Laboratoire de Gologie Seismic energy radiation from dynamic faulting Ral Madariaga Ecole Normale Suprieure (from Aochi and Madariaga, BSSA 2003) Some inferred properties of seismic ruptures
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? Earthquake energy balance
U 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) Es= Gc(qs) Gc(dyn) Radiation from a simple circular crack This model has just 3 parameters: Radius R Thisdrop
Stress Rupture velocity vr Plus elasticity Actually it has only one : R w Gc, vr
Radiated Energy Er ~ R3 Gc ~ R Displacement field Mo ~ R3 Etc.
Possible rupture scenarios for the Izmit Earthquake Possible models A seismic (Bouchon) B GPS (Wright) C Spot Images D FDM Harris E Aochi Madariaga
Modelling complex fault geometries SEM/BIEM Fault model BIE Rupture propagation model FD Wave propagation model
Two reasonable models of the Izmit earthquake Bouchon like smooth model Harris-like rough model After Aochi and Madariaga (2003 Model B Model E The smooth fault model
develops 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 Es A lot of high frequency radiation Subshear
The higher the speed, the less energy is absorved, the less is radiated Seismic radiation from a kink in an antiplane fault ( Adda-Bedia et al, 2003-2005) At t = tc the crack kinks Emits a strong high frequency wave of ---2 type (Jump in velocity)
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 kink
Shear stress Particle velocity 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
quasistatic Is this localizable ? dynamic How are High Frequencies generated ? Constant radiation a t s
n o C ra t n io t a
di n Local strain energy Radiation density Es =Gc(qs)-Gc(Dyn) High frequency S wave front
Along the fault 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,Fukuyam a, Aochi, Tada, Kame,Yamashita) Displacement field for a rupture moving along a kink Wrinkle
Slip discontinuity X component Slip is frustrated by the kink Residual stress concentration (Williams, 1952) Y component (King, Yamashita, Kame, Polyakov, etc)
Vorticity of the particle velocity field Computed by Festa and Vilotte April 2005 Rupture moves along the kink Velocity along x Velocity along y CONCLUSIONS 1. High frequencies play a fundamental rle 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 Along x Along y kink
P S R Figures show particle velocity at three succesive instants of time Radiation from a suddenly starting antiplane crack
(or stopping) Velocity Stress Analytical solution from Madariaga (1977) (Madariaga, 1977) Why ? Energy Partition into radiation, fracture and Kostrov energies Simple mode II fault kink model
rupture onset by Aochi et al, 2004 Normal displacementP . arallel displacement Stopping phase Supershear
After Aochi et al (2004) Rupture stops rapidly after the kink Horizontal displacement Vertical displacement Rupture moves along the kink Horizontal displacement
Vertical displacement Seismic energy radiated by an earthquake Strain energy release >0 .T stress change T
stress change rate u displacement Gc energy release rate Kostrov Term any value Rupture energy >0