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We present a novel numerical method for simulating the generation andpropagation of surface gravity waves by vertical seabed displacements. Thecornerstone of our method is the computation of a time dependent conformal mapwhich incorporates the time dependent geometry of the seabed and the waveprofile along the free surface. This enables us to handle general geometricconfigurations of the seabed and the wave. As benchmark we reproduce theresults of Hammack on tsunami generation and propagation. Our results show thatHammack's linear theory accurately predicts wave generation. However, as thevelocity of the sea bed displacement increases, nonlinear effects becomeincreasingly noticeable. Notably, when the seabed uplift occurs rapidly, thefollowing nonlinear dynamics of the wave differ significantly from the lineardynamics usually associated with tsunami propagation.

Full Euler equations for waves generated by vertical seabed displacements