After an earthquake, numerous smaller shocks are triggered over distances comparable to the dimensions of the mainshock fault rupture, although they are rare at larger distances. Here we analyse the scaling of dynamic deformations (the stresses and strains associated with seismic waves) with distance from, and magnitude of, their triggering earthquake, and show that they can cause further earthquakes at any distance if their amplitude exceeds several microstrain, regardless of their frequency content. These triggering requirements are remarkably similar to those measured in the laboratory for inducing dynamic elastic nonlinear behaviour, which suggests that the underlying physics is similar.