GEOPHYSICAL RESEARCH LETTERS, VOL. 25, NO. 4, PAGES 551-554, FEBRUARY 15, 1998
Large earthquake nucleation associated with stress
exchange between middle and upper crust
MireilleHuc, 1 Rind H•ss•ni,e •nd JeanChary
Laboratoire de G•ophysiqueet Tectonique,UMR CNRS 5573, Universit• Montpellier II, France.
Abstract. Earthquake nucleationand propagationcan
be explainedusingtwo basicconcepts,crustal strength
and fault theology. Despite numerousexperimentaland
modelingstudies,the way in which a faulted crust generates a seismic cycle under loading is still controversial. We discussearthquake generation using a 2-D
out that frictional stick-slip on a fault could be the
main operating mechanism for earthquake generation
and distribution. This view comes from the extrapo-
lation of experimentson crustalrocksfrom laboratory
to geologicalscale, which suggestsa velocity weaken-
ing of the frictionlaw. The transitionfrom weakening
to strengtheningwith velocityoccursat approximately
of geodynamicalproblemssuch as theologicallayering, 3500 C [$tesky,1975]in quartz-richrocks,supportdynamic Coulomb faulting and relative plate velocity. ing the idea that the limit of earthquakesis causedby
The occurrence of a deep nucleation is explained by the transition from unstable to stable slip with depth
the strong viscosity drop at the base of the seismo- [$cholz,1988].Because
we think that crustalstrength
genic layer, without any transition of frictional prop- and fault rheologyare both deeplyinvolvedin the mechFinite
Element
Model
which includes relevant
features
erties of the fault. Rather, viscosity contrast causes a
anism of earthquakes, we combined them in a finite el-
stress transfer
ement model of continental
around
the fault
that
reloads
the fault
plane during the postseismicphase. We argue that this
mechanismmay explain the seismiccyclefor large faults
in the continental
extension.
2. Mechanical modeling
crust.
A classicview of the strength of continental crust is
providedby Brace and Kohlstedt[1980], who showed
1.
Introduction
pressure and temperature effects on differential stress
for quartz-rich rocks. At shallow depth, low confining
pressurein the brittle field restricts stresslevels to low
A fairly good correlationexistsbetweenthe base of
the seismogenic
layer and expectedtemperaturesin the values.At intermediatedepths(4-12 km), higherconcontinental crust. Earthquakes that nucleate at 10-15
fining pressureand moderately high temperature perkm depth are typical for hot continental crust, like the
mits higherstress.At greaterdepth, increasingtemperBasin and Range province in the Western US, while ature beyond 3500 C leads to stress decay due to visdeeperearthquakes(15-30 km) are mainly represented cousdissipation. In order to describethis peak strength
in regionsof coldercrust(Rhinegraben,Baikal). Meiss- within the crust, we divide the crust into three visher and $trehlau[1982]and $ibson[1982],pointedout coelasticlayers(Figure 1). This layeredsystemis cut
this fact, and proposed that the seismicity cut-off at
by a planar,high-angle,deeply-rooted
(16 km) fault in
depth is controlled mainly by temperature. Beyond this
the low-viscositylayer, with an infinite out-of-plane ex-
correlation,$ibson[1982],stated that "the nucleation tension accordingto the plane strain geometry of our
of larger earthquakesnear the base of the seismogenic
zone, in the regionof inferredpeak resistance,suggestsa
causal relationship". In this paper we show that such a
relationship appears in our modeling of the earthquake
cycle, and demonstrate how this modifies our current
understandingof earthquakemechanics.
While our approachimplicitly refers to crustal strength
for explaining earthquake distribution, some authors
model. We assumethat the dynamic friction coefficient
/•d is lower(0.24) than the staticoneits (0.30).
In any mechanical modeling, the way in which the
crust-fault system behaves is strongly dependent on
boundary conditions. Becausewe want to study the interaction between fault rheology and crustal strength,
we do not prescribe any boundary condition near the
fault zone. We rather impose a constant plate velocity
[Braceand Byedee,1966;$cholz,1990],havepointed far from the fault [Lyzengaet al., 1991]as donefor a
long-termgeological
model(Figure1). The baseof the
box
(low
viscosity
zone)
is chosendeepenough(30 km)
1Nowat Universityof Edinburgh,ScotlandUK.
to not influence the numerical
2Now at ENSAM, University of Bordeaux,France.
