Are Earthquake Magnitudes Clustered?

The question of earthquake predictability is a long-standing and important challenge. Recent results [Phys. Rev. Lett. 98, 098501 (2007); Phys. Rev. Lett.100, 038501 (2008)] have suggested that earthquake magnitudes are clustered, thus indicating that they are not independent in contrast to what is typically assumed. Here, we present evidence that the observed magnitude correlations are to a large extent, if not entirely, an artifact due to the incompleteness of earthquake catalogs and the well-known modified Omori law. The latter leads to variations in the frequency-magnitude distribution if the distribution is constrained to those earthquakes that are close in space and time to the directly following event.

Figure 1

Differences in the cumulative distributions as a function of magnitude, $\delta P(m_0)$, for different magnitude thresholds $m_{\mathrm{th}}$. The (blue) dashed curve corresponds to $m_{\mathrm{th}}=2.5$ after correcting for STAI due to $m\ge 6$ earthquakes, while the (blue) dash-dotted curve excludes in addition all event pairs that are separated by less than 2 min. In the latter case the error bars correspond to the $3\sigma$ confidence intervals. In all other cases $1\sigma$ confidence intervals are shown. Inset: The (orange) solid curve corresponds to $m_{\mathrm{th}}=3.4$ after correcting for STAI. The (green) dashed curve corresponds to $\delta P_{l=5}(m_0)$ for $m_{\mathrm{th}}=2.5$ after correcting for STAI. $2\sigma$ confidence intervals are shown.

Figure 2

Differences in the cumulative distributions as a function of magnitude $m_0$, for $r_0=10\mathrm{km}$ and $m_{\mathrm{th}}=2.5$ after correcting for STAI due to $m\ge 6$ earthquakes. See text for details on the definitions. The error bars correspond to the $1\sigma$ confidence intervals.

Figure 3

Conditional and unconditional frequency-magnitude distributions for $r_0=10\mathrm{km}$ and $t_0=1\mathrm{h}$.