Statistical physics approach to understanding the multiscale dynamics of earthquake fault systems

Abstract

[1] Earthquakes and the faults upon which they occur interact over a wide range of spatial and temporal scales. In addition, many aspects of regional seismicity appear to be stochastic both in space and time. However, within this complexity, there is considerable self-organization. We argue that the occurrence of earthquakes is a problem that can be attacked using the fundamentals of statistical physics. Concepts of statistical physics associated with phase changes and critical points have been successfully applied to a variety of cellular automata models. Examples include sandpile models, forest fire models, and, particularly, slider block models. These models exhibit avalanche behavior very similar to observed seismicity. A fundamental question is whether variations in seismicity can be used to successfully forecast the occurrence of earthquakes. Several attempts have been made to utilize precursory seismic activation and quiescence to make earthquake forecasts, some of which show promise. INDEX

Acoustic emission monitoring of medieval towers considered as sensitive earthquake receptors

“…Removing earthquakes lower than M L =2.5, a good agreement with the linear trend is found (see Fig. 7b), this skimming is consistent with the observational evidence that small earthquakes behave like background noise (Rundle et al, 2003). The intriguing observation on the similarity of the two b-values suggests that the b-value could be considered as an universal exponent characterizing both the earthquakes distribution and the AE activity monitored on the urban system.…”

Richter's laws at the laboratory scale interpreted by acoustic emission

“…10 The validity of this analogy has been confirmed by various authors, who demonstrated how the amplitude of the AE signals, associated with the formation of microcracks in the structural elements monitored, follows the GR power law frequency-magnitude statistics. 5,8,11 They also measured the cumulative energy in the acoustic emission activity and found that this activation is very similar to the power law seismic activation in the geological faults, as demonstrated by the second GR law.…”

“…10,11,14 In this section their theoretical interpretation based on the fractal approach is suggested.…”

“…This approach made it possible to verify the two semi-empirical GR laws, 10 widely used in seismology, whose fractal interpretation is very close to the essence of the AE phenomenon. 11,12 The fractal theory, based on the geometrical self-similarity of structural defects, has the aim of defining simple but rigorous laws, useful to evaluate the energy progressively released by a compressed structural element.…”

Entropy in Natural Time and the Associated Complexity Measures

“…where b is a constant, which varies only slightly from region to region in the range 0.8 ≤ b ≤ 1.2 [104]. Considering that the seismic energy E released during an earthquake is related [105] to the magnitude through E ∼ 10 cm -where c is around 1.5-Eq.…”