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Chaotic behavior of earthquakes induced by a nonlinear magma up flow

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  • Pelap, F.B.
  • Kagho, L.Y.
  • Fogang, C.F.

Abstract

This paper considers the dynamics of a modified 1D nonlinear spring-block model for earthquake subjected to the strengths induced by the motion of the tectonic plates and the up flow of magma during volcanism. Based on the multiple time scales method, we establish that after the slip, the fault remains active and the frictions increase with the power of the earthquake. We also obtain in the non-resonance case that the appearing probability of an event decreases with these frictions. In the resonance case, the dynamics of harmonic oscillations show that the rocks constituting the block will fracture or resist to the effects induced by the magma motion. Our analytical investigations are complemented by numerical simulations from which it appears that, for given values of the magma thrust strength magnitude, the friction coefficient, the quadratic and cubic nonlinear parameters, the system exhibits chaotic behavior.

Suggested Citation

  • Pelap, F.B. & Kagho, L.Y. & Fogang, C.F., 2016. "Chaotic behavior of earthquakes induced by a nonlinear magma up flow," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 71-83.
    • Handle: RePEc:eee:chsofr:v:87:y:2016:i:c:p:71-83
    DOI: 10.1016/j.chaos.2016.03.018
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    References listed on IDEAS

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    1. Montagne, Raúl & Vasconcelos, Giovani L., 2004. "Complex dynamics in a one-block model for earthquakes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 178-185.
    2. Vasconcelos, Giovani L. & de Sousa Vieira, Maria & Nagel, Sidney R., 1992. "Phase transitions in a spring-block model of earthquakes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 69-74.
    3. Kostić, Srđan & Vasović, Nebojša & Perc, Matjaž & Toljić, Marinko & Nikolić, Dobrica, 2013. "Stochastic nature of earthquake ground motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 4134-4145.
    4. Christopher H. Scholz, 1998. "Earthquakes and friction laws," Nature, Nature, vol. 391(6662), pages 37-42, January.
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    Cited by:

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    3. Nkomom, Théodule Nkoa & Okaly, Joseph Brizar & Mvogo, Alain, 2021. "Dynamics of modulated waves and localized energy in a Burridge and Knopoff model of earthquake with velocity-dependant and hydrodynamics friction forces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).

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