Fractal properties of spatial distributions of aftershocks and active faults

The relationship between the fractal dimensions of spatial distributions of aftershocks and pre-existing active faults is examined. Fourteen mainshocks taking place in Japan were followed by aftershocks, and the aftershocks occur in swarms around the mainshocks. The epicentral distributions of the aftershocks exhibit fractal properties, and the fractal dimensions are estimated by using the two-point correlation integral. The pre-existing active fault systems observed in the 14 aftershock regions have fractal structures, and the fractal dimensions are estimated by using the box-counting method. A positive correlation between the estimated fractal dimensions is found, and it is independent on the mainshock magnitude. The correlation shows that aftershock distributions become less clustered with increasing the fractal dimensions of active fault systems. Namely, the fractal clusters of aftershocks are put under the constraint of the fractal properties of the pre-existing active fault systems. If the fractal dimension of active fault system is the upper limit value of the fractal dimension of actual rock-fracture geometries, then the spatial clustering of aftershocks shows completely random and unpredictable. The fractal structure of active fault systems is discussed to relate with self-organized criticality in a nonconservative model of earthquakes and "cumulative Benioff strain-release relationship" associating the total sum of the square root of the energy released for sequential fracture events to the time prior to the collapse failure.