13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- Assisi [14,15]. Progressively lower frequencies of detected AE seemed consistent with the theory that high-frequency AE can be associated with the progress of small lesions of the crust, which later coalesce to form defects growing bigger and bigger. In order to correlate the peaks of AE activity to seismic precursors mentioned earlier, it was observed that the fumes of radon occur almost simultaneously with the AE peaks about 7-8 months before the earthquake. Therefore, the potential of earthquake prediction related to the AE monitoring appears promising, since the AE signals may be picked up in advance [14]. 4.1. Correlation algorithms between AE and seismic events Among the various studies on the earthquakes space-time correlation, there is a statistical method that allows to calculate the degree of correlation both in space and time between a series of AE and the local seismic recordings, collected in the same period. This analysis is based on the generalization of the space-time correlation known as the integral of Grassberger-Procaccia [17], defined as follows: 1 1 1 ( , ) ( ) ( ) EQ AE N N k j k j k j EQ AE C r r x x t t N N τ τ = = ≡ Θ − − Θ − − ∑∑ (1) where NAE is the number of peaks of AE activity registered in site and in a defined time window, NEQ is the number of earthquakes recorded in the surrounding area during the same time window, and Θ is the step function of Heaviside ( ( ) 0 x Θ = if 0 x≤ , ( ) 1 x Θ = if 0 x > ). The index k refers to the recorded seismic events { } , k k x t , while the index j refers to the recorded AE events { } , j j x t . Therefore, between all possible pairs of recorded AE and seismic events, the sum expressed by the integral of Grassberger-Procaccia is valid for those having the epicentral distance k j x x r − ≤ and the temporal distance k j t t τ − ≤ . Hence, C(r, τ ) is the probability of occurrence of two events, an earthquake and an AE event, whose mutual spatial distances are smaller than r and mutual temporal distances are smaller than τ. Anyway, this approach does not consider the chronological order of the two types of event. Since the AE time series and the earthquake sequences are closely intertwined in the time domain, the problem of the predictive ability of the AE peaks is still open, and the records of noise could be the consequences of the progressive development of micro damage. However, a probabilistic response sought by considering the first AE events as precursors and later as aftershocks of an earthquake is utilized. This analysis is performed by using a modified correlation integral [7]: ( ) ( ) ( ) ( ) ( ) j k j k N k N j j k EQ AE t t t t r x x N N C r EQ AE Θ − − Θ − − Θ± − ≡ ∑∑ = = ± τ τ 1 1 1 , (2) where "+" and "-" in the Heaviside function are used to take into account that the AE events could be respectively seismic precursors and aftershocks.
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