View
218
Download
0
Tags:
Embed Size (px)
Citation preview
A DECADE OF PROGRESS :FROM EARTHQUAKE KINEMATICS TO DYNAMICS
Raúl Madariaga
Laboratoire de Géologie, Ecole Normale Supérieure
At the beginning ...
Earthquake Kinematics
1. Elastic model + attenuation
2.. Dislocation model
3.. Modeling program
4.. Seismic data
Slip model
Rupture process
Parkfield 2004
(after Liu et al 2006)
inversionmod
elin
g
Wave propagation around and on a fault
Parkfield 2004
Kinematic model by Liu, Custodio andArchuleta (2006)
Modeling by Finite DifferencesStaggered gridThin B.C.
Full 4th order in spaceNo dampingdx=100m dt=0.01 HzComputed up to 3 Hz
Few hours in intel linux cluster
A very simplified version of Liu et al (2006) model
After K. Sesetyan, E. Durukal, R. Madariaga and M. Erdik
Full 3D velocity model
65 km65 km
up to 60 km
Resolution power up to 3 Hz
yet data resolved only 0.3 Hz !
0 5 10 15 20 25-5
0
5G
H2E
Vp (cm/sec)
Observed
Synthetic
0 5 10 15 20 25-2
0
2Vn (cm/sec)
0 5 10 15 20 25-2
0
2Vz (cm/sec)
0 5 10 15 20 25-5
0
5
GH
3E
0 5 10 15 20 25-2
0
2
0 5 10 15 20 25-1
0
1
0 5 10 15 20 25-5
0
5
GH
1W
0 5 10 15 20 25-5
0
5
0 5 10 15 20 25-2
0
2
0 5 10 15 20 25-10
0
10
GH
2W
0 5 10 15 20 25-5
0
5
0 5 10 15 20 25-2
0
2
0 5 10 15 20 25-10
0
10
GH
3W
0 5 10 15 20 25-2
0
2
0 5 10 15 20 25-2
0
2
0 5 10 15 20 25-5
0
5
GH
4W
0 5 10 15 20 25-5
0
5
0 5 10 15 20 25-2
0
2
0 5 10 15 20 25-5
0
5
GH
5W
0 5 10 15 20 25-5
0
5
0 5 10 15 20 25-2
0
2
0 5 10 15 20 25-5
0
5
GH
6W
time (sec)0 5 10 15 20 25
-1
0
1
time (sec)0 5 10 15 20 25
-2
0
2
time (sec)
Parkfield 2004
Data high pass filtered to 1 Hz.
Synthetics computed For the slip model ofLiu et al up to 3HzOn a 100 m grid
Structure from Chen Ji 2005
Earthquake Quasidynamics m
odel
ing
From Fukuyama and Mikumo (1993)
Earthquake dynamics
Slip is due to stress
relaxation
under the control of friction
Slip evolution is controlled
by geometry
and
stress relaxation
Earthquake Dynamics
1. Elastic model + attenuation
2.. Stress model
4.. Modeling program
5.. Seismic data
Landers 1992
(after OMA, 1997)
mod
elin
g
3.. Friction law
inversion
Wald and Heaton, 1992Peyrat Olsen Madariaga, 2001
Computed
and observed
accelerogram
s
Landers 28/06/92
Olsen et al, 97
Bouchon, 97
Ide and Takeo, 97
Peyrat et al '01
Ill possedness of the inverse problem, the hidden assumptions
Three inverted models that fit the data equally well
Peyrat, Olsen, Madariaga
Global Energy Balance
Seismologists mesure Es directly (still difficult)
Estimate Wc from seismic moment (easily measured)
L = length scaleS = surfaceE
s = radiated energy
W
s = strain energy change
Gc
= surface energy
Kt
= Kostrov's term
L
W
s
KostrovSGWE css
Main result Gc is large w.r.t radiation
For Landers: Moment Mo ~ 1020 Nm
Radiated Energy: Es~1015 J
Surface S~109 m2
Energy spent in fracture: Gc S ~1015 J
Strain Energy change: Ws~1016 J
Similar result for Kobe (Ide and Takeo,1997)
Red is 20 MJ/m2
Kappa ES
An open, but essential question is how to quantify energy release
Asperity
Barrier 1
Barrier 2
Scaling of energy
Landers Gc ~ Es ~ DW ~ 106 J/m2
Sumatra Gc ~ Es ~ DW ~ 107 J/m2W~150 km
W~15 km
= U/Gc
1
1.2
-1 = Es/G
c
0
0.2
Tsunami EQ
Kunlun EQ
How to reduce speed? increase Gc
vr= 0
vr > v
s
What controls rupture propagation?
