Origin of Traveltime anomaies of distant tsunami

After the implementation of DART Buoys in the deep open sea, two major earthquakes along deep oceanic trenches, the 2010 Chile earthquake and the 2011 Tohoku earthquake, excited large trans-Pacific tsunamis. The long-period DART tsunami record avoids complex near coast effects, and unequivocally showed that teleseismic tsunami travels slower by 2-3 % than the numerically predicted tsunami with hydrodynamic non-linear effects and the Coriolis force and the basal viscosity on the ocean floor included. If the ocean current is the cause, the reciprocal position of two earthquakes will show a distinct directional pattern, but observation eliminates the possibility of ocean current effects. We measured the phase velocity difference between the theoretical tsunami waveforms and those observed at DART buoys propagated from the earthquake source to the buoys. The difference is large at longer period (or wavelength) of tsunami. At 1000 km or more, the phase velocity difference reaches to about 3% of the synthetic tsunami. At 100 km, the difference diminishes to a fraction of percent. The phase difference dispersion pattern is consistent among buoys and two earthquakes. We computed tsunami phase and group velocities for the self-gravitating PREM earth model including the effect of elasticity of the ocean and the solid Earth. The dispersion relation of PREM tsunami deviates from the dispersion of tsunami with rigid-bottom boundary at long period. The deviation pattern is consistent observed phase difference from two mega-earthquakes and recorded by DART buoys. We conclude that the traveltime anomaly is the problem in the current 2D or 3D tsunami numerical computation which does not include the effect of elasticity and self gravity of the Earth. The 2-3% difference of speed of tsunami after one day propagation results in a 30 min arrival time difference, and more advanced tsunami computation techniques should be developed for accurate prediction of long-distance tsunami propagation.