Copyright1998by theAmericanGeophysical
Union.
results.
The crustal medium is discretizedusing3-node linear
finite elements. The fault zone is simulated by contact
betweennodesof differentelements [Jeanand Touzot,
1988]. Time discretizationis derivedusingthe dynamic
Papernumber98GL00091.
0094-8534/98/98GL-00091505.00
551
552
HUC ET AL.' EARTHQUAKE
Vn=6mm/y
freesurface
::-
NUCLEATION
faultplane
;-'.........!!g....::•
\"
AND STRESS EXCHANGE
Vn=6mm/y
event•
3
' 1.02Opa..;-:'"'•:•
......
:•"
'...............
'.....
.-:._
.......
-::i;?
....... -'-':
IN THE CRUST
event•35
events62
[1',[I,',111
IIJIIIl'11illl
I[1111UlI,II[111111
I !ø
ß' "'"'•I'"TIII•I
' l'l'l"l'l'
':'
10600
5oho
6
•5boo
Time (years)
Vn=O
Figure 1. Geometry,rheological
layering,andbound- Figure 2. Earthquake distribution with time. Vertiary conditions of the model. Lateral and lower sides are cal linesrepresentfault-rupture length, and dots nuclefree slip, with a fixed normal velocity V, Mechanical ation points. Time before t=4500 yrs correspondsto a
model correspondsto a finite-element mesh with 3000 quasi-static evolution where the critical shear stress on
triangularelements,partly drawnin the lowerrightcor- the fault is not reached. Mean recurrence time stabiner. The stress-strainrelationsfor the crust are pro- lizes around 170 yrs after t=7000 yrs. Events3, 35 and
62 are shown on Figure 3.
vided by the viscoelasticmodel:
o
o P_3Kd,•ot
where • is the viscosityof the layer, G and K are shear
and bulk modulusrespectively.Valuesof respectively at the first point wherethe condition]ertl= /• er• is
4.10lø and6.66.10lø Pa areusedfor all layers.da•,and satisfied. The condition lertl= tta er,,is then usedfor
d•ot are the deviatoricand volumetricpart respectively slippingnodes. As extensionproceeds,earthquakesnuof the strain-rate tensord. aa• is the deviatoricpart cleateat deeperlevelsnear the baseof the high viscosity
of the stresstensor a, and P is the pressure.
layer (Figure2). Maximumcoseismic
motionsreach3-5
m and are damped out within the first 1-2 km in the
low viscositylayer (Figure3). All nucleationpointsare
relaxationmethod [Cundalland Board,1988],that al- contained in the high-viscositylayer. Between seismic
lows us to compute the velocity field for both inertial events,the fault is lockedbecauselertl</• er,•,and ex(coseismic)
and quasi-static(inte.
rseismic)phasesin a tension only results in a bulk viscoelasticstrain in the
time continuum [Huc, 1997]. The time step At is ad- crust. Accumulated topography is similar to that ex-
justedfromshort(10-2 s) to long(107s) timescales. pectedfor an half-graben, with an uplifted footwall and
Earthquakeoccurrenceis controlledby the friction law a subsidinghangingwall. Coseismic
motionof the 35th
on the fault plane. As long as I•tl < • • every- event (Figure 2 and 3) is typicalof largeearthquakes
where on the fault, relative fault motion is locked and
the model behaves in a quasi-static mode. As stress in-
creasesin the continuummedium,]ertlreaches/• er,at
generated by our model: nucleation at depth, downward rupture which dampsin the middle crust, upward
rupture that breaks the free surface. Slip envelopesof
some point on the fault. The friction coefficient then Figure 3 result from a high-velocitymotion according
switches to tta for this point, that causesearthquake to the elastodynamic equation of motion. Becausethe
triggering and propagationwith respectto the friction total time of coseismicmotion is less than 10 seconds,
law. The velocity (v) and displacement(u) computa- viscosity does not play a role, and coseismicdeforma-
tions involvegravity forces,(F•), internal forces(Fi) t.ion is similar to an
and contactforceson the fault (F•), as follows,for one viscosity medium.
degreeof freedom:
vt-[-1/2= vt--1/2q_[Feq_/7/q_Fcq_Fd]
Ut+l
At
elastic dislocation
even in the low
The most surprising property of this mechanicalmodel
is that earthquakesspontaneouslynucleate at depth, as
for most large natural earthquakes. It is unexpectedbe-
• ut q-vt+l/2At
Event 35
Event 3
I
....
