Natural time analysis of global seismicity: the identification of magnitude correlations

Natural time [1-6] can reveal novel dynamical features hidden behind the time series of complex systems, for a review see Ref.[7]. In a time series comprising N earthquakes, the natural time χk = k/N serves as an index for the occurrence of the k-th event[1, 5, 6], and is smaller than or equal to unity. In natural time analysis of seismicity, the evolution of the pair of two quantities (χk, Ek) is considered, where Ek denotes the energy emitted during the k-th earthquake. It has been proposed[5] that the variance κ1 of natural time can play the role of an order parameter for seismicity. Moreover, when using natural time the identification of temporal correlations-even in the presence of heavy tails in the data- becomes possible[6]. Thus, natural time analysis enables the identification of magnitude correlations between successive earthquakes[8]. By analyzing in natural time[9] the worldwide seismicity from the Harvard Global Centroid Moment Tensor Catalog as reported by the United States Geological Survey as well as the most recent version (1900-2007) of the Centennial earthquake Catalog[10], we find non-trivial magnitude correlations for earthquakes of magnitude greater than or equal to 7.