Earth and Planetary Science Letters 618 (2023) 118277
Contents lists available at
ScienceDirect
Earth
and
Planetary
Science
Letters
journal
homepage:
www.elsevier.com/locate/epsl
Absolute
stress
levels
in
models
of
low-heat
faults:
Links
to
geophysical
observables
and
differences
for
crack-like
ruptures
and
self-healing
pulses
Valère Lambert
a
,
∗
,
Nadia Lapusta
b
,
c
a
Department
of
Earth
and
Marine
Sciences,
University
of
California,
Santa
Cruz,
CA,
USA
b
Seismological
Laboratory,
California
Institute
of
Technology,
Pasadena,
CA,
USA
c
Department
of
Mechanical
and
Civil
Engineering,
California
Institute
of
Technology,
Pasadena,
CA,
USA
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Article
history:
Received
19
December
2022
Received
in
revised
form
4
May
2023
Accepted
12
June
2023
Available
online
28
June
2023
Editor:
R.
Bendick
Dataset
link:
https://
data
.caltech
.edu
/records
/1619
Dataset
link:
https://
data
.caltech
.edu
/records
/1620
Keywords:
fault
stress
earthquake
ruptures
enhanced
dynamic
weakening
self-healing
pulse
crack-like
rupture
undershoot
Absolute
levels
of
stress
on
faults
have
profound
implications
for
earthquake
physics
and
fault
mechanics.
A
number
of
observations
suggest
that
well-developed,
mature
faults
such
as
the
San
Andreas
Fault
are
generally
“weak,”
i.e.
operate
at
much
lower
levels
of
shear
stress
compared
to
the
higher
expected
shear
resistance
∼
100
MPa
at
seismogenic
depths.
In
particular,
low
heat
flow
measurements
suggest
shear
stress
levels
of
∼
10
MPa
or
less
on
highly
localized
faults.
Geodynamic
constraints
based
on
topography
and
similar
considerations
also
support
“weak”
fault
operation,
and
are
comparable
with
heat-based
constraints
for
some
mature
faults,
but
potentially
higher
for
regions
with
substantial
topography.
Here,
we
investigate
measures
of
average
fault
shear
stress
and
their
relationship
to
geophysically
inferable
quantities
using
numerical
simulations
of
earthquake
sequences
on
rate-and-state
faults
with
low
heat
production,
due
to
chronic
fluid
overpressure
and/or
enhanced
dynamic
weakening
from
the
thermal
pressurization
of
pore
fluids.
We
review
the
earthquake
energy
balance,
focusing
on
energy-
based
definitions
of
average
shear
stress
and
how
the
average
fault
prestress
(a
measure
of
fault
strength
plausibly
relevant
to
geodynamic
constraints)
can
be
expressed
as
the
sum
of
the
dissipation-
based
average
rupture
stress
(which
can,
in
principle,
be
inferred
from
shear-heating
constraints),
and
seismologically
inferable
source
properties,
such
as
the
static
stress
drop
and
apparent
stress.
Our
modeling
demonstrates
that
rapid
dynamic
weakening
and
healing
of
shear
resistance
during
ruptures,
as
exhibited
in
self-healing
pulses,
allows
faults
to
maintain
higher
average
interseismic
stress
levels
despite
low
dynamic
resistance
and
realistic
static
stress
drops,
providing
a
physical
explanation
for
potential
differences
between
topography-based
and
heat-based
constraints
on
fault
shear
stress.
In
our
models,
the
difference
is
related
to
stress
undershoot
and
apparent
stress,
which
can
be
as
large
as
1-3
times
the
static
stress
drop
based
on
our
simulations.
Yet
suitably
large
values
of
apparent
stress
(and
hence
radiated
energy)
are
rarely
inferred
for
natural
earthquakes,
either
because
radiated
energy
is
underestimated,
or
suggesting
that
most
large
earthquakes
do
not
propagate
as
sharp
enough
self-healing
pulses
with
sufficiently
large
undershoot.
Our
results
emphasize
the
distinction
between
dynamic
versus
static
stress
changes
when
relating
earthquake
source
observations
to
absolute
levels
of
fault
stress
and
suggest
that
reviewing
estimates
of
radiated
energy
and
static
stress
drop
from
large
earthquakes,
with
input
from
finite-fault
numerical
modeling,
may
improve
constraints
on
absolute
fault
stress
levels.
©
2023
The
Author(s).
Published
by
Elsevier
B.V.