0
I
Event 62
I
where mi is the mass of the node i. The damping
force Fa is added only during the quasi-static phase.
The model is initially in isostatic equilibrium with no
deviatoric stress. We apply a constant velocity of ex-
tensionof 1.2 cm/yr betweenthe lateral sidesover a
period of 15000 yrs.
3. Seismic cycle and stress change
In the model, small earthquakesoccur at the begin-
ning of extension(Figure 2), with a mean dislocation
length of 4 km and a coseismicmotion of 1 m. These
eventsnucleate under the top of the high viscositylayer
16
2
3
4
5
0
I
2
3
4
5
0
1
2
3
4
5
Coseismic slip (m)
Figure 3.
Coseismicslip occurring during inertial
phase of modeling. left: Small event nucleation at the
top of the high-viscositylayer. middle and right: Nucleation of large events mainly occursat depth near zone
of viscosity drop. Rupture breaks the whole crust above
and is rapidly damped below, within the low-viscosity
layer.
HUC ET AL.- EARTHQUAKE
NUCLEATION
MPa
150
120
90
60
30
-30
0
MPa
5
3
1
---1
__i_3
.5
MPa
5
AND STRESS EXCHANGE
lution
mirrors
IN THE CRUST
coseismic evolution:
553
the middle
crust is
unloaded while the upper crust is reloaded in the faultplane vicinity. While coseismicstresschangeis sudden,
postseismicstresschangein the middle crust is slowand
is controlledby the relaxation time of the low viscosity
layerthat scales
with shear,,iscositv
modulus
' Thisratiois about
2.5 109s (m 80 yrs) for our experiment.Althoughthe
true time scale is probably dependent on geometric effects, one can predict that stress release of the middle
crust is almost complete when the next event occurs
with a mean recurrence time of 170 years. Because the
relaxation time of the high-viscositylayer is 1000 tinms
higher(80000years)than that of the middlecrust,the
3
upper crust respondselastically during the post-seismic
1
stage.
---1
5
We found by modelingthat stressdecreasein the middle crust is the cause of a rapid stress increase at the
baseof the uppercrust(Figure4c). Fault-planereloadFigure 4.
a: Deviatoric stressintensity beforethe ing during the postseismicphase is therefore largely
35tn event. High stressis mainlyconfinedin the high depth dependent because the main stresssource comes
viscositylayer. b: Coseismic
stresschange(10 s) asso- from below. This modeling result is well illustrated by
ciatedto the35tnevent(between
tl andt2 onfigure5). the transient evolution of • with time for three points
Stressrelease(light areas)mainly occursin the upper on the fault at increasing
depths(10.9, 12.0,and 13.2
crust. Stressincrease(dark areas)mainlyoccursin the kin, Figure 5). Becausethe stressincreaseof the shalmiddle crust. Labelled points p, q and r refer to stress
lowerpoint (10.9 kin) is lowerthan the stressincrease
evolutionon figure 5. c: Postseismic
stresschange(53
of the deeperpoint of the seismogenic
layer, the next
yrs)following
the35tnevent(between
t2 andt3 onfigure
earthquake
occurs
preferentially
at
a
greater
depth. Al5). Oppositeevolutionof the coseismic
stresschangeis
a variabilityin coseismic
slip(comrecorded. Stress rate is controlled by relaxation time thoughweobserve
of the middle crust. Fault reloading in the upper crust pare event 35 and 62, Figure 3) which correspondsto
appears as very inhomogeneous.
variable coseismicstressrelease,a rapid post-seismic
stressincreaseat the baseof the seismogenic
layer is
a persistentfeattire of our model. Consequently,
we
cause1) the increasein normalstresswith depth pre- claim that, in our modeling,the stresstransfermechavents shear stressfrom increasingto its critical value nism,causedby a viscositydropat middlecrustallevels,
Fs '•,,, and 2) constantpropertiesof the friction law favorsthe nucleationof deep earthquakes.
with depth do not favor nucleationat any givendepth.
