Why earthquakes correlate weakly with the solid Earth tides: Effects of periodic stress on the rate and probability of earthquake occurrence

We provide an explanation why earthquake occurrence does not correlate well with the daily solid Earth tides. The explanation is derived from analysis of laboratory experiments in which faults are loaded to quasiperiodic failure by the combined action of a constant stressing rate, intended to simulate tectonic loading, and a small sinusoidal stress, analogous to the Earth tides. Event populations whose failure times correlate with the oscillating stress show two modes of response; the response mode depends on the stressing frequency. Correlation that is consistent with stress threshold failure models, e.g., Coulomb failure, results when the period of stress oscillation exceeds a characteristic time tn; the degree of correlation between failure time and the phase of the driving stress depends on the amplitude and frequency of the stress oscillation and on the stressing rate. When the period of the oscillating stress is less than tn, the correlation is not consistent with threshold failure models, and much higher stress amplitudes are required to induce detectable correlation with the oscillating stress. The physical interpretation of tn is the duration of failure nucleation. Behavior at the higher frequencies is consistent with a second-order dependence of the fault strength on sliding rate which determines the duration of nucleation and damps the response to stress change at frequencies greater than 1/tn. Simple extrapolation of these results to the Earth suggests a very weak correlation of earthquakes with the daily Earth tides, one that would require >13,000 earthquakes to detect. On the basis of our experiments and analysis, the absence of definitive daily triggering of earthquakes by the Earth tides requires that for earthquakes, tn exceeds the daily tidal period. The experiments suggest that the minimum typical duration of earthquake nucleation on the San Andreas fault system is ???1 year.