Fault friction Fault friction and and

seismic nucleation phasesseismic nucleation phases

Jean-Paul AmpueroJean-Paul AmpueroPrinceton UniversityPrinceton University

J.P. Vilotte (IPGP), F.J. SJ.P. Vilotte (IPGP), F.J. Sáánchez-Sesma (UNAM)nchez-Sesma (UNAM)

Data from: W. Ellsworth, B. Shibazaki, H. ItoData from: W. Ellsworth, B. Shibazaki, H. Ito

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Seismic nucleation phase: Seismic nucleation phase: – DefinitionDefinition– ObservationsObservations– Open Open questionsquestions

A mechanical model for dynamic nucleationA mechanical model for dynamic nucleation::– IngredientsIngredients– Characterization by numerical simulationCharacterization by numerical simulation– Analytic argumentsAnalytic arguments

Applications: Applications: – Kobe earthquakeKobe earthquake– Broad Broad magnitude magnitude range observationsrange observations

Implications: Implications: – SScale-dependent or non-linear friction ?cale-dependent or non-linear friction ? – Nucleation size / earthquake size ?Nucleation size / earthquake size ?

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SSeismic nucleation phaseeismic nucleation phases s : : – DefinitionDefinition– ObservationsObservations– Open Open questionsquestions

A mechanical model for dynamic A mechanical model for dynamic nucleationnucleation

ApplicationsApplications ImplicationsImplications

Definition of a seismic Definition of a seismic nucleation phasenucleation phase

Progressive onset Progressive onset of of a a seismogramseismogram, , inconsistent withinconsistent with classical self-classical self-similar source similar source model (model (constant constant rupture velocity)rupture velocity)

Iio (1992)

How to observe them ?How to observe them ?

Needs high quality data: high sampling rate, Needs high quality data: high sampling rate, low attenuation, high S/Nlow attenuation, high S/N,, high gain high gain … …

Proper instrument response deconvolutionProper instrument response deconvolution AvoidAvoid azimuth azimuth effect on STFeffect on STF EGF appreciatedEGF appreciated to avoid path/site effects to avoid path/site effects

What to measure ?What to measure ? Duration is ill-defined (onset time depends on Duration is ill-defined (onset time depends on

S/N)S/N) Measures of the shape are preferred (tMeasures of the shape are preferred (tnn,…),…)

Observed propertiesObserved properties

Not always observedNot always observed source source effect / effect / recording recording conditions?conditions?

Shape is not universal Shape is not universal from smooth to bumpyfrom smooth to bumpy

ScalingScaling durationduration3 3 // M M00

Nucleation MNucleation M00 / total M / total M00

Open questions:Open questions: Nucleation size Nucleation size mechanically mechanically related to related to earthquake size ?earthquake size ? How to objectively define measurable How to objectively define measurable properties ?properties ? How to relate them to fault friction ?How to relate them to fault friction ?

Why focus on the Why focus on the nucleation phase ?nucleation phase ?

Once started earthquakes are increasingly Once started earthquakes are increasingly complex: complex: • multiple radiation zonesmultiple radiation zones• rupture path depends on details of the initial stress rupture path depends on details of the initial stress

OOn their initial stage earthquakes are simplern their initial stage earthquakes are simpler ? ?• a single radiation zone (the nucleation zone)a single radiation zone (the nucleation zone)• controlled by intrinsic properties of the faultcontrolled by intrinsic properties of the fault

Laboratory observationsLaboratory observations

A brief history of fault A brief history of fault frictionfriction Coulomb friction: Coulomb friction:

strengthstrength

SLIP

STRESS

STRENGTH

A brief history of fault A brief history of fault frictionfriction Coulomb frictionCoulomb friction::

strengthstrength Static/dynamic Static/dynamic

friction: stress dropfriction: stress drop

SLIP

STRESS

Static

Dynamic

Stress drop

A brief history of fault A brief history of fault frictionfriction Coulomb frictionCoulomb friction::

strengthstrength Static/dynamic Static/dynamic

frictionfriction:: stress dropstress drop Cohesion models: Cohesion models:

fracture energy Gfracture energy Gcc

Nucleation sizeNucleation size

LLcc ~ ~ GGcc//

SLIP

STRESS

Fracture energy

Gc

A brief history of fault A brief history of fault frictionfriction Coulomb frictionCoulomb friction: :

strengthstrength Static/dynamic Static/dynamic

frictionfriction: stress drop: stress drop Cohesion modelsCohesion models: :

fracture energy Gcfracture energy Gc Slip weakening Slip weakening

friction: critical slip friction: critical slip Dc, weakening rate Dc, weakening rate WW