This
is
an
open
access
article
under
the
CC
BY
license
(
http://creativecommons
.org
/licenses
/by
/4
.0/
).
1.
Introduction
Assessing
the
absolute
levels
of
stress
on
faults
is
a
topic
of
many
geological
and
geophysical
investigations,
with
substantial
implications
for
fault
mechanics,
earthquake
physics,
and
geody-
*
Corresponding
author.
E-mail
address:
valerelambert@ucsc.edu
(V. Lambert).
namics.
Some
of
the
most
notable
constraints
on
the
shear
stress
state
of
mature
faults,
of
∼
20
MPa
or
less,
are
based
on
mea-
surements
indicating
a
lack
of
substantial
heat
flow
around
ma-
ture
faults
(e.g
Brune
et
al.,
1969
;
Lachenbruch
and
Sass,
1980
;
Tanikawa
and
Shimamoto,
2009
;
Fulton
et
al.,
2013
;
Gao
and
Wang,
2014
)
and
the
existence
of
long-lived
narrow
shear
zones
that
do
not
exhibit
evidence
of
melting
(Sibson,
1975
;
Rice,
2006
;
Chester
and
Chester,
1998
;
Wibberley
and
Shimamoto,
2003
).
Ther-
mal
measurements
surrounding
mature
faults
are
in
principle
re-
https://doi.org/10.1016/j.epsl.2023.118277
0012-821X/
©
2023
The
Author(s).
Published
by
Elsevier
B.V.
This
is
an
open
access
article
under
the
CC
BY
license
(
http://creativecommons
.org
/licenses
/by
/4
.0/
).
V. Lambert and N. Lapusta
Earth and Planetary Science Letters 618 (2023) 118277
lated
to
the
average
shear
stress
associated
with
shear
heating
during
substantial
fault
motion.
Such
observations
can
thus
provide
constraints
for
the
average
dynamic
shear
resistance
at
seismic
slip
rates
during
large
earthquakes.
Studies
of
exhumed
mature
faults
suggest
that
shear
motion
can
be
accommodated
within
narrow
layers,
less
than
one
to
several
millimeters
wide
(e.g.
Chester
and
Chester,
1998
;
Wibberley
and
Shimamoto,
2003
).
In
order
to
avoid
pervasive
melt
production
during
dynamic
rupture,
upper
bounds
for
the
average
shear
stress
associated
with
shear
heating
are
ex-
pected
to
be
on
the
order
of
10
MPa
or
less
for
shear
localized
between
1
to
10
mm
(Lachenbruch
and
Sass,
1980
;
Rice,
2006
;
Lambert
et
al.,
2021b
).
Such
low
shear
stress
values
during
fast
slip
on
mature
faults
are
supported
by
in-situ
temperature
mea-
surements
soon
after
major
earthquake
events
(Tanikawa
and
Shi-
mamoto,
2009
;
Fulton
et
al.,
2013
).
Further
evidence
for
the
sim-
ilarly
low-stress
operation
of
mature
faults
arise
from
inferences
of
steep
angles
between
the
principal
stress
direction
and
fault
trace
(Townend
and
Zoback,
2004
)
and
the
geometry
of
thrust-belt
wedges
and
their
internal
faults
(Suppe,
2007
;
Dielforder,
2017
).
Several
studies
have
estimated
the
absolute
stress
levels
along
major
plate
boundary
faults,
such
as
the
San
Andreas
Fault
system,
by
considering
the
force
balance
of
tectonic
block
motion,
topogra-
phy
and
mantle
buoyancy
(Fialko
et
al.,
2005
;
Fay
and
Humphreys,
2006
;
Luttrell
and
Smith-Konter,
2017
),
inferring
shear
stress
levels
of
20
to
30
MPa
averaged
over
seismogenic
depths.
Similar
stud-
ies
suggest
that
the
topography
associated
with
most
subduction
and
collisional
megathrusts
can
be
maintained
by
average
shear
stresses
ranging
from
7
to
25
MPa
(Lamb,
2006
;
Luttrell
et
al.,
2011
;
Dielforder,
2017
;
Dielforder
et
al.,
2020
),
which
are
largely
consistent
with
constraints
based
on
heat
flow
and
other
shear
heating
considerations
for
these
regions
below
20-30
MPa
(e.g.
Gao
and
Wang,
2014
).
Some
calculations
suggest
that
regions
with
more
substantial
topography,
such
as
the
North
Chilean
subduction
zone
and
portions
of
the
San
Andreas
and
San
Jacinto
fault
zones,
may
require
average
shear
stresses
up
to
40
MPa
(Lamb,
2006
;
Fay
and
Humphreys,
2006
).
