Microscopic
and
Macroscopic
Physics
of
Earthquakes
Hiroo
Kanamori
and
Thomas
H.
Heaton
Seismological
Laboratory,
California
Institute
of
Technology,
Pasadena
California
91125
Frictional
melting
and
fluid
pressurization
can
play
a key
role
in
rupture
dynamics
of
large
earthquakes.
For
faulting
under
frictional
stress
ar,
the
temperature
increases
with
cr.r
and
the
earthquake
magnitude,
Mw.
If
the
thickness
of
the
heated
zone,
w,
is
of
the
order
of
a few
mm,
then,
even
for
a
modest
a
1
,
the
temperature
rise,
ll.T,
would
exceed
1000°
for
earthquakes
with
Mw=5
to
6,
and
melting
is
likely
to
occur,
and
reduce
friction
during
faulting.
If
fluid
exists
in
a fault
zone,
a
modest
ll.T
of
1
00
to
200°
would
likely
increase
the
pore
pressure
enough
to significantly
reduce
friction
for
earthquakes
with
Mw=3
to
4.
The
microscopic
state
of
stress
can
be
tied
to
macroscopic
seismic
parameters
such
as
the
seismic
moment,
M
0
,
and
the
radiated
energy,
ER,
by
averaging
the
stresses
in
the
microscopic
states.
Since
the
thermal
process
is
important
only
for
large
earthquakes,
the
dynamics
of
small
and
large
earthquakes
can
be
very
different.
This
difference
is
reflected
in
the
observed
relation
between
the
scaled
energy
e
=ERIM
0
and
Mw.
The
observed
e
for
large
earthquakes
is
1
0
to
1
00
times
larger
than
for
small
earthquakes.
Mature
fault
zones
such
as
the
San
Andreas
are
at
relatively
moderate
stress
levels,
but
the
stress
in
the
plate
interior
can
be
high.
Once
slip
exceeds
a threshold,
runaway
rupture
could
occur,
and
could
explain
the
anomalous
magnitude-frequency
relationship
observed
for
some
mature
faults.
The
thermally
controlled
slip
mechanism
would
produce
a
non-linear
behavior,
and
under
certain
circumstances,
the
slip
behavior
at
the
same
location
may
vary
from
event
to
event.
Also,
slip
velocity
during
a large
earthquake
could
be
faster
than
what
one
would
extrapolate
from
smaller
earthquakes.
INTRODUCTION
Modem
broad-band
seismic
data
have
allowed
seismologists
to
determine
important
seismic
source
parameters
such
as
seismic
moment,
M
0
,
radiated
energy,
ER,
rupture
parameters,
and
stress
drops
of
earthquakes
over
a large
magnitude
range.
However,
at
short
length
scales,
GeoComplexity
and
the
Physics
of
Earthquakes
Geophysical
Monograph
120
Copyright
2000
by
the
American
Geophysical
Union
resolution
of
seismic
methods
is
limited
because
of
the
complex
propagation
and
wave
attenuation
effects
near
the
Earth's
surface,
and
it
is
difficult
to
determine
the
details
of
rupture
process
below
some
length
scale.
The
complex
wave
forms
at
high
frequency
must
be
controlled
by
microscopic
processes
on
a fault
plane.
Such
microscopic
processes
include
frictional
melting
[Jeffreys,
1942;
McKenzie
and
Brune,
1972;
Richards,
1977;
Sibson,
1977;
Cardwell
et
at.,
1978],
fluid
pressurization
[Sibson,
1973;
Lachenbruch,
1980;
Mase
and
Smith,
1985,
1987],
acoustic
fluidization
[Melosh,
1979,
1996],
dynamic
unloading
effects
[
Schallamach,
1971;
Brune
et
a/.,
1993;
Weertman,
1980;
Ben-Zion
and
Andrews,
1998;
Mora
and
Place,
1998,
1999]
and
geometrical
effects
[Scott,
1996].
147
148
MICROSCOPIC
AND
MACROSCOPIC
PHYSICS
OF
EARTHQUAKES
The
importance
of
thermal
processes
in
earthquake
mechanics
has
long
been
recognized.
Sibs
on
[
I977]
discussed
the
implication
of
frictional
heating
for
fault
dynamics.
He
suggested
that
melt
formation
and
transient
increases
in
fluid
pressure
caused
by
frictional
heating
may
decrease
the
friction
to
near-zero
values
once
slip
is
initiated.
Here,
we
extend
the
model
discussed by
Sibson
in
light
of
recent
seismological
data.
