Transcript Diapositive 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
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
Let us back track 40 years:
The good old circular crack explains Brune’s spectrum

r

c 2.34
r
1

(
) 2 2
1

/
c
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
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
The usual view of this variation
Following Ide and Beroza
An alternative view
Deviation of self-similarity over 7 orders of magnitude
μEr β 3  a
Cr = 2 3 
M o f 0 
Decreasing
damping
Boatwright’s
Mw
Brune spectrum
Scaling of energy with earthquake size
Er
For Brune’s model
3 3
r
f0
E
32
r
 C
r
3

W 7 
W
Brune used
Gc

WE
G
r
cS

f0 0.3724
r
Er
0.466
W
Scaling of Energy release rate Gc
Er
W
Gc
Rupture process for a circular crack
Slip rate
P st.phase
Rupture front grows
Slip
Rayleigh
S
Radiation is controlled by wave propagation inside the fault!
Far field radiation from circular crack
rupture
-2
-2
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 = 1. 1019 Nm
Far field body wave
inversion
Peyrat et al, 2007
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
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.
Friction law: slip weakening
Fault
Propagation to surface with Axitra
(Bouchon-Coutant)
Paraxial absorbing BC. on the faces
Dynamic inversion friction law
stress
Tu
Barrier
Gc
Dc
Te shear stress
slip
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
Applied stress
Rupture resistance
barrier
Friction
Te Applied stress
Asperity radius and value at peak
Tu Dc
geometry
a, b , , x0, y0
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
Dynamic inversion of the 16/12/2007 earthquake
Convergence of the algorithm
Te2 b

 Gc

=0.62
0.18
Critical value for
Circular crack is
c = 0.6 MOA 1998
Dynamic inversion of 16/12/2007 earthquake in Northern Chile
Inverted 9 near field 3-comp displacement records
Start phase
0.02-2 Hz band
Main stopping phase
Start phase
Displacement [m]
stopping phase
EW component
Residual RMS 0.18
Dynamic inversion of 16/12/2007 earthquake in Northern Chile
Inverted 9 near field 3-comp displacement records
Start phase
0.02-2 Hz band
Main stopping phase
Start phase
Displacement [m]
stopping phase
Z component
Residual RMS 0.18
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
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
Cinca 95, Ancorp 96 profile
From Oncken et al, 2003
Summary of Dynamic inversion of 16/12/2007 earthquake
1 1019 N m
Moment
Stress Drop
15 MPa
Peak Stress
23.7 MPa
Gc
Dc
Semi minor axis
Rupture Speed
2.5 MJ/m2
0.2 m
5 km
1.5 km/s
Radiation dominated by stopping Phase
Resolution of Inversion
Best solution
Resolution of Inversion
forbidden
Best solution
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
Convert Barrier into asperity model
Initial stress
Frictional resistance
Barrier
Asperity
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
Dynamic inversion of the 16/12/2007 earthquake
Asperity
Barrier
Dynamic inversion of 16/12/2007 earthquake in Northern Chile
Inverted 9 near field 3-comp displacement records
Start phase
0.02-2 Hz band
Main stopping phase
Start phase
Displacement [m]
stopping phase
EW component
Residual RMS 0.20
An exotic model of the 16 December 2010 earthquake
Initial stress
Asperity model
Rupture process
And slip
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
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
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
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
(non-radiative)
(~ 100 m)
Microscale
vr
Dynamic parameters are not independent
From kinematics
Stress drop
b
fault size
Barrier
a
Te2 b

 Gc
Initial patch radius R
Tu R
asp
1
D
c
Gc: choosen so that
rupture ocurs and is subshear
( iff 1<<1.2)