GNGTS 2015 - Atti del 34° Convegno Nazionale

14 GNGTS 2015 S essione 2.1 p(t,t+ τ ) = [F(t+ τ )-F(t)]/[1/r-F(t)] . It has been demonstrated that a frequency distribution of anomaly time can be successfully analysed by making use of a Weibull distribution (Rikitake, 1989). Being so, the cumulative probability of earthquake occurrence is obtained by F(t) = 1-exp[-Kt m+1 /(m+1)] , where K and m can be evaluated with R(t) = exp[-Kt m+1 /(m+1)] and taking the double natural logarithms of 1/R, one obtains ln[ln(1/R)] = ln[K/(m+1)] + (m+1)ln(t) , which is linearly related to ln(t) . ln[K/(m+1)] and (m+1) can be obtained by the least square method and so that parameters K and m can readily determined. The mean value of the precursor time t of the electric anomaly is given as E(t) = [K/(m+1)] -1/(m+1) Γ [(m+2)/(m+1)] where Γ is the gamma function, while the standard deviation of the mean value is given as σ = E(t) {Γ[ (m+3)/(m+1) ]-Γ 2 [ (m+2)/(m+1) ]} 1/2 / Γ[ (m+2)/(m+1) ]. Given that there is no clear cut-way of omitting spurius electric anomalies coming from meteorology, the parameter r must be evaluated. This can be done by counting the anomalies recorded during days with significant earthquakes near a CIEN station and without any meteorological (rainfall) activity for a radius of 100 km; called Ne . Therefore, the number of anomalies recorded during days with significant earthquakes and meteorology near the same CIEN station is called Nem . Furthermore, the number of anomalies recorded during days with meteorological activity near the CIEN station but not significant seismic activity (M < 2) inside a radius of 100 km is called Nm. Whereas, the number of anomalies with no seismic or meteorological activities near the CIEN station is called N . The parameter r can be proposed as r = Sqrt[(1 – N/Ne)(1 – Nm/Nem)/(1 + Nm/Ne)] . The probability defined in this way increases discontinuously when an anomaly is observed, whereas the probability decreases subsequently if no earthquake is observed. Randomoccurrence of anomalies leads to an appreciable increase in probability at an early period, although the probability during this period decreases fairly quickly. If many electric anomalies are observed, the probability tends to increase monotonically, see for example a calculation made for the 1923 Kanto earthquake in Fig. 3. Conclusions. Magnetic data recorded at the Chieti, Città di Castello and Avigliano CIEN stations suggest that electric perturbations recorded a these stations were characterised by magnetic intensities so small that, probably under the natural and anthropic noise levels, they are undetectable. The proposed model to explain electric perturbations (Fidani and Martinelli, 2015) seems to Fig. 3 – Changes in synthetic probability in logarithm of earthquake occurrence within one day (τ = 1) for the Kanto earthquake with r = 0.01; from p.166 of Rikitake (2001).