Fault friction and seismic nucleation phases Jean-Paul Ampuero Princeton University J.P. Vilotte (IPGP), F.J. Sánchez-Sesma (UNAM) Data from: W. Ellsworth, B. Shibazaki, H. Ito

Outline Seismic nucleation phase: Seismic nucleation phase: –Definition –Observations –Open questions A mechanical model for dynamic nucleation: A mechanical model for dynamic nucleation: –Ingredients –Characterization by numerical simulation –Analytic arguments Applications: Applications: –Kobe earthquake –Broad magnitude range observations Implications: Implications: –Scale-dependent or non-linear friction ? –Nucleation size / earthquake size ?

Outline Seismic nucleation phases : Seismic nucleation phases : –Definition –Observations –Open questions A mechanical model for dynamic nucleation A mechanical model for dynamic nucleation Applications Applications Implications Implications

Definition of a seismic nucleation phase Progressive onset of a seismogram, inconsistent with classical self-similar source model (constant rupture velocity) Progressive onset of a seismogram, inconsistent with classical self-similar source model (constant rupture velocity) Iio (1992)

How to observe them ? Needs high quality data: high sampling rate, low attenuation, high S/N, high gain … Needs high quality data: high sampling rate, low attenuation, high S/N, high gain … Proper instrument response deconvolution Proper instrument response deconvolution Avoid azimuth effect on STF Avoid azimuth effect on STF EGF appreciated to avoid path/site effects EGF appreciated to avoid path/site effects What to measure ? Duration is ill-defined (onset time depends on S/N) Duration is ill-defined (onset time depends on S/N) Measures of the shape are preferred (t n,…) Measures of the shape are preferred (t n,…)

Observed properties Not always observed source effect / recording conditions? Not always observed source effect / recording conditions? Shape is not universal from smooth to bumpy Shape is not universal from smooth to bumpy Scaling duration 3 / M 0 Scaling duration 3 / M 0 Nucleation M 0 / total M 0 Nucleation M 0 / total M 0 Open questions:  Nucleation size mechanically related to earthquake size ?  How to objectively define measurable properties ?  How to relate them to fault friction ?

Why focus on the nucleation phase ? Once started earthquakes are increasingly complex: Once started earthquakes are increasingly complex: multiple radiation zonesmultiple radiation zones rupture path depends on details of the initial stressrupture path depends on details of the initial stress On their initial stage earthquakes are simpler ? On 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 observations Laboratory observations

A brief history of fault friction Coulomb friction: strength Coulomb friction: strength SLIP STRESSSTRESS STRENGTH

A brief history of fault friction Coulomb friction: strength Coulomb friction: strength Static/dynamic friction: stress drop Static/dynamic friction: stress drop SLIP STRESSSTRESS Static Dynamic Stress drop

A brief history of fault friction Coulomb friction: strength Coulomb friction: strength Static/dynamic friction: stress drop Static/dynamic friction: stress drop Cohesion models: fracture energy G c Cohesion models: fracture energy G c Nucleation size L c ~  G c /   SLIP STRESSSTRESS Fracture energy GcGc

A brief history of fault friction Coulomb friction: strength Coulomb friction: strength Static/dynamic friction: stress drop Static/dynamic friction: stress drop Cohesion models: fracture energy Gc Cohesion models: fracture energy Gc Slip weakening friction: critical slip Dc, weakening rate W Slip weakening friction: critical slip Dc, weakening rate W Lc ~  / W SLIP STRESSSTRESS W = weakening rate DcDc

A brief history of fault friction Coulomb friction: strength Coulomb friction: strength Static/dynamic friction: stress drop Static/dynamic friction: stress drop Cohesion models: fracture energy Gc Cohesion models: fracture energy Gc Slip weakening friction: critical slip Dc, weakening rate W Slip weakening friction: critical slip Dc, weakening rate W Rate-and-state friction: healing, velocity weakening (a,b) Rate-and-state friction: healing, velocity weakening (a,b) SLIP RATE STRESSSTRESS STATE

Seismological constraints on fault friction Smaller earthquakes: macroscopic quantities, radiated energy/moment scalings Smaller earthquakes: macroscopic quantities, radiated energy/moment scalings Are these dynamic properties relevant for nucleation ? Are these dynamic properties relevant for nucleation ? OUR GOAL: get the slope W of the friction law during the nucleation phase OUR GOAL: get the slope W of the friction law during the nucleation phase Importance: gives nucleation size (…?) Importance: gives nucleation size (…?) Large earthquakes: strong motion data (band-limited < 1Hz) Large earthquakes: strong motion data (band-limited < 1Hz) → estimates of Gc but poorly resolved strength and Dc ( > lab)

Outline Seismic nucleation phases Seismic nucleation phases A mechanical model for dynamic nucleation: A mechanical model for dynamic nucleation: –Ingredients –Characterization by numerical simulation –Analytic arguments Applications Applications Implications Implications

