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## Seismic energy radiation from dynamic faulting

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**Seismic energy radiation from dynamic faulting**Laboratoire de Géologie Raúl Madariaga Ecole Normale Supérieure (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 DU 6. Local control of rupture 7. How about Energy and High frequencies?**Slip weakening model with healing**All the terms scale with earthquake size (Aki, 1967) Eventdependent This is an average global model not a local model (Rivera and Kanamori, 2004)**Radiation from a simple circular crack**This model has just 3 parameters: Radius R Stress dropDs Rupture velocity vr Plus elasticity This Actually it has only one : R**w-2**w Radiated Energy Gc, vr 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**Fault model BIE Rupture propagation model FD SEM/BIEM 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 Why? Detailed energy balance The « rough » fault models produces subshear ruptures**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**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)**Displacement**Shear stress Radiation from an antiplane crack moving along a kink Analytical solution from Adda-Bedia et al (2003-2005)**Radiation from an antiplane crack moving along a kink**Particle velocity Shear stress**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 Kostrov’s term dynamic quasistatic Is this localizable ?**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**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)**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)**Vorticity of the particle velocity field**Computed by Festa and Vilotte April 2005**Rupture moves along the kink**Velocity along y Velocity 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**Along x Along y Figures show particle velocity at three succesive instants of time P S R**Velocity**Stress Radiation from a suddenly starting antiplane crack (or stopping) Analytical solution from Madariaga (1977) (Madariaga, 1977)**Energy Partition into radiation, fracture and Kostrov**energies Simple mode II fault kink model by Aochi et al, 2004 Why ? rupture onset**Normal displacement.**Parallel displacement Stopping phase Supershear After Aochi et al (2004)**Rupture stops rapidly after the kink**Horizontal displacement Vertical displacement**Rupture moves along the kink**Vertical displacement Horizontal displacement**Seismic energy radiated by an earthquake**Kostrov Term any value Rupture energy >0 T stress change T stress change rate u displacement Gc energy release rate . Strain energy release >0