روابط مقیاس گذاری داده های لرزه ای زمین لرزه Scaling relation of earthquake seismic data

1. Introduction Earthquake is one of the most important and common natural phenomenon that directly affects human life and property. Therefore, scientists have been studying the genesis of earthquakes, earthquake forecast, hazard evaluation and other dynamics of earthquakes for a long history [1, 2]. It is widely believed that seismicity can be characterized by extremely rich phenomenology, and then some known empirical laws are summarized, for example, the Omori law [3] for the temporal pattern of aftershocks showing slow relaxation and the Gutenberg-Richter law [4] for describing the frequency of tremors of a given magnitude. In addition, physicists take earthquake dynamics as a scale invariant process and study the correlation between different shocks. Some studies claim that the spatial positions of earthquake epicenters can form fractal sets [5, 6]. The fractal dimension D proposed by Aviles, for instance, is used to measure the irregularity of the fault trace in the selected band and may changes significantly from the short-length band to the long-length band [5]. Kagan analyzed the fractal distribution of epicenters and discovered that seismicity is controlled by scale-invariant statistical distributions [6]. Burridge and Knopoff proposed a model for describing the slow creeping of the continental plates along the fault lines as a stick-slip process [7]. Bak et al. believed that the earthquake phenomenon can be regarded as a Self-Organized Critical process for studying the evolution of earthquakes and the scaling relations [8]. Although the correlations among different shocks have been studied, the actual mechanism of the underlying dynamics of this complex phenomenon has not been possible yet [1]. In a real complex system, detailed information on properties of system elements may not always be available, especially the interaction or correlation among them [9]. In such a situation, the network description offers a useful tool to build the relationships of system elements and mine the interactions between them. Scientists widely believe that complex network theory plays an increasingly pivotal role in revealing the complicated dynamics of real systems [10-13]. The vertices and the links connecting them respectively represent elements and their interaction or correlation.