In order to explain this phenomenon,we explorehow 4. Summary and Discussion
stresschangesduring the 35tn event and the followAlthoughthe rheologicallayeringof our modelis siming interseismicphase. Figure 4 showssnapshotsof
ilar
to that usedin previousworks[e.g. Li and Rice,
deviatoricstressintensitybeforethe earthquake(4a),
1987],
we usea differentviewpointto setupboundary
and changesrelatedto coseismic
(4b) and postseismic
conditions.
As for a long term geodynamicalexper(4c) changes.As alreadystated, coseismicmotionon
the normal fault is similar to a dislocation in an elastic
iment, we assumethat only relative plate velocityis
medium.
Relative motion across the fault modifies the
deviatoricstressnorm in the fault vicinity, mainly above
andbelowthe nucleation
point(Figure4b). Stressis releasedin the seismogenic
layer, mainly in the footwall,
and stressis gained in the low viscositylayer around
the fault tip. Maxinmm stresschangeis about 50 Mpa.
The far field stresschange is larger than what is expected for a finite dislocation, due to the 2D nature of
our model. The zoneaffectedby k 5 MPa stresschange
extends up to 10 km around fault. Coseismicstressincreasecorrespondsto a potential energy stored in the
low-viscositymiddle crust. Becausethis layer is viscoelastic,this energystorageis only transient. Figure
4c showshow stressis redistributedduring the post-
0.3
0.0
tr
0
a)
100
gd
200
300
0
100
200
300
b) Time
(years)
0
100
200
300
c)
Figure 5.
• evolutionon the fault after the 35tn
event,for the three pointsshownon Figure 4. Depths
of points p, q and r are 10.9, 12, and 13.2 km. Most
rapid post-seismic
stressloadingoccurson point q at
the viscositydrop,corresponding
to stressunloadingat
seismicstage,53 yrs after the 35th event. This evo- point r in the middle crust below.
554
HUC ET AL.: EARTHQUAKE NUCLEATION AND STRESSEXCHANGE IN THE CRUST
relevant.We thinkthat prescribing
staticor kinematic References
boundary
conditions
nearthefaultis misleading
beW.F., and J.D. Byerlee,Stick-slipas a mechanism
cause
1)these
conditions
arebasically
unknown
2)such Brace,
for earthquakes,Science,153, 990-991,1966.
a choiceconstrains
stressandslip historyaroundthe Brace,W.F. and D.L. Kohlstedt,Limitson lithospheric
fault to be consistent
with theseboundary
conditions. stressimposedby laboratoryexperiments,J. Geophys.
Weratherimpose
a more"neutral"boundary
condition Res., 85, 6248-6252, 1980.
program
that shouldcorrespond
to the general
hypothesis
that Cundall,P.A., and M. Board,A microcomputer
lowdeviatoric
stress
is always
present
at depthforgeologicalstrainrates.This hypothesis
is consistent
with
for modellinglargestrainplasticityproblems,in Numeri-
calmethods
in Geomechanics,
editedby G. Swoboda,
pp.
2101-2108,Balkema, Rotterdam, 1988.
theuseof linearviscosities
lowerthan102•Pa.s, ac- Das, S., and C.H. Scholz,Why largeearthquakes
do not
cordingto viscousrheologyof quartz-rich-rocks.
nucleateat shallowdepths,Nature,305,621-623,1983.
par la mdthodedes
Usinga constantvelocityof extension,linearvis- Huc, M., Moddlisationdu cyclesismique
coelastic
laws,andthesimplest
frictionlaw
dldmentsfinis, 192 pp., Th;esede Doctorat,Universitdde
Montpellier II, 1997.
bothconstants),
wegenerate
a seismic
cyclethatisnei- Jean,M., and G. Touzot, Implementationof unilateralcontherperiodic,
norchaotic.Asfor naturalearthquakes tactanddryfrictionin computercodesdealingwithlarge
[Dasand$cholz,1983],almostall largeevents
nucleate deformation
problems,J. Mec. Theor.Appl.,7, suppl.1,
145-160, 1988.
at depthnearthe baseof theviscosity
transition.Anal-
in greatCalysisof stresstransfermechanisms
relatedto this model Li, V.C., and J.R. Rice,Crustaldeformation
ifornia earthquakecycles,J. Geophys.Res., 92, 11533leadsus to the followingpropositions:
11551, 1987.
