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Earth and Planetary Science Letters 194 (2001) 277^286
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Postseismic stress transfer explains time clustering of
large earthquakes in Mongolia
Jean Chëry *, Sëbastien Carretier, Jean-Franc°ois Ritz
Laboratoire de Gëophysique, Tectonique et Sëdimentologie, CNRS and Universitë de Montpellier II, 34095 Montpellier, France
Received 13 July 2001; received in revised form 20 September 2001; accepted 12 October 2001
Abstract
Three M s 8 earthquakes have occurred in Mongolia during a 52-year period (1905^1957). Since these earthquakes
were well separated in space (400 km), the coseismic stress change is far too low (0.001 bar) to explain mutual
earthquake triggering. By contrast, postseismic relaxation gradually causes a significant stress change (0.1^0.9 bar) over
large distances. Using a spring-slider model to simulate earthquake interaction, we find that viscoelastic stress transfer
may be responsible for the earthquake time clustering observed in active tectonic areas. Therefore, revealing postseismic
strain by satellite geodesy and modeling earthquake clusters could improve our understanding of earthquake
occurrence, especially in zones where large earthquakes have already struck in past decades. ß 2001 Elsevier Science
B.V. All rights reserved.
Keywords: earthquake cluster; fault; Mongolia; stress transfer; postseismic
1. Earthquake time clusters
The occurrence of several earthquakes after a
long period of quiescence in a tectonic province,
called earthquake clustering, is a perturbing behavior of the lithosphere. It means that a large
earthquake occurring in an apparently dormant
zone could be a warning signal for a subsequent
one in the years or decades to follow. These clustering phenomena have been documented since
the 1980s for rapid faults on certain plate boundaries. For example, paleoseismic investigations
on the Southern San Andreas Fault produced evi-
* Corresponding author. Tel.: +33-4-67-14-36-85;
Fax: +33-4-67-52-39-08.
E-mail address: [email protected] (J. Chëry).
dence of clusters of three to four large earthquakes during 200-year periods followed by a
long quiescence of 400 years [1]. In addition, historical sequences on the North Anatolian Fault
reveal that this major fault was relatively quiescent for centuries [2,3] prior to the destructive sequence of 10 M 6^7 earthquakes starting in 1939
and ending with the Duzce earthquake in 1999 [4].
Due to the low occurrence of earthquakes, fault
activity on plate interiors where the lithosphere is
slowly deforming is more di¤cult to document. In
such cases, fault motion with long-term slip rates
of 0.01^1 mm/year may be di¤cult to prove since
no historical record exists. However, the occurrence of earthquake clusters is documented in numerous areas such as the eastern Mediterranean
[3,5,6], Iran [7] or in the Great Basin in the western USA [8]. Understanding why earthquakes oc-
0012-821X / 01 / $ ^ see front matter ß 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 0 1 2 - 8 2 1 X ( 0 1 ) 0 0 5 5 2 - 0
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J. Chëry et al. / Earth and Planetary Science Letters 194 (2001) 277^286
cur in clusters, rather than in an evenly distributed manner, is a key point in assessing earthquake probability on faults. We propose that
this behavior may be physically described using
the idea that postseismic stress relaxation of the
lithosphere after one large event may increase the
crustal stress up to the failure threshold on other
faults.
We test our model using a sequence of large
earthquakes that occurred in Mongolia during
the 20th century (Fig. 1). This sequence is due
to crustal shortening between India and Eurasia
(e.g. [9]). Under this slow compression, three
M s 8 earthquakes have occurred during the last
century: Bolnay (1905, July 23), Fuyun (1931,
August 10) and Gobi^Altay (1957, December 4)
[10,11]. An M 7.8 earthquake also occurred 14
days prior to the Bolnay earthquake (Tsetserleg,
1905, July 9). All these earthquakes were located
on very large faults showing a clear geomorpho-
logical expression, suggesting the occurrence of
repeated earthquakes. Given that historical records of earthquakes are quite scarce in Mongolia, and that paleoseismic data are preliminary, it
is still unknown whether other earthquake clusters
have occurred in the past. However, recurrence
time of large Mongolian earthquakes is assessed
by direct ¢eld measurements. Preliminary paleoseismic studies on the Bogd Fault along which the
1957 Gobi^Altay M 8 earthquake occurred show
large recurrence times of ``thousands of years''
[12]. In addition, 100 m o¡sets of 80 000-yr-old
alluvial fans along this fault lead to a long-term
slip rate of 1.2 mm/yr [13] in accordance with a
time return of 4000 years for 5 m of average slip
for one earthquake. If we assume for the purpose
of this argument that the mean recurrence times
on Bolnay, Fuyun, and Gobi^Altay faults are in
the order of 4000 years, then there is only a small
probability that each of these faults undergoes a
Fig. 1. Simpli¢ed schematic tectonic setting of Mongolia. Thick lines represent the surface fault rupture during the 20th century.
