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