1. Deviatoricstressis storedat deptharoundthe fault Lyzenga,G.A., A. Raefsky,and S.G. Mulligan,Modelsof
tipin anelastic
manner
during
coseismic
motion.
Then, recurrent strike-slip earthquakecyclesand the state of
thisstress
isprogressively
released
in themiddle
crust, crustalstress,J. Geophys.Res.,96, 21623-21640,1991.
providing
a newstressbuild-upat the baseof upper Meissner,R., and J. Strehlau, Limits of stressesin continentalcrustsand their relationsto the depth-frequency
crust.Originally
proposed
by Nut andMavko[1974], distributionof shallowearthquakes,Tectonics,1, 73-89,
this stresstransfereffectcouldbe a generalmecha- 1982.
viscoelastic
rebound,
nismfor clustering
and aftershocks,
as alreadysug- Nur, A., and G. Mavko,Postseismic
Science,
183,
204-206,
1974.
gested[$ibson,
1982;Unruhet al., 1996;Rigoet al.,
Rigo, A., H. Lyon-Caen,R. Armijo, A. Deschamps,
D.
Hatzfeld, K. Makropoulos,P. Papadimitriou,I. and Kas2. The fault-loadingrate after an earthquake
is theresaras,A microseismic
study in the westernpart of the
forea combination
ofa long-term
stress
loading
ratedue
to relative plate velocity,and a short term stressloading rate due to stressrelaxationin the middlecrust.
GulfofCorinth(Greece):
implications
forlarge-scale
normalfaultingmechanisms,
Geophys.
J. Int., 126,663-688,
1996.
C.H., Thebrittle-plastic
transition
andthedepth
Thisshorttermrateis highnearthefaulttip, andis Scholz,
seismic
faulting,
Geologische
Rundschau,
77,319-328,
thecause
of inhomogeneous
faultloading,
asalready of
1988.
shown
by Lyzenga
et al. [1991]forantiplane
faults.We Scholz,
C.H., Themechanics
of earthquakes
andfaulting,
suggest
that thisstress-rate
partitioning
isthephysical 439 pp., Cambridge,Universitypress,1990.
R.H., Faultzonemodel,heatflow,andthedepth
causefor thegeneration
of largeearthquakes,
whatever Sibson,
the slip direction.
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3. If we acceptthat viscosityrapidlydecreases
with Stesky,R. M., The mechanicalbehaviorof faultedrock at
hightemperature
andpressure,
Ph.D.Thesis,275pp.,
depthnearthe300- 3500C isotherm,/•d
_</•sisonly
requiredin the high-viscosity
zone.The frictionlaw at
Mass.Inst. of Technol.,Cambridge,
Mass.,1975.
greaterdepthis not of primaryimportance
because
the Unruh,J.R.,Twiss,R.J.,andHauksson,
E., Seismogenic
deformation
in theMojaveblockandimplications
fortecshearstresson fault planesneverreachesthe critical
tonics
of
the
eastern
California
shear
zone,
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Geophys.
value/• .a•. Thisinterpretation
doesnot preclude
slip-hardening
law at hightemperature,
but ratherindicatesthat thefrictionlawisnotnecessarily
thecause
for seismicitycutoffat depthas is oftenstated.
Res., 101, 8335-8361,1996.
M. HucandJ. Chdry,LaboGdophysique
et Tectonique,
4 pl. Bataillon,34095,Universitd
MontpellierII, France.
(e-mail:[email protected])
R. Hassani,
LEPT,EcoleNationale
desArtset Metiers,
Esplanade
des
Arts
et
Metiers,
33405
Talence
Cedex.
(email:
We are gratefulto M. Jeanwhoprovidedus his contact
hassani
@lept-ensam.
u-bordeaux.fr)
Acknowledgments.
algorithm
to compute
frictiononfaults.Thisworkwassupportedin 1995by INSU-CNRSthrougha PNRN granton (Received
June26,1997;revised
December
1, 1997;
seismic risk.
accepted
December18, 1997.)