We have used observations from Felzer and Brodsky (2006) of the variation of linear aftershock densities (i.e., aftershocks per unit length) with the magnitude of and distance from the main shock fault to derive constraints on how the probability of a main shock triggering a single aftershock at a point, P(r, D), varies as a function of distance, r, and main shock rupture dimension, D. We find that P(r, D) becomes independent of D as the triggering fault is approached. When r ??? D P(r, D) scales as Dm where m-2 and decays with distance approximately as r-n with n = 2, with a possible change to r-(n-1) at r > h, where h is the closest distance between the fault and the boundaries of the seismogenic zone. These constraints may be used to test hypotheses about the types of deformations and mechanisms that trigger aftershocks. We illustrate this using dynamic deformations (i.e., radiated seismic waves) and a posited proportionality with P(r, D). Deformation characteristics examined include peak displacements, peak accelerations and velocities (proportional to strain rates and strains, respectively), and two measures that account for cumulative deformations. Our model indicates that either peak strains alone or strain rates averaged over the duration of rupture may be responsible for aftershock triggering.