Lc ~ Lc ~ / W/ W

SLIP

STRESS

W = weakening rate

Dc

A brief history of fault A brief history of fault frictionfriction Coulomb frictionCoulomb friction: :

strengthstrength Static/dynamic Static/dynamic

frictionfriction: stress drop: stress drop Cohesion modelsCohesion models: :

fracture energy Gcfracture energy Gc Slip weakening Slip weakening

frictionfriction: critical slip : critical slip Dc, weakening rate WDc, weakening rate W

Rate-and-state Rate-and-state friction: healing, friction: healing, velocity weakening velocity weakening (a,b)(a,b)

SLIP RATE

STRESS

STATE

Seismological Seismological constraints on fault constraints on fault friction friction

Smaller earthquakes: macroscopic Smaller earthquakes: macroscopic quantities, radiated energy/moment quantities, radiated energy/moment scalingsscalings

Are these dynamic properties relevant for Are these dynamic properties relevant for nucleation ?nucleation ?

OUR GOAL: get the slope W of the OUR GOAL: get the slope W of the friction law during the nucleation phasefriction law during the nucleation phase

Importance: gives nucleation size (…?)Importance: gives nucleation size (…?)

Large earthquakes: Large earthquakes: strong motion data strong motion data (band-limited < 1Hz) (band-limited < 1Hz) → → estimates of Gc estimates of Gc but poorly resolved but poorly resolved strength and Dc ( strength and Dc ( >> lab)lab)

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Seismic nucleation phaseSeismic nucleation phasess A mechanical model for dynamic A mechanical model for dynamic

nucleationnucleation::– IngredientsIngredients– Characterization by numerical Characterization by numerical

simulationsimulation– Analytic argumentsAnalytic arguments

ApplicationsApplications ImplicationsImplications

A dynamic nucleation A dynamic nucleation model: ingredientsmodel: ingredients Planar fault in elastic Planar fault in elastic

mediummedium

Linear slip weakening frictionLinear slip weakening friction

Heterogeneous initial stress Heterogeneous initial stress + uniform + uniform tectonic loadtectonic load

SLIP

STRESS

W

Numerical simulationNumerical simulation

We characterize the nucleation phase We characterize the nucleation phase using a simplified boundary element using a simplified boundary element methodmethod

Exponential shape of the

seismic nucleation

phase:

M0(t) ~ exp(Sm t)

Characteristics of the Characteristics of the nucleation phasenucleation phaseI.I. Quasi-static nucleationQuasi-static nucleation: :

stable slip in a slowly stable slip in a slowly expanding zone, up to a expanding zone, up to a critical size Lc ~ critical size Lc ~ /W/W

II.II. Dynamic nucleationDynamic nucleation::a.a. Early stage dominated Early stage dominated

by lateral growthby lateral growthb.b. Late stage dominated Late stage dominated

by by exponentialexponential slip slip accelerationacceleration

Phase IIb leads to an Phase IIb leads to an observable quantity, observable quantity, the growth rate sthe growth rate smm, , related to an related to an effective property, effective property, the weakening rate the weakening rate W.W.

I

IIa

IIb

Elastodynamics:Elastodynamics:

Fault stress = Fault stress =

½ ½ VVSS ×× slip rate slip rate

+ dynamic interactions+ dynamic interactions

Analytical arguments: Analytical arguments: case of infinite case of infinite nucleation zonenucleation zone

Friction:Friction:

Fault stress = - WFault stress = - W××slipslip

radiation damping = radiation damping = - fault impedance - fault impedance ×× slip slip raterate

When integrated over the whole fault plane: When integrated over the whole fault plane:

Fault impedance Fault impedance ×× slip rateslip rate = W = W × × slipslip

Moment Moment exp(S exp(Smm t) t) where where

SSmm = weakening rate / fault = weakening rate / fault impedanceimpedance

Analytic arguments: case Analytic arguments: case of growing nucleation of growing nucleation zonezone

When L = L(t),When L = L(t),

MM00 rate = s(L) rate = s(L) ×× M M00

Where:Where:

S(L) ~ SS(L) ~ Smm (1-L (1-Lcc22/L/L22))½½

Rapidly S(L) Rapidly S(L) → → SSmm

→ → The result is asymptotically preservedThe result is asymptotically preserved

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Seismic nucleation phaseSeismic nucleation phase A mechanical model for dynamic A mechanical model for dynamic

nucleationnucleation Applications:Applications:

