Statistical relations between the parameters of aftershocks in time, space, and magnitude

The correlation between statistical parameters of seismicity, such as the b value of the Gutenberg and Richter [1954] relation, the p value of the modified Omori formula [Utsu, 1961], the p and alpha value of the Epidemic Type Aftershock Sequence (ETAS) model [Ogata, 1992], and the fractal dimension D of the hypocenter distribution, is analysed for 34 aftershock sequences in Japan from 1971 to 1995. All the parameters are estimated using maximum likelihood methods along with their error assessments. For the majority of the aftershock sequences, the ETAS model fits statistically better than the modified Omori formula, which suggests existence of clusters within the aftershock sequence. Most of the scatterplots between the estimates of the seismicity parameters in time, space, and magnitude distributions are clearly seen to be either positively or negatively correlated. The contrasting correlation patterns are revealed between the estimated parameters for the intraplate and interplate earthquakes, except for the two pairs (b, D) and (alpha,p) in which similar correlation patterns are found. We focus our attention on these patterns as a source of interesting contrasts between the two earthquake groups. In particular, the significant dependence of these parameters on the depth appears to be a key to understanding: the correlation pattern for interplate aftershocks, while a different interpretation is made for intraplate aftershocks because no significant dependence on depth is observed.