ss=*+(a-b) ln(V/V*)

a-b > 0

stable sliding

a-b < 0

slip is potentially unstable

Correspond to T~300 °C

For Quartzo-Feldspathic rocks

Stationary State Frictional Sliding

(Blanpied et al, 1991)

a-b

Slip as a function of depth over the seismic cycle of a strike–slip fault, using a frictional model containing a transition from unstable to stable friction at 11 km depth

(Sholz, 1998)

Modeling the Seismic Cyclefrom Rate-and-state friction(e.g., Tse and Rice, 1986)

Model of afterslipEvolution of afterslip on BCFZ with time Slip velocity (or slip rate) on BCFZ

Figure 2, 2004

background loading rate afterslip duration

Model of aftershock rateKey assumption: seismicity rate is proportional to the stress rate (time derivative of applied stress, or loading)

Figure 4, 2004

C = 100

Note: the decrease in seismicity rates lasts longer than increase in seismicity rate.

slope of 1/t

Figure 5, 6 and 7, 2004

(Svarc and Savage, 1997)

CPA analysis show that all GPS stations follow about

the same time evolution f(t)

Postseismic Displacements following the Mw 7.2 1992 Landers Earthquake

Modeling Landers afterslip

Step 4: Compute displacement U(r,t) in a bulk:

Modeling Landers afterslip Step 5: Find the best-fitting model parameters to the geodetic data

Figure 4, 2007

too small: maybe due to high pore-pressure

maybe due to dynamic stress change

Observed and predicted Displacements relative to

Sanh Cumulative displacements after 6 yr

rms=16mm

CFF on 340ºE striking fault planesat 15 km depth due to afterslip

CFF (bar)

6 months 6 yr

Figure 9, 2007

CFF on 340ºE striking fault planesat 5, 10, and 15 km depth due to afterslip

Figure 10, 2007

Aftershocks tend to fall preferentially in area of static Coulomb stress increase but there are also earthquakes in area of decrease Coulomb stress

>> the stress history at the location of each aftershocks is a step function and a static Coulomb failure criterion is rejected. Failure needs being a time depend process.

Aftershocks follow the Omori Law (seismicity rate decays as 1/t)

>> the postseismic stress is time dependent in a way that controls the seismicity rate.

OR

Ge277-Experimental Rock Frictionimplication for Aftershocks triggering

Dieterich, J. H. (1994). A constitutive law for rate of earthquake production and its application to earthquake clustering. JGR 99, 2601–2618.

Gomberg, J. (2001), The failure of earthquake failure models, Journal of Geophysical Research-Solid Earth, 106, 16253-16263.

Gross, S., and C. Kisslinger (1997), Estimating tectonic stress rate and state with Landers aftershocks, Journal of Geophysical Research-Solid Earth, 102, 7603-7612.

King, G.C.P., and M. Cocco (2001). Fault interaction by elastic stress changes: New clues from earthquake sequences. Adv. Geophys. 44.

Perfettini, H., J. Schmittbuhl, and A. Cochard (2003a). Shear and normal load perturbations on a two-dimensional continuous fault: 1. Static triggering. JGR 108(B9), 2408.

Perfettini, H., J. Schmittbuhl, and A. Cochard (2003b). Shear and normal load perturbations on a two-dimensional continuous fault: 2. Dynamic triggering. JGR 108(B9), 2409.

Time Delay Explanations

• Failure model involving a nucleation phase (rate-and-state friction, static fatique)

• fluid flow

• postseismic relaxation / creep in the crust, either on faults or distributed through a volume

• viscoelastic relaxation of the lithosphere and asthenosphere

• continued progressive tectonic loading adding to postearthquake stresses

Rate-and-State Friction

• Constitutive laws can be described by two coupled equations:

• the governing equationgoverning equation, which relates sliding resistance (or shear stress) to slip velocity V and state variables i :

= F (V, i, a, b, 0, n)

where a and b are positive parameters, 0 is a reference friction,and n is normal stress

• the evolution equationevolution equation, which provides time evolution of the state variable:

/t = G (V, L, , b)

• Dieterich (1994) uses :

King & Cocco (2001)

Rate-and-State FrictionDieterich (1994)

• Dieterich derives two likely equations to describe seismicity rate as a function of time:

• Note that (13) has the form of Omori’s lawOmori’s law:

R = K / (c + t)

• Similarly (12) gives Omori’s lawOmori’s law for t/ta<1 but seismicity rate merges to the steady state background rate for t/ta>1

• This makes (12) preferable in general

The inferred value of a is around 3-6 10-4

For a small stress change :

Rate-and-State FrictionPerfettini et al. (2003a,b)

Rate-and-State FrictionPerfettini et al. (2003a,b)

Rate-and-State FrictionPerfettini et al. (2003a,b)

Rate-and-State FrictionPerfettini et al. (2003a,b)

Rate-and-State FrictionPerfettini et al. (2003a,b)

Rate-and-State FrictionPerfettini et al. (2003a,b)

Rate-and-State Friction

• In the previous figures, Perfettini et al. considered permanent

variations of the normal stress (loading or unloading step)

• Perfettini et al. show more generally that all stresses for which

CFF(,) are the same are equivalent for this purpose

Perfettini et al. (2003a,b)

Rate-and-State Friction

• Except near the end of the earthquake cycle, the prediction of the Coulomb failure criterion, in terms of clock advance/decay, agrees to the first order (i.e., neglecting the small oscillations)

• This agreement may explain the success of the Coulomb failure criterion in modeling many earthquake sequences

• The discrepancy at the end of the cycle comes from the fact that varies significantly at the end of the cycle

• The departure from a Coulomb-like behavior later in the cycle is the self-accelerating phase

• The transition from the locked to the self-accelerating phase occurs when the state variable becomes greater than its steady state value, i.e., when > ss = Dc/V or when > ss

Perfettini et al. (2003a,b)

Rate-and-State Friction

• One major difference between the Coulomb failure model and

their results is that, at the end of the earthquake cycle, the clock

delay due to unloading steps drops to zero; one example of

such an effect is the 1911 Morgan Hill event occurring in the

1906 stress shadow

• In other words, a fault at the end of its cycle seems to be only

slightly sensitive to external stress perturbations, the nucleation

process being underway

Perfettini et al. (2003a,b)

Influence of Pulse Duration in Dynamic Triggering Perfettini et al. (2003a,b)