GNGTS 2018 - 37° Convegno Nazionale

GNGTS 2018 S essione 2.1 347 with cov (EQ,EB) = [ P (EQ ∩ EB)− P (EQ) P (EB)], (4) and where P (EQ) and P (EB) are the independent probabilities of the earthquake and the electron burst occurrence, respectively. However, the correlation term appearing in relations (2) and (3) is not the same as the binary correlation defined in the past publications, which was ∑ {EQ;EB} (EQ x EB); (5) in fact, in (2) the cross-correlation coefficient can be both positive and negative. To find a link using (4) to obtain (3), the following expression can be used for the cross-correlation coefficient corr (EQ,EB) = ( E [EQ,EB] – E [EQ] E [EB])/√( E [EQ 2 ]- E 2 [EQ])( E [EB 2 ]− E 2 [EB]), (6) where E [] is the expectation. Being EQs ab EBs binary events E [EQ] = E [EQ 2 ] = P (EQ), E [EB] = E [EB 2 ] = P (EB) and the relation (6) can be rewritten throughout the population formula cov (EQ,EB) = [ N h ∑ {EQ;EB} (EQ x EB) – N EQ N EB ] / N h 2 , (7) where N EQ and N EB are the number of EQ and EB which participated in the correlation, respectively; while N h is the number of total hours considered for the correlation. Being so, the probabilities of single events are P (EQ) = N EQ / N h and P (EB) = N EB / N h . To evaluate them it can be considered that the observed correlation was calculated only when the geomagnetic activity was very low (Fidani, 2015; Fidani, 2018). It corresponds to only 996 days over 16.5 years, equal to 23,906 hours. Furthermore, the NOAA satellite moves in a synchronous orbit to the Sun’s position, going intermittently high offshore the USA and South American West Coasts only for about half a days time, the effective hours of detection reducing to N h = 11,953 hours. During the same time intervals, there were detected N EB = 1,051 EBs, so defining a P (EB) = 0.088, in other words the average of one EB every 11.4 hours. A total of 2,023 main shocks struck the earth surface in 16.5 years, which correspond to N EQ = 167 and therefore 122 EQs/ year, defining a P (EQ) = 0.014, in other words an average of one main shock with M ≥ 6 every 3 days. The cross-correlation coefficients were recalculated using (7) and the cross-correlation plot is shown in Figure 6, which now assumes both positive and negative values. Based on (7), the expression (2) can be simplified in P (EQ|EB) = ∑ {EQ;EB} (EQ x EB) / N EB , (8) and tell that the previous calculated correlations is proportional to the conditional probability, see Figure 3. Using the 2 – 3 hour correlation peak equal to 34 of Figure 1, the conditional EQ forecasting probability can be calculated in P (EQ|EB) = 0.032, and referring it to (6) it Fig. 3 - The conditional probability P (EQ|EB) calculated over 48 hours of T EQ -T EB time differences; the probability of a strong earthquake in one hour P (EQ), indicated by a dotted line, is the average of this histogram.