All
these
estimates
are
much
lower
than
the
expected
seismo-
genic-depth-averaged
shear
resistance
of
about
100-200
MPa,
given
typical
quasi-static
friction
measurements
of
0.6-0.8
in
the
lab
and
confining
conditions
assuming
hydrostatic
fluid
pressures
(Byerlee,
1978
).
However,
some
of
the
higher
topography-based
estimates
of
average
fault
shear
stress
(20-40
MPa)
may
also
be
higher
than
estimates
from
shear
heating,
particularly
if
heat-
based
constraints
limit
average
shear
stresses
to
around
10
MPa
or
less
for
faults
with
highly
localized
shear,
as
evidenced
along
some
mature
strike-slip
faults
such
as
the
San
Andreas
Fault
(e.g.
Brune
et
al.,
1969
;
Lachenbruch
and
Sass,
1980
;
Rice,
2006
;
Lambert
et
al.,
2021a
).
Note
that
evidence
for
low-stress,
low-heat
operation
predominantly
pertains
to
mature
plate
boundary
faults,
whereas
a
number
of
studies
suggest
that
less
mature
active
faults
may
op-
erate
at
stress
levels
consistent
with
Byerlee
values
of
friction
and
hydrostatic
pore
pressures
(Byerlee,
1978
;
Townend
and
Zoback,
2000
).
In
this
work,
we
study
average
shear
stress
levels
in
two
types
of
models
of
low-stress,
low-heat
mature
faults
based
on
field
observations
and
laboratory
experiments,
with
a
focus
on
the
re-
lationship
between
averaged
shear
stress
quantities
relevant
to
heat-based
and
topography
or
geodynamic-based
constraints.
In
the
first
model,
the
fault
is
persistently
weak
due
to
the
presence
of
anomalously
low
quasi-static
friction
coefficients
and/or
low
ef-
fective
confinement
from
pervasive
fluid
overpressure
(e.g.
Brown
et
al.,
2003
;
Lockner
et
al.,
2011
).
In
the
second
model,
the
shear
resistance
at
seismic
slip
rates
is
significantly
lower
than
the
quasi-
static
shear
resistance
on
faults
during
periods
of
slow
aseismic
slip
and
interseismic
locking
with
negligible
motion,
due
to
en-
hanced
dynamic
weakening
at
seismic
slip
rates
(e.g.
Tsutsumi
and
Shimamoto,
1997
;
Rice,
2006
;
Tullis,
2007
;
Di
Toro
et
al.,
2011
).
Recent
numerical
simulations
of
earthquake
ruptures
in
these
two
types
of
fault
models
have
demonstrated
that
they
can
be
po-
tentially
distinguished
by
seismological
observations
(Lambert
et
al.,
2021b
).
Earthquake
ruptures
in
persistently
weak
fault
mod-
els
with
typically
inferred
static
stress
drops
(i.e.
the
difference
in
average
fault
shear
stress
before
and
after
the
earthquake)
be-
tween
1
to
10
MPa
(e.g.
Shearer
et
al.,
2006
;
Allmann
and
Shearer,
2009
;
Ye
et
al.,
2016
)
propagate
as
crack-like
ruptures.
In
such
rup-
tures,
seismic
slip
at
each
fault
location,
once
initiated,
continues
until
arrest
waves
arrive
from
the
edges
of
the
fault
or
other
het-
erogeneities
in
the
problem;
as
a
result,
the
portion
of
the
fault
that
slips
at
a
given
time
during
rupture
is
comparable
to
the
final
rupture
size
and
the
local
slip
duration
at
different
points
is
com-
parable
to
the
total
rupture
duration
(Fig.
1
A).
The
word
“crack”
in
the
name
refers
to
analogy
with
opening
cracks
that
also
typically
continue
to
open
until
the
crack
arrests
at
a
barrier.
In
contrast,
ruptures
in
quasi-statically
strong,
dynamically
weak
fault
models
with
1
to
10
MPa
static
stress
drops
typically
propagate
as
self-
healing
pulses
(e.g.
Heaton,
1990
;
Noda
et
al.,
2009
),
in
which
slip
spontaneously
arrests
behind
the
rupture
front
due
to
rapid
local
weakening
and
then
healing;
as
a
result,
only
a
small
portion
of
the
fault
slips
at
a
given
time
and
the
local
slip
duration
is
short
relative
to
the
rupture
duration
(Fig.
