1. Earthquake dynamics at the crossroads between seismology, mechanics and geometry Raúl Madariaga, Mokhtar Adda-Bedia ENS Paris, Jean-Paul Ampuero, ETH Zürich, Valparaiso, 17 August 2006, another big Earthquake of 1906 M=8.4

2. . Lo f seismic waves Hi f seismic waves Different scales in earthquake dynamics Macroscale Mesoscale Microscale Steady state mechanics vrvr (< 0.3 Hz  5 km) (>0.5 Hz  <2 km) (non-radiative ) ( < 1 Km) Geometry Mechanics

3. Example from Northern Chile Tarapacá earthquake Iquique From Peyrat et al, 2006 13 June 2005 M=7.8 Mo = 5x10 20 Nm

4. 2003 Tarapaca earthquake recorded by the IQUI accelerometer Thanks to Rubén Boroschev U de Chile IQUI displacement IQUI ground velocity IQUI energy flux Small oscillations are equivalent to M>6 events What are them? Accelerogram filtered from 0.01 to 1 Hz and integrated Stopping phase 0 4020 10cm/s 18cm 60

5. Solution by spectral elements Propagation solved by SEM (Vilotte, Ampuero, Festa and Komatisch) Polynomial order 7 Fracture solved by slip weakening friction on a split interface Clayton Engquist absorbing boundaries ttypical grid A multiply kinked rupture T X Antiplane shear

6. A complex antiplane (Mode III) crack  Multiple kink phases  Low rupture speeds  Residual stresses  Diffraction Time Rms stress Velocity rupture front Kink waves Residual stresses (Dieterich, 2005)

7. Energy flux through a line parallel to the fault trend Kink waves 10 km

8. time position Slip Shear stress shear wave speed Complex geometry reduces rupture speed Lower rupture speed Upper side Lower side

9. Energy release rate G c Energy flow and rupture speed Seismic energy E s Energy release rate: Radiated energy per unit surface : From Kostrov, Husseini, Freund v

10. Energy release rate reduction by one kink Energy release rate reduction by n kinks Number of kinks per unit length Effect of geometrical complexity on rupture propagation Energy Balance n

11. CONCLUSIONS 1. Fault kinks break simple symmetry of faulting 2. They generate simple   radiation 3. Kinks reduce available energy G c 4. They reduce rupture speed 4. Kinks may stop rupture 5. Kinks are the site of residual stress concentrations

12. How are High Frequencies generated ? High frequency S wave front Radiation density Local strain energy Along the fault vrvr v’ r EsEs Es'Es' EsEs Es'Es'

13. Radiation from an antiplane crack with a kink S kink S wave (  -2 ) Starting asperity Velocity z Stress  zy Stress  zx Rupture front v r < v s Corner stresses    

14. Comparison of kinked crack with a flat crack propagating at the same apparent speed Velocity z Stress  zy Stress  zx Rupture front Residual stresses S waves

15. There is an apparent paradox: Supershear Little high frequency radiation along the way Subshear strong high frequency radiation Es The higher the speed, the less energy is absorbed, the more energy is radiated