Fig. 3

Dispersive and non-dispersive tsunami propagation simulations for a 4 km deep ocean. a An initial Gaussian-shaped tsunami observed at x = 0 km traveling in the positive \(x\) direction, where \(u\left(0,t\right)=0.5*\mathrm{exp}\left(-{\left(t-{t}_{o}\right)}^{2}*{\omega }_{a}^{2}\right)\) m, \({f}_{a}\) = 0.0015 Hz, \({\omega }_{a}=2\pi {f}_{a}\), and \({t}_{o}\)= 1920 s. The time series was computed at every 30 s for 2048 samples, giving a total time length of 1024 min. b–d Simulated tsunami waveforms at \(x\) = 9000 km that were computed for constant long-wave phase speed, i.e., \(\sqrt{gd}\), linear surface gravity wave phase speed in a homogeneous incompressible ocean, i.e., \(\omega /k=\sqrt{g(\mathrm{tanh}kd)/k}\), and the phase speed in an ocean coupled with the PREM having a 4 km deep ocean layer, respectively. The arrival times of the peak amplitude in Fig. 3c and d are delayed by 3 min and 8.5 min, respectively, relative to that in Fig. 3b. Note that in Fig. 3d, a small-amplitude initial phase with reversed polarity relative to the main peak precedes the main peak. The figure has been adapted from Fig. 6 of Watada et al. (2014)