14:15 〜 14:30
[SCG39-09] Feasibility of periodic solution in Rate-State friction Law
キーワード：速度状態依存摩擦法則、非線形解析
Slow earthquakes are phenomena with a wide range of time scales and a variety of characteristics. Among them, slow slip event (SSE) has a remarkable feature of periodic motion. For example, off the coast of Tohoku, the subduction rate fluctuates with a period of about three years. In addition to that, interestingly, relatively large earthquakes have occurred at the timing of accelerated slip (Uchida et al., 2016).
Since the mechanism of periodic occurrence of SSE is not clear, various models have been proposed. As a quasi-static model, the "fault patch model" has been used in many studies. In this model, a patchy sliding region is considered to exist on the fault plane. The sliding behavior is determined by considering the balance between elastic forces and friction (determined by the Rate-State friction law) on the patch region. However, there is a problem with this model. When the sliding behavior is examined numerically, the solution diverges. To prevent divergence, the effect of elastic wave radiation (radiation damping) is conventionally used (Rice 1993). However, since this model is quasi-static, elastic waves are not generated. Also, if elastic waves do occur, the model cannot be used as an SSE. Therefore, radiation damping is not a solution to the problem.
First, in this study, we reconsider what kind of behavior appears after the slip becomes unstable without radiation damping. For this calculation, we use a nonlinear analysis method called Dulac's criterion. Using this method, the nonlinearity of friction is rigorously taken into account to determine the feasibility of the periodic solutions. As a result, it is shown that there are no periodic solutions and the solution diverges when the aging law, slip law, and Nagata's law (Nagata et al., 2012) is used.
In this study, we further devise a new evolution law that avoids divergence. Considering the wear effect, we create a new evolution law. By applying this law to the model, we show that it is possible to realize periodic solutions without divergence. We also confirm that the velocity dependence of the friction coefficient in steady-state is similar in the granite experiment (Kilgore et al., 1993). Finally, the period of the sliding behavior derived from the new law is discussed. Then, we consider what values of the parameters are suitable for SSE.
Since the mechanism of periodic occurrence of SSE is not clear, various models have been proposed. As a quasi-static model, the "fault patch model" has been used in many studies. In this model, a patchy sliding region is considered to exist on the fault plane. The sliding behavior is determined by considering the balance between elastic forces and friction (determined by the Rate-State friction law) on the patch region. However, there is a problem with this model. When the sliding behavior is examined numerically, the solution diverges. To prevent divergence, the effect of elastic wave radiation (radiation damping) is conventionally used (Rice 1993). However, since this model is quasi-static, elastic waves are not generated. Also, if elastic waves do occur, the model cannot be used as an SSE. Therefore, radiation damping is not a solution to the problem.
First, in this study, we reconsider what kind of behavior appears after the slip becomes unstable without radiation damping. For this calculation, we use a nonlinear analysis method called Dulac's criterion. Using this method, the nonlinearity of friction is rigorously taken into account to determine the feasibility of the periodic solutions. As a result, it is shown that there are no periodic solutions and the solution diverges when the aging law, slip law, and Nagata's law (Nagata et al., 2012) is used.
In this study, we further devise a new evolution law that avoids divergence. Considering the wear effect, we create a new evolution law. By applying this law to the model, we show that it is possible to realize periodic solutions without divergence. We also confirm that the velocity dependence of the friction coefficient in steady-state is similar in the granite experiment (Kilgore et al., 1993). Finally, the period of the sliding behavior derived from the new law is discussed. Then, we consider what values of the parameters are suitable for SSE.