INTRODUCTION TO EARTHQUAKE MECHANICS The seismic cycle Elastic

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. • The condition for instability is simply: • The area between B and C is equal to that between C and D.

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

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

Slip Stress Frictional instabilities governed by static-kinetic friction Time

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

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

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

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.

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

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

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

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

Summary 1 st part • Single spring-slider systems governed by either static-kinetic, or rate- and state-dependent friction give rise to periodic earthquakelike 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? ? ?

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.