“III. Amplification: 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.”

Citation source:http://www.owlnet.rice.edu/~esci108/108_EQ_Lec_4.ppt