Spatial distribution of aftershocks and the fractal structure of active fault systems

The relationship between the fractal dimensions of aftershock spatial distr ibution and of pre-existing fracture systems is examined. Fourteen main sho cks occurring in Japan were followed by aftershocks, and the aftershocks oc curred in swarms around the main shock. Epicentral distributions of the aft ershocks exhibit fractal properties, and the fractal dimensions are estimat ed by using correlation integral. Observable pre-existing active fault syst ems in the fourteen aftershock regions have fractal structures, and the fra ctal dimensions are estimated by using the box-counting method. The estimat ed fractal dimensions derive positive correlation. showing independence fro m the main-shock magnitude. The correlation shows that aftershock distribut ions become less clustered with increasing fractal dimensions of the active fault system. That is, the clusters of the aftershocks are constrained und er the fractal properties of the pre-existing active fault systems. If the fractal dimension of the active fault system is the upper limit value of th e fractal dimension of the actual fracture geometries of rocks, then the cl ustering aftershocks manifest completely random and unpredictable distribut ion.