Dynamic rupture propagation on a 2D fault with fractal frictional properties

摘要

We study dynamic rupture propagation on a 2D fault with a spatially heterogeneous slip-weakening friction law under a homogeneous stress condition. The slip-weakening distance D_c is determined based on fault topography, characterized by the fractal dimension δ and a normalized slip-weakening distance D_{c 0}. Assuming different combination of these parameters, we carry out a large number of dynamic rupture simulations to discuss event size statistics and the scaling relations of macroscopic parameters such as seismic moment, rupture velocity, seismic energy, and radiation efficiency. All stopped events obey an approximately power-law size-number relation. However, statistically self-similar rupture propagation is observed only for selfsimilar fault topography with δ = 1, where the average rupture velocity is controlled by D_{c 0}. This suggests that a power-law size-number relation does not simply mean the self-similarity of rupture process. Both upper and lower fractal limits in fault topography disturb the power-law statistics and the lower fractal limit results in excess of events of the characteristic size. The facts that slow ruptures can radiate large seismic energy and that fast ruptures are not always efficient suggest the importance of local acceleration, deceleration, and arrest of rupture. We also show that the spatial regularity of slip-weakening distance is essential to make the above results.