Pp
!
∆σ11
∆σ21
∆σ12
∆σ22
"
∆σe
∆τ
∆CF F = ∆τ + µs ∆σe
fau
where
lt
(σe = σn + Pp )
∆σe (+)
largest +∆CF F :
• unclamping
• shear stress increase
!
∆σ11
∆σ21
∆σ12
∆σ22
"
∆τ (+)
∆CF F = ∆τ + µs ∆σe
where
(σe = σn + Pp )
no
rm
Monday’s class activity
al
fa
ult
!
∆σ11
0
0
0
"
∆CF F = ∆τ + µs ∆σe
(right below building)
α
• clamping
• shear stress increase
• these almost cancelled
for our fault dip and
friction coefficient
• ∆CF F = 0 if tan(α) = 1/µs
∆σn (−)
∆σn = ∆σe
(if Pp = 0)
∆τ (+)
no
rm
• the answer also depends on relative
position of hypocentre and applied load
al
fa
ult
Monday’s class activity - Q3
!
∆σ11
0
0
0
"
(right below building)
• Pore pressure increases
when rock compacts. This
pressure acts to reduce the
compression (clamping) of
the asperities along the fault
Monday’s class activity - Q4
∆CF F = ∆τ + µs ∆σe
where
(σe = σn + Pp )
∆σn (−) ∆σe = ∆σn +∆Pp
+∆τ
no
rm
al
fa
ult
Coulomb stress changes from large
earthquakes can be sufficient to
trigger other earthquakes
This is the main reason for
aftershocks
+x2
+x2
+x1
∆τ is +
+x1
∆τ is −
From King et al (BSSA, 1994)
From King et al (BSSA, 1994)
From King et al (BSSA, 1994)
from Todal et al (JGR, 2005)
from Todal et al (JGR, 2005)
1992 M=7.3 Landers shock
increases stress
at Big Bear
Landers
Big
Bear
Los
Angeles
First 3 hr of
Landers
aftershocks
plotted
from Stein
(Nature, 2003)
1992 M=7.3 Landers shock
promotes the M=6.5 Big
Bear shock 3 hr later
Landers
Big
Bear
Los
Angeles
First 3 hr of
Landers
aftershocks
plotted
from Stein
(Nature, 2003)
…and promotes the
M=7.1 Hector Mine
shock 7 yr later
Hector Mine
Los
Angeles
First 7 yr of
aftershocks
plotted
from Stein
(Nature, 2003)
Bay area shocks during the 75 years before 1906
from Stein (Nature, 2003)
The 1906 SAF Earthquake caused a stress shadow here
Bay area shocks during the 75 years after 1906
from Stein (Nature, 2003)
from Lin & Stein (JGR, 2004)
from Lin & Stein (JGR, 2004)
Random population of creeping but not unstable fault
patches (CFF = or > 0)
slip speed (microns / s)
close to instability
far from
instability
Time remaining to instability (s)
Stress change boosts slip speed of all creeping patches by ∆vslip
Because faster slipping patches are so much closer to failure, small
stress change temporarily causes a profound increase in seismicity
∆vslip ∝ ∆τ
∆vslip
∆vslip
∆vslip
typical aσe :
1 bar?
∆τ = 5 bar
150 times as
many earthquakes
as before
earthquake rate
decreases as 1/t