Analytical solutions for estimating tsunami propagation speeds: Fid-Bau Portal

Analytical solutions for estimating tsunami propagation speeds

An, Chao / Liu, Philip L-F.

Abstract Recent studies suggest that the tsunami speed can be slowed down by around 1% due to Earth elasticity, water compressibility and density stratification. Analytical solutions of wave dispersion relationship, accounting for such effects, were found in previous studies. In this paper, we investigate the additional effects of water viscosity, ocean stratification due to temperature/salinity and numerical dispersion. Theoretical solutions are derived and checked with known solutions. All the formulas are then simplified for long tsunamis waves so that the propagation speed can be calculated explicitly. The simplified solutions are evaluated using realistic geophysical parameters. For a typical tsunami wavelength of ∼200km, the viscous effect is found to be negligible; ocean stratification due to temperature/salinity causes significant speed reduction because of the high density change rate, which has been ignored before. We also evaluate the numerical dispersion of tsunami simulations, which is shown to be potentially comparable to physical dispersion.

Highlights • Effects of water viscosity, ocean stratification and numerical dispersion on tsunami speeds are theoretically derived. • The latter two effects are found to be the same order as the effects of Earth elasticity and water compressibility. • All formulas are simplified to explicit forms and verified using realistic geophysical parameters.