¶ … Tsunamis Are Formed Earthquakes are often linked to ground shaking that is a ramification of elastic waves traveling through the solid earth. However, close to the heart and origin of submarine earthquakes, the seafloor is "permanently" uplifted and down-dropped, pushing the entire water column up and down.

The potential energy (as opposed to kinetic energy) that is the consequence of pushing water above mean sea level is then transferred to horizontal propagation of the tsunami wave (kinetic energy as opposed to potential energy). In most cases, the earthquake rupture occurs at the base of the continental slope in relatively deep water. Situations can also arise where the earthquake rupture occurs beneath the continental shelf in much shallower water.

Within just moments of the original submarine earthquake, the initial tsunami is divided into a tsunami that travels out to the deep ocean (distant tsunami) and yet one more tsunami that travels towards the nearby coast...

The speed at which both tsunamis travel varies as the square root of the water depth. Because of this, the deep-ocean tsunami travels faster than the local tsunami near shore.
Several occurrences happen as the local tsunami courses over the continental slope. Most fundamentally, the amplitude increases. Not to be outdone, the wavelength decreases. This results in steepening of the leading wave -- an important control of wave runup at the coast.

One must observe in addition 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, just as with the local tsunami discussed above.

As the tsunami wave travels from the deep-water, continental slope region…