Regional-scale triggering of local earthquakes in the crust by seismic waves from distant main shocks has now been robustly documented for over a decade. Some of the most thoroughly recorded examples of repeated triggering of a single site from multiple, large earthquakes are measured in geothermal fields of the western United States like Long Valley Caldera. As one of the few natural cases where the causality of an earthquake sequence is apparent, triggering provides fundamental constraints on the failure processes in earthquakes. We show here that the observed triggering by seismic waves is inconsistent with any mechanism that depends on cumulative shaking as measured by integrated energy density. We also present evidence for a frequency-dependent triggering threshold. On the basis of the seismic records of 12 regional and teleseismic events recorded at Long Valley Caldera, long-period waves (>30 s) are more effective at generating local seismicity than short-period waves of comparable amplitude. If the properties of the system are stationary over time, the failure threshold for long-period waves is ~0.05 cm/s vertical shaking. Assuming a phase velocity of 3.5 km/s and an elastic modulus of 3.5 x 10¹⁰Pa, the threshold in terms of stress is 5 kPa. The frequency dependence is due in part to the attenuation of the surface waves with depth. Fluid flow through a porous medium can produce the rest of the observed frequency dependence of the threshold. If the threshold is not stationary with time, pore pressures that are >99.5% of lithostatic and vary over time by a factor of 4 could explain the observations with no frequency dependence of the triggering threshold.