Hierarchical seismic sources model and recent observational evidence

Earthquakes are multiscale phenomena with several scale invariant parameters, such as stress drop, apparent stress, and rupture propagation velocity, and dynamic rupture grows almost self-similarly. While the rupture process is always complex, the location of sources is not completely random, but nearly predetermined, especially along a well-developed fault system like a plate interface. To explain such behavior, some hierarchical structure is required, and one candidate is the hierarchical circular patch (fractal asperity) model suggested by Ide and Aochi (JGR, 2005) and Aochi and Ide (JGR, 2009), in which fracture energy inside a patch is proportional to the patch radius. In this paper, we review the characteristics of the model and show some observational evidence, which has been recently discovered mainly for subduction-type earthquakes in the Tohoku-Oki, Japan, region. Some hierarchical patch-like structure has been identified for several repeating earthquakes of M~5 (Uchida et al., GRL, 2012; Okuda and Ide, EPS, 2018). Identical onsets of seismic waves were observed for many pairs of large (M>4.5) and small (M<4.0) earthquakes (Okuda and Ide, Nature Communications, 2018; Ide, Nature, 2019). We can also observe long-term increase of seismicity before the rupture of system-size events (Okuda et al., Zishin, 2018). These lines of evidence suggest the qualitative validity of the hierarchical model and will be useful to improve the quantitative aspects of the model, such as patch density and the slip-weakening rate, to numerically simulate realistic earthquakes and seismicity (e.g., Aochi and Ide, EPS, 2011; Ide and Aochi, Tectonophysics, 2013; Aochi and Twardzik, Pageoph, 2019).