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This paper deals with the study of the behaviour of a one spring-block model subjected to the strengths due to the motion of the tectonic plates and the upflow of magma during volcanism. Using the direct integration method, we show that the sound velocity decreases (or increases) with the amplitude of the block’s oscillation when the external frequency is zero (or not). It appears that this amplitude grows with the amplitude of the magma thrust strength. For the resonance case, where this external frequency equals the pseudofrequency of the block’s oscillation, we establish that the slip which occurs during the periodic movement of a block is a stick-slip motion instead of a creep motion as usually known; therefore, the transition does not occur. We also obtain that the event probability decreases with the amplitude of the magma thrust strength while the power of the earthquake increases with it.

The study of 1D spring-block model of earthquake dynamics with consideration of water effects in preexisting fault deals with new forms of frictional force. An analytical study of the equation of motion enables us to establish that motion of geological fault is accelerated by water pressure. In the same setting the critical value of frictional velocity for which appears the discontinuous (first-order) transition from a stick-slip behavior to a creep motion strongly depends on water pressure. The investigation also displays the magnitude and probability of events as a function of water pressure; these two quantities decrease and increase, respectively, with the variation of water pressure.

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