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 spat ial distributions of three geological systems in Japan, namely those of ear thquake epicentres, active faults, and rivers. Our results show that, in th e scale range from 1 to 100 km, all geological systems have a common charac teristic scale of similar to 13 km, which divides the spatial distribution into two bands: a smaller scale r < 13 km and larger scale r > 13 bm (where r is the box size). In both bands, the three systems obey a power law dist ribution, and therefore it is proposed that all geological systems have a b and-limited fractal structure. Since the characteristic scale of similar to 13 km is in agreement with the depth of the brittle-ductile transition zon e of the crust, we suggest that it is a common feature of the heterogeneity of the crust.