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