Turbulencelike Behavior of Seismic Time Series

We report on a stochastic analysis of Earth’s vertical velocity time series by using methods originally developed for complex hierarchical systems and, in particular, for turbulent flows. Analysis of the fluctuations of the detrended increments of the series reveals a pronounced transition in their probability density function from Gaussian to non-Gaussian. The transition occurs 5–10 hours prior to a moderate or large earthquake, hence representing a new and reliable precursor for detecting such earthquakes.

Figure 1

Continuous deformation of the increments’ PDFs for the $M=7.1$ earthquake for, from top to bottom, $s=200$, 400, 600, and 800 ms and (a) far from and (b) close to the earthquake. Solid curves are the PDFs based on Eq. (2), while dashed curves are the Gaussian PDF.

Figure 2

Scale dependence of ${\lambda }_s^2$ vs $\log s$. (a) The $M=7.1$ event, far from [data set (I)] and close to [data set (II)] the earthquake. For data set (I) and $s>700\mathrm{ms}$, ${\lambda }_s^2\to 0$, implying that the increments’ PDF is Gaussian, but, for data set (II), ${\lambda }_s^2$ deviates strongly from 0 for $700\mathrm{ms}<s<1500\mathrm{ms}$. (b) The same as in (a), but for the $M=6.1$ event. When ${\lambda }_s\to 0$ the error bars are about the same size as the symbols.

Figure 3

The correlation function $C^{(s)}(\tau )$ for the data; bold symbols, data set (I) far from, and open symbols, set (II) close to, the $M=7.1$ event.

Figure 4

The local temporal dependence of ${\lambda }_s^2$ and the flatness for $s=800\mathrm{ms}$, over a one-hour period, for the $M=7.1$ and $M=6.1$ events, indicating a gradual, systematic increase on approaching the earthquakes.

Figure 5

(a) The data for the $M=5.4$ earthquake in California. (b) and (c) show the local temporal dependence of ${\lambda }_s^2$ for $s=500\mathrm{ms}$, collected at stations with a distance $d$ from the epicenter. The station at $d=128\mathrm{km}$ provides the alert, whereas the other station does not.