Electromagnetic Signature of Prefracture Criticality in Heterogeneous Media

Fractal statistical analysis under the critical point (CP) hypothesis is applied to electromagnetic (EM) signals emitted before failure. A new approach to the analysis of a possible EM fractal pattern evolution toward CP is suggested. The analysis reveals characteristic signs of approaching the CP: the emergence of memory effects; the increase of the spatial correlation; the decrease of the antipersistence behavior; the appearance of persistence properties in the tail of the precursors, a loss of multifractality, and, finally, the divergence of the energy release rate. These critical features are compatible with the percolation theory of fracture process.

Figure 1

(a) Histograms of probability distribution of the correlation coefficient $r$ and exponent $\beta$ calculated on 1024 measurements segments for three consecutive time intervals (blue frames) marked in (b). Insets show the percentage of segments with $r>0.94$. (b) The time series of the 41 MHz field strength [4]. The star indicates the time of the earthquake occurrence. (c) The probability distribution of the exponent $\beta$ and the percentage of segments with $r>0.98$ for $3$ consecutive subintervals (purple frames) of $6\mathrm{h}$ duration each as marked in (b).

Figure 2

(a) The $\beta$ values are confined in the narrow range $\beta =1.5\pm 0.2$ during the last few hours of the prefailure period while the fit to the power law model remains excellent ($r>0.98$) for the whole extent of this period (see text). In the fence, the red stripes refer to 1024 measurements segments with ($1.3<\beta <1.7$ and $r>0.98$). A progressive increase of the time intervals showing these characteristics as the failure approaches is observed. (b) The temporal evolution of the spectral amplification $\alpha$ corresponding to segments with $r>0.98$, reveals a nearly exponential increase during the last several hours prior to the main event. The red circles correspond to segments with $r>0.98$. (c) The wavelet power spectrum of the 41MHz EM time series.

Figure 3

Two segments of the precursory 41 MHz EM signal, recorded on 12 May 1995 (upper row) and 13 May 1995 (lower row). On the right part of the figure the corresponding fractal dimensions $D(h)$ are presented.

Figure 4

(a) The 3 kHz EM emission before the K-G EQ [4]. (b) The power spectral density of the signal versus frequency. The straight lines reveal that the lower and higher frequencies follow a power law model with exponent $\beta$ taking values 1.04 and 2.91, respectively. (c) The fractal dimension $D(h)$ at small scales, which correspond to higher frequencies.

Figure 5

(a) The time series of the 10 kHz magnetic field variations [4]. The star indicates the time of the Athens EQ occurrence. (b) Histograms of probability distribution of the exponent $\beta$ calculated on 1024 measurements segments for four consecutive time intervals as marked in (a). Insets show the percentage of segments with $r>0.85$. (c) The distributions of the statistically dominant local Hurst exponents $h^{*}$ (see text) for two time periods (P1), (P2) noted in (b). (d) The evolution of Benioff cumulative strain release (BCS) and the Benioff cumulative EM energy release (BCEM) (see text). Provenance of seismicity data is http://www.gein.noa.gr/services/cat.html