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Fault friction and seismic nucleation phases

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### 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:
- Definition
- Observations
- Open questions

- A mechanical model for dynamic nucleation:
- Ingredients
- Characterization by numerical simulation
- Analytic arguments

- Applications:
- Kobe earthquake
- Broad magnitude range observations

- Implications:
- Scale-dependent or non-linear friction ?
- Nucleation size / earthquake size ?

Outline

- Seismic nucleation phases :
- Definition
- Observations
- Open questions

- A mechanical model for dynamic nucleation
- Applications
- Implications

Definition of a seismic nucleation phase

- Progressive onset of a seismogram, inconsistent withclassical 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 …
- Proper instrument response deconvolution
- Avoid azimuth effect on STF
- EGF appreciated to avoid path/site effects
What to measure ?

- Duration is ill-defined (onset time depends on S/N)
- Measures of the shape are preferred (tn,…)

Observed properties

- Not always observedsource effect / recording conditions?
- Shape is not universal from smooth to bumpy
- Scalingduration3 / M0
- Nucleation M0 / total M0

- 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:
- multiple radiation zones
- rupture path depends on details of the initial stress

- On their initial stage earthquakes are simpler ?
- a single radiation zone (the nucleation zone)
- controlled by intrinsic properties of the fault

- Laboratory observations

Coulomb friction:strength

Static/dynamic friction: stress drop

A brief history of fault frictionSTRESS

Static

Stressdrop

Dynamic

SLIP

Coulomb friction:strength

Static/dynamic friction:stress drop

Cohesion models: fracture energy Gc

Nucleation size

Lc ~ mGc/Dt2

A brief history of fault frictionSTRESS

Fracture energy

Gc

SLIP

Coulomb friction: strength

Static/dynamic friction: stress drop

Cohesion models: fracture energy Gc

Slip weakening friction: critical slip Dc, weakening rate W

Lc ~ m / W

STRESS

W = weakening rate

SLIP

A brief history of fault frictionDc

Coulomb friction: strength

Static/dynamic friction: stress drop

Cohesion models: fracture energy Gc

Slip weakening friction: critical slip Dc, weakening rate W

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

A brief history of fault frictionSTRESS

STATE

SLIP RATE

Seismological constraints on fault friction

- Smaller earthquakes: macroscopic quantities, radiated energy/moment scalings
- Are these dynamic properties relevant for nucleation ?
- OUR GOAL: get the slope W of the friction law during the nucleation phase
- Importance: gives nucleation size (…?)

- Large earthquakes: strong motion data (band-limited < 1Hz)
→ estimates of Gc

but poorly resolved strength and Dc ( > lab)

Outline

- Seismic nucleation phases
- A mechanical model for dynamic nucleation:
- Ingredients
- Characterization by numerical simulation
- Analytic arguments

- Applications
- Implications

W

SLIP

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

Exponential shape of the seismic nucleation phase:

M0(t) ~ exp(Sm t)

Numerical simulation- We characterize the nucleation phase using a simplified boundary element method

Quasi-static nucleation: stable slip in a slowly expanding zone, up to a critical size Lc ~ m/W

Dynamic nucleation:

Early stage dominated by lateral growth

Late stage dominated by exponential slip acceleration

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

I

IIa

IIb

Characteristics of the nucleation phaseFault stress =

-½ r VS× slip rate

+ dynamic interactions

Friction:

Fault stress = - W×slip

radiation damping =

- fault impedance × slip rate

Analytical arguments: case of infinite nucleation zoneWhen integrated over the whole fault plane:

Fault impedance ×slip rate = W × slip

Moment exp(Sm t) where

Sm = weakening rate / fault impedance

Analytic arguments: case of growing nucleation zone

When L = L(t),

M0 rate = s(L) × M0

Where:

S(L) ~ Sm (1-Lc2/L2)½

Rapidly S(L) → Sm

→ The result is asymptotically preserved

Outline

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

- 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 Sm of the Kobe earthquake

D ≈ 100 km

- Observed Sm ≈ 5 Hz
- → Dc ≈ 10 cm : huge compared to lab values !
- Transition lab/geo scales ?

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

Sm

Broad magnitude range observations- 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 …

Sm ~ M0-1/3

Very short time scale observations:

- M0(t) ~ tnwith n=4~5 (self-similar is n=3)
- No systematic M dependence
- Similar observation: Ito (1992) for M<3
- Is this phase IIa ?
- … but attenuation !

Outline

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

Scale-dependent friction?

Moment ~ size3

W ~ 1/size

In the lab, effect of fault roughness on friction:

W ~ 1/scale

Ohnaka et al.

Ohnaka et al.

Non-linear friction ?

Moment ~ slip3

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.
- 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.
- A single weakening rate is not compatible with seismological observations.
- The observed properties of a single earhquake cannot lead to a universal nucleation size.

Nucleation size / earthquake size scaling ?

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

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