| Summary: | Numerical simulations were generated to investigate the propagation processes of distant tsunamis, using a set of wave equations based on the variational principle considering both the strong nonlinearity and strong dispersion of waves. First, we proposed estimate formulae for the time variations of the tsunami height and wavelength of the first distant tsunami, by assuming that the initial tsunami profile was a long crest in a uniform bathymetry. Second, we considered the plate elasticity and upper-mantle fluidity of Earth, to examine their effects on the distant tsunami propagation. When the plate and upper mantle meet certain conditions with both a large depth and moderately large density of the upper mantle, the internal-mode tsunamis with a significant tsunami height propagated slower than the tsunamis in the corresponding one-layer problems, leading to the delay of the arrival time observed in distant tsunamis from that evaluated by the one-layer calculation.
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