Effect of Non-Linearity of Stiffness during the Nucleation Phase of an Earthquake

Stiffness plays an important role in the earthquake rupture dynamics. At the main slip zone, the response of the system following a solicitation is both a function of stiffness and the heterogeneity of the surroundings. This work studies the effect of heterogeneity of Earth crust, particularly the effect of spatial dependence of stiffness during the nucleation phase of an earthquake. Based on Burridge Knopoff's ۱D model, we have redesigned the dynamics of an earthquake, taking into account the spatial variation of stiffness. Given the complexity of the differential system obtained, a digital approach was used to trace solutions to the problem. We represented the variation curves of temperature, energy and displacement as well as the speed obtained when the rigidity is constant (CS) and when the stiffness is nonlinear (NLS). Then a comparative study was conducted between the two cases. The result show that by considering the space-dependent of stiffness, the stick-slip movements occurred and a succession of oscillations with decreasing amplitude in time, separate to the case where it was considering to be constant. The non-linearity of the stiffness reveals that each oscillation is separated from the next by a coseismic phase. For non-linearities of order one and in the presence or absence of a fluid, the spatial dependence of stiffness suggests the existence of a seismic motion with decreasing amplitude, which always precedes by a steady state when the stiffness is nonlinear, which is not the case when the stiffness is constant; moreover, the amplitude of the movement decreases with the increase in the pore-fluid ratio. For nonlinearities of order three and in the presence of a fluid, the introduction of heterogeneity into the motion reduced the charging time before any seismic activity. Besides, it reveals existence of a transient phase that appears before steady state during nucleation phase. When going from TP to SH law and also to VW law, a quantitative difference is observed, which is not the case for a qualitative difference on these different laws. This work shows that before observing a steady state during nucleation, there are a multitude of micro seismic activity characterized by oscillations with time decreasing amplitudes.

کلیدواژه ها:

Nucleation phase ، Non-linearity ، anisotropy ، Elasticity coefficient ، Dimensional Velocity