ABSTRACT
Fractal nature has been widely found in geology and seismology under a variety of circumstances. It is concluded, from the studies of Okubo & Aki and Aviles et al. on fractal characteristics of the San Andreas Fault system, that fractal concepts can be applied in quantitative analyses of fault geometry. Thus, fractal temporal clustering of earthquakes is more representative since timing of events and the total length of time provide quite a wide range of scales for analyses. In this chapter, the authors focus on introducing the temporal fractal clustering of earthquakes. The basic idea of a fractal approach to clustering earthquakes proposed by Smalley et al. is that if the seismic events are taken as a 'point process' on the time axis, then the seismicity can be simulated by a random Cantor set. The computer-generated fractal topographies such as landscapes have been made by Voss, Feder, Clarke, Yfanitis et al. and Falconer by means of the fractional Brownian model.
