Discussions on fractals, aftershocks, and active faults: Diffusion and seismo-electromagnetism

Aftershocks following a mainshock can be quantified by using fractal concepts, and active faults observed in the Earth's surface are fractal objects. Here, fractals, aftershocks, and active faults are discussed, reviewing the rates of aftershock decay and the fractal structure of pre-existing active-fault systems and referring to fractal properties of spatial distributions of aftershocks and pre-existing active faults. Moreover, the discussion is extended to aftershock diffusion, invoking our result of the correlation between aftershock spatial distributions and earthquake fault lengths. Finally, the fractal structures of active faults' are discussed with: seismo-electromagnetism (seismo-electromagnetic phenomena and seismo-electric/magnetic fields), in relation to the concepts of self-organized criticality in a non-conservative earthquake model and "cumulative Benioff strain-release relationship" that can suggest the discrete scale-invariant process of sequential fractures. This paper demonstrates that the message of the importance of pre-existing geometrical structures is a crucial one. The examinations of the geometrical structures of pre-existing active-fault systems with aftershock diffusion and seismo-electromagnetism are open challenges in the Earth Sciences.