Figure 1

Manner in which information on the latest occurrence rate reduces the uncertainty in the interevent interval before the next earthquake. (a) Earthquakes with magnitudes greater than or equal to a given threshold ($M⩾M_c$) are treated here as unit events. Their occurrence rate $\lambda$ is defined as the number of events in the observation window that terminates at the most recent event divided by the duration $w$ of the window, and $\tau$ is the interevent interval between the most recent event and the next event. (b) A scatter plot of the interevent interval $\tau$ versus the latest rate $\lambda$. (Data were taken from the SCSN catalog for a threshold magnitude $M_c=2.0$ and for an observation window $w=$10 hours) The raw distribution of interevent intervals $P(\tau )$ is condensed into the conditional distribution $P(\tau |\lambda )$ due to information regarding the latest rate $\lambda$, as shown by the red line in (b).Reuse & Permissions

Figure 2

Dependence of the mutual information $I(\tau ,\lambda )$ between the interevent interval $\tau$ before the next earthquake and the latest occurrence rate $\lambda$ on the observation window $w$ (over which the occurrence rate is defined). Various threshold magnitudes $M_c$ are examined for four seismic catalogs: southern California, New Zealand, Japan, and the entire earth.Reuse & Permissions

Figure 3

Comparison of the latest rate $\lambda$ with the preceding interevent interval ${\tau }_{-1}$, with respect to the relevance to the next interevent interval $\tau$. (a) The average number of events contained in the 10 hours observation window. (b) The difference between $I(\tau ,\lambda )$ and $I(\tau ,{\tau }_{-1})$ for various seismic data examined in Fig. 2. That the values are positive indicates that information based on the latest rate $\lambda$ is superior to information based on the preceding interevent interval ${\tau }_{-1}$ for reducing the uncertainty in the occurrence of the next earthquake.Reuse & Permissions

Figure 4

(a) A method for segmenting an entire sequence to construct active and inactive sequences according to whether the event intervals belong to the aftershock periods of mega-earthquakes or not. (b) and (c) The mutual information computed for the active and inactive sequences, respectively. Various aftershock periods defined for a range of mega-earthquakes are tested [32]. Data were taken from the SCSN catalog with $M_c=2.0$.Reuse & Permissions

Figure 5

(a) Conditional distributions of interevent intervals given low and high latest rates, $P(\tau |$ the lowest 1/8 $\lambda )$ and $P(\tau |$the highest 1/8 $\lambda )$. (The optimal observation window sizes are 8.0, 10.5, 8.0, and 18.4 h for $M_c=$ 2.0, 2.5, 3.0, 3.5, respectively.) (b) Those given short and long preceding interevent intervals, $P(\tau |$ the lowest 1/8 ${\tau }_{-1})$ and $P(\tau |$the highest 1/8 ${\tau }_{-1})$. In (a) and (b), an open (solid) symbol represents the distribution for a low (high) value for the latest occurrence rate $\lambda$ (a) or the long (short) preceding interevent interval ${\tau }_{-1}$ (b). (c) The variances of the interevent intervals given the latest rate, $\langle \Delta {\tau }^2\rangle {}_{\lambda }$ (solid line), and those given the previous interevent interval, $\langle \Delta {\tau }^2\rangle {}_{{\tau }_{-1}}$ (dashed line). Data were taken from the SCSN catalog.Reuse & Permissions