Large earthquakes can trigger distant earthquakes in geothermal areas. Some triggered earthquakes happen while the surface waves pass through a site, but others occur hours or even days later. Does this prolonged seismicity require a special mechanism to store the stress from the seismic waves that differs from ordinary aftershock mechanisms? These questions have driven studies of long-range triggering since the phenomenon's discovery. Here I attempt to answer the questions by examining the statistics of triggered sequences. Two separate observations are consistent with the prolonged sequences being simply local aftershocks of earthquakes triggered early in the wave train. First, the sequences obey Omori's Law over both short (1 hour) and longer (5 day) time intervals. Secondly, the number of observed triggered earthquakes in the first hour after the wave train can be predicted from the number of earthquakes triggered during the wave train. Even the very vigorous 10-day triggering at Long Valley from the 1992 Landers Mw 7.3 earthquakes can be interpreted as the aftershocks of either a local M ≈ 4.1 earthquake or an equivalent combination of several smaller mainshocks. Therefore, long-range triggering does not need to include a mechanism to produce sustained stresses other than the process that generates aftershocks of the earthquakes that occur while the wave train is passing.