– Kobe earthquakeKobe earthquake– Broad Broad magnitude magnitude range observationsrange observations

ImplicationsImplications

An example: the nucleation An example: the nucleation of the Kobe earthquake M of the Kobe earthquake M 7.27.2

Shibazaki et al. (2002)

EGF + short term kinematic inversion (the first 0.7 secs)Δ=103 km. Observed

nucleation phase ≈ 0.6 s

Measure of the growth Measure of the growth rate Srate Smm of the Kobe of the Kobe earthquakeearthquake

Observed SObserved Smm ≈ 5 Hz ≈ 5 Hz → → DDcc ≈ 10 cm : huge ≈ 10 cm : huge

compared to lab values !compared to lab values ! Transition lab/geo scales ?Transition lab/geo scales ?

≈

100

km

≈

30 k

m,

EG

F deco

nvolv

ed

Effect of the fault zone Effect of the fault zone ??

The structure of the damaged fault zone can have an The structure of the damaged fault zone can have an effect on dynamic nucleation (speed-up)effect on dynamic nucleation (speed-up)

Highly damaged core zone is needed to match W≈ 3 Highly damaged core zone is needed to match W≈ 3 MPa/m estimated from strong motion dataMPa/m estimated from strong motion data

Broad magnitude Broad magnitude range observationsrange observations

Sm ~ M0-1/3

Sm

Sm

From Ellsworth and Beroza (1994) catalog of nucleation phases (50):

A selected subset (7) shows exponential nucleation.

Large events are more complex → Sm is an effective

(average) property

Small events are harder to analyse: slow sampling,

attenuation …

Very short time scale Very short time scale observations:observations:

MM00(t) ~ t(t) ~ tnn with n=4~5with n=4~5 (self-similar is n=3)(self-similar is n=3)

No systematic M No systematic M dependencedependence

Similar observation: Similar observation: Ito (1992) for M<3Ito (1992) for M<3

Is this phase IIa ?Is this phase IIa ? … … but attenuation !but attenuation !

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Seismic nucleation phaseSeismic nucleation phase A mechanical model for dynamic A mechanical model for dynamic

nucleationnucleation ApplicationsApplications Implications: Implications:

– SScale-dependent or non-linear friction cale-dependent or non-linear friction ??

– Nucleation size / earthquake size ?Nucleation size / earthquake size ?

Scale-dependent Scale-dependent friction?friction?

Moment ~ Moment ~ sizesize33

W ~ 1/sizeW ~ 1/size

In the lab, In the lab, effect of effect of fault fault roughness roughness on friction:on friction:

W ~ 1/scaleW ~ 1/scaleOhnaka et al.

Ohnaka et al.

Non-linear friction ?Non-linear friction ?

Moment ~ slipMoment ~ slip33

W ~ 1/slipW ~ 1/slip Support from lab Support from lab

(Chambon et al.)(Chambon et al.) Support from Support from

apparent apparent stress/moment scaling stress/moment scaling (Abercrombie-Rice)(Abercrombie-Rice)

Enhances complexity Enhances complexity in continuum models in continuum models of seismic cycle (Shaw of seismic cycle (Shaw and Rice)and Rice)

Chambon et al.

Conclusions:Conclusions:

We explored the implications of a linear slip We explored the implications of a linear slip weakening model of dynamic nucleation.weakening model of dynamic nucleation.

Robust properties of the seismic nucleation Robust properties of the seismic nucleation phase can be related to mechanical properties phase can be related to mechanical properties of the fault.of the fault.

The seismic nucleation phase is a The seismic nucleation phase is a latelate dynamic dynamic stage. stage.

A single weakening rate is not compatible with A single weakening rate is not compatible with seismological observations.seismological observations.

The observed properties of a single earhquake The observed properties of a single earhquake cannot lead to a universal nucleation size.cannot lead to a universal nucleation size.

Nucleation size / Nucleation size / earthquake size earthquake size scaling ?scaling ? Still an open question …Still an open question … … … but our results point towards a but our results point towards a new new

paradigmparadigm: multi-scale/non-linear : multi-scale/non-linear friction.friction.

Ongoing work: simulations of Ongoing work: simulations of nucleation with steep power law nucleation with steep power law frictionfriction

More observations: improving EGF More observations: improving EGF analysisanalysis