I just recently read an article about this...

"Around 150 to 200 fiber-optic cable breaks are recorded each year. Between 65% and 75% occur in water depths of < 200 m and result mainly from fishing and shipping activities. In contrast, breaks attributed to geohazards comprise < 10% of the world average. However, seaward of the busy continental shelf and upper continental slope, geohazards account for at least one-third of breaks."

-- "Insights into Submarine Geohazards from Breaks in Subsea Telecommunication Cables"

PDF: https://www.iscpc.org/documents/?id=1794

An earthquake took out a section of undersea fiber in Alaska recently, so it has definitely happened before:

http://www.adn.com/article/20140725/59-earthquake-causes-tel...

I wondered about the earthquake as well. Context/maps:

http://www.bloomberg.com/news/articles/2016-03-02/magnitude-...

They are designed with this in mind, and certainly hold up better than oil pipelines, which also have to be engineered to withstand earthquakes.

I expect it is unlikely for an earthquake itself to sever a cable, but knocking out power / knocking over a building that then destroys the cables landing site is possible, if rare.