1
B).
Numerical
simulations
show
that
self-healing
pulse-like
rup-
tures
have
much
higher
radiated
energy
than
crack-like
ruptures
with
the
same
seismic
moment,
average
static
stress
drop,
and
av-
erage
slip
(Lambert
et
al.,
2021b
).
This
finding
implies
that
the
two
types
of
low-stress,
low-heat
models
can
be
distinguished
based
on
the
radiated
energy
per
seismic
moment
of
the
result-
ing
earthquake
ruptures,
which
is
proportional
to
the
apparent
stress
(McGarr,
1999
;
Beeler
et
al.,
2003
).
Persistently
weak
models
with
crack-like
ruptures
result
in
the
radiated
energy
per
mo-
ment
comparable
to
teleseismic
estimates
from
large
megathrust
earthquakes,
while
quasi-statically
strong,
dynamically
weak
fault
models
with
self-healing
pulses
produce
radiated
energy
per
mo-
ment
which
is
much
larger
than
typical
teleseismic
estimates
for
large
megathrust
earthquakes,
yet
comparable
to
limited
regional
estimates
from
large
crustal
earthquakes
(Ye
et
al.,
2016
;
Choy
and
Boatwright,
1995
;
Perez-Campos
and
Beroza,
2001
).
The
substan-
tial
difference
in
radiated
energy
results
from
difference
in
rupture
dynamics
and
shear
stress
variations
on
the
fault,
as
discussed
further
in
section
4
.
Specifically,
increasingly
sharper
self-healing
pulses
have
increasingly
larger
stress
undershoot.
Here,
we
consider
the
implications
of
the
qualitatively
differ-
ent
rupture
dynamics
between
crack-like
ruptures
and
self-healing
pulses
for
average
fault
stresses.
Further,
we
consider
the
link
between
fault
stresses
to
seismological
and
other
observables
us-
ing
energy
balance
considerations,
building
on
prior
work.
To
ex-
amine
average
shear
stress
quantities
in
numerical
fault
models
consistent
with
the
inferred
low-heat,
low-stress
operation
of
ma-
ture
faults,
we
use
numerical
simulations
of
sequences
of
earth-
quakes
and
aseismic
slip
(SEAS)
on
rate-and-state
faults
with
dif-
ferent
levels
of
chronic
fluid
overpressure
and
enhanced
dynamic
weakening
due
to
the
thermal
pressurization
of
pore
fluids
(sec-
tion
2.1
).
We
perform
simulations
with
sets
of
parameters
based
on
prior
studies
that
reproduce
the
typical
stress
drops
of
1-10
MPa
and
comply
with
the
heat-generation
constraints.
In
section
2.2
,
we
use
our
simulations
to
review
previously
identified
concep-
tual
differences
in
shear-stress
evolution
between
the
simulated
ruptures
of
differing
rupture
style,
crack-like
vs.
pulse-like.
In
sec-
tion
3
,
we
recall
the
earthquake
energy
budget,
focusing
on
the
energy-based
definition
of
average
shear
stress
and
review
how
the
average
fault
prestress
can
be
expressed
as
the
sum
of
the
dissipation-based
average
rupture
stress
(which
can,
in
principle,
2
V. Lambert and N. Lapusta
Earth and Planetary Science Letters 618 (2023) 118277
Fig. 1.
Evolution
of
slip
rate
and
shear
stress
with
time
for
representative
fault
models
hosting
crack-like
(fault
model
TP3
from
Supplementary
Table
2)
and
self-healing
pulse-like
(fault
model
TP6)
ruptures.
(A-B)
The
fault
models
are
composed
of
a
velocity-weakening
(VW)
seismogenic
region
surrounded
by
two
velocity-strengthening
(VS)
sections.
Local
seismic
slip
duration
during
(A)
crack-like
ruptures
is
proportional
to
the
overall
rupture
duration
whereas
only
a
small
portion
of
the
fault
slips
at
a
given
time
during
(B)
self-healing
pulse-like
ruptures.
(C-D)
Evolution
of
local
slip
rate
and
shear
stress
at
the
center
of
the
fault
over
sequences
of
earthquakes
with
low
dynamic
resistance
and
moderate
static
stress
drops.
Time
series
are
centered
at
t=0
corresponding
to
the
ruptures
shown
in
(A-B).
(C)
Most
points
within
the
VW
region
are
locked
during
the
interseismic
period
between
dynamic
ruptures,
with
slip
rates
far
below
the
loading
plate
rate.
