Stress III The domino effect Stress transfer and the Coulomb Failure Function Aftershocks Dynamic triggering Volcano-seismic coupling.

Stress III

• The domino effect• Stress transfer and the Coulomb Failure Function• Aftershocks• Dynamic triggering• Volcano-seismic coupling

Example from California:

Figure from www.earthquakecountry.info

Stress III: The domino effect

Example from the North Anatolia Fault (NAF):

Stress III: The domino effect

Figure from Stein et al., 1997

Animation from the USGS site

Slip on faults modifies the stress field:

Stress III: The Coulomb Failure Function

Stress III: The effect of a stress step

Stresses in the crust may change slowly due to the steady plate motion, and may change abruptly due to earthquakes, volcanic activity and other more.

time

abruptperturbations

steady platemotion

stress

Stress III: 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.

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Δtime =Δstress

dstress /dtime .

A function that measures the enhancement of the failure on a given plane due to a stress perturbation is the Coulomb Failure Function (ΔCFF):

where:S is the shear stress (- positive in the direction of slip)N is the normal stress (- positive in compression)M is the coefficient of friction

Failure on the plane in question is enhanced if ΔCFF ispositive, and is delayed if it is negative.

Stress III: The Coulomb Failure Function

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ΔCFF = Δσ S − μΔσ N ,

Stress III: The Coulomb Failure Function

The figures above show the change in the fault-parallel shear stress and fault-perpendicular normal stress, due to right-lateral slip along a dislocation embedded in an infinite elastic medium

Stress III: The Coulomb Failure Function

Stress III: The Coulomb Failure Function

The area affected by the stress perturbation scales with the rupture dimensions.

The change in CFF due to the eight largest earthquakes of the 20th century.

Figure from: legacy.ingv.it/~roma/attivita/fisicainterno/modelli/struttureattive

Alaska, 1964, Mw9.2

Chile, 1969, Mw9.5

Animations from the USGS site

Stress III: The Coulomb Failure Function

Example from NAF

The 1906 Great California stress shadow:

Stein, 2002

So the CFF concept works not only for positive, but also for negative stress change.

Stress III: Stress shadows

Stress III: Multiple stress transfers - The Landers and Hector Mine example

Maps of static stress changes suggest that the Landers earthquake did not increase the static stress at the site of the Hector Mine rupture, and that Hector Mine ruptured within a “stress shadow”.

Kilb, 2003

This map shows the change in CFF caused by the Landers quake on optimally oriented planes at 6km depth. The arrows point to the northern and southern ends of the mapped surface rupture.

Figure downloaded from www.seismo.unr.edu/htdocs/WGB/Recent.old/HectorMine

Stress III: Multiple stress transfers - The Landers and Hector Mine example

Stress III: Multiple stress transfers - The Landers and Hector Mine example

• Most Landers aftershocks in the rupture region of the Hector Mine were not directly triggered by the Landers quake, but are secondary aftershocks triggered by the M 5.4 Pisgah aftershock.• The Hector Mine quake is, therefore, likely to be an aftershock of the Pisgah aftershock and its aftershocks.

Felzer et al., 2002

Stress III: Aftershock triggering

Maps of ΔCFF calculated following major earthquakes show a strong tendency for aftershocks to occur in regions of positive ΔCFF.

The Landers earthquake (CA):

King and Cocco (2000);Stein et al., 1992.

Stress III: Aftershock triggering

The Homestead earthquake (CA):

King and Cocco (2000).

Ziv, 2006

Stress III: Remote aftershock triggering

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˙ N Landers + 10 days( ) − ˙ N Landers - 100 days( )˙ N 1985 - 2002( )

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˙ N HM + 10 days( ) − ˙ N HM - 100 days( )˙ N 1985 - 2002( )

Stress III: Remote aftershock triggering

The Mw7.4 Izmit (Turkey):

Mw5.8Two weeks later

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˙ N Izmit + 10 days( ) − ˙ N Izmit - 100 days( )˙ N 1985 - 2002( )

Stress III: Remote aftershock triggering

The decay of M7.4 Izmit aftershocks throughout Greece is very similar to the decay of M5.8 Athens aftershocks in Athens area (just multiply the vertical axis by 2).

Stress III: Dynamic triggering

Figure from Kilb et al., 2000

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ΔCFF(t) = Δσ S (t) − μΔσ N (t) ,

• The magnitude of static stress changes decay as disatnce-3.• The magnitude of the peak dynamic stress changes decay as distance-1.• At great distances from the rupture, the peak dynamic stresses are much larger than the static stresss.

Stress III: Dynamic triggering

Str

ess

Time Time

Instantaneous triggering No triggering

Stress III: Dynamic triggering

Brodsky et al., 2000

Indeed, distant aftershocks are observed during the passage of the seismic waves emitted from the mainshock rupture.

Izmit aftershocks in Greece.

Stress III: Dynamic triggering

• Dynamic stress changes trigger aftershocks that rupture during the passage of the seismic waves.

• But the vast majority aftershocks occur during the days, weeks and months after the mainshock.

• Dynamic stress changes cannot trigger “delayed aftershocks”, i.e. those aftreshocks that rupture long after the passage of the seismic waves emitted by the mainshock.

• It is, therefore, unclear what gives rise to delayed aftershocks in regions that are located very far from the mainshock.

Stress III: Volcano-seismic coupling - the Apennines and Vesuvius example

How normal faulting in the Apennines may promote diking and volcanic eruptions in the Vesuvius magmatic system, and vice versa.

Nostro et al. (1998)

Nostro et al. (1998)

Stress III: Volcano-seismic coupling - the Apennines and Vesuvius example

Coulomb Failure Function calculationsStress on a dike striking

parallel to the Apennines

Stress on a dike strikingPerpendicular to the

Apennines

Pressure change on a spherical magma

chamber

Nostro et al. (1998)

Stress III: Volcano-seismic coupling - the Apennines and Vesuvius example

Volcano-seismic coupling?

Further reading:

• Scholz, C. H., The mechanics of earthquakes and faulting, New-York: Cambridge Univ. Press., 439 p., 1990.• Harris, R. A., Introduction to special section: Stress triggers, stress shadows, and implications for seismic hazard, J. Geophys. Res., 103, 24,347-24,358, 1998.• Freed, A. M., Earthquake triggering by static, dynamic and postseismic stress transfer, Annu. Rev. Earth Planet. Sci., 33, 335-367, 2005.