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

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

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

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

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

The usual view of this variation Following Ide and Beroza

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

Scaling of energy with earthquake size WW ErEr GcGc For Brune’s model Brune used

Scaling of Energy release rate Gc WW ErEr GcGc

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

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

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)

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

IPOC + GFZ Task Force Instruments

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

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

Numerical simulation by staggered grid Finite Differences Dynamic Forward problem FD Cube 32 km 3  x = 200 m  t = 0.01 s Friction law: slip weakening Fault at center of cube, thin B.C. 32 km Fault Paraxial absorbing BC. on the faces Propagation to surface with Axitra (Bouchon-Coutant)

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

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

Parameters for the inversion of a barrier model geometry a, b, , x 0, y 0 Te Applied stress Asperity radius and value at peak Tu Dc Friction Applied stress Rupture resistance barrier

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

0.18  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

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

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

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

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

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

Moment N m Stress Drop 15 MPa Peak Stress 23.7 MPa Gc 2.5 MJ/m 2 Dc 0.2 m Semi minor axis 5 km Rupture Speed 1.5 km/s Radiation dominated by stopping Phase Summary of Dynamic inversion of 16/12/2007 earthquake

Resolution of Inversion Best solution

Resolution of Inversion Best solution forbidden

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

Convert Barrier into asperity model Barrier Asperity Initial stress Frictional resistance

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

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

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

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

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

CONCLUSIONS Dynamic inversion is now possible in the barrier and Asperity formulation Error of fit is < 0.20 Converges is about 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)

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

. BB Seismic waves Hifi 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) ( ~ 100 m)

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