Earthquake dynamics at the crossroads between seismology,

mechanics and geometry

Raúl Madariaga, Mokhtar Adda-Bedia ENS Paris,

Jean-Paul Ampuero, ETH Zürich,

Valparaiso, 17 August 2006, another big Earthquake of 1906 M=8.4

.Lo f seismic waves

Hi f seismic waves

Different scales in earthquake dynamics

Macroscale

Mesoscale

MicroscaleSteady state mechanics

vr

(< 0.3 Hz 5 km)

(>0.5 Hz <2 km)

(non-radiative)

(< 1 Km)

Geometry

Mechanics

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

Small oscillationsare equivalent to M>6 events

What are them?

Accelerogram filteredfrom 0.01 to 1 Hz

and integrated

Stopping phase

0 4020

10cm/s

18cm

60

Solution by spectral elements

Propagation solvedby SEM

(Vilotte, Ampuero, Festa and Komatisch)

Polynomial order 7

Fracture solvedby slip weakening

frictionon a split interface

Clayton Engquist absorbing boundaries

ttypical grid

A multiply kinked rupture

T

X

Antiplane shear

A complex antiplane

(Mode III) crack

Multiple kink phases Low rupture speeds Residual stresses Diffraction

Tim

eRms stress Velocity

rupture front

Kink waves

Residual stresses (Dieterich, 2005)

Energy flux through a line parallel to the fault trend

Kink waves

10 km

tim

eti

me

position

Slip

Shear stress

shear wave speed

Complex geometry reduces rupture speed

Lower rupture speed

Upper side

Lower side

Energy release rate Gc

Energy flow and rupture speed

Seismic energy Es

)(Gγ(v)=(v)G cc 0 Energy release rate:

Radiated energy per unit surface : )(Gγ(v)][=vE cs 0 1)( From Kostrov, Husseini, Freund

v)(vf

G

E

c

s

23 1 λH Energy release rate reduction by one kink

Energy release rate reduction by n kinks LλnH 23 1

Number of kinks per unit length

Effect of geometrical complexity on rupture propagation

)(GLλn)γ(v=)(vG crrc 0 1 2

Energy Balance

n

CONCLUSIONS

1. Fault kinks break simple symmetry of faulting

2. They generate simple radiation

3. Kinks reduce available energy Gc

4. They reduce rupture speed

4. Kinks may stop rupture

5. Kinks are the site of residual stress concentrations

How are High Frequencies generated ?

High frequency S wave frontRadiation density

Local strain energy

Along the fault

vr

v’rEs

Es'

Es

Es'

Radiation from an antiplane crack with a kink

S

kink S wave(-2 )

Starting asperity

Velocity z Stress zy

Stresszx

Rupture front

vr < v

s

Corner stresses

Comparison of kinked crack with a flat crack propagatingat the same apparent speed

Velocity z Stresszy Stress zx

Rupture front

Residual stressesS waves

There is an apparent paradox:

Supershear

Little high frequency

radiation along the

way

Subshear

strong high frequency radiation

Es

The higher the speed, the less energy is absorbed,

the more energy is radiated