Thin lines represent the Quaternary faults [51]. Solid arrows indicate the approximate shortening direction.
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J. Chëry et al. / Earth and Planetary Science Letters 194 (2001) 277^286
279
large rupture in a 52-yr interval. Given that this
did occur, we postulate that a causal relation exists between these earthquakes, and investigate
physical reasons that may cause such behavior.
2. Earthquake recurrence model and
coseismic stress triggers
Our current understanding of earthquake occurrence is based on the simple idea that a fault
plane is progressively loaded during slow plate
motion. As a ¢rst approximation, we consider
that both the interseismic stress rate c between
two earthquakes and plate velocity is constant
far from active zones. When the shear stress acting on the fault reaches a static stress dyield , slip
instability occurs and elastic motion of the crust
releases the stress on the fault plane until the static stress dbase is reached. In this simple model, the
recurrence time T of the fault is given by vdco /c
where vdco = dyield 3dbase is the local (static) stress
drop. The model is periodic if dyield and dbase do
not evolve with time. Variation in one of these
stresses (Fig. 2a) leads to an irregular earthquake
occurrence [14].
Due to the elastic behavior of the lithosphere
over short time periods, a permanent strain and
stress change is caused on surrounding faults after
the occurrence of an earthquake (e.g. [15]). Such a
distant trigger may increase the slow secular loading rate that would advance the time of an earthquake [16]. Alternatively, the fault plane may be
unloaded which would delay the occurrence of the
upcoming earthquake [17,18]. Because the limit
stress on a fault is generally thought to be controlled by the fault friction W, the static stress
change due to the coseismic fault motion of the
distant earthquake should depend on the shear
stress change vct , the normal stress change vcn ,
and the £uid pressure change vP within the
fault. The resulting stress change vCFSco called
the Coulomb failure stress (CFS) change, is given
by:
vCFSco ˆ vc t 3 W W…vc n 3vP†
…1†
CFS changes as low as 0.1 bar have been invoked
Fig. 2. Stress cycle on a fault due to elastic stress change:
(a) the local stress evolution is controlled by the loading
stress rate c and the coseismic stress drop vdco , (b) a distant
earthquake induces a coseismic stress change vCFSco that
causes a clock advance vt, (c) coseismic stress change induced by the 1931 Fuyun earthquake on the Gobi^Altay
Fault. Modeled values are small due to the limited extension
of coseismic motions.
in many cases to be the cause of a signi¢cant
seismicity increase in zones where the stress approaches to the Coulomb limit (e.g. [15,16,19]).
Alternatively, a stress decrease with respect to
the CFS change often correlates with a microseismicity decay or even suppression of large earthquakes [17,20]. The e¡ect of CFS change on
earthquake time occurrence can be evaluated using the concept of `clock advance' vt [21^23]. This
time di¡erence is de¢ned as the time by which an
earthquake is advanced (or delayed if negative)
due to a distant stress triggering. If the secular
stress loading rate is linear, vt is given by
vCFSco /c (see Fig. 2b). Since c can be evaluated
as vdco /T (see Fig. 2a), the clock advance depends
on the static stress drop, the CFS change, and the
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recurrence time of the fault:
vt ˆ
co
vCFS
WT
vd co
…2†
Modeling earthquake cycles on a group of faults
therefore requires a knowledge of the ratio between the distant stress change vCFSco and the
local stress drop vdco . Static stress drop during a
large earthquake is generally estimated with a dislocation model and is expressed as:
vd co ˆ CWG
u
W
…3†
where C is a geometrical constant close to 1 (see
[24]), G the elastic shear modulus, uš the average
displacement during an earthquake and W the
fault width. For values of 5 m and 15 km for uš
and W respectively, a stress drop of 100 bar is
found. Such a stress drop corresponds to the
upper bound given by moment magnitude analysis [25] and is compatible with estimates deduced
from radiated energy during earthquakes [26].
