Seismicity has fractal structures in space, time, and magnitude distributions, as expressed by the fractal dimension D, Omori's exponent p, and the b value, respectively. We expect that there is correlation among these scaling parameters. Aki (1981) speculated that there is a relation D = 3b/c (c = 1.5) between the b value and the fractal dimension D of fault planes. We point out that Aki's fractal dimension corresponds to the capacity dimension D0 and may be compared with the correlation dimension D2, obtained from the spatial distribution of earthquakes. By analyzing the actual earthquake catalogue, we calculated the fractal dimension D2 and the b value. Our result does not support Aki's speculation that D0 = 3b/c, but shows, on the contrary, that there is a negative correlation (D = 2.3 − 0.73b) between the b value and the fractal dimension of the spatial distribution of earthquakes in the Tohoku region.

A constant stress fracture experiment of Oshima granite was carried out at the confining pressure of 40MPa. Hypocentres of 2064 acoustic emissions were located during the experiment. Using the 'correlation integral', we found that the spatial distribution of hypocentres of acoustic emission is a fractal, and that the fractal dimension decreases with the evolution of rock fracturing. The spatial distribution of earthquake's hypocentres reveals fractals ranging from regional to worldwide distribution. If we extrapolate from laboratory measurements, it is possible to predict the occurrence of large earthquakes by the decrease in the fractal dimension.

A time series of acoustic emissions (AE) in basalt was measured under constant uniaxial compression. Some bursts of AE events considered to be the main shock and aftershock sequences were observed. Two models describing the aftershock sequences (the exponential decay model, n(t)= K exp (--pt), and the Omori's power law model, n(t) = K/(c + t) •', where n(t) denotes the occurrence rate of aftershocks at time t) were examined. With the progress of the fracturing process, the bursts changed from the exponential decay type to Omori's power law type, and the p value of Omori's power law aftershock sequences decreased. These results indicate that microfracturing gains a longer tail with the evolution of the fracture ....... ThP reproduction nr C}mnri'.q nower law aftershock seauences of AE events suggests that the self-similarity of rock fracturing holds good over a range from microfracturing to large earthquakes.

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