Abstract
Abstract. The behaviour of seismogenic faults is generally investigated under the assumption that they are subject to a constant strain rate. We consider the effect of a slowly variable strain rate on the recurrence times of earthquakes generated by a single fault. To this aim a spring-block system is employed as a low-order analog of the fault. Two cases are considered: a sinusoidal oscillation in the driver velocity and a monotonic change from one velocity value to another. In the first case, a study of the orbit of the system in the state space suggests that the seismic activity of the equivalent fault is organized into cycles that include several earthquakes and repeat periodically. Within each cycle the recurrence times oscillate about an average value equal to the recurrence period for constant strain rate. In the second case, the recurrence time changes gradually from the value before the transition to the value following it. Asymptotic solutions are also given, approximating the case when the amplitude of the oscillation or of the monotonic change is much smaller than the average driver velocity and the period of oscillation or the duration of the transition is much longer than the recurrence times of block motions. If the system is not isolated but is subject to perturbations in stress, the perturbation anticipates or delays the subsequent earthquake. The effects of stress perturbations in the two cases of strain rate oscillations and monotonic change are considered.
Highlights
If we consider the simplest stick-slip model for the earthquake mechanism, such as the one proposed one century ago by Reid (1911), fault slip events are found to be periodic and predictable
The behaviour of seismogenic faults is generally investigated under the assumption that they are subject to a constant strain rate
Asymptotic solutions are given, approximating the case when the amplitude of the oscillation or of the monotonic change is much smaller than the average driver velocity and the period of oscillation or the duration of the transition is much longer than the recurrence times of block motions
Summary
If we consider the simplest stick-slip model for the earthquake mechanism, such as the one proposed one century ago by Reid (1911), fault slip events are found to be periodic and predictable. When investigating the long-term behaviour of a fault system, models with a finite number of degrees of freedom are often preferable to descriptions based on continuum mechanics, since they allow long-term properties to be studied in a finite-dimensional state space Such low-order analogs of seismic sources are spring-block systems that were first proposed by Burridge and Knopoff (1967). In writing Eq (5), we have assumed that v is much smaller than the block velocity, since the ratio between the velocity of tectonic plates and the slip rate of a fault is in the order of 10−9 This means that the driver is virtually stationary during the motion of the block. Variations of , fs or v with time may render aperiodic the motion: we investigate the effect of varying v
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