Do Earthquakes Exhibit Self-Organized Criticality?

If earthquakes are phenomena of self-organized criticality (SOC), statistical characteristics of the earthquake time series should be invariant after the sequence of events in an earthquake catalog are randomly rearranged. In this Letter we argue that earthquakes are unlikely phenomena of SOC because our analysis of the Southern California Earthquake Catalog shows that the first-return-time probability $P_M(T)$ is apparently changed after the time series is rearranged. This suggests that the SOC theory should not be used to oppose the efforts of earthquake prediction.

Figure 1

First-return-time distribution for actual data of the earthquake catalog. The Omori law is shown as the solid line. The inset shows the distribution for small $T$s in semilog coordinates—a straight line indicates an exponential distribution. For Figs. 1, 2, 3, 4 each data point represents an average of $P_{\mathrm{M}}(T)$ in a bin. In log-log plots a decade of $T$ is divided into three bins. In semilog plots uniform bin size is used. $T_{\mathrm{maximum}}(M)$ is the largest time separation for events of magnitude $m\ge M$.

Figure 2

Same as Fig. 1 but for magnitude-rearranged data. The Omori law is shown as the solid line.

Figure 3

Same as Fig. 1 but for totally rearranged (both magnitude and time of occurrence) data. The Omori law is shown as the solid line.

Figure 4

Same as Fig. 3 but with log-linear scale. The straight-line effect indicates an exponential distribution. $T_{\mathrm{maximum}}(M)$ is the largest time separation for events of magnitude $m\ge M$.

Figure 5

An analysis showing how SOC systems can have a power-law distribution for the first-return-time distribution. The falloff rate of the power law is “$-2$”.