spatial distribution of aftershocks as a hallmark for ... · describing the asthenosphere as...
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SeisMath IP 2013 12 July
Spatial distribution of aftershocks as a hallmark for different stress regimes
E. L. Dep. of Mathematics and Physics (Second University of Naples)Lucilla de Arcangelis, Ferdinando Giacco Cataldo Godano, Warner Marzocchi (INGV)
Dina Dargo
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Spatial distribution of aftershocks as a hallmark for different stress regimes
First PART: From Modeling in Statistical Physics toModeling in Statistical Seismology
Second PART: Insights from modeling concerning the aftershock spatial organization
Third PART: Test of theoretical predictions in experimental catalogs
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Statistical Physics: Phase transitions and critical points
Critical point were discovered by Cagniard de la Tour in 1822 and named by Dmitri Mendeleev in 1860 and Thomas Andrews in 1869.
Most insights of phase transitions were appreciated only later after The introduction of minimal models such as the Ising model invented by Wilhelm Lenz (1920), and studied by his student Ernst Ising.
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1894
Omori law Gutenberg-Richter law
2000-1980
Burridge-Knopoff model
Self-organized criticalityOFC model
TIME AXIS1894 1932-35
PHYSICAL MODELS
Energy-spatio-temporal correlationsDependence on the fault geometry….........................
2000-
Productivity law
1970
Spatial Clustering
1980
1967 1987
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Statistical Seismology: Minimal model for aftershock occurrence
Most simple description of a seismic fault: A single elastic layer (Burridge-Knopoff, OFC model)
ROUGH SUBSTRATE
MOVING SUBSTRATE
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Statistical Seismology: Minimal model for aftershock occurrence
Most simple description of a seismic fault: - We reach a stable configuration- We stop the external drive- We apply a Stress perturbation in the middle of the system
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Statistical Seismology: Minimal model for aftershock occurrence
When we apply a Stress perturbation in the middle of the system
Yellow-Red indicate more unstable regions
Violet-Black indicate more stable regions
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Statistical Seismology: Minimal model for aftershock occurrence
When we apply a Stress perturbation in the middle of the system
The whole extra stress is relaeased during the “mainshock”
Aftershocks are not observed
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Statistical Seismology: Minimal model for aftershock occurrence
When we apply a Stress perturbation in the middle of the system
The whole extra stress is relaeased during the “mainshock”
No aftershock is observed
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When we apply a Stress perturbation in the middle of the system
There remain unstable regions that relax at subsequent times
Aftershocks are observed
1st INGREDIENT : SPATIAL HETEROGENEITIES IN THE FRICTION LEVELS
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1st INGREDIENT : SPATIAL HETEROGENEITIES IN THE FRICTION LEVELS
Aftershocks are present but they abruptly stop
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Describing the Asthenosphere as Maxwell Viscoelasic medium We obtain a Diffusive equation for the stress in the Crust
2nd INGREDIENT : COUPLING WITH A VISCOELASTIC MEDIUM(Hainzl, et al 1999, Pellettier 2000, Jagla et al 2014)
dσdt=D
d 2 σdx2
D=YH lH a
η
Y= Young modulus Lithosphereη= Viscosity AsthenosphereH
l=Lithosphere depth
Hl=Asthenosphere depth
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When we apply a Stress perturbation in the middle of the system
Aftershocks are observed with patterns very similar to experimental data
2nd INGREDIENT : COUPLING WITH A MAXWELL VISCOELASTIC MEDIUM
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When we apply a Stress perturbation in the middle of the system
2nd INGREDIENT : COUPLING WITH A MAXWELL VISCOELASTIC MEDIUM
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When we apply a Stress perturbation in the middle of the system
Aftershocks are observed
2nd INGREDIENT : COUPLING WITH A MAXWELL VISCOELASTIC MEDIUM
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For a whole temporal evolution with the applied external drive
MINIMAL MODEL: Only one variable on a discrete latticeOnly two model parameters: - one controlling the heterogeneity level - one fixing the time scale of diffusion
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The magnitude distribution follows the GR law
MINIMAL MODEL: Only one variable on a discrete latticeOnly two model parameters: - one controlling the heterogeneity level - one fixing the time scale of diffusion
The b-value is in agreement with experimental values b=1.1 Independently of model parameters
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Second PART: Insights from modelling and experimental results for aftershock spatial organization
HIGH STRESS REGIMEThe stress is concentrated in a smaller region
