The majority of earthquakes are aftershocks, yet aftershock physics is not well understood. Many studies suggest that static stress changes trigger aftershocks, but recent work suggests that shaking (dynamic stresses) may also play a role. Here we measure the decay of aftershocks as a function of distance from magnitude 2-6 mainshocks in order to clarify the aftershock triggering process. We find that for short times after the mainshock, when low background seismicity rates allow for good aftershock detection, the decay is well fitted by a single inverse power law over distances of 0.2-50km. The consistency of the trend indicates that the same triggering mechanism is working over the entire range. As static stress changes at the more distant aftershocks are negligible, this suggests that dynamic stresses may be triggering all of these aftershocks. We infer that the observed aftershock density is consistent with the probability of triggering aftershocks being nearly proportional to seismic wave amplitude. The data are not fitted well by models that combine static stress change with the evolution of frictionally locked faults.