VII. The seismic cycle

1. VII. The seismic cycle VII. 1 Conceptual and kinematic models VII.2 Interseimic coupling VII.3 Comparison with observations

2. Premises • Slip on any point on a fault results from seismic slip event and/or aseismic creep • Faults are separating domains with negligible deformation in the long term : slip at any point on the fault must be consistent with the rate predicted from the block motion of one side of the fault with respect to the other.

3. The ‘elastic rebound’ theory The medium is purely elastic only if, over a long period of time cumulative coseismic slip near the surface equals slip due to creep at depth. In other words, the fault walls act as rigid blocks that pass each other without internal strain. = + Long Term = Interseismic + Coseismic

4. The ‘elastic rebound’ model A testable implication: Long term fault slip rate = average interseismic rate = +

5. The ‘backslip’ model of interseimsic strain interseismic strain = - Co-seismic strain (except on the fault where the co-seismic strain has a singularity) Strain on each side of the fault is equivalent to that obtained from a fault that would slip ‘backward’. This works because by virtue of linear elasticity: -Coseismic (S) = coseismic (-S) = + (Savage, 1983)

6. Backslip = - Coseismic Strain on each side of the fault is equivalent to that obtained from a fault that would slip ‘backward’ (this is because by virtue of linear elasticity: -Coseismic (S)=coseismic (-S) = +

7. Infinite strike-slip fault Interseismic Velocity • Strain rate is constant (velocity field is stationary) if creep rate and locking depths are constant. • Peak strain occurs at the fault: • For x>>h displacements decrease as 1/x and strain decreases as 1/x2 with distance from the fault. Interseismic strain rate Co-seismic displacements

8. Infinite Strike-Slip fault = Interseismic= Long Term - Coseismic + with, Interseismic velocity // Oy:

9. A simplified view of a sequence of earthquakes 1: a fault is embedded in the elastic crust. Peltzer, JPL Lecture, 2003

10. 2- The fault is locked; plate motion is accommodated by elastic deformation loading shear stress on the fault plane Peltzer, JPL Lecture, 2003

11. 3- Shear stress reaches failure level and an earthquake occurs, locally releasing stress Peltzer, JPL Lecture, 2003

12. 4- Stress is redistributed on fault after first event, bringing other section closer to failure and eventually leading to other earthquakes Peltzer, JPL Lecture, 2003

13. 5- Earthquake sequence goes on… Peltzer, JPL Lecture, 2003

14. Some events are small and do not break the surface Peltzer, JPL Lecture, 2003

15. Other are large and produce a surface break Peltzer, JPL Lecture, 2003

16. In the long run the fault slip uniformly Peltzer, JPL Lecture, 2003

17. Are there any Eqs characteristics which can be predicted? • Area of slip events (‘segment’) • Amount of slip in individual event • Timing of slip event

20. Conceptual Recurrence Models • The characteristic Earthquake Model: A given fault segment always produce the same earthquake (Schwartz and Coppersmith, 1981)

21. Sometime 1 segment breaks alone, sometimes 2 go together. Slip is similar at the same location

22. Conceptual Recurence Models • The characteristic Slip Model: At a given point along a fault co-seismic slip is always the same (Sieh, 2000)

23. (Scholz, 1990)

24. Conceptual Recurrence Models - Two cases of variable slip models- Stress Slip Time Time Time Periodic model Time-predictable model Slip-predictable model • EQs occur when the stress reaches a critical similar value. • EQs have various stress drop. • If you know the slip on a EQ, you can predict the the Time (but not the slip!) of the next EQ • EQs occur at variable stress states. • EQs have same stress drop. • If you know the Time of an EQ, you can predict the Slip (but not the time!) of the next EQ • EQs occur when the stress reaches a critical similar value. • All EQs have same stress drop. (Shimazaki and Nakata, 1980)

25. Earthquakes rupturing repeatedly one location on a fault also tend to cluster in time. (Weldon et al. 2004)

26. Wrightwood Example • NB: This plot assumes constant interseismic rate (Weldon et al. 2004) Earthquakes are not periodic and seem to be neither time predictable nor slip-predictable.

27. Earthquakes are not periodic: • they tend cluster in time and space • returning events rupturing a same fault segments may have different rupture length (but eventually similar slip?)

28. VII. The seismic cycle VII. 1 Conceptual and kinematic models VII.2 Interseimic coupling VII.3 Comparison with observations

29. Interseismic couplingImplications for LargesTEarThquakes magnitude and recurrence

30. before 2005 earthquake after

32. Interseismic coupling Definition: χi =deficit of slip/long term slip (assigned to a fault, varies in time and space) Long term slip rate Determination: Elastic Dislocation Modeling of Interseismic geodetic displacements χi=1 χi=0

33. Interseismic coupling Relation to Seismic slip: If deformation of the hanging wall in the long term is negligible then seismic slip and aseismic transients must balance ISC Long term slip rate Implication: The ISC pattern should determine the location, amplitude/frequency of seismic and aseismic transients. χi=1 χi=0

34. Long Term Subduction rate: V

35. Long Term Subduction rate: V

36. Scalar Moment of ‘characteristic’ EQ: (G: Shear Modulus) • Deficit of Momentrate accumulation Long Term Subduction rate: V

37. Slope: -3/2 Moment Magnitude: Long Term Subduction rate: V

38. EQs follow the Gutenberg-Richter law with b≈ 1 b=0.94 (Sumatra Megathrust, 1976-2014)

39. Frequency of largest EQ in the GR distribution

40. VII. The seismic cycle VII. 1 Conceptual and kinematic models VII.2 Comparison with observations

41. References Bouchon, M., M. Campillo, and F. Cotton, Stress field associated with the rupture of the 1992 Landers, California, earthquake and its implications concerning the fault strength at the onset of the earthquake, Journal of Geophysical Research-Solid Earth, 103, 21091-21097, 1998. Cattin, R., and J. P. Avouac, Modeling mountain building and the seismic cycle in the Himalaya of Nepal, Journal of Geophysical Research-Solid Earth, 105, 13389-13407, 2000. Marone, C., Laboratory-derived friction laws and their application to seismic faulting, Annual Review of Earth and Planetary Sciences, 26, 643-696, 1998. Perfettini, H., and J. P. Avouac, Stress transfer and strain rate variations during the seismic cycle, Journal of Geophysical Research-Solid Earth, 109, 2004. Schwartz, D. P., and Coppersmith, K. J., Fault behavior and characteristic earthquakes: examples from the Wasatch and San Andreas fault zones: J. Geophys. Res., v. 89, p. 5681-5698, 1984. Sieh, K., The repetition of large earthquake ruptures: Hokudan International Symposium and School on Active, p. 465-468, 2000. Shimazaki, K., and T. Nakata, Time-predictable recurrence model for large earthquakes, Geophys. Res. Lett., 7, 279-282, 1980. Scholz, C., The Mechanics of Earthquakes and Faulting: New York, Cambridge University Press, 439 p, 1990. Weldon, R., T. Fumal, and G. Biasi, Wrightwood and the earthquake cycle: What a long recurrence record tells us about how faults works, GSA Today, 14, 4-10, 2004.