**6. Interpretation of precursory kHz EM activity in terms of Intermittent Criticality**

The Intermittent Criticality (IC)-viewpoint of EQ dynamics is based on the hypothesis that a large regional EQ is the end result of a process in which the stress field becomes correlated over increasingly long scale-lengths, which set the size of the largest EQ that can be expected at any given time. The largest event on the fault network cannot occur until regional criticality has been achieved and stress is consequently correlated at all length scales up to the size of the region. The growth of the spatial correlation length obeys a power law with a singularity in the critical point [92-102]. This large event destroys, after its occurrence, the criticality on its associated network, creating a period of relative quiescence, after which the process repeats by rebuilding correlation lengths towards criticality and the next large event. In contrast to self-organized criticality, in which the system is always at or near criticality, intermittent criticality implies time-dependent variations in the activity during a seismic cycle. Before the large EQ, the growing correlation length manifests itself as an increase in the frequency of intermediate-magnitude earthquakes. This is commonly referred to as the "accelerating moment release model", and has been discussed by a number of authors [97,98]. Briefly, IC-approach includes self-organized criticality, growing spatial correlation length, and accelerating energy release.

A kHz EM anomaly can be interpreted as an EM confirmation of the IC-hypothesis. Indeed, a power-law type increase in the rate of EM energy release as the global instability approaches is observed [27,28,78]. The recorded acceleration of the EM emission leading up to EM large event and "EM shadow" following this is in harmony with the IC-hypothesis. Notice, the rate of seismic energy release computed around the epicenter of the EQ follows a similar 14 Will-be-set-by-IN-TECH

It is expected that a positive feedback mechanism results in a finite-time singularity. The kHz EM time series under study shows such a behaviour by means of the "cumulative Benioff type EM energy release". A clear finite-time singularity of this type has been reported in [27,28,78]. *Remark*: The estimated Hurst exponents through the R/S analysis are in harmony with those estimated from the fractal spectral analysis via the hypothesis that the time series follows the fBm-model [35,36]. This fact supports the hypothesis that the profile of kHz EM precursors follow the persistent fBm-model. The last hypothesis has been further verified by

**5.3 Footprints of universal roughness value of fracture surfaces in the kHz EM activity**

The Hurst exponent, *H*, specifies the strength of the irregularity ("roughness") of the fBm surface topography: the fractal dimension is calculated from the relation *D* = (2 − *H*) [83]. The Hurst exponent *H* ∼ 0.7 has been interpreted as a universal indicator of surface fracture, weakly dependent on the nature of the material and on the failure mode [86-90]. Importantly, the surface roughness of a recently exhumed strike-slip fault plane has been measured by three independent 3D portable laser scanners [91]. Statistical scaling analyses show that the striated fault surface exhibits self-affine scaling invariance that can be described by a scaling roughness exponent, *H*<sup>1</sup> = 0.7 in the direction of slip. In Section 5.2.1 we showed that the "roughness" of the profile of the kHz EM precursors, as it is represented by the Hurst exponent, is distributed around the value 0.7. This result has been verified by means of both fractal spectral analysis and R/S analysis [35,36]. Thus, the universal spatial roughness of fracture surfaces nicely coincides with the roughness of the temporal profile of the recorded kHz EM precursors.

**6. Interpretation of precursory kHz EM activity in terms of Intermittent Criticality** The Intermittent Criticality (IC)-viewpoint of EQ dynamics is based on the hypothesis that a large regional EQ is the end result of a process in which the stress field becomes correlated over increasingly long scale-lengths, which set the size of the largest EQ that can be expected at any given time. The largest event on the fault network cannot occur until regional criticality has been achieved and stress is consequently correlated at all length scales up to the size of the region. The growth of the spatial correlation length obeys a power law with a singularity in the critical point [92-102]. This large event destroys, after its occurrence, the criticality on its associated network, creating a period of relative quiescence, after which the process repeats by rebuilding correlation lengths towards criticality and the next large event. In contrast to self-organized criticality, in which the system is always at or near criticality, intermittent criticality implies time-dependent variations in the activity during a seismic cycle. Before the large EQ, the growing correlation length manifests itself as an increase in the frequency of intermediate-magnitude earthquakes. This is commonly referred to as the "accelerating moment release model", and has been discussed by a number of authors [97,98]. Briefly, IC-approach includes self-organized criticality, growing spatial correlation length, and

A kHz EM anomaly can be interpreted as an EM confirmation of the IC-hypothesis. Indeed, a power-law type increase in the rate of EM energy release as the global instability approaches is observed [27,28,78]. The recorded acceleration of the EM emission leading up to EM large event and "EM shadow" following this is in harmony with the IC-hypothesis. Notice, the rate of seismic energy release computed around the epicenter of the EQ follows a similar

a DFA-analysis [35,36].

accelerating energy release.

power-law type increase [27,28,78]. This experimental fact supports the hypothesis that both the seismicity and the preseismic EM activity represent two cuts in the same underlying fracture mechanism. Moreover, the spectral scaling exponent *β* (see Section 5.2) is a measure of the strength of time correlations. The *β*-values are significantly shifted to higher values as the EQ is approaching [27,28,78], namely, the correlation length in the time series increases as the catastrophic event approaches. Consequently, the two basic signatures predicted by the IC-model are included in the candidate kHz EM precursors.
