Earthquake clustering in space as a percolation problem

The clustering of earthquakes in space is a well established observational fact. This effect is directly related to the space-time correlations between events which play a critical role in earthquake processes. One of the main aims of this work is to investigate the dynamic evolution in time and statistical properties of earthquake clusters defined using the framework of a percolation problem. A seismogenic zone is divided into a grid of square boxes. We consider earthquakes greater than a specified magnitude that occur within a specified time window. A spatial box is occupied if one or more earthquakes occur within it. Adjacent occupied boxes define a cluster. Using this approach one can define the radius of gyration for each cluster and calculate the correlation length in the seismogenic region. The correlation length can be used as a measure of spatial correlations of seismicity and plays a fundamental role in studies of critical phenomena. Well defined variations in radii of gyration and correlation lengths are found for aftershock sequences. The change in correlation length might be also used as a precursor to large events, although this effect is not well observed and remains controversial. In the work, the physical basis of spatial correlations of earthquakes will be discussed in the context of critical phenomena and percolation problem. In addition we have obtained scaling laws for the correlation functions of earthquake clusters. We have also obtained the variations in time of the correlation function and correlation length associated with the spatial and temporal processes in seismogenic regions.