seismic energy radiation from dynamic faulting raúl madariaga ecole normale supérieure laboratoire...
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Seismic energy radiation from dynamic faulting
Raúl MadariagaEcole Normale Supérieure
Laboratoire de Géologie
(from Aochi and Madariaga, BSSA 2003)
1. Slip distributions and ruptures are complex at all scales.
2. Very large variations of stress change.
3. Slip weakening is a substantial fraction of static slip
4. Self-healing rupture (Heaton pulses) is the rule.
5. Energy release rate (Gc) is of the same order as strain energy density U
6. Local control of rupture
7. How about Energy and High frequencies?
Some inferred properties of seismic ruptures
Earthquake energy balance
U
Slip weakening model with healing
This is an average
global model
not a local model
(Rivera and Kanamori, 2004)
All the terms scale with
earthquake size (Aki, 1967)
Event dependent
Es= Gc(qs) – Gc(dyn)
Radiation from a simple circular crack
This
This model has just 3 parameters:Radius R
Stress drop Rupture velocity vr
Plus elasticity
Actually it has only one : R
Gc, vr
Radiated Energy
Displacement field
w
Er ~ R3
Gc ~ R
Etc.
Mo ~ R3
Possible rupture scenarios for the Izmit Earthquake
Possible modelsA seismic (Bouchon)B GPS (Wright)C Spot ImagesD FDM HarrisE Aochi Madariaga
Modelling complex fault geometries
Fault model
Rupture propagation model
Wave propagation model
BIE
FD
SE
M/B
IEM
Bouchon like « smooth » model Harris-like « rough» model
Two reasonable models of the Izmit earthquake
After Aochi and Madariaga (2003)
Model B Model E
The « smooth » fault modeldevelops supershear shocks
The « rough » fault models produces
subshear ruptures
Why? Detailed energy balance
There is an apparent paradox:
Supershear
Little high frequency radiation along the way
Subshear
A lot of high frequency radiation
Es
The higher the speed, the less energy is absorved, the less is radiated
Seismic radiation from a kink in an antiplane fault
At t = tc the crack kinks
Emits a strong highfrequency wave
of ---2 type
(Jump in velocity)
( Adda-Bedia et al, 2003-2005)
Radiation from an antiplane crack moving along a kink
Displacement Shear stress
Analytical solution from Adda-Bedia et al (2003-2005)
Radiation from an antiplane crack moving along a kinkRadiation from an antiplane crack moving along a kink
Shear stress Particle velocity
Energy balance
If rupture propagates very slowly there is no seismic radiation
If rupture does not absorb available strain energy, Rupture accelerates and radiates. Neglecting Kostrov’s term
Is this localizable ?
(Kostrov, Husseini, Freund, etc )
quasistatic dynamic
Constant radiation
Es =Gc(qs)-Gc(Dyn)
Constant ra
diation
How are High Frequencies generated ?
High frequency S wave frontRadiation density
Local strain energy
Along the fault
Solution by spectral elements
Propagation solvedby SEM
(Vilotte, Ampuero, Festa and Komatisch)
Fracture solvedby BIEM-like
boundary conditions
(Cochard,Fukuyama, Aochi, Tada,
Kame,Yamashita)
Typical grid
The in-plane kink
Displacement field for a rupture moving along a kinkWrinkle
Slip discontinuity
Slip is frustrated by the kink
Residual stress concentration
(King, Yamashita, Kame, Polyakov, etc)(Williams, 1952)
X component
Y component
Vorticity of the particle velocity field
Computed by Festa and Vilotte April 2005
Rupture moves along the kinkVelocity along yVelocity along x
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
Rupture stops rapidly after the kink
P
S
R
Figures show particlevelocity at three
succesive instantsof time
Along x Along y
Radiation from a suddenly starting antiplane crack
Velocity Stress
(Madariaga, 1977)Analytical solution from Madariaga (1977)
(or stopping)
Why ?
Energy Partition into radiation, fracture and Kostrov energies
rupture onset
Simple mode II fault kink model
by Aochi et al, 2004
Stopping phase
Normal displacement.Parallel displacement
Supershear
After Aochi et al (2004)
Rupture stops rapidly after the kinkVertical displacementHorizontal displacement
Rupture moves along the kink
Horizontal displacement Vertical displacement
Seismic energy radiated by an earthquake
Strain energy release>0
Kostrov Termany value
Rupture energy>0
T stress changeT stress change rateu displacementGc energy release rate
.