Is there an increase in seismic activity corresponding with underground nuclear testing?
Yes, but but only of very small events, which can be considered as
aftershocks of the explosion (i.e., strains readjusting themselves).
Testing has never materially altered seismic risk: there is no
convincing evidence that nuclear tests trigger large earthquakes. The
explosion of the Cannikin shot beneath Amchitka Island in the
Aleutians in the seventies did not change the statistics of Aleutian
earthquakes at all, neither did testing at the Nevada Test Site,
which is also a seismically active area.
It is only very rarely that earthquakes trigger other earthquakes (one recent example was the Landers/Big Bear sequence of 1992, which spawned a succession of small earthquakes up the east side of the Sierra and in the vicinity of Lassen). Earthquakes are much more efficient at putting energy into the ground than explosions; since earthquakes only rarely seem to trigger other earthquakes there is little reason to believe that mere explosions will be capable of doing so. If a large earthquake were to follow a nuclear test that earthquake was probably about to happen anyway.
Hawaii Inst. of Geophysics & Planetology
University of Hawaii, Honolulu, HI 96822