  We present a novel numerical method for simulating the generation and
propagation of surface gravity waves by vertical seabed displacements. The
cornerstone of our method is the computation of a time dependent conformal map
which incorporates the time dependent geometry of the seabed and the wave
profile along the free surface. This enables us to handle general geometric
configurations of the seabed and the wave. As benchmark we reproduce the
results of Hammack on tsunami generation and propagation. Our results show that
Hammack's linear theory accurately predicts wave generation. However, as the
velocity of the sea bed displacement increases, nonlinear effects become
increasingly noticeable. Notably, when the seabed uplift occurs rapidly, the
following nonlinear dynamics of the wave differ significantly from the linear
dynamics usually associated with tsunami propagation.
