Anomalous fluctuations of vertical velocity of Earth and their possible implications for earthquakes

High-quality measurements of seismic activities around the world provide a wealth of data and information that are relevant to understanding of when earthquakes may occur. If viewed as complex stochastic time series, such data may be analyzed by methods that provide deeper insights into their nature, hence leading to better understanding of the data and their possible implications for earthquakes. In this paper, we provide further evidence for our recent proposal [P. Mansour et al., Phys. Rev. Lett. 102, 014101 (2009)] for the existence of a transition in the shape of the probability density function (PDF) of the successive detrended increments of the stochastic fluctuations of Earth’s vertical velocity $V_z$, collected by broadband stations before moderate and large earthquakes. To demonstrate the transition, we carried out extensive analysis of the data for $V_z$ for 12 earthquakes in several regions around the world, including the recent catasrophic one in Haiti. The analysis supports the hypothesis that before and near the time of an earthquake, the shape of the PDF undergoes significant and discernable changes, which can be characterized quantitatively. The typical time over which the PDF undergoes the transition is about 5–10 h prior to a moderate or large earthquake.

Figure 1

(Color online) (a) The increments’ PDFs for the $M=7.2$ event near south of coast of western Honshu, Japan, for $s=800\text{ms}$, and for far from, and close to, the event. Solid curves are the PDFs based on the cascade model. (b) Scale-dependence of ${\lambda }_s^2$ versus $\text{log}s$. (c) The local temporal dependence of ${\lambda }_s^2$ for $s=800\text{ms}$, over a 1 h period, indicating a gradual, systematic increase as the earthquake approaches.

Figure 2

(Color online) Time-dependence of the non-Gaussian parameter ${\lambda }_s^2$ for the 9 earthquakes that were analyzed. See the text for the location and date of the events.

Figure 3

(Color online) The correlation functions $C^{\left(s\right)}\left(\tau \right)$ for the 9 earthquakes that are analyzed in Fig. 2. See the text for the location and date of the events.

Figure 4

(Color online) Continuous deformation of the increments’ PDFs for the 2010 Haiti earthquake for, from top to bottom, $s=250$, 500, 750, 1000, 1250 ms, and (a) far from, and (b) close to the earthquake. The solid curves are the PDFs based on Eq. (2), while the dashed curves are the Gaussian PDF.

Figure 5

(Color online) Dependence of the non-Gaussian parameter ${\lambda }_s^2$ on the time scale $s$, both close to the earthquake and away from it. The results are for the 2010 Haiti earthquake.

Figure 6

(Color online) Dependence of ${\lambda }_{s=250}^2$ (see Fig. 5) of the time as the Haiti earthquake is approached. The results indicate that 5 h before the earthquake the value of ${\lambda }_{s=250}^2$ suddenly increases, hence signaling the transition in the PDF. On the scale of the figure the velocity appears flat, but its fluctuations can be seen on a more refine horizontal axis.