Several things happen as the local tsunami travels over the continental
slope. Most obvious is that the amplitude increases. In addition, the
wavelength decreases. This results in steepening of the leading wave, an
important control of wave run-up at the coast. Note also that the deep ocean
tsunami has traveled much farther than the local tsunami because of the
higher propagation speed. As the deep ocean tsunami approaches a distant
shore, amplification and shortening of the wave will occur."