Scaling characteristics in aftershock sequence of earthquake

The possible scale-invariant behavior and the clustering characteristics in aftershock sequence of Chi-Chi (Taiwan) main earthquake (ASCCME) that occurred in 1999/9/20/17/47 were investigated by means of some statistical tools: histogram, spectral analysis, and fractal theory. The examined data were constructed from the aftershocks that occurred at the locations defined at longitude 120.1-121.3 and latitude 23.3-24.5 during the 1999/9/20/17/47-1999/9/24/08/13 period. It was found that the aftershock sequence exhibited the characteristic right-skewed frequency distribution and could be well described with the lognormal distribution. Long-term memory and the possibility of scale invariance were first roughly identified through the analysis of autocorrelation and power spectrum, respectively. Scale invariance was clearly revealed with the aid of box-counting method and the box dimension was shown to be a decreasing function of the threshold magnitude level, i.e., the weak and intense regions scaled differently. To verify the existence of multifractal characteristics, the aftershock sequence was transferred into a useful compact form through the multifractal formalism, namely, the τ(q)-q and f(α)-α plots. The analysis confirmed the existence of multifractal characteristics in the examined aftershock sequence. The origin of both the pronounced right-skewness and multifractal phenomena in aftershock sequence might be interpreted in terms of the multiplicative cascade process of the stress in the Earth's crust. A simple two-scale Cantor set with unequal scales and weights was then used to fit the calculated τ(q)-q plot. This model fitted remarkably well the entire spectrum of scaling exponents of the examined ASCCME.