Earthquake Dynamics and Inversion for source characteristics Raul Madariaga

1. Earthquake Dynamics and Inversion for source characteristics Raul Madariaga Sergio Ruiz and Maria Lancieri Laboratoire de Géologie CNRS ENS Paris, France Departamento de Geofisica, Universidad de Chile Thanks to SPICE, ANR DEBATE and CONICYT

2. Earthquakes as dynamic shear ruptures Preexisting Fault system in the Mojave desert Rupture modelled on the complex fault system determined from Geology, Geodesy and Seismology Aochi et al. 2003

3. Let us back track 40 years: The good old circular crack explains Brune’s spectrum  r

4. The Tocopilla earthquake sequence in Northern Chile With Maria Lancieri Main event Mw 7.7 on 14 November 2007 Two main aftershocks on 15 November 2007 Lancieri et al analyzed several 100s small events

5. Spectral stack of small earthquakes in Tocopilla Following Prieto et al. , 2004 Main event poor From these spectra we can compute 3 quantities Mo, Er and fc that define a second order harmonic oscillator

6. The usual view of this variation Following Ide and Beroza

7. An alternative view Deviation of self-similarity over 7 orders of magnitude Decreasing damping Boatwright’s Mw Brune spectrum

8. Er W Gc Scaling of energy with earthquake size For Brune’s model Brune used

9. Er W Gc Scaling of Energy release rate Gc

10. Rupture process for a circular crack Slip Slip rate Rupture front grows Rayleigh P st.phase S Radiation is controlled by wave propagation inside the fault!

11. Far field radiation from circular crack -2 rupture -2

12. Can devise the equivalent of Brune’s model for near field data ? Work done in collaboration with Sara DiCarli (ENS Paris), Caroline Holden-François (New Zealand), Maria Lancieri (ENS, Paris), And Sergio Ruiz and Sophie Peyrat (U of Chile)

13. The Tocopilla earthquake sequence in Northern Chile Main event Mw 7.7 on 14 November 2007 Two main aftershocks on 15 November 2007 Deep slab push aftershock 16 December 2007

14. IPOC + GFZ Task Force Instruments

15. Far and Near-field kinematic inversion of the 16/12/2007 Mw 6.8 earthquake Mo = 1. 1019 Nm Far field body wave inversion Peyrat et al, 2007

16. Near-field kinematic inversion of the 16/12/2007 earthquake EW displacement Result of non-linear Inversion with NA. Residual rms 0.22 Main feature: vr ~ 1.5 km/s Data Filtered 0.05 - 0.2 Hz

17. Dynamic Forward problem Numerical simulation by staggered grid Finite Differences FD Cube 32 km3 x = 200 m t = 0.01 s 32 km Fault at center of cube, thin B.C. Fault Friction law: slip weakening Propagation to surface with Axitra (Bouchon-Coutant) Paraxial absorbing BC. on the faces

18. stress Gc Tu slip Dc Dynamic inversion friction law Te shear stress Barrier Problem: radiation does not know about absolute stress value

19. The most important feature: The dynamic problem is fundamentally ill-posed we can either invert a Barrier or an Asperity model Asperity: variable initial stress, homogenous rupture resistance (Kanamori, Stewart, Ruff, Lay, …) Barrier: initial stress is homogenous, rupture resistance is variable and stops rupture (Das, Aki) Seismic waves can not distinguish asperities and barriers

20. Parameters for the inversion of a barrier model Rupture resistance Applied stress barrier Friction Tu Dc Te Applied stress Asperity radius and value at peak geometry a, b , , x0, y0

21. Dynamic inversion of the 16/12/2007 earthquake We use the NA Algorithm : a Monte Carlo technique with memory Each iteration consists in a full FD simulation Slip and isochrones for best model Final slip

22. Dynamic inversion of the 16/12/2007 earthquake Convergence of the algorithm  =0.62 Critical value for Circular crack is c = 0.6 MOA 1998 0.18

23. Dynamic inversion of 16/12/2007 earthquake in Northern Chile Inverted 9 near field 3-comp displacement records 0.02-2 Hz band Start phase Main stopping phase Start phase Displacement [m] stopping phase EW component Residual RMS 0.18

24. Dynamic inversion of 16/12/2007 earthquake in Northern Chile Inverted 9 near field 3-comp displacement records 0.02-2 Hz band Start phase Main stopping phase Start phase Displacement [m] stopping phase Z component Residual RMS 0.18

25. Dynamic inversion of 16/12/2007 earthquake in Northern Chile Slip-rate Snapshots Rupture process of the best model start Total rupture time ~ 3.7 s arrest

26. Dynamic inversion of 16/12/2007 earthquake in Northern Chile Snapshots of Stress drop Te=15.7 MPa Tu=23.7 MPa

27. General situation of the Tocopilla earthquake Cinca 95, Ancorp 96 profile From Oncken et al, 2003

28. Summary of Dynamic inversion of 16/12/2007 earthquake Moment 1 1019 N m Stress Drop 15 MPa Peak Stress 23.7 MPa Gc 2.5 MJ/m2 Dc 0.2 m Semi minor axis 5 km Rupture Speed 1.5 km/s Radiation dominated by stopping Phase

29. Resolution of Inversion Best solution

30. Resolution of Inversion forbidden Best solution

31. Partial Conclusions Like Brune’s model, barrier inversion is dominated by stopping phases Dynamic parameters (stress and Gc) are connected by . Dynamic inversion is non-unique Barrier inversion is dominated by geometry Dynamic inversion is possible now for M~7 events

32. Convert Barrier into asperity model Frictional resistance Initial stress Barrier Asperity

33. Dynamic inversion of 16/12/2007 earthquake Slip-rate Snapshots Rupture process of the Asperity model start Total rupture time ~ 3.7 s arrest Residual RMS 0.20

34. Dynamic inversion of the 16/12/2007 earthquake Asperity Barrier

35. Dynamic inversion of 16/12/2007 earthquake in Northern Chile Inverted 9 near field 3-comp displacement records 0.02-2 Hz band Start phase Main stopping phase Start phase Displacement [m] stopping phase EW component Residual RMS 0.20

36. An exotic model of the 16 December 2010 earthquake Initial stress Asperity model Rupture process And slip

37. Exotic model of the 16/12/2007 earthquake in Northern Chile 0.02-2 Hz band Start phase Main encircling phase Start phase Displacement [m] stopping phase EW component Residual RMS 0.22

38. CONCLUSIONS Dynamic inversion is now possible in the barrier and Asperity formulation Error of fit is < 0.20 Converges is about 10000 models for 11 parameters (few days in Cluster with larege memory > 2GO/node Barrier and asperity models produce very similar Results There exist exotic solutions (supershear, rupture encircles the border of the asperity)

39. Conclusions Dynamic inversion is possible now for M~7 events Like Brune’s model, inversion is dominated by stopping phases Dynamic parameters (stress and Gc) are connected by . Dynamic inversion is non-unique Dynamic inversion is dominated by geometry

40. Different scales in earthquake dynamics . BB Seismic waves Macroscale (< 0.3 Hz  5 km) Hifi Seismic waves Mesoscale (>0.5 Hz <2 km) Steady state mechanics Microscale vr (non-radiative) (~ 100 m)

41. Dynamic parameters are not independent From kinematics Stress drop fault size b Barrier a Initial patch radius R Gc: choosen so that rupture ocurs and is subshear ( iff 1<<1.2)