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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. - PowerPoint PPT Presentation
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Earthquake Dynamics andInversion for source characteristics
Raul Madariaga Sergio Ruiz and Maria Lancieri
Laboratoire de Géologie CNRS ENS Paris, FranceDepartamento de Geofisica, Universidad de Chile
Thanks to SPICE, ANR DEBATE and CONICYT
Earthquakes as dynamic shear ruptures
Preexisting Fault systemin the Mojave desert
Rupture modelled on the complex faultsystem determined from Geology, Geodesy andSeismology
Aochi et al. 2003
The good old circular crack explains Brune’s spectrum
22 /1
1)(
c
rc
34.2
r
Let us back track 40 years:
The Tocopilla earthquake sequence in Northern Chile
Main event Mw 7.7on 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
a
o
rr f
β
M
μE=C
30
3
2
An alternative view
Mw
Scaling of energy with earthquake size
W
Er
Gc
For Brune’s model
3
30
3
7
32
fr
CW
Er
r
Brune used
rf
3724.00
466.0WErSGEW cr
Scaling of Energy release rate Gc
W
Er
Gc
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 7.7on 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 = 1. 1019 Nm
Far field body waveinversion
Peyrat et al, 2007
Near-field kinematic inversion of the 16/12/2007 earthquake
Residual rms
Data Filtered
0.05 - 0.2 Hz
Result of non-linear Inversion with NA.
0.22
EW displacement
Main feature:
vr ~ 1.5 km/s
Numerical simulation by staggered grid Finite Differences
Dynamic Forward problem
FD Cube 32 km3
x = 200 mt = 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
Dc
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
modelAsperity: 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 , , x0, y0
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 earthquakeConvergence of the algorithm
c
e
G
bT
2
=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 0.02-2 Hz band
Main stopping phaseStart phase
stopping phase
Start phase
EW component
Disp
lace
men
t
[m]
Residual RMS 0.18
Dynamic inversion of 16/12/2007 earthquake in Northern Chile
Inverted 9 near field 3-comp displacement records 0.02-2 Hz band
Main stopping phaseStart phase
stopping phase
Start phase
Z component
Disp
lace
men
t
[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 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
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 theAsperity 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 0.02-2 Hz band
Main stopping phaseStart phase
stopping phase
Start phase
EW component
Disp
lace
men
t
[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
0.02-2 Hz band
Main encircling phaseStart phase
stopping phase
Start phase
EW component
Disp
lace
men
t
[m]
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)
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
MicroscaleSteady state mechanicsvr
(< 0.3 Hz 5 km)
(>0.5 Hz <2 km)
(non-radiative)
(~ 100 m)
a
Gc: choosen so that
rupture ocurs and is subshear( iff 1<<1.2)
Initial patch radius R
Barrier
1c
uasp D
RT
c
e
G
bT
2
Stress drop fault size
Dynamic parameters are not independent
From kinematics
b