Remainder of the course:
• forecasting
• earthquake triggering
• local earthquake hazard
Short Assignment 4 given Friday, due last
day of class (April 5)
Course evaluation survey closes April 10
Final exam is here (EOSC M 135), April 20, 8:30 AM
Good conditions for rupture propagation
rupture
not slipping (yet)
shear stress
shear stress
shear stress
required for failure
= µs σn
shear stress before
earthquake started
distance along the fault
*biggest for high normal stress
and velocity weakening (big
frictional force drop with slipping)
shear stress on unbroken fault next
to the rupture increases!
the shear stress increase is
proportional to the earthquake stress
drop* and (1/ the square root of
distance to the rupture tip)
neighboring parts of the fault can be
driven to failure by this domino effect
if they are already close to failure
A process favoring large stress drops: “extreme
weakening” of the fault
Recent lab experiments show that if slip speed gets going really fast
(up to about 0.1-0.2 m/s) dynamic friction may drop to near zero
this large drop
in frictional
strength will
encourage the
earthquake to
keep going.
Bad conditions for rupture propagation
shear stress
rupture
not slipping (yet)
shear stress
required for failure
= µs σn
shear stress
shear stress before
earthquake started
distance along the fault
• Long, continuous fault (no need for rupture to jump from segment to
segment, which costs energy)
• Shear stress near the Coulomb threshold along the whole fault
• Big stress drop and large “kick” to adjacent parts of the fault make big quake
more likely (large normal stress and very velocity weakening friction)
1906 M 8
as
re
nd
nA
Sa
1992 M 7.4
1857 M 7.?
• Segmented faults (rupture must jump from segment to segment,
which costs energy)
• Shear stress or Coulomb failure stress heterogeneous
• Weak stress drop and small “kick” to adjacent parts of the fault
make larger quake unlikely
smaller
earthquakes
as
re
nd
nA
Sa
σ2
σ1
σn
τ
Coulomb failure criterion:
The fault can slip if:
τ = µσn
What if shear stress varies along the fault?
What if effective normal stress varies along the fault?
What if BOTH vary along the fault (eek)?
• Segmented (discontinuous) faults - rupture must jump from segment
to segment, which takes energy OR long continuous fault
• Heterogeneous fault frictional strength and shear stress (so whole
fault NOT close to Coulomb failure threshold) OR whole fault close
to Coulomb failure.
• Small stress drop and small “kick” to adjacent parts of the fault (due
to low
x a-b) OR large stress drop and “kick” to adjacent parts
of the fault (high
x a-b).
Variations in frictional strength
and in velocity weakening (a-b)
may be due to variations in
caused by pore fluid pressure
Consider the effect of water on the fault.
Consider liquefaction of saturated sand
Grains are not
touching. This is a
fluid with grains
floating in it.The
load is supported
by the water.
Image from Stanford
University
Rock Physics Lab
Grains are
touching and
are supporting
the load
(stressed parts
of grains are
red).
just add water
at high
pressure.
what will
happen?
C. Scholz 2002
Groundwater is present throughout the upper crust
from Plummer et al., Physical Geology
(text for EOSC 110)
water level in porous, permeable rock = water level in well
water pressure at depth is same as for a column of water
(“unconfined” shallow aquifer)
In some aquifers, and deeper
in the crust, water in pores and
cracks may become trapped.
Fluid cannot flow out faster
than compaction is occurring,
so water pressure goes up.
“pore fluid pressure” can
approach the lithostatic pressure!
(same as for a column of fluid
with the density of saturated rock,
about 2700 kg / m3!)
from Plummer et al., Physical Geology
(text for EOSC 110)
Water trapped inside low-permeability faults
may be at hogh pressure, effectively opposing the normal stress
on the fault (pushing the two sides apart)
low permeability
pore pressure
may increase
dramatically!
Pore fluid pressure can dramatically
reduce the effective normal stress
|σe | = |σn | − Pp
normal stress
or effective normal stress
σe
σe
if water is not overpressured?
depth
At a depth of 10 km:
σn
if pore pressure is close to
lithostatic pressure?
Pore fluid pressure can dramatically
reduce the effective normal stress
|σe | = |σn | − Pp
What does this do to the faultʼs
frictional strength ( µs σe )?
depth
normal stress
or effective normal stress
σn
What does this do to stress drop
(which depends on (a − b)σe )?
Rocky Mt. Arsenal (US Army base) near
Denver Colorado, early 1960’s: 3670 m deep
well was drilled and used for disposal of
wastewater...
Human-triggered earthquakes: wastewater
injection wells
Still happens, recently in Arkansas and Switzerland.
Problem: for most faults we do not know
enough about these three things
• Long, continuous fault (no need for rupture to jump from segment to
segment, which costs energy)?
We have maps and seismicity data to inform us about fault geometry (and
seismic gaps) but some faults are not seen at the surface at all, or look
discontinuous at the Earth’s surface but are continuous at depth.
• Shear stress near the Coulomb threshold along the whole fault?
We do not know shear stress on faults. With GPS we can estimate stressing
RATE only. We also do not know frictional strength of faults in detail. It can
vary a LOT along a fault due to pore fluid pressure variations.
• Large normal stress and velocity weakening friction (big stress drop and large
“kick” to adjacent parts of the fault make a big quake more likely) ?
We do not know how (a-b) and effective normal stress vary along a fault.
(Extreme drop in friction during fast sliding may also happen.)
This makes it hard to predict when earthquakes will
happen based on the physics...
If all else fails,
we can count toads.
R. Grant, J. Zoology, 2010
What about precursors?
Changing well water levels, ground-hugging fog, low-frequency
electromagnetic emission, “earthquake lights”, magnetic field
anomalies up to 0.5% of the Earthʼs dipole field, temperature
anomalies by several degrees over wide areas as seen in
satellite images, changes in the plasma density of the
ionosphere, strange animal behavior, radon and helium
emission, methane emission and formation of colored clouds,
changes in seismicity patterns, bulging of the Earthʼs surface...
Some of these are seen for some quakes but not for
all (or even for many) quakes. Reports of these fail to
address cases where the phenomenon wasnʼt
followed by a major quake).
Most earthquake forecasting is based statistics of past
earthquakes (how often, magnitude, how regular)
In western Canada we know something about:
• The Queen Charlotte Fault
• The Cascadia Subduction zone Fault
In other regions we must use seismicity catalogues and
the Gutenberg-Richter relationship, together with
assumptions about the maximum earthquake size, to
forecast probability of damaging earthquakes.
Mazzotti et al., 2011
Mazzotti et al., 2011