Fractal structure and characteristic scale in the distributions of earthquake epicentres, active faults and rivers in Japan

Using a box-counting method, we examined the fractal structures of the spatial distributions of three geological systems in Japan, namely those of earthquake epicentres, active faults, and rivers. Our results show that, in the scale range from 1 to 100  km, all geological systems have a common characteristic scale of ~13  km, which divides the spatial distribution into two bands: a smaller scale r < 13  km and larger scale r > 13  km (where r is the box size). In both bands, the three systems obey a power law distribution, and therefore it is proposed that all geological systems have a band-limited fractal structure. Since the characteristic scale of ~13  km is in agreement with the depth of the brittle–ductile transition zone of the crust, we suggest that it is a common feature of the heterogeneity of the crust.