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Stress III
• The domino effect
• Stress transfer and the Coulomb Failure Function
• Aftershocks
• Dynamic triggering
• Volcano-seismic coupling
Stress III: The domino effect
Example from California:
Figure from www.earthquakecountry.info
Stress III: The domino effect
Example from the North Anatolia Fault (NAF):
Figure from Stein et al., 1997
Stress III: The Coulomb Failure Function
Slip on faults modifies the stress field:
Animation from the USGS site
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.
steady plate
motion
stress
abrupt
perturbations
time
Stress III: The effect of a stress step
The effect of a stress
perturbation is to modify the
timing of the failure according
to:
stress
time 
.
dstress /dtime
That means that the amount
of time advance (or delay) is
independent of when in the
cycle the stress is applied.
Stress III: The Coulomb Failure Function
A function that measures the enhancement of the failure on a
given plane due to a stress perturbation is the Coulomb Failure
Function (CFF):
CFF   S   N ,
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 CFF is
positive, and is delayed if it is negative.
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.
Alaska, 1964, Mw9.2
Chile, 1969, Mw9.5
Figure from: legacy.ingv.it/~roma/attivita/fisicainterno/modelli/struttureattive
Stress III: The Coulomb Failure Function
Example from NAF
Animations from the USGS site
Stress III: Stress shadows
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: 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
Stress III: Multiple stress transfers - The Landers and Hector Mine
example
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
• 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 CFF calculated following major earthquakes show a
strong tendency for aftershocks to occur in regions of positive
CFF.
The Landers earthquake (CA):
King and Cocco (2000);
Stein et al., 1992.
Stress III: Aftershock triggering
The Homestead earthquake (CA):
King and Cocco (2000).
Stress III: Remote aftershock triggering
NÝLanders + 10 days   NÝLanders - 100 days 
NÝ1985 - 2002

Ziv, 2006
NÝHM + 10 days   NÝHM - 100 days 
NÝ1985 - 2002
Stress III: Remote aftershock triggering
NÝIzmit + 10 days   NÝIzmit - 100 days 
NÝ1985 - 2002
The Mw7.4 Izmit (Turkey):

Mw5.8
Two weeks later
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
CFF(t)   S (t)   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.
Figure from Kilb et al., 2000
Stress III: Dynamic triggering
Instantaneous triggering
Time
No triggering
Time
Stress III: Dynamic triggering
Indeed, distant aftershocks are observed during the passage of
the seismic waves emitted from the mainshock rupture.
Izmit aftershocks in Greece.
Brodsky et al., 2000
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)
Stress III: Volcano-seismic coupling - the Apennines and Vesuvius
example
Coulomb Failure Function calculations
Stress on a dike striking
parallel to the
Apennines
Nostro et al. (1998)
Stress on a dike striking
Perpendicular to the
Apennines
Pressure change on a
spherical magma
chamber
Stress III: Volcano-seismic coupling - the Apennines and Vesuvius
example
Volcano-seismic coupling?
Nostro et al. (1998)
Further reading:
• Scholz, C. H., The mechanics of earthquakes and faulting, NewYork: 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, 335367, 2005.