GNGTS 2022 - Atti del 40° Convegno Nazionale

GNGTS 2022 Sessione 2.1 209 EQs and NOAA EBs. In fact, starting from Matthews correlations (Matthews, 1975), it can be shown that the conditional probabilities can be defined between EQs and EBs (Fidani, 2018). Moreover, correlation histograms calculated in past publications (Fidani, 2015), Σ {EQ;EB} (EQ x EB) (see Fig. 2), were put in relation with the Matthews correlation coefficients corr(EQ,EB) (Fidani, 2020). Being so, the next relations need to be evaluated retrieving the relations (4) and (5): P(EQ ∩ EQ+1|EB+Δt) = (6) = P(EQ ∩ EQ+1) + corr(EQ ∩ EQ+1,EB+Δt) {[1 – P(EQ ∩ EQ+1)] P(EQ ∩ EQ+1) [1/P(MA) − 1]}^½, P(EQ+1|EB+Δt) = P(EQ+1) + corr(EQ+1,EB+Δt) {[1 – P(EQ)] P(EQ) [1/P(MA) − 1]}^½, (7) P(EQ+1|EQ) = P(EQ+1) + corr(EQ+1,EQ) [1 – P(EQ)], (8) P(EB+Δt|EQ) = P(EB+Δt) + corr(EB+Δt,EQ) {[1 – P(EB)] P(EB) [1/P(EQ) − 1]}^½, (9) where P(EQ+1) = P(EQ), and corr(EB+Δt,EQ) = − corr(EQ,EB+Δt). The number of EQs that occurred during the 6953 pairs of hours were considered, which is N EQ = 57, and P(EQ) = 0.0082 EQs for each pair of hours. A N EB = 1892 EBs was considered in the same time interval, so that P(EB) = 0.27. Finally, a N EQ ∩ EQ+1 = 6 resulted in the same time interval, so that P(EQ ∩ EQ+1) = 0.000863 for each pair of hours. Then, calculating quantities (6-8) and summing in (4) for the couples of digital events, the transfer entropy is retrieved and shown in Figure 3, where mall negative terms of TE were set to 0 as by definition. A second peak, which does not appear in the correlation histogram of Figure 2, appears in the transfer entropy at a negative time delay Δt = 58.5 - 56.5 h. It represents a real novelty that arises from this analysis (Fidani, 2022). It means that EB shares a maximum amount of information with past EQs occurring around 2 days and 9.5 h before EBs. Given the significant reduction in the EQ auto-correlation due to the Cluster 2000 algorithm application (Reasenberg, 1985), the second peak in the present case is not very significant. Nevertheless, this is an example of how linear and non-linear contributions could be separated, making a distinction between correlation and auto-correlation in the particular case of binary events, respectively. Fig. 2 - The correlation event histogram between EQs and EBs with a Δt range of -48 to 48 hours, in intervals of 2 hours, which are shifted by 1.5 hours with respect to the origin.