Limits...
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 aftershock decay rate on the global shear stress.(a) Occurence rate of MA ∈ [1, 3] aftershocks for different ranges of shear stress value and a volume fraction ϕ = 0.644. Aftershocks i ∈ {0, 1, 2, 3} are classify according to the global shear stress value σi ∈ [exp(i − 10), exp(i − 9)] at the inititation of the avalanches. The time delay before the onset of the power-law decay rate is systematically decreasing with the level of stress (i.e., an increasing i-value). (b) Negative dependence of the c-value on the global shear stress. Circles: ϕ = 0.644, MM ∈ [3, 4], and MA ∈ [1, 3]; Squares: ϕ = 0.645, MM ∈ [3, 4], and MA ∈ [1, 3]. Diamonds: ϕ = 0.644, MM ∈ [2, 3], and MA ∈ [1, 2].
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4508663&req=5

f7: Dependency of the aftershock decay rate on the global shear stress.(a) Occurence rate of MA ∈ [1, 3] aftershocks for different ranges of shear stress value and a volume fraction ϕ = 0.644. Aftershocks i ∈ {0, 1, 2, 3} are classify according to the global shear stress value σi ∈ [exp(i − 10), exp(i − 9)] at the inititation of the avalanches. The time delay before the onset of the power-law decay rate is systematically decreasing with the level of stress (i.e., an increasing i-value). (b) Negative dependence of the c-value on the global shear stress. Circles: ϕ = 0.644, MM ∈ [3, 4], and MA ∈ [1, 3]; Squares: ϕ = 0.645, MM ∈ [3, 4], and MA ∈ [1, 3]. Diamonds: ϕ = 0.644, MM ∈ [2, 3], and MA ∈ [1, 2].

Mentions: Next, we analyse how the time constant c depends on the magnitude of the shear stress. We define for aftershocks the stress range [σmin, σmax] and select only aftershocks that belong to this stress range and the magnitude range . The aftershock rates are shown in Figure 7a, in which the MOL (with p = 1) holds clearly and c is a decreasing function of shear stress. We estimate the c-values by fitting the data with A/(τ + c) using the maximum-likelihood method. As shown in Fig. 7b, the c-value has a negative dependence on the shear stress. We confirm this stress dependence for two volume fractions (ϕ = {0.644, 0.645}) and for two magnitude ranges (MM ∈ [3, 4], MA ∈ [1, 3] and MM ∈ [4, 5], MA ∈ [2, 4]). This negative shear-stress dependence of the c-value for aftershocks is consistent with the trend inferred from seismological observations53435.


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

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

Dependency of the aftershock decay rate on the global shear stress.(a) Occurence rate of MA ∈ [1, 3] aftershocks for different ranges of shear stress value and a volume fraction ϕ = 0.644. Aftershocks i ∈ {0, 1, 2, 3} are classify according to the global shear stress value σi ∈ [exp(i − 10), exp(i − 9)] at the inititation of the avalanches. The time delay before the onset of the power-law decay rate is systematically decreasing with the level of stress (i.e., an increasing i-value). (b) Negative dependence of the c-value on the global shear stress. Circles: ϕ = 0.644, MM ∈ [3, 4], and MA ∈ [1, 3]; Squares: ϕ = 0.645, MM ∈ [3, 4], and MA ∈ [1, 3]. Diamonds: ϕ = 0.644, MM ∈ [2, 3], and MA ∈ [1, 2].
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f7: Dependency of the aftershock decay rate on the global shear stress.(a) Occurence rate of MA ∈ [1, 3] aftershocks for different ranges of shear stress value and a volume fraction ϕ = 0.644. Aftershocks i ∈ {0, 1, 2, 3} are classify according to the global shear stress value σi ∈ [exp(i − 10), exp(i − 9)] at the inititation of the avalanches. The time delay before the onset of the power-law decay rate is systematically decreasing with the level of stress (i.e., an increasing i-value). (b) Negative dependence of the c-value on the global shear stress. Circles: ϕ = 0.644, MM ∈ [3, 4], and MA ∈ [1, 3]; Squares: ϕ = 0.645, MM ∈ [3, 4], and MA ∈ [1, 3]. Diamonds: ϕ = 0.644, MM ∈ [2, 3], and MA ∈ [1, 2].
Mentions: Next, we analyse how the time constant c depends on the magnitude of the shear stress. We define for aftershocks the stress range [σmin, σmax] and select only aftershocks that belong to this stress range and the magnitude range . The aftershock rates are shown in Figure 7a, in which the MOL (with p = 1) holds clearly and c is a decreasing function of shear stress. We estimate the c-values by fitting the data with A/(τ + c) using the maximum-likelihood method. As shown in Fig. 7b, the c-value has a negative dependence on the shear stress. We confirm this stress dependence for two volume fractions (ϕ = {0.644, 0.645}) and for two magnitude ranges (MM ∈ [3, 4], MA ∈ [1, 3] and MM ∈ [4, 5], MA ∈ [2, 4]). This negative shear-stress dependence of the c-value for aftershocks is consistent with the trend inferred from seismological observations53435.

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