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INTRODUCTION TO EARTHQUAKE MECHANICS: The seismic cycle Elastic rebound theory

INTRODUCTION TO EARTHQUAKE MECHANICS: The seismic cycle Elastic rebound theory. The simplistic view is too simple…. The elastic rebound theory (according to Raid, 1910). The spring-slider analog. Frictional instabilities. The common notion is that earthquakes are frictional instabilities.

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INTRODUCTION TO EARTHQUAKE MECHANICS: The seismic cycle Elastic rebound theory

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  1. INTRODUCTION TO EARTHQUAKE MECHANICS: • The seismic cycle • Elastic rebound theory The simplistic view is too simple…

  2. The elastic rebound theory (according to Raid, 1910)

  3. The spring-slider analog

  4. Frictional instabilities The common notion is that earthquakes are frictional instabilities. • The condition for instability is simply: • The area between B and C is equal to that between C and D.

  5. Frictional instabilities governed by static-kinetic friction static friction stress kinetic friction Lc slip The static-kinetic (or slip-weakening) friction: experiment Constitutive law Ohnaka (2003)

  6. What are the conditions for instabilities in the spring-slider system? static friction stress kinetic friction Lc slip The static-kinetic friction: Thus, the condition for instability is:

  7. Frictional instabilities governed by static-kinetic friction Stress Slip Time

  8. The Parkfield example Magnitude Year A sequence of magnitude 6 quakes have occurred in fairly regular intervals. 2004 The next magnitude 6 quake was anticipated to take place within the time frame 1988 to 1993, but ruptured only on 2004.

  9. So the occurrence of major quakes is non-periodic - why?

  10. The role of stress transfer Every earthquake perturb the stress field at the site of future earthquakes. Animation from the USGS site

  11. The effect of a stress step The effect of a stress perturbation is to modify the timing of the failure according to: That means that the amount of time advance (or delay) is independent of when in the cycle the stress is applied.

  12. A 0-D spring-slider system is too simple… • Fault networks are extremely complex. • More complex models are needed. • In terms of spring-slider system, we need to add many more springs and sliders. Figure from Ward, 1996

  13. System of two blocks During static intervals: During dynamic intervals: • To simplify matters we set: We define: Several situations:

  14. System of two blocks symmateric ( ) asymmateric ( ) Next we show solutions for: Were: Turcotte, 1997 Breaking the symmetry of the system gives rise to a chaotic behavior.

  15. Frictional instabilities in the lab • Frictional instabilities are commonly observed in lab experiments and are referred to as stick-slip. • Note that the occurrence of stick-slip in the lab is non-periodic as well! Brace and Byerlee, 1966

  16. Summary 1st part • Single spring-slider systems governed by either static-kinetic, or rate- and state-dependent friction give rise to periodic earthquake-like episodes. • The effect of stress change on the system is to modify the timing of the instability. For a fault governed by static-kinetic friction, the time advance depends linearly on the magnitude of the stress step and the stressing rate. • Breaking the symmetry of two spring-slider system results in a chaotic behavior. • If such a simple configuration gives rise to a chaotic behavior - what are the chances that natural fault networks are predictable???

  17. Recommended reading • Scholz, C., Earthquakes and friction laws, Nature, 391/1, 1998. • Scholz, C. H., The mechanics of earthquakes and faulting, New-York: Cambridge Univ. Press., 439 p., 1990. • Turcotte, D. L., Fractals and chaos in geology and geophysics, New-York: Cambridge Univ. Press., 398 p., 1997.

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