The reason that southern Alaska is so geologically active is basically that the Pacific plate, which is sliding northwestward (arrows on map, below), is being pushed, or 'subducted' (click here for a quick read on tectonics, courtesy UC-Berkeley) under the North American plate. As the top of the Pacific plate grinds against the bottom of the North American plate earthquakes occur (note on this map that the earthquake epicenters generally get deeper to the northwest, as the subducted Pacific plate angles downward). Hundreds of miles to the southeast these same two plates slide past each other in California forming the complex of faults there.
This map provides a general view
the situation. It shows active faults, rupture zones, significant
and their dates, arrows showing the motion of the Pacific plate. What
doesn't show is that the whole arc of the Aleutian Islands and Alaska
is dotted with active volcanos, which are also a result the subduction
of the Pacific plate. As it dives into the Earth's mantle under the
American plate it begins to melt and some of this melted rock is forced
back up to the surface as lava.
The Alaska Range mountains (SE to SW of Fairbanks) are also the result of this titanic collision. In the process of being forced down into the Earth's mantle, the Pacific plate crumples the North American plate and forces it upward into mountains. Strangely, there doesn't seem to be any current volcanic activity in the Alaska Range, though there is plenty of evidence that there has been in the past, and there are several active volcanoes in the Wrangell Mountains to the southeast of the Range.
The Fairbanks area itself has been subject
to some large earthquakes, bigger than typical of California, and seems