A dynamic nucleation model: ingredients Planar fault in elastic medium Planar fault in elastic medium Linear slip weakening friction Linear slip weakening friction Heterogeneous initial stress + uniform tectonic load Heterogeneous initial stress + uniform tectonic load SLIP STRESSSTRESS W

Numerical simulation We characterize the nucleation phase using a simplified boundary element method We characterize the nucleation phase using a simplified boundary element method Exponential shape of the seismic nucleation phase: M 0 (t) ~ exp(S m t)

Characteristics of the nucleation phase I. Quasi-static nucleation: stable slip in a slowly expanding zone, up to a critical size Lc ~  /W II. Dynamic nucleation: a.Early stage dominated by lateral growth b.Late stage dominated by exponential slip acceleration Phase IIb leads to an observable quantity, the growth rate s m, related to an effective property, the weakening rate W. I IIa IIb

Elastodynamics: Fault stress = Fault stress =  ½  V S × slip rate  ½  V S × slip rate + dynamic interactions Analytical arguments: case of infinite nucleation zone Friction: Fault stress = - W×slip Fault stress = - W×slip radiation damping = - fault impedance × slip rate When integrated over the whole fault plane: Fault impedance ×  slip rate  = W ×  slip  Moment  exp(S m t) where S m = weakening rate / fault impedance

Analytic arguments: case of growing nucleation zone When L = L(t), M 0 rate = s(L) × M 0 Where: S(L) ~ S m (1-L c 2 /L 2 ) ½ Rapidly S(L) → S m → The result is asymptotically preserved

Outline Seismic nucleation phase Seismic nucleation phase A mechanical model for dynamic nucleation A mechanical model for dynamic nucleation Applications: Applications: –Kobe earthquake –Broad magnitude range observations Implications Implications

An example: the nucleation of the Kobe earthquake M 7.2 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 rate S m of the Kobe earthquake Observed S m ≈ 5 Hz Observed S m ≈ 5 Hz → D c ≈ 10 cm : huge compared to lab values ! → D c ≈ 10 cm : huge compared to lab values ! Transition lab/geo scales ? Transition lab/geo scales ?  ≈ 100 km  ≈ 30 km, EGF deconvolved

Effect of the fault zone ? The structure of the damaged fault zone can have an effect on dynamic nucleation (speed-up) The structure of the damaged fault zone can have an effect on dynamic nucleation (speed-up) Highly damaged core zone is needed to match W≈ 3 MPa/m estimated from strong motion data Highly damaged core zone is needed to match W≈ 3 MPa/m estimated from strong motion data

Broad magnitude range observations S m ~ M 0 -1/3 Sm From Ellsworth and Beroza (1994) catalog of nucleation phases (50):  A selected subset (7) shows exponential nucleation.  Large events are more complex → S m is an effective (average) property  Small events are harder to analyse: slow sampling, attenuation …

Very short time scale observations: M 0 (t) ~ t n with n=4~5 (self-similar is n=3) M 0 (t) ~ t n with n=4~5 (self-similar is n=3) No systematic M dependence No systematic M dependence Similar observation: Ito (1992) for M<3 Similar observation: Ito (1992) for M<3 Is this phase IIa ? Is this phase IIa ? … but attenuation ! … but attenuation !

Outline Seismic nucleation phase Seismic nucleation phase A mechanical model for dynamic nucleation A mechanical model for dynamic nucleation Applications Applications Implications: Implications: –Scale-dependent or non-linear friction ? –Nucleation size / earthquake size ?

Scale-dependent friction? Moment ~ size 3 W ~ 1/size In the lab, effect of fault roughness on friction: W ~ 1/scale Ohnaka et al.

Non-linear friction ? Moment ~ slip 3 W ~ 1/slip  Support from lab (Chambon et al.)  Support from apparent stress/moment scaling (Abercrombie-Rice)  Enhances complexity in continuum models of seismic cycle (Shaw and Rice) Chambon et al.

Conclusions: We explored the implications of a linear slip weakening model of dynamic nucleation. We explored the implications of a linear slip weakening model of dynamic nucleation. Robust properties of the seismic nucleation phase can be related to mechanical properties of the fault. Robust properties of the seismic nucleation phase can be related to mechanical properties of the fault. The seismic nucleation phase is a late dynamic stage. The seismic nucleation phase is a late dynamic stage. A single weakening rate is not compatible with seismological observations. A single weakening rate is not compatible with seismological observations. The observed properties of a single earhquake cannot lead to a universal nucleation size. The observed properties of a single earhquake cannot lead to a universal nucleation size.

Nucleation size / earthquake size scaling ? Still an open question … Still an open question … … but our results point towards a new paradigm: multi-scale/non-linear friction. … but our results point towards a new paradigm: multi-scale/non-linear friction. Ongoing work: simulations of nucleation with steep power law friction Ongoing work: simulations of nucleation with steep power law friction More observations: improving EGF analysis More observations: improving EGF analysis