Indeed all buildings in Anchorage have to meet strict earthquake building standards. Unfortunently, downtown Anchorage sits on what is known as "bootleggers clay" which is very weak ground that liquifys during a strong earthquake. As a result during the 1964 Good Friday quake (the strongest in the history of North America), downtown Anchorage along with the former neighborhood of Turnagain Heights suffered the worse damage as the clay they sat on slid down, much of it going into Cook Inlet.
After the quake, geologists suggested that downtown be moved away from Cook Inlet, but of course as you'd expect, money won over as former governor Wally Hickel among others wanted to prove Anchorage's comeback by building large scale hotels and office buildings on the same site were the worse damage occured. Thankfully, Midtown Anchorage is located on land that is much more stable. BTW Downtown actually has 4 buildings at or over 20 stories while the proposed Augustine Energy Center will be at 21 stories. In 2005, a 22 story building was also planned in downtown but seems to have fell through. From what I know of, the current height limit is 30 stories.
4th Avenue in Downtown Anchorage, 1964
The seven story Four Seasons apartment complex that was supposedly
equipped with the latest in earthquake resistent technology.
Government Hill Elementary School near Downtown.