A tsunami can be generated when converging or destructive plate boundaries abruptly move and vertically displace the overlying water. It is very unlikely that they can form at divergent (constructive) or conservative plate boundaries. This is because constructive or conservative boundaries do not generally disturb the vertical displacement of the water column. Subduction zone related earthquakes generate the majority of all tsunamis.
On 1st April, 1946 a Magnitude 7.8 (Richter Scale) earthquake occurred near the Aleutian Islands, Alaska. It generated a tsunami which inundated Hilo on the island of Hawai'i with a 14 m high surge. The area where the earthquake occurred is where the Pacific Ocean floor is subducting (or being pushed downwards) under Alaska.
Examples of tsunami being generated at locations away from convergent boundaries include - Storegga during the Neolithic era, Grand Banks 1929, Papua New Guinea 1998 (Tappin, 2001). In the case of the Grand Banks and Papua New Guinea tsunamis an earthquake caused sediments to become unstable and subsequently fail. These slumped and as they flowed down slope a tsunami was generated. These tsunami did not travel transoceanic distances.
It is not known what caused the Storegga sediments to fail. It may have been due to overloading of the sediments causing them to become unstable and they then failed solely as a result of being overloaded. It is also possible that an earthquake caused the sediments to become unstable and then fail. Another theory is that a release of gas hydrates (methane etc.,) caused the slump.
The "Great Chilean earthquake" (19:11 hrs UTC) 22nd May 1960 (9.5 Mw), the 27th March 1964 "Good Friday earthquake" Alaska 1964 (9.2 Mw), and the "Great Sumatra-Andaman earthquake" (00:58:53 UTC) 26th December 2004 (9.2 Mw), are recent examples of powerful megathrust earthquakes that generated a tsunami that was able to cross oceans. Smaller (4.2 Mw) earthquakes in Japan can trigger tsunami that can devastate nearby coasts within 15 minutes or less.
In the 1950s it was hypothesised that larger tsunamis than had previously been believed possible may be caused by landslides, explosive volcanic action e.g., Santorini, Krakatau, and impact events when they contact water. These phenomena rapidly displace large volumes of water, as energy from falling debris or expansion is transferred to the water into which the debris falls at a rate faster than the ocean water can absorb it. They have been named by the media as "mega-tsunami."
Tsunami caused by these mechanisms, unlike the trans-oceanic tsunami caused by some earthquakes, may dissipate quickly and rarely affect coastlines distant from the source due to the small area of sea affected. These events can give rise to much larger local shock waves (solitons), such as the landslide at the head of Lituya Bay 1958, which produced a wave with an initial surge estimated at 524m. However, an extremely large gravitational landslide might generate a so called "mega-tsunami" that may have the ability to travel trans-oceanic distances. This though is strongly debated and there is no actual geological evidence to support this hypothesis.