(D)
The
shear
stress
over
the
persistently
weak
fault
model
(TP3)
which
hosts
the
crack-like
rupture
is
always
low
(
<
20
MPa).
For
self-healing
pulse-like
ruptures
on
quasi-statically
strong,
dynamically
weak
fault
model
(TP6),
the
shear
stress
before
the
rupture
is
relatively
high
compared
to
the
persistently
weak
fault
(
>
30
MPa),
then
drops
to
low
values
below
10
MPa
during
seismic
slip,
and
recovers
to
around
20
MPa
over
most
of
the
ruptured
region.
be
inferred
from
shear-heating
constraints),
and
seismologically
inferable
source
properties,
such
as
the
static
stress
drop
and
ap-
parent
stress.
We
then
analyze
our
simulations
with
a
focus
on
the
average
stress
values
(section
4
)
and
show
that
the
energy-based
shear
stress
is
significantly
higher
for
self-healing
pulses,
due
to
their
higher
apparent
stress,
in
comparison
with
crack-like
rup-
tures
of
the
same
average
stress
drop
and
slip.
While
averaged
shear
stresses
for
crack
ruptures
are
within
one
static
stress
drop
from
the
dissipation-based
average
shear
stress,
the
averaged
shear
stresses
before
and
after
self-healing
pulses
can
be
2-4
static
stress
drops
higher
than
shear
stresses
related
to
shear
heating,
providing
a
potential
physical
explanation
for
higher
estimates
of
fault
stress
based
on
geodynamics
and
topography.
We
discuss
related
seismo-
logical
observations
in
section
5
and
conclusions
in
section
6
.
2.
Numerical
simulations
of
crack-like
versus
self-healing
pulse-like
ruptures
2.1.
Model
description
We
conduct
numerical
simulations
of
sequences
of
earthquakes
and
aseismic
slip
following
the
methodological
developments
of
Lapusta
et
al.
(
2000
),
Noda
and
Lapusta
(
2010
),
and
Lambert
et
al.
(
2021b
).
Our
simulations
consider
mode
III
slip
on
a
1-D
fault
em-
bedded
into
a
2-D
uniform,
isotropic,
elastic
medium
(Supplemen-
tary
Figure
S1).
The
resulting
slip
on
the
fault
includes
sequences
of
earthquakes
and
aseismic
slip,
including
the
nucleation
process,
dynamic
rupture
propagation,
postseismic
slip
that
follows
each
seismic
event,
and
interseismic
period
between
seismic
events
that
3
V. Lambert and N. Lapusta
Earth and Planetary Science Letters 618 (2023) 118277
Fig. 2.
Spatial
distribution
of
slip
rate
(top)
and
shear
stress
(bottom)
for
the
same
representative
ruptures
as
in
Fig.
3
.
Both
ruptures
nucleate
with
prestress
levels
(gray
line)
that
are
near
the
local
steady-state
quasi-static
shear
resistance
(dashed
orange
line),
however
the
ruptures
propagate
over
lower
prestress
conditions
depending
on
the
efficiency
of
weakening.
The
slip
rate
and
shear
stress
at
the
same
instance
are
shown
by
the
black
lines,
illustrating
the
concentrated
stress
changes
at
the
rupture
front,
with
slip
continuing
throughout
the
entirety
of
the
rupture
for
the
crack-like
rupture
(A),
but
not
the
self-healing
pulse
(B).
can
last
up
to
tens
or
hundreds
of
years
and
host
steady
and
tran-
sient
slow
slip.
Our
fault
models
are
governed
by
a
form
of
the
laboratory-
derived
Dieterich-Ruina
rate-and-state
friction
law
(Dieterich,
1979
;
Ruina,
1983
)
as
well
as
enhanced
dynamic
weakening
during
rapid
slip
due
to
the
thermal
pressurization
of
pore
fluids
(Sibson,
1973
;
Rice,
2006
,
further
details
in
the
Supplementary
Text).
The
effects
of
off-fault
yielding
are
approximated
through
a
limit
on
slip
ve-
locity
(Supplementary
Text).
The
simulated
fault
contains
a
24-km
region
vw
with
velocity-weakening
(VW)
frictional
properties
where
earthquakes
can
nucleate
and
propagate,
surrounded
by
velocity-strengthening
(VS)
regions
that
inhibit
rupture
propaga-
tion
(Fig.
1
).
The
fault
is
loaded
by
a
region
outside
these
frictional
regions
slipping
at
a
prescribed
tectonic
plate
rate.