Dynamic rupture of the Landers earthquake of June 28, 1992
Aochi et al 2003
following
Peyrat et al 2001
.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)
o Seismic data has increased dramatically in quality and
number.
o Opens the way to better kinematic and dynamic models
o Earthquake Modeling has become a well developed
research field
o There are a number of very fundamental problems that
need careful study (geometry, slip distribution, etc)
o Main remaining problem: non-linear dynamic inversion
CONCLUSIONS
No surface rupture observationM
w 6.6~6.8
Pure left-lateral strike slip eventHypocentral depth poorly constrained
Tottori accelerograms have absolute time
Hypocentre determined directly from raw records
The 2000 Western Tottori earthquake
Kinematic inversion of Tottori earthquake
Small slip around the hypocentre
Slip increases towards the upper northern edge of the fault
Velocity Waveforms
EW component
T05
S02 OK015T07OK05
OK04
S15
S03
T06T08
T09
Good fit at nearfield stations (misfit=3.4 L2)
Circular crack dynamics
Starts fromInitial patch
Longitudinal stopping phase
Transverse stopping phase
Stopping phase (S wave)
Slip rate Slip Stress change
Fully spontaneousrupture propagation
underslip weakening friction
Stress drop
P st.phase Rayleigh
S
Slip rate Slip
Rupture process for a circular crack
The rupture process is controlled by wave propagation!
Computational grid
Inversion grid
The main problem with dynamic inversion
Inversion grid has about 30 elements (degrees of freedom)
Computational grid has > 1000 elements
This method was used by Peyrat and Olsen
Inversion of a simple geometrical initial stress field and/or friction laws
Based on an idea by Vallée et Bouchon (2003)
An ellipse has only 7 independentDegrees of freedom (position, angle, axes, stress level)
Finite difference grid is independentof inverted object and has many more(>1000) degrees of freedom.
The initial stress field
Rupture is forced to start from an asperity located at 18 km in depth
Then we modify the elliptical slip distribution until the rupture propagates and the seismograms are fitted
Slip rate Slip Stress change
Dynamic modelling of Tottori
t=2s
t=4s
t=6s
t=8s
Main Results
Velocity waveforms fit observations less well than the kinematic model.
For each station both amplitude and arrival phases match satisfactorily
T05
S04OK015
T07
OK05
OK04
S15
S03
T06T08
T09
Velocity Waveform fitting for EW component
Influence of different rupture patches
S15
T09
Final slip distribution
NS component
NS component
The stopping phase (red) exerts the primary control on the waveform
realsynth
realsynth
OutlookTwo approaches to study the rupture process
The non linear kinematic inversion gives a very good wavefits controlled by a diagonal stopping phase.
The dynamic rupture inversion allows to fit very well both amplitude and arrival phases. The horizontal stopping phase controls the waveforms.
A dynamic inversion with a slip distribution controlled by 2 elliptical patches is in progress.
Far field radiation from circular crack
SpectrumDisplacement pulse
4s
0.25 Hz
Example of velocity data processing
Time measured w/r to origin time
P
S
Data integrated and filtered between 0.1 - 5 Hz
We relocate the hypocentre close to 14 km depth
Example from Northern Chile Tarapacá earthquake
Iquique
From Peyrat et al, 2006
13 June 2005
M=7.8
Mo = 5x1020 Nm
2003 Tarapaca earthquake recorded by the IQUI accelerometer
Thanks to Rubén Boroschev U de Chile
IQUI displacement
IQUI ground velocity
IQUI energy flux
What are them?
Accelerogram filteredfrom 0.01 to 1 Hz
and integrated
Stopping phase
0 4020
10cm/s
18cm
60
Spectrum of Tarapaca earthquakedi
spla
cem
ent
spec
tral
am
plitu
de
-2 slope
20s
0.2