Effects of mesoscopic-scale fault structure on dynamic earthquake ruptures: Dynamic formation of geometrical complexity of earthquake faults

We develop a new hierarchical earthquake rupture model that takes into account mesoscopic-scale fault structure; shear branches nucleated on the main fault are specifically assumed as an example of mesoscopic-scale fault structure. We numerically investigate dynamic formation of fault geometry and its effects on dynamic earthquake rupture process based on this rupture model. As long as the length of the main fault is below a certain threshold L-m, the growth of these branches is shown to be arrested spontaneously soon after their nucleation. The spatial distribution of arrested branches is shown to form a self-similar geometrical structure. This suggests the existence of a simple scaling relationship between small and large events as long as the length of the main fault is below the threshold Lm. However, once the length of the main fault exceeds Lm, a limited number of branches begin unstable growth, and their sizes soon become comparable to that of the main fault. In other words, mesoscopic-scale branches are spontaneously transformed into macroscopic-scale ones. This finding indicates the critical importance of the consideration of mesoscopic-scale fault structure in understanding rupture dynamics: Once macroscopic-scale branches are formed, they change the fault geometry, which will considerably affect the rupture dynamics. The emergence of macroscopic branches suggests that the above mentioned simple scaling relation is never valid above a critical length Lm. Our study thus indicates that relationship between small and large earthquakes is complicated by the spontaneous transformation of a mesoscopic-scale fault structure into a macroscopic-scale one.