The one-dimensional Frenkel-Kontorova ͑FK͒ model, well known from the theory of dislocations in crystal materials, is applied to the simulation of the process of nonelastic stress propagation along transform faults. Dynamic parameters of plate boundary earthquakes as well as slow earthquakes and afterslip are quantitatively described, including propagation velocity along the strike, plate boundary velocity during and after the strike, stress drop, displacement, extent of the rupture zone, and spatiotemporal distribution of stress and strain. The three fundamental speeds of plate movement, earthquake migration, and seismic waves are shown to be connected in framework of the continuum FK model. The magnitude of the strain wave velocity is a strong ͑almost exponential͒ function of accumulated stress or strain. It changes from a few km/s during earthquakes to a few dozen km per day, month, or year during afterslip and interearthquake periods. Results of the earthquake parameter calculation based on real data are in reasonable agreement with measured values. The distributions of aftershocks in this model are consistent with the Omori law for temporal distribution and a 1 / r for the spatial distributions.

The seismic moment for regular earthquakes is proportional to the cube of rupture time. A second class of phenomena, collectively called slow earthquakes, has very different scaling. We propose a model, inspired from the phenomenology of dislocation dynamics in crystals, that is consistent with the scaling relations observed in the Cascadia episodic tremor and slip (ETS) events. Two fundamental features of ETS are periodicity and migration. In the northern Cascadia subduction zone, ETS events appear every 14.5 months or so. During these events, tremors migrate along‐strike with a velocity of 10 km/day and simultaneously zip back and forth in the relative plate‐motion direction with a typical velocity of 50 km/h. Our model predicts the formation of a sequence of slip pulses on the boundary of the plates, which describes the major features of fault dynamics, including periodicity and the migration pattern of tremors.

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Abstract.A model for seismo-electromagnetic (SEM) phenomena is described. The electromagnetic signals generated by mechanical disturbances in the earths crust have been calculated and compared with reported seismo-electromagnetic signals (SEMS). The major known SEM phenomena, namely, tectonomagnetic variations, electrotelluric anomalies, geomagnetic variations in the ultra-low frequency range and electromagnetic emission in the radio frequency range, have been considered. We have calculated the spectral densities associated with various types of sources. The set of formulas necessary to calculate the detected (filtered and averaged) electric and magnetic fields generated by mechanical disturbances for a wide range of frequencies and at various distances from the source are presented. Based on these formulas, we discuss the conditions under which electrokinetic, piezomagnetic and piezolectric effects could be responsible for SEMS. A comparison of estimated values of SEMS with reported field measurements leads to the conclusion that the sources of most anomalous SEMS are relatively close to the detector. In other words, the source of the signal is local, although the source of the mechanical disturbance which activates it, i.e. the epicenter of an earthquake, may be far away. Recommendations for field experiments (appropriate detector sitting, detector parameters and frequency range) following from the model developed here are presented.