INTERMEDIATE STRESS REGIME
LOW STRESS REGIMEThe stress is distributed over a wider region
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Second PART: Insights from modelling and experimental results for aftershock spatial organization
HIGH STRESS REGIMEThe stress is concentrated in a smaller
INTERMEDIATE STRESS REGIME
LOW STRESS REGIMEThe stress is distributed over a wide regionr
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Second PART: Insights from modelling and experimental results for aftershock spatial organization
HIGH STRESS REGIMEThe stress is concentrated in a smaller
INTERMEDIATE STRESS REGIME
LOW STRESS REGIMEThe stress is distributed over a wider region
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Second PART: Insights from modelling and experimental results for aftershock spatial organization
HIGH STRESS REGIMEThe stress is concentrated in a smaller
INTERMEDIATE STRESS REGIME
LOW STRESS REGIMEThe stress is distributed over a wider
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Second PART: Insights from modelling and experimental results for aftershock spatial organization
HIGH STRESS REGIMEThe stress is concentrated in a smaller
INTERMEDIATE STRESS REGIME
LOW STRESS REGIMEThe stress is distributed over a wider
smaller c-values in higher stressed regionsIn agreement with experimental findings(Narteau et al. 2009)
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Second PART: Insights from modelling and experimental results for aftershock spatial organization
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Second PART: Insights from modelling and experimental results for aftershock spatial organization
smaller b-values in higher stressed regionsIn agreement with experimental findings(Schorlemmer et al. 2005)
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Second PART: Insights from modelling and experimental results for aftershock spatial organization
HIGH STRESS REGIMEA SMALLER SIZE of the AFTERSHOCK AREAL
a is defined as the average main-aftershock
distance
INTERMEDIATE STRESS REGIME
LOW STRESS REGIMEA LARGER SIZE of the AFTERSHOCK AREA
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Second PART: Insights from modelling and experimental results for aftershock spatial organization
HIGH STRESS REGIMEA SMALLER SIZE of the AFTERSHOCK AREALa is defined as the average main-aftershock distance
INTERMEDIATE STRESS REGIME
LOW STRESS REGIMEA LARGER SIZE of the AFTERSHOCK AREA
smaller sizes of the aftershock area in higher stressed regions
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Second PART: Insights from modelling and experimental results for aftershock spatial organization
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Second PART: Insights from modelling and experimental results for aftershock spatial organization
Proportionality among the b-value, the c-value and the size of the aftersock area
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3rd PART: Test on experimental catalogs
Southern California Region
Schorlemmer et al, 2005Larger b-value in normal faulsSmaller b-value in thrust faullts
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3rd PART: Test on experimental catalogs
Southern California Region
Narteau et al.(2009)For mainshock magnitudes in [2.5:4.5]
Larger c-value in normal faulsSmaller c-value in thrust faullts
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3rd PART: Test on experimental catalogs
Southern California RegionWe adopt the same criterion by Narteau et al.
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3rd PART: Test on experimental catalogs
Southern California RegionWe adopt the same criterion by Narteau et al.
A larger La-value in normal fauls
Smaller c-value in thrust faullts
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3rd PART: Test on experimental catalogs
Southern California Region: Parametric Plots
Black crosses are results for SCEC m<4.5Blue lines are behaviors of the numerical model
Southern California Region: Parametric Plots
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3rd PART: Test on experimental catalogs
Southern California Region: Parametric PlotsWe extend the analysis to other geographic regions considering big mainshocks: All events with m>6.5 recorded in Southern California, Northern California, Alaska, Japan mainland and m>5.9 in Italy.
For ecah sequence we evaluate the b-value, c-value, La-
value
and obtain parametric plots
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3rd PART: Test on experimental catalogs
Black crosses are results for SCEC m<4.5Red squares are world wide m>6.5 main-aftershock sequencesBlue lines are behaviors of the numerical model
Parametric Plots
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SUMMARY & CONCLUSIONS
First PART: We have presented a “minimal” model for seismic occurrence;
Second PART: The model indicates proportionality among b-value, c-value and the size of the aftershock area
Third PART: Theoretical predictions are recovered in experimental catalogs for different magnitude ranges and geographic regions.
Also the size of the aftershock area can be used as a probe for different stress regimes