spatial distribution of aftershocks as a hallmark for ... · describing the asthenosphere as...

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