We
refer
to
rup-
tures
that
span
the
entire
VW
region
and
arrest
in
the
VS
region
as
model-spanning
ruptures.
We
define
the
beginning
and
end
of
dynamic
rupture,
t
ini
and
t
fin
respectively,
as
well
as
the
ruptured
region
rupt
,
using
a
slip-velocity
threshold
(
V
thresh
=
1 cm/s)
for
seismic
slip,
based
on
previous
studies
(Perry
et
al.,
2020
;
Lambert
et
al.,
2021b
).
We
study
the
evolution
of
shear
stress
and
average
stress
mea-
sures
in
fault
models
which
produce
ruptures
with
typically
ob-
served
static
stress
drops
of
1-10
MPa
(e.g.
Shearer
et
al.,
2006
;
Allmann
and
Shearer,
2009
;
Ye
et
al.,
2016
)
and
which
are
consis-
tent
with
low
heat
production,
where
the
shear
stresses
associated
with
shear
heating
are
below
20
MPa.
We
conduct
simulations
with
varying
levels
of
background
fluid
overpressure
in
terms
of
the
effective
normal
stress,
as
well
as
varying
degrees
of
efficiency
in
enhanced
weakening
due
to
thermal
pressurization.
The
param-
eter
values
we
have
chosen
(Supplementary
Tables
S1
-S2)
are
motivated
by
prior
studies
(Rice,
2006
;
Noda
and
Lapusta,
2010
;
Perry
et
al.,
2020
;
Lambert
et
al.,
2021b
)
and
our
goal
of
examining
ruptures
with
varying
efficiency
in
enhanced
dynamic
weakening
and
different
rupture
styles.
For
realistic,
lab-derived
fault
constitutive
relations
such
as
rate-and-state
friction,
the
concept
of
a
local
“static
friction”
co-
efficient
that
must
be
reached
for
the
slip
to
occur
is
ill-defined,
since
slip
rate
is
non-zero
for
any
non-zero
shear
stress.
We
choose
a
representative
value
for
the
classical
notion
of
local
quasi-static
fault
strength,
which
we
call
the
local
steady-state
quasi-static
(SSQS)
shear
resistance
and
define
as
the
product
of
the
inter-
seismic
drained
effective
normal
stress
and
the
quasi-static
friction
coefficient
during
steady
creep
f
ss
(
V
)
at
the
prescribed
tectonic
plate
rate
V
pl
:
τ
V
pl
ss
(
z
,
t
)
=
(
σ
−
p
int
)
f
ss
(
V
pl
).
(1)
Here
σ
is
the
normal
stress
and
“drained”
refers
to
the
effective
stress
with
ambient
interseismic
pore
pressure
p
int
unaffected
by
slip
processes
such
as
dilatancy
or
thermal
pressurization.
Previous
numerical
studies
have
shown
that
the
local
SSQS
shear
resistance
τ
V
pl
ss
is
comparable
to
the
spatially-averaged
prestress
during
rup-
ture
nucleation
(Supplementary
Figure
S2;
Lambert
et
al.,
2021a
).
2.2.
Local
fault
behavior
in
simulated
crack-like
and
self-healing
pulse-like
ruptures
All
of
our
simulated
ruptures
nucleate
in
regions
with
locally
high
prestress
near
the
corresponding
local
SSQS
resistance,
but
then
propagate
over
areas
of
varying,
and
particularly
lower,
pre-
stress
conditions
depending
on
the
efficiency
of
dynamic
weaken-
ing
(Fig.
2
;
Lambert
et
al.,
2021a
,
b
).
For
persistently
weak
faults,
the
shear
stress
is
always
low
(
<
20 MPa;
Fig.
1
D).
In
contrast,
the
local
shear
resistance
on
quasi-statically
strong,
dynamically
weak
faults,
and
hence
the
local
shear
stress,
is
generally
higher
during
periods
of
negligible
motion
before
and
after
ruptures,
and
quite
high
at
the
peak
of
the
propagating
rupture,
but
drops
dramati-
cally
to
lower
values
below
10
MPa
during
most
of
seismic
slip
(Figs.
1
C-D);
in
these
models,
ruptures
with
realistic
stress
drops
tend
to
be
pulse-like
(Lambert
et
al.,
2021b
)
In
crack-like
ruptures,
the
local
shear
resistance
drops
at
high
slip
rates
and
remains
low
throughout
the
remainder
of
the
rup-
4