Study of the 2010 and 2015 Chilean tsunamis

The trans-pacific propagation of the 2010 and 2015 Chilean tsunamis have been simulated by resolving both the Saint-Venant and the Boussinesq equations, these latter equations taking into account the frequency dispersion of waves. Numerical results show that the frequency dispersion simulation must be considered to reproduce the wave heights and arrival times recorded by several DART buoys in the Pacific Ocean. Several grid resolutions have been tested using either the Saint-Venant or the Boussinesq model (10′, 5′ and 2′). Only the Saint-Venant simulation at a 5′ resolution and the Boussinesq simulation at a 2′ resolution allow to reproduce the amplitudes and arrival times of the first waves. Numerical results indicate that frequency dispersion has a significant impact on the computed waveforms and suggest that the Saint-Venant code generates numerical dispersion similar to the physical frequency dispersion. It has been confirmed by one dimensional sensitivity tests. By comparing both events (2010 and 2015), we show that the frequency dispersion is stronger for the second event and it has been confirmed by the analysis of the Absolute Pressure Gages KSR1 and MRT1 spectrograms at some 17000 km from the source. Indeed, the main wave energy is contained in the first waves for the 2010 events and in the following waves for the 2015 event. Nevertheless, for the 2010 event, we also detect some late arrival waves at the APG KSR1, three hours after the first arrival time, with energy only two times lower than the first wave one.