Triggering and synchronization of stick slip: Waiting times and frequency-energy distribution

Triggering and synchronization are encountered in many geophysical phenomena, including geodynamics. Both these effects are generated by the action of additional forcing, which is much smaller than the main driving force. That means that triggering and synchronization are connected with nonlinear interactions of objects, in this case with initiation of instability in systems that are close to the critical state. In seismic process the main component is the tectonic stress and the additional forcing is exerted by various external impacts like tides, reservoir exploitation, big explosions, magnetic storms, etc.In the paper, the results of laboratory and field experiments on the electromagnetic (EM) initiation and synchronization of mechanical instability (slip) are presented. Slip events were recorded as acoustic emission bursts. In the first series of experiments strong EM pulses were applied to the mechanical system driven close to the critical state, namely, to the (dry) rock samples placed on an inclined supporting sample at the slope angle less than, but close to the critical slip angle. It has been found that EM impact initiates slip with probability P ≈ 0.07 at the voltage ΔV = 1.3 kV and with probability P ≈ 0.2 at ΔV ≈ 10 kV if the EM field is applied parallel to the slip surface (first mode). On the other hand, the application of EM pulse hampers the slip considerably if the EM field is directed perpendicularly to the slip surface (second mode): the slip was not observed even at the angle that was larger than the critical one.In the second series of experiments the periodic EM and mechanical forcing were applied to the standard slider-spring system. It was discovered that periodic EM force of frequency f superimposed on the constant driving force excites periodic microslips of rock samples with double frequency 2f. Combined impact of periodic and constant voltages invokes transition from double frequency synchronization to 1:1 synchronization if the direct component of voltage is larger than the periodic one. Synchronization affects not only waiting times, but also frequency-energy distribution: i. the energy of bursts emitted in synchronized mode have much less scatter than in the absence of the periodic forcing, ii. the sudden decrease of synchronizing forcing is followed by acoustic burst of much larger energy than during forcing.The elementary theory of EM triggering and synchronization is given: the effects are explained by the action of EM ponderomotive (electrostriction) forces, which modify Coulomb stress similar to the well known pore pressure model. The formalism of transition from 1:2 to 1:1 synchronization is considered.