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[SCG44-12] Condition for the transition from slow to fast earthquakes analyzed by the BK model with the interaction among heat, fluid pressure, and porosity
Keywords:slow earthquake, fast earthquake, transition, heat, fluid pressure, porosity
Transition from slow to fast earthquakes is a controversial problem. The purpose of this presentation is giving the condition for the transition using the quasi-1D Burridge-Knopoff (BK) model with the interaction among the heat, fluid pressure, and porosity. The blocks are considered to be thermoporoelastic media, and we put them on the thermoporoelastic substrate. They are connected with the upper substrate by the upper-springs, and they are also connected to the adjacent blocks by the side-springs. The interaction among three quantities is considered within the zone above the contact plane between the blocks and substrate. This zone, referred to as slip zone, is assumed to have finite height. The upper substrate is assumed to move rightward with the constant speed, and the accumulated strain in the upper-springs due to the motion induces dynamic slip. During the dynamic slip, the generation of pores (frictional heating) reduces (raises) the fluid pressure, increases (reduces) the friction stress and reduces (increases) the slip velocity. The slow and fast earthquakes are dominated by the generation of pores and the frictional heating, respectively. Moreover, the porosity decreases in the interval between successive earthquakes, which is called the porosity-healing effect. We also consider the heat and fluid diffusion effects in that interval. Based on this model, repeating of the slow earthquakes is confirmed to be quasi-cyclic, and finally the transition to the fast earthquakes emerges.
We now discuss the condition thatthe transition emerges. From the governing equations for the temperature T, fluid pressure p, and porosity phi within the slip zone, we can express p as a function of the slip u. We employ the initial condition just before the first slow earthquake, and obtain p as a function of u, which is referred to as the original p-u curve. After that the observed p-u curve differs from the original p-u curve because the system repeats the stick-slip behavior. However, the discussion of the condition for the transition to occur was confirmed to be possible based on the original p-u curve as follows.
With the original p-u curve, we can obtain the slip distance um with which p takes the minimum value. Note that the fluid pressure tends to decrease and increase during the slow and fast earthquakes, respectively. We can expect that the transition never occurs before the accumulated slip exceeds um for the original p-u curve. We confirmed that um gives a lower bound of the critical slip distance for the transition for the observed p-u curve. Note that even if u exceeds um, we cannot conclude that the transition occurs. The condition u > um is a necessary condition, and not a sufficient condition, for the transition to occur.
We now discuss the condition thatthe transition emerges. From the governing equations for the temperature T, fluid pressure p, and porosity phi within the slip zone, we can express p as a function of the slip u. We employ the initial condition just before the first slow earthquake, and obtain p as a function of u, which is referred to as the original p-u curve. After that the observed p-u curve differs from the original p-u curve because the system repeats the stick-slip behavior. However, the discussion of the condition for the transition to occur was confirmed to be possible based on the original p-u curve as follows.
With the original p-u curve, we can obtain the slip distance um with which p takes the minimum value. Note that the fluid pressure tends to decrease and increase during the slow and fast earthquakes, respectively. We can expect that the transition never occurs before the accumulated slip exceeds um for the original p-u curve. We confirmed that um gives a lower bound of the critical slip distance for the transition for the observed p-u curve. Note that even if u exceeds um, we cannot conclude that the transition occurs. The condition u > um is a necessary condition, and not a sufficient condition, for the transition to occur.