A mega-tsunami is a tidal wave with far greater destructive power than a tsunami. They are over 100 meters in height and about 10 km in wavelength.

How they were discovered

In 1953, two geologists looking for sources of oil explored Lituya Bay in Alaska. They noticed something strange: that all the trees below a certain line (which they named the "trim line") were of a younger age than those above. This suggested that something devastating had occurred that wiped out the trees below that line. Looking at a cross-section of a tree that came from just above the trim line indicated that the tree had suffered a great impact at about the same period of time. However, as the trim line was high above sea level, the scientists did not have a clue as to what had happened until 1958.

On the 9th of July, 1958, a mega-tsunami swept into Lituya Bay, utterly destroying all the trees below 520 meters. Eyewinesses report seeing an explosion followed by a huge wall of water. The geologists returned and found that a landslide had occurred nearby, displacing the water and causing the mega-tsunami. They realised that they had discovered a force of destruction greater than the ordinary tsunami.

How a mega-tsunami differs from a tsunami

A tsunami is caused by earthquakes at sea. Therefore, there is only a certain height a tsunami can reach.
```   1) --------------------------------------
- -       -    -    -         -
- -       -      -        -    -   -
______________________________________
Sea floor at rest

2) --------------------|   }Height of tsunami
- -       -   _|------------------
- -       -      -        -    -   -
__________________
|____________________

Fault in sea-bed occurs. The wave of the tsunami is
determined by how much the sea-bed is lowered/raised.
```

Most tsunamis reach 10 to 15 meters in height at the highest. However, as mega-tsunamis are caused by landslides, the height of the wave is determined by how much soil is falling into the sea and the force and velocity at which it hits the sea.
```  1) \ooo
\ooo
\ooo
\oo
\o
\------------------------------------
\ -  -      - --         ---       -
\   - -   -       -  -     -- -    -

Sea at rest just before rocks (o) collapse into it.

2) \ooo   Air      | \            }
\ooo  cavity    | \           }Height of
\oooooooo       | \          }mega-tsunami
\ooooooooo     |  \         }
\oooooooooo  \    \\ \     }
\ oooooooooo     \    ------------------
\ooooooooo           ---       -
\ ooooooo            -  -     -- -    -

As the rocks crash into the sea, it causes the waves to
rise by displacement. An air cavity is formed because the
water does not have time to rush in and fill it. This is what
gives the mega-tsunami its height and destructive power.
```

Mega-tsunamis can also be caused by asteroid impact and volcanic eruptions.

With regard to wavelength, a mega-tsunami can reach up to hundreds of kilometers in length.
```         {.......wavelength.....}
--------------------\
/                     \
---/                       \---------
- ---         -  --     --
- -       -      -        -    -   -
______________________________________
```

This means that it can get pretty destructive, because unlike waves that break on the beach, the mega-tsunami will continue rolling in, threatening even those cities situated miles inland. In comparison, tsunamis only reach 100 to 200 meters in wavelength.

As with tsunamis, mega-tsunamis can also travel across entire oceans to wreck havoc on another continent.

Where does the danger come from?

Scientists have realised the greatest danger comes from volcanic islands, which build up over time and expand in size as volcanic rock from previous eruptions crumble into the sea.

Evidence of such collapses could be found off the islands of Hawaii, where pieces of debris, one of them 10 times the volume of Mount Everest, were found.

When and where will it strike next?

It is postulated that the origin of the next mega-tsunami will come from La Palma, one of the Canary Islands off the coast of North Africa. An island with an active volcano, it has shown signs of an impending collapse. A fault stretching across part of the island was formed after an earthquake.

If this piece of island collapses as a whole, a mega-tsunami would be sent rushing towards the eastern coast of America. The duration of its passage across the Atlantic is estimated at about 8 hours and scientists believe it would destroy some major cities like Miami and New York.

However, there is no major cause for worry right now, as the volcano on La Palma erupts about once every two centuries, and the last one occurred in 1949.

Sources:

The BBC
http://www.bbc.co.uk/science/horizon/2000/mega_tsunami.shtml

U. S. Department of Energy