A
recent
study
of
the
deep
Bolivian
earthquake
(M=8.3,
depth=637
km)
[
Kanamori
et
a/.,
1998]
presented
an
interesting
observational
case
which
suggests
a
dominant
role
of
thermal
processes
during
faulting.
For
this
earthquake,
the
released
potential
energy,
1.4xi0
18
J,
is
at
least
30
times
larger
than
the
radiated
energy,
with
a large
amount
of
non-
radiated
energy
(comparable
to
the
total
thermal
energy
released
during
the
I980
Mount
St.
Helens
eruption)
deposited
in
a relatively
small
fault
zone
over
a time
scale
of
less
than
a minute.
The
thermal
process
during
faulting
would
cause
a
complex
sequence
of
events
including
local
melting,
freezing,
fluid
pressurization,
micro-fracturing
and
injection
of
fluids.
Although
these
microscopic
processes
are
important
for
understanding
rupture
dynamics,
it
is
difficult
to
determine
how
these
processes
work
in
detail
during
faulting
because
of
the
limited
resolution
of
seismic
methods.
In
this
paper,
we
investigate
the
effects
of
frictional
melting
and
fluid
pressurization
and
relate
them
to
macroscopic
seismic
source
parameters
such
as
M
0
and
ER·
This
approach
is
somewhat
similar
to
that
of
statistical
mechanics
in
which
the
physics
applied
to
small-scale
processes
is
used
to
determine
the
average
macroscopic
parameters
such
as
pressure
and
temperature.
THERMAL
BUDGET
DURING FAULTING
The
possibility
of
frictional
melting during
faulting
has
been
suggested
by
several
investigators.
In
particular,
McKenzie
and
Brune
[
1972]
quantitatively
investigated
this
problem
as
a
one-dimensional
heat
conduction
problem.
They
assumed
that
the
fault
surface
is
simultaneously
heated
during
slippage
(i.e.
infinite
rupture
speed)
over
a finite
time,
and
concluded
that
if
both
the
frictional
and
driving
stresses
are
of
the order
of
I kbar,
melting
can
occur
for
fault
slips
as
small
as
one
millimeter.
Richards
[
1977]
solved
elasto-dynamic
equations
for
a
propagating
elliptical
crack,
estimated
frictional
heating
rate
behind
the
rupture
front,
and
showed
that
if
the
driving
stress
is
100
bars
and
the
fault
particle
velocity
is
I
0
em/sec
at
nucleation,
a temperature
rise
of
about
1000°
can
occur
within
a few
seconds.
These
studies
indicate
that
frictional
melting
is
likely
to
occur
during
seismic
faulting,
at
least
locally.
Here
we
consider
a gross
thermal
budget
during
faulting
under
a frictional
stress
a!-
Let
S
and
D
be
the
fault
area
Lines
of
constant
stress
drop
(bars)
10
1
10
10
10
4
10
5
Source
Dimension
{m)
Figure
1.
Static
stress
drop
of
earthquakes.
Modified
from
[Abercrombie
and
Leary,
1993].
and
the
displacement
offset
respectively.
Then
the
total
heat
generated
during
faulting
is
Q=aps.
If
we
assume
that
the
heat
is distributed
during
seismic
faulting
within
a
layer
of
thickness
w
around
the
rupture
plane,
the
average
temperature
rise
!l.T
is
given
by
!l.T=
Q/CpSw=
a
1
D!Cpw
(1)
where
C
is
the
specific
heat,
and
p
is
the
density.
In
general
D
increases
with
the
earthquake
magnitude,
M
w·
Here
we
use
a simple
circular
model
in
which
the
static
stress
drop
is
!l.as
[Eshelby,
1957].
Then,
where
M
0
is the
seismic
moment
and
J.l
is the
rigidity.
From
(1)
and
(2),
we
obtain
(2)
!l.T
=
(16
I
7)
213
(1
I
1r)a
1
t1a;
13
M6
13
I
pCpw
(3)
The
seismic
moment
M
0
is
related
to
MwbY
IogM
0
=1.5Mw
+9.1
(M
0
in
Nm)
(4)
The
static
stress
drop,
!l.as,
for
most
earthquakes
is
in
the
range
of
1
0
to
1
00
bars,
as
shown
in
Figure
1
[Kanamori
and
Anderson,
1975,
Hanks,
1977,
Abercrombie
and
Leary,
1993].
However,
higher
stress
drops
have
been
reported
for
some
earthquakes
for
which
the
source
dimension
was
determined
well
[e.g.
Kanamori
et
al.,
1990;
Wald,
1992].
Also,
there
is
evidence
that
the
stress
drop
can
be
locally
very
high
(up
to
25
kbar)
around
small
asperities
[Nadeau
and
Johnson,
1998].
Since
the