Fig. 46.

Interoccurrence time series and DFA from the Israeli, Italian and ETAS catalogs. (a) Interoccurrence time series between earthquake events from the Israeli (a) and Italian (b) catalogs using magnitude threshold $M_z$. DFA of the interoccurrence times from the (c) Israeli and (d) Italian catalogs with different $M_z$ values. (d) DFA of the interoccurrence times from the ETAS model, with parameters $A=6.26$, $\mu =0.2$, $p=1.1$, ${\alpha }_M=1.5$ and $c=0.007$, see Eq. (139). The solid line is the best fitting line with slope $\alpha =0.75$, R-square $>0.99$. For comparison, the shuffled data with slope $\alpha =0.5$, indicating no memory, are presented in (d).

Reprinted figure from Ref. [212].