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Common dependence on stress for the statistics of granular avalanches and earthquakes.

Hatano T, Narteau C, Shebalin P - Sci Rep (2015)

Bottom Line: The faulting style dependence may be related to the magnitude of the differential stress, but no model so far has been able to reproduce this behaviour.Here we investigate the statistical properties of avalanches in a dissipative, bimodal particulate system under slow shear.These results are consistent with recent seismological observations of earthquake size-distribution and aftershock statistics.

View Article: PubMed Central - PubMed

Affiliation: Earthquake Research Institute, University of Tokyo, 113-0032 Tokyo, Japan.

ABSTRACT
Both earthquake size-distributions and aftershock decay rates obey power laws. Recent studies have demonstrated the sensibility of their parameters to faulting properties such as focal mechanism, rupture speed or fault complexity. The faulting style dependence may be related to the magnitude of the differential stress, but no model so far has been able to reproduce this behaviour. Here we investigate the statistical properties of avalanches in a dissipative, bimodal particulate system under slow shear. We find that the event size-distribution obeys a power law only in the proximity of a critical volume fraction, whereas power-law aftershock decay rates are observed at all volume fractions accessible in the model. Then, we show that both the exponent of the event size-distribution and the time delay before the onset of the power-law aftershock decay rate are decreasing functions of the shear stress. These results are consistent with recent seismological observations of earthquake size-distribution and aftershock statistics.

No MeSH data available.


Related in: MedlinePlus

Dependency of the avalanche magnitude-frequency distribution on the global shear stress.(a) The avalanche magnitude-frequency distributions for different ranges of shear stress value, a volume fraction ϕ = 0.643 and a shear rate . Events i are classify according to the value of the global shear stress at the inititation of the avalanches (See text for the exact ranges of shear stress value). (b) The slope of the magnitude-frequency distribution with respect to the global shear stress. The β-value is a decreasing function of the global shear stress.
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f4: Dependency of the avalanche magnitude-frequency distribution on the global shear stress.(a) The avalanche magnitude-frequency distributions for different ranges of shear stress value, a volume fraction ϕ = 0.643 and a shear rate . Events i are classify according to the value of the global shear stress at the inititation of the avalanches (See text for the exact ranges of shear stress value). (b) The slope of the magnitude-frequency distribution with respect to the global shear stress. The β-value is a decreasing function of the global shear stress.

Mentions: To discuss the effect of shear stress on the β-value, we introduce the shear stress σ at the beginning of an event as an additional argument to the magnitude-frequency distribution. Then, P(M, σ) is the conditional probability of observing a magnitude M avalanche under the (global) shear stress value σ. For convenience, σ is integrated in a certain interval Si ∫ [10−i/2, 10−i/2+0.5] (i = {1, 2, ···, 9}). Thus, we obtain the following distribution function: . Figure 4a shows the behaviours of Pi(M) at ϕ = 0.643. We can see that the probability of observing a larger avalanche increases as the shear stress increases. More importantly, the distribution function at each stress level develops a power-law tail with a β-value, which is a decreasing function of the shear stress (Fig. 4b). We confirm that this stress dependence is independent of the volume fraction in the range 0.642 ≤ ϕ ≤ 0.645. In addition, the shear stress dependence of the β-value is qualitatively the same as that in rock fracture experiments7.


Common dependence on stress for the statistics of granular avalanches and earthquakes.

Hatano T, Narteau C, Shebalin P - Sci Rep (2015)

Dependency of the avalanche magnitude-frequency distribution on the global shear stress.(a) The avalanche magnitude-frequency distributions for different ranges of shear stress value, a volume fraction ϕ = 0.643 and a shear rate . Events i are classify according to the value of the global shear stress at the inititation of the avalanches (See text for the exact ranges of shear stress value). (b) The slope of the magnitude-frequency distribution with respect to the global shear stress. The β-value is a decreasing function of the global shear stress.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4508663&req=5

f4: Dependency of the avalanche magnitude-frequency distribution on the global shear stress.(a) The avalanche magnitude-frequency distributions for different ranges of shear stress value, a volume fraction ϕ = 0.643 and a shear rate . Events i are classify according to the value of the global shear stress at the inititation of the avalanches (See text for the exact ranges of shear stress value). (b) The slope of the magnitude-frequency distribution with respect to the global shear stress. The β-value is a decreasing function of the global shear stress.
Mentions: To discuss the effect of shear stress on the β-value, we introduce the shear stress σ at the beginning of an event as an additional argument to the magnitude-frequency distribution. Then, P(M, σ) is the conditional probability of observing a magnitude M avalanche under the (global) shear stress value σ. For convenience, σ is integrated in a certain interval Si ∫ [10−i/2, 10−i/2+0.5] (i = {1, 2, ···, 9}). Thus, we obtain the following distribution function: . Figure 4a shows the behaviours of Pi(M) at ϕ = 0.643. We can see that the probability of observing a larger avalanche increases as the shear stress increases. More importantly, the distribution function at each stress level develops a power-law tail with a β-value, which is a decreasing function of the shear stress (Fig. 4b). We confirm that this stress dependence is independent of the volume fraction in the range 0.642 ≤ ϕ ≤ 0.645. In addition, the shear stress dependence of the β-value is qualitatively the same as that in rock fracture experiments7.

Bottom Line: The faulting style dependence may be related to the magnitude of the differential stress, but no model so far has been able to reproduce this behaviour.Here we investigate the statistical properties of avalanches in a dissipative, bimodal particulate system under slow shear.These results are consistent with recent seismological observations of earthquake size-distribution and aftershock statistics.

View Article: PubMed Central - PubMed

Affiliation: Earthquake Research Institute, University of Tokyo, 113-0032 Tokyo, Japan.

ABSTRACT
Both earthquake size-distributions and aftershock decay rates obey power laws. Recent studies have demonstrated the sensibility of their parameters to faulting properties such as focal mechanism, rupture speed or fault complexity. The faulting style dependence may be related to the magnitude of the differential stress, but no model so far has been able to reproduce this behaviour. Here we investigate the statistical properties of avalanches in a dissipative, bimodal particulate system under slow shear. We find that the event size-distribution obeys a power law only in the proximity of a critical volume fraction, whereas power-law aftershock decay rates are observed at all volume fractions accessible in the model. Then, we show that both the exponent of the event size-distribution and the time delay before the onset of the power-law aftershock decay rate are decreasing functions of the shear stress. These results are consistent with recent seismological observations of earthquake size-distribution and aftershock statistics.

No MeSH data available.


Related in: MedlinePlus