Earthquake nucleation

1. Earthquake nucleation Related questions: • How do they begin? • Are large and small ones begin similarly? • Are the initial phases geodetically or seismically detectable?

2. Slip nucleation in the lab Ohnaka’s (1990) stick-slip experiment Figures from Shibazaki and Matsu’ura, 1998

3. Slip nucleation in the lab The hatched area indicates the breakdown zone, in which the shear stress decrease from a peak stress to a constant friction stress. Ohnaka, 1990

4. Slip nucleation in the lab • The 3 phases according to Ohnaka are: • Stable quasi-static nucleation phase (~1 cm/s). • Unstable, accelerating nucleation phase (~10 m/s). • Rupture propagation (~2 km/s).

5. The critical stiffness and the condition for slip acceleration The critical stiffness: In the case of the slip-weakening law: Rice and Ruina (1983) provided a minimum estimate for kcrit, that is relevant for small perturbations from steady state: Slope=k The condition for slip acceleration:

6. The critical stiffness and the self-accelerating approximation Recall that: It is convenient to write this equation as follows: where now contains all the constant parameters. The state evolution law (the aging law) is:

7. The critical stiffness and the self-accelerating approximation For large sliding speeds, the following approximation holds: the solution of which is: and the quasi-static (i.e., slider mass=0) spring-slider force balance equation may be written as:

8. The critical stiffness and the self-accelerating approximation The block neither accelerates nor decelerates if Thus, to obtain the critical stiffness, one needs to take the slip derivative of the force balance equation for This approach leads to: The block will accelerate if:

9. Slip instability on a crack embedded within an elastic medium So far we have examined spring-slider systems. We now consider a crack embedded within an elastic medium. In that case, Hook’s law is written in terms of the shear modulus, G, and the shear strain, , as: Were  is a geometrical constant with a value close to 1. Writing the stress balance equation, and taking the slip derivative as before leads to:

10. Slip instability on a crack embedded within an elastic medium • So now, the equivalent for critical stiffness in the spring-slider system is the critical crack length: • In conclusion: • The condition for unstable slip is that the crack length be larger than the critical crack length. • The dimensions of the critical crack scale with b.

11. Numerically simulated nucleation Dieterich, 1992

12. What controls the size of the nucleation patch? • Lcrit provides only a minimum estimate of the nucleation patch size. • The actual size of the nucleation patch is asymptotic to Lcrit for small a/b, but increases with decreasing a/b. Rubin and Ampuero, 2005

13. What controls the size of the nucleation patch? patches of a>b ? • Precise location of seismicity on the Calaveras fault (CA) suggest that a/b~1. • Slip episodes on patches of a/b>1 may trigger slip on patches of a/b<1, and vice versa. • It is, therefore, instructive to examine slip localization around a/b~1. Rubin et al., 1999

14. What controls the size of the nucleation patch? • Positive stress changes applied on a>b interfaces can trigger quasi-static slip episodes. • Similar to the onset of ruptures on a<b, the creep on intrinsically stable fractures too are preceded by intervals, during which the slip is highly localized. Ziv, 2007

15. What controls the size of the nucleation patch? • The size of the nucleation patch depends not only on the constitutive parameters, but also on the stressing history. Ziv, 2007

16. The effect of negative stress perturbations

17. The effect of negative stress perturbation • Following a negative stress step, sliding velocity drops below the load point velocity, and the system evolves towards restoring the steady-state. • The path along which the system evolves overshoots the steady-state curve, and the amount of overshoot is proportional to the magnitude of the stress perturbation. • Consequently, a crack subjected to a larger negative stress perturbation intersects the steady state at a higher sliding speed, undergoes more weakening and more slip during the nucleation stage. • Similar to the results for positive stress changes, the size of the localization patch depends on the magnitude of the stress perturbation. The greater the stress change is, the smaller is the localization patch.

18. Implications for prediction • The bad news is that small and large quakes begin similarly. • The good news is that, under certain circumstances, the nucleation phase may occupy large areas - therefore be detectable. Calculations employ: a/b=0.7. If a/b is closer to a unity and actual Dc is much larger than lab values, premonitory slip should be detectable. Dieterich, 1992

19. Seismically observed earthquake nucleation phase? Near source recording of the 1994 Northridge earthquake Ellsworth and Beroza, 1995 Note that real seismograms do not show the linear increase of velocity versus time that is predictable by the self-similar model predicts.

20. Seismically observed earthquake nucleation phase? Ellsworth and Beroza, 1995 For a given event, it’s initial seismic phase is proportional to it’s final size; but this conclusion is inconsistent with the inference (a few slides back) that the dimensions of the nucleation patch depend on the constitutive parameters and the normal stress.

21. Seismically observed earthquake nucleation phase? • Recall that: • Some of the previously reported seismically observed initial phases are due to improper removal of the instrumental effect (e.g., Scherbaum and Bouin, 1997). • Some claim that the slow initial phase observed in teleseismic records are distorted by anelastic attenuation or inhomogeneous medium.

22. Further reading • Dieterich, J. H., Earthquake nucleation on faults with rate- and state-dependent strength, Tectonophysics, 211, 115-134, 1992. • Iio, Y., Observations of slow initial phase generated by microearthquakes: Implications for earthquake nucleation and propagation, J.G.R., 100, 15,333-15,349, 1995. • Shibazaki, B., and M. Matsu’ura, Transition process from nucleation to high-speed rupture propagation: scaling from stick-slip experiments to natural earthquakes, Geophys. J. Int., 132, 14-30, 1998. • Ellsworth, W. L., and G. C. Beroza, Seismic evidence fo an earthquake nucleation phase, Science, 268, 851-855, 1995.