Origin and Nonuniversality of the Earthquake Interevent Time Distribution

Many authors have modeled regional earthquake interevent times using a gamma distribution, whereby data collapse occurs under a simple rescaling of the data from different regions or time periods. We show, using earthquake data and simulations, that the distribution is fundamentally a bimodal mixture distribution dominated by correlated aftershocks at short waiting times and independent events at longer times. The much-discussed power-law segment often arises as a crossover between these two. We explain the variation of the distribution with region size and show that it is not universal.

Figure 1

Interevent time histogram for the Southern California Earthquake Center (SCEC) catalog, plotted (a) without and (b) with normalization by the bin widths. Events larger than magnitude 2.4 between 1984 and 2000 were used. Interevent time histogram for the worldwide Preliminary Determination of Epicenters (PDE) catalog, plotted (c) without and (d) with normalization by the bin widths. Events larger than magnitude 5.0 between 1970 and 2006 were used.

Figure 2

Cartoon illustrating how varying the independent event rate changes the proportion of correlated to independent interevent times as a consequence of the degree of overlap of triggered aftershock sequences. (a) Regional catalogs tend to resolve aftershock sequences; (b) Because of the increased independent event rate, global catalogs tend to contain more temporal overlapping and thus more independent interevent times.

Figure 3

Synthetic interevent time histograms for three ETAS simulations with $\mu$ values as indicated, plotted (a) without and (b) with normalization by the bin widths. These few examples demonstrate the range of behavior observed in real earthquake interevent time distributions (Fig. 1). The other ETAS parameters used were $A=10$, $\alpha =1$, $c=0.01$, and $p=1.2$.

Figure 4

Interevent time histograms for four ETAS simulations with $\mu$ values (a) 10.751, (b) 0.187, (c) 0.047, and (d) 0.002, plotted without normalization by the bin widths. Correlated (triangle) and uncorrelated (cross) interevent times are shown together with their sum, all interevent times (circle). The other ETAS parameters used were $A=10$, $\alpha =1$, $c=0.01$, and $p=1.2$.

Figure 5

Interevent time (IET) histograms for 11 ETAS simulations with $\mu$ values as indicated, plotted with normalization by the bin widths, rescaled by the mean event rate $\mathrm{r}$ in the manner of Corral. Data collapse is not observed. The other ETAS parameters used were $A=10$, $\alpha =1$, $c=0.01$, and $p=1.2$.