Detecting Quasi-Harmonic Factors Synchronizing Relaxation Processes: Application to Seismology

Abstract

Investigations conducted during the last 20-30 years demonstrate some very deep, fundamental regularity in the statistics of earthquakes time and space distribution that lead to the concept that the earthquake phenomenon is a system-defined complex of interacting events.

In the final stage of earthquake preparation, the epicentral area becomes sensitive to weak global disturbances such as tides, geophysical disturbances caused by solar activity, and variations of Earth rotation rate. One can consider the earthquake source as an analogue of nonlinear relaxation oscillator, storing the energy during dozens or hundreds of years. The “discharge”, i.e., an earthquake, happens suddenly, when the stress on the fault reaches the critical value. Close to this limit, the epicentral area becomes sensitive even to weak external disturbances. The additional stresses caused by varying external factors contribute to premature “discharge” of relaxation oscillator, i.e., earthquake. In seismically active regions, varying external factors may operate as synchronizers of earthquake release moments.

Investigation of synchronizing effect of external factors in a certain region requires development of special methods, because the data of earthquakes are presented as unequally-spaced sequences of phenomena.

According to the synchronization theory of relaxation process, discharges (earthquakes) mainly happen when influencing external factor is in a certain phase. It is possible to determine these moments by means of analysis of discharge recurrence and forms of distributions of event occurrence times’ moments. The distribution corresponding to the period of an external synchronizing factor demonstrates a characteristic gap or modulation. All external influencing periodicities may be determined by an analysis of distributions for all virtual forcing periods and detection of typical characteristic forms.

A simple model describes the principles of the used approach. The stress $P(t) = P_o+ b(t - t_0 )$ increases monotonically and undergoes the influence of external small stress with amplitude, frequency and phase denoted by $a,\bar {\omega}\varpi,\,{\rm and}\ f$, respectively. The resulting stress and the critical stress $P_m$, determining the discharge moment, which are connected by the equation $P_0+ b(t - t_0 ) + a\cos (\bar {\omega} t + f) = P_m$, will be obtained. The initial moment of energy integration process is unknown. If one examines a set of N different stress accumulation starting moments separated by a step $\varepsilon$, one will obtain N equations of type $b(t - t_0+ \varepsilon n) = P_m- P_0- a\cos (\bar {\omega} t + f), n = 0,1,2,\ldots N.$ The solutions of equations correspond to relaxation oscillator discharge moments for stress processes, started at different time moments. Solutions obviously reveal the “gaps”, or time intervals when discharges are forbidden, and also demonstrate that the width of the gap depends on the stress growth velocity. The examination of the distribution of phases of discharges inside the period of external forcing shows that strong and slowly growing earthquakes triggered by a stable external forcing demonstrate wider gaps. Fast growth of stress gives birth to narrow gaps or modulation of distribution. An analysis of distributions for different forcing frequencies and appearance of gaps or modulation is the way for distinguishing different external synchronizing factors.

All of these considerations, and the validity of “gap” method for the discovery of external synchronizing factors, are tested and confirmed in model laboratory experiments on electromagnetic and mechanical control of slip, namely, laboratory experiments with spring-slider system.

In order to investigate the influence of external factors triggering earthquakes, the “gap” method was applied to Caucasus earthquakes. The results reveal a set of regularities for strong earthquakes (the earthquakes with $M > 6$ that occurred during the last 100 years). The spectrum of recurrence periods of earthquakes contains 19 components which have clear astronomical and geophysical meaning; spectral distribution of time series of such earthquakes indicates that release mechanism of tectonically prepared strong earthquakes correlates with different tidal effects - the positional relationship of Sun, Earth and the Moon and periodicities of their orbital movement.