CFS change cannot be estimated as simply as
for the local stress drop vdco because the stress
vector variation on a triggered fault is dependent
on the relative position and orientation of the two
faults. Using the geometry of Fuyun and Gobi^
Altay faults, we compute the coseismic CFS
change induced by the 1931 Fuyun earthquake
on the Gobi^Altay Fault (Fig. 2c). We assume
that the 1931 Fuyun earthquake can be modeled
as a vertical, rectangular strike-slip fault (L = 180
km, W = 20 km, uš = 10 m) embedded in an in¢nite
half-space. We use the formulation of Okada [27]
in order to compute the stress perturbation cn
and ct on the Gobi^Altay Fault. We compute
the coseismic stress change vCFSco assuming
that the Gobi^Altay Fault friction W is equal to
0.3, which is an intermediate value between a
weak fault such as the San Andreas Fault
(WW0.1) and a fault as strong as the crust (W in
the range of 0.6^0.8). Our calculation yields a
positive vCFSco of V0.001 bar (Fig. 2c). Under
these circumstances, it is unlikely that a large
earthquake on the Fuyun Fault would a¡ect, either positively or negatively, the earthquake occurrence on the Gobi^Altay Fault. Computing
similar CFS values between the Bolnay, Fuyun
and Gobi^Altay faults using the same principle
as above yields CFS values consistently smaller
than 0.05 bar. This indicates that coseismic triggering between these distant faults is highly unlikely. Because static stress is clearly too small to
cause distant triggering, seismic waves interacting
with crustal £uids have been cited to explain
anomalous distant microseismicity, as it happened
in the days following the Landers earthquake
[28,29]. Therefore, this mechanism may have
been e¤cient for the triggering of the 1905 Bolnay
earthquake 14 days after the Tsetserleg earthquake. However, the Fuyun earthquake and the
Gobi^Altay earthquake occurred decades after
the 1905 pair. For this reason we explore how
postseismic stress relaxation slowly modi¢es the
local stress drop vd and the distant stress change
vCFS during the seismic cycle.
3. Postseismic stress relaxation
Postseismic motion at the surface occurs in response to the coseismic dislocation and seems to
involve deep changes in the lower crust or in the
mantle [30^32]. The progressive decay of postseismic motion can be characterized by a relaxation
time R ranging from a few days to several decades
such as after the 1906 San Francisco earthquake
[33]. Detailed postseismic motion distribution at
depth is di¤cult to assess from surface measurement only, and can be attributed either to fault
afterslip [34] or to a viscoelastic crustal relaxation
[35]. In both cases, this induces a slow `reloading'
of the seismogenic layer [36] that brings the fault
plane stress closer to the yield limit than in a
model where relaxation does not occur [37]. As
a consequence, the coseismic stress drop vdco
evolves towards a relaxed stress drop vdrel as depicted in Fig. 3a. Because postseismic relaxation
occurs aseismically, the associated local fault
stress change cannot be estimated by seismological means. This stress change may, however, be
inferred if a postseismic slip model is assumed for
the deep part of the fault. In this case, the lower
crustal stress relaxes to zero in this layer during
the postseismic phase, meaning that the stress singularity that occurred at depth W during the co-
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seismic stage progressively vanishes. The corresponding relaxed stress after the postseismic relaxation becomes controlled by a dislocation of
length L with an in¢nite width. This new fault
scaling leads to values of 5^20 bar for L values
ranging from 300 km to 75 km when replacing L
by W in Eq. 3. In this simple model, the ratio
between the relaxed local stress vdrel and the coseismic local stress vdco is therefore given by W/L.
Away from the fault, the local stress change promotes a larger strain distribution as demonstrated
by the remote geodetic motions detected after the
Alaska earthquake in 1964 [38]. As a result, the
net e¡ect of the CFS change on a remote fault
superimposes a slowly evolving postseismic
change vCFSpost (Fig. 3b) on a sudden coseismic
change vCFSco . The sum e¡ects result in a relaxed stress change vCFSrel after complete lower
crustal relaxation.
