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

The relationship between the fractal dimensions of aftershock spatial distribution and of pre-existing fracture systems is examined. Fourteen main shocks occurring in Japan were followed by aftershocks, and the aftershocks occurred in swarms around the main shock. Epicentral distributions of the aftershocks exhibit fractal properties, and the fractal dimensions are estimated by using correlation integral. Observable pre-existing active fault systems in the fourteen aftershock regions have fractal structures, and the fractal dimensions are estimated by using the box-counting method. The estimated fractal dimensions derive positive correlation, showing independence from the main-shock magnitude. The correlation shows that aftershock distributions become less clustered with increasing fractal dimensions of the active fault system. That is, the clusters of the aftershocks are constrained under 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 the fractal dimension of the actual fracture geometries of rocks, then the clustering aftershocks manifest completely random and unpredictable distribution.