Prsentation PowerPoint

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Raúl Madariaga Ecole Normale Supérieure
(from Aochi and Madariaga, BSSA 2003)
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Earthquake energy balance
D U
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Slip weakening model with healing
All the terms scale with earthquake size (Aki,
1967)
Event dependent
This is an average global model not a local
model
(Rivera and Kanamori, 2004)
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Es Gc(qs) Gc(dyn)
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This model has just 3 parameters Radius R Stress
drop Ds Rupture velocity vr Plus elasticity
This
Actually it has only one R
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w-2
w
Radiated Energy
Gc, vr
Er R3
Gc R
Displacement field
Mo R3
Etc.
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Possible rupture scenarios for the Izmit
Earthquake
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SEM/BIEM
Wave propagation model
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The  rough  fault models produces subshear
ruptures
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There is an apparent paradox
Little high frequency radiation along the way
Supershear
Es
A lot of high frequency radiation
Subshear
The higher the speed, the less energy is
absorved, the less is radiated
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(Jump in velocity)
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Radiation from an antiplane crack moving along a
kink
Analytical solution from Adda-Bedia et al
(2003-2005)
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Radiation from an antiplane crack moving along a
kink
Shear stress
Particle velocity
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Energy balance
(Kostrov, Husseini, Freund, etc )
If rupture propagates very slowly there is no
seismic radiation
If rupture does not absorb available strain
energy, Rupture accelerates and radiates.
Neglecting Kostrovs term
dynamic
quasistatic
Is this localizable ?
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How are High Frequencies generated ?
Constant radiation
Constant radiation
Local strain energy
High frequency S wave front
Radiation density
Es Gc(qs)-Gc(Dyn)
Along the fault
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The in-plane kink
Solution by spectral elements
Typical grid
Propagation solved by SEM (Vilotte, Ampuero,
Festa and Komatisch)
Fracture solved by BIEM-like boundary
conditions (Cochard,Fukuyama, Aochi, Tada,
Kame,Yamashita)
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Displacement field for a rupture moving along a
kink
Wrinkle
Slip discontinuity
X component
Slip is frustrated by the kink
Residual stress concentration
Y component
(Williams, 1952)
(King, Yamashita, Kame, Polyakov, etc)
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Vorticity of the particle velocity field
Computed by Festa and Vilotte April 2005
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Rupture moves along the kink
Velocity along y
Velocity along x
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CONCLUSIONS
1. High frequencies play a fundamental rôle in
energy balance 2. Fault kinks produce radiation
so that they reduce available energy 3. Kinks
reduce rupture speed 4. Kinks can stop
rupture 5. Kinks are the site of residual stress
concentrations
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Rupture stops rapidly after the kink
Along x
Along y
Figures show particle velocity at three succesive
instants of time
P
S
R
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Radiation from a suddenly starting antiplane crack
(or stopping)
Analytical solution from Madariaga (1977)
(Madariaga, 1977)
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Why ?
rupture onset
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Rupture stops rapidly after the kink
Vertical displacement
Horizontal displacement
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Rupture moves along the kink
Vertical displacement
Horizontal displacement
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Strain energy release gt0