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Dynamics of Simple Earthquake Model with Time Delay and Variation of Friction Strength : Volume 20, Issue 5 (29/10/2013)

By Kostić, S.

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Book Id: WPLBN0003990677
Format Type: PDF Article :
File Size: Pages 9
Reproduction Date: 2015

Title: Dynamics of Simple Earthquake Model with Time Delay and Variation of Friction Strength : Volume 20, Issue 5 (29/10/2013)  
Author: Kostić, S.
Volume: Vol. 20, Issue 5
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Vasović, N., Franović, I., Todorović, K., & Kostić, S. (2013). Dynamics of Simple Earthquake Model with Time Delay and Variation of Friction Strength : Volume 20, Issue 5 (29/10/2013). Retrieved from

Description: University of Belgrade Faculty of Mining and Geology, Ðušina 7, Belgrade, Serbia. We examine the dynamical behaviour of the phenomenological Burridge–Knopoff-like model with one and two blocks, where the friction term is supplemented by the time delay Τ and the variable friction strength c. Time delay is assumed to reflect the initial quiescent period of the fault healing, considered to be a function of history of sliding. Friction strength parameter is proposed to mimic the impact of fault gouge thickness on the rock friction. For the single-block model, interplay of the introduced parameters c and Τ is found to give rise to oscillation death, which corresponds to aseismic creeping along the fault. In the case of two blocks, the action of c1, c2, Τ1 and Τ1 may result in several effects. If both blocks exhibit oscillatory motion without the included time delay and frictional strength parameter, the model undergoes transition to quasiperiodic motion if only c1 and c2 are introduced. The same type of behaviour is observed when Τ1 and Τ2 are varied under the condition c1 = c2. However, if c1, and Τ1 are fixed such that the given block would lie at the equilibrium while c2 and Τ2 are varied, the (c2, Τ2) domains supporting quasiperiodic motion are interspersed with multiple domains admitting the stationary solution. On the other hand, if (c1, Τ1) warrant oscillatory behaviour of one block, under variation of c2 and Τ2 the system's dynamics is predominantly quasiperiodic, with only small pockets of (c2, Τ2) parameter space admitting the periodic motion or equilibrium state. For this setup, one may also find a transient chaos-like behaviour, a point corroborated by the positive value of the maximal Lyapunov exponent for the corresponding time series.

Dynamics of simple earthquake model with time delay and variation of friction strength

Aronson, D., Ermentout, G., and Kopell, N.: Amplitude response of coupled oscillators, Physica D, 41, 403–449, 1990.; Bak, P. and Tang, C.: Earthquakes as a self-organized critical phenomenon, J. Geophys. Res., 94, 15635–15637, 1989.; Behnsen, J. and Faulkner, D. R.: The effect of mineralogy and effective normal stress on frictional strength of sheet silicates, J. Struct. Geol., 30, 1–13, 2012.; Beltrami, H. and Mareshal, J.: Strange seismic attractor?, Pure Appl. Geophys., 141, 71–81, 1993.; Burić, N. and Todorović, D.: Dynamics of delay-differential equations modeling immunology of tumor growth, Chaos Soliton. Fract., 13, 645–655, 2002.; Burridge, R. and Knopoff, L.: Model and theoretical seismicity, B. Seismol. Soc. Am., 57, 341–371, 1967.; Byerlee, J. D.: Frictional characteristics of granite under high confining pressure, J. Geophys. Res., 72, 36390–36448, 1967.; Byerlee, J. D. and Summers, R.: A note on the effect of fault gouge thickness on fault stability, Int. J. Rock Mech. Mining Sci. Geomech. Abstr., 13, 35–36, 1976.; Carlson, J. M. and Langer, J. S.: Mechanical model of an earthquake fault, Phys. Rev. A, 40, 6470–6484, 1989.; Das, S., Boatwright, J., and Scholz, C. H. (Eds.): Earthquake source mechanics, Am. Geophys. Union Monogr., Washington DC, 1986.; De Sousa Vieira, M.: Chaos in a simple spring-block system, Phys. Lett. A, 198, 407–414, 1995.; De Sousa Vieira, M.: Chaos and synchronized chaos in an earthquake model, Phys. Rev. Lett., 82, 201–204, 1999.; Dieterich, J. H.: Modeling of rock friction: 1. Experimental results and constitutive equations, J. Geophys. Res., 84, 2161–2168, 1979.; Engelder, J. T., Logan, J. M., and Handin, J.: The sliding characteristics of sandstone on quartz fault-gouge, Pure Appl. Geophys., 113, 69–86, 1975.; Erickson, B., Birnir, B., and Lavallee, D.: A model for aperiodicity in earthquakes, Nonlinear Proc. Geoph., 15, 1–12, 2008.; Gopalsamy, K. and Leung, I.: Delay induced periodicity in a neural netlet of excitation and inhibition, Physica D, 89, 395–426, 1996.; Horowitz, F. G. and Ruina, A.: Slip patterns in a spatially homogeneous fault model, J. Geophys. Res., 94, 10279–10298, 1989.; Langer, J. S., Carlson, J. M., Myers, C. R., and Shaw, B. E.: Slip complexity in dynamics models of earthquake faults, Proc. Natl. Acad. Sci. USA, 93, 3825–3829, 1996.; Marone, C.: The effect of loading rate on static friction and the rate of fault healing during the earthquake cycle, Nature, 391, 69–72, 1998.; Marone, C. and Scholz, C. H.: The depth of seismic faulting and the upper transition from stable to unstable slip regimes, Geophys. Res. Lett., 15, 621–624, 1988.; Marone, C., Raleigh, C. B., and Scholz, C. H.: Frictional behaviour and constitutive modeling of simulated fault gouge, J. Geophys. Res., 95, 7007–7025, 1990.; Marsan, D., Bean, C. J., Steacy, S., and McCloskey, J.: Observation of diffusion processes in earthquake populations and implications for the predictability of seismicity systems, J. Geophys. Res., 105, 28081–28094, 2000.; Mizoguchi, K., Fukuyama, E., Kitamura, K., Takahasi, M., Masuda, K., and Omura, K.: Depth dependent strength of the fault gouge at the Atotsugawa fault, central Japan: a possible mechanism for its creeping motion, Phys. Earth Planet. In., 161, 115–125, 2007.; Morrow, C. A., Moore, D. E., and Lockner, D. A.: The effect of mineral bond strength and adsorbed water on fault gouge frictional strength, Geophys. Res. Lett., 27, 815–818, 2000.; Okubo, P. G. and Aki, K.: Fractal geometry in the San Andreas fault system, J. Geophys. Res., 92, 345–355, 1987.; Pomeau, Y. and Le Berre, M.: Critical speed-up vs critical slow-down: a new kind of relaxation oscillation with application to stick-slip phenomena, arXiv: 1107.3331v1, 2011.; Reddy, D., Sen, A., and Johnston, G.: Time delay induced death in coupled limit cycle oscillators, Phys. Rev. Lett., 80, 5109–5112, 1998.; Rice, J. R.: Constitutive relations for fault slip and earthquake instabilities, Pure Appl. Geophys


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