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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

The aftershock decay rate.(a) Occurence rate of magnitude MA ∈ [1, 3] aftershocks for different mainshock magnitude ranges and a volume fraction ϕ = 0.644. The dashed line is proportional to 1/t (i.e., the Omori Law). (b) Occurence rate of MA ∈ [1, 3] aftershocks for different volume fractions and magnitude MM ∈ [3, 4] mainshocks. (c) Occurence rate of MA  ∈ [2, 4] aftershocks for different volume fractions and magnitude MM ∈ [4, 5]. In all cases, the shear rate  and individual aftershocks are stacked according to their main shock times to compensate for the small number of events in each sequence. There are at least 10 mainshocks and 1000 aftershocks in each sequence. Note the time delay before the onset of a power-law aftershock decay rate.
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f6: The aftershock decay rate.(a) Occurence rate of magnitude MA ∈ [1, 3] aftershocks for different mainshock magnitude ranges and a volume fraction ϕ = 0.644. The dashed line is proportional to 1/t (i.e., the Omori Law). (b) Occurence rate of MA ∈ [1, 3] aftershocks for different volume fractions and magnitude MM ∈ [3, 4] mainshocks. (c) Occurence rate of MA  ∈ [2, 4] aftershocks for different volume fractions and magnitude MM ∈ [4, 5]. In all cases, the shear rate and individual aftershocks are stacked according to their main shock times to compensate for the small number of events in each sequence. There are at least 10 mainshocks and 1000 aftershocks in each sequence. Note the time delay before the onset of a power-law aftershock decay rate.

Mentions: Figure 6a shows the aftershock rates with respect to the time τ from the mainshock for several ranges of mainshock magnitude, which is denoted by MM. The magnitude of aftershocks is denoted by MA. The studied ranges of MM and MA-values are chosen so that we have enough events in the numerical output to get sufficient statistics. We find that the MOL (Eq. 2) holds with the exponent p ≃ 1 irrespective of the magnitude range of mainshocks. Figure 6b,c show the dependence of the aftershock rate on the volume fraction. We test several volume fractions (ϕ = {0.642, 0.643, 0.644, 0.645} and shear rate ) to verify the existence of the MOL irrespective of these parameters. This relaxation process, characterised by an initial plateau followed by a power law decay, remains stable across the entire parameter space of the model. This is not the case for the GR law (Fig. 3). In addition, the time constant c is insensitive to the volume fraction, as shown in Fig. 6b,c.


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

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

The aftershock decay rate.(a) Occurence rate of magnitude MA ∈ [1, 3] aftershocks for different mainshock magnitude ranges and a volume fraction ϕ = 0.644. The dashed line is proportional to 1/t (i.e., the Omori Law). (b) Occurence rate of MA ∈ [1, 3] aftershocks for different volume fractions and magnitude MM ∈ [3, 4] mainshocks. (c) Occurence rate of MA  ∈ [2, 4] aftershocks for different volume fractions and magnitude MM ∈ [4, 5]. In all cases, the shear rate  and individual aftershocks are stacked according to their main shock times to compensate for the small number of events in each sequence. There are at least 10 mainshocks and 1000 aftershocks in each sequence. Note the time delay before the onset of a power-law aftershock decay rate.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f6: The aftershock decay rate.(a) Occurence rate of magnitude MA ∈ [1, 3] aftershocks for different mainshock magnitude ranges and a volume fraction ϕ = 0.644. The dashed line is proportional to 1/t (i.e., the Omori Law). (b) Occurence rate of MA ∈ [1, 3] aftershocks for different volume fractions and magnitude MM ∈ [3, 4] mainshocks. (c) Occurence rate of MA  ∈ [2, 4] aftershocks for different volume fractions and magnitude MM ∈ [4, 5]. In all cases, the shear rate and individual aftershocks are stacked according to their main shock times to compensate for the small number of events in each sequence. There are at least 10 mainshocks and 1000 aftershocks in each sequence. Note the time delay before the onset of a power-law aftershock decay rate.
Mentions: Figure 6a shows the aftershock rates with respect to the time τ from the mainshock for several ranges of mainshock magnitude, which is denoted by MM. The magnitude of aftershocks is denoted by MA. The studied ranges of MM and MA-values are chosen so that we have enough events in the numerical output to get sufficient statistics. We find that the MOL (Eq. 2) holds with the exponent p ≃ 1 irrespective of the magnitude range of mainshocks. Figure 6b,c show the dependence of the aftershock rate on the volume fraction. We test several volume fractions (ϕ = {0.642, 0.643, 0.644, 0.645} and shear rate ) to verify the existence of the MOL irrespective of these parameters. This relaxation process, characterised by an initial plateau followed by a power law decay, remains stable across the entire parameter space of the model. This is not the case for the GR law (Fig. 3). In addition, the time constant c is insensitive to the volume fraction, as shown in Fig. 6b,c.

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