Using the same approach used to evaluate the
coseismic CFS change induced by 1931 Fuyun
earthquake on the Gobi^Altay Fault, we now
compute the relaxed CFS change. We assume
that a complete postseismic relaxation after an
earthquake may be simply approximated by a
deep postseismic slip [39] as done, for example,
for the postseismic motion of the 1999 Izmit
earthquake [4], and for the tectonic loading in
southern California [40]. We therefore add to
the coseismic slip a deep patch between 20 km
and an arbitrary large depth (1500 km). Doing
so, we model a thin elastic plate overriding a relaxed lower crust [15,41,42]. Signi¢cant relaxed
stress change vCFSrel then occurs at a larger distance from the Fuyun Fault (Fig. 3c). The Gobi^
Altay Fault now su¡ers a positive (loading) stress
of +0.15 bar on its western termination and +0.08
bar on its eastern termination. Since only 26 years
separate the Fuyun earthquake and the Gobi^Altay earthquake, the stress relaxation caused by the
Fuyun event could not have been complete at the
time of the 1957 event. As a consequence, the
stress change on the Gobi^Altay Fault should
have been smaller than 0.15 bar. Also, our fault
geometry neglects local fault complexities. Nevertheless, postseismic stress relaxation seems to have
a signi¢cant e¡ect between distant faults such as
Bolnay, Fuyun and Gobi^Altay faults.
281
Fig. 3. Stress cycle on a fault due to viscoelastic stress
change: (a) the local postseismic stress evolves until the relaxed stress drop vdrel , (b) a distant earthquake induces a
postseismic stress change that magni¢es the initial value
vCFS co and converges toward the relaxed value vCFSrel ,
(c) relaxed stress change induced by the 1931 Fuyun earthquake on the Gobi^Altay Fault. Modeled values are two orders of magnitude larger than those predicted by coseismic
motion only.
4. Earthquake cycle on the Bolnay, Fuyun and
Gobi^Altay faults
We explore the possible consequence of postseismic stress relaxation on the seismic cycle. In
modeling this cycle, one needs to generate hundreds or thousands of events in order to statistically quantify the e¡ect of stress transfer on the
earthquake timing. Until now, numerical modeling of earthquake series on a fault system has
been done to study the generic fault properties,
such as for example earthquake predictability
[43], faults interaction [44,45] or earthquake activ-
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J. Chëry et al. / Earth and Planetary Science Letters 194 (2001) 277^286
ity mode switching [46]. We attempt here to explicitly model coseismic and postseismic stress interactions between large Mongolian faults and
compute earthquake occurrence along a time
span.
We consider a model in which each fault is
represented by a 1-degree of freedom spring-slider
model [47]. Because the 1905 Tsetserleg earthquake probably triggered the Bolnay earthquake
2 weeks later, and because of the rupture complexity, we model the 1905 pair as a unique event.
We use the geometry of the largest rupture (Bolnay) in order to compute the interaction with the
Fuyun and Bogd faults. Our deterministic model
may therefore be viewed as a three-fault system
generating earthquakes. The stress evolution for
each spring-slider only depends on the loading
rate c, the local stress relaxation (see Fig. 3a)
and the distant stress change between faults (see
Fig. 3b). To de¢ne the stress transfer between the
Bolnay, Fuyun, and Gobi^Altay faults, we use the
3D formulation of Okada to compute two interaction matrices vCFSCO and vCFSREL accounting for maximum coseismic or relaxed CFS
changes, respectively :
0
vCFSCO
1
3
0:040 30:080 Bolnay trigger
ˆ @ 0:001
3
0:000 A Fuyun trigger
0:019 0:007
3
Gobi ÿ Altay trigger
…4†
0
vCFSREL
1
3 0:85 0:26 Bolnay trigger
ˆ @ 0:07 3 0:15 A Fuyun trigger
0:73 0:22 3
Gobi ÿ Altay trigger
…5†
where the line number represents the fault j where
the stress is coming from, and the column number
represents the fault i where the stress is acting on.
For example, the value 0.15 bar corresponds to
the relaxed stress coming from Fuyun (j = 2) and
acting on Gobi^Altay (i = 3) as shown in Fig. 3c.
We make the simpli¢ed assumption that the postseismic stress change on a fault i coming from an
earthquake on a distant fault j at tj evolves from
vCFSCO at tj to vCFSREL
at the end of the relaxij
ation process. If the postseismic relaxation is controlled by a relaxation time R, the postseismic
stress for t s tj is given by:
vCFSPOST
…t† ˆ …13e3…t3tj †=R †W…vCSFREL
3vCFSCO
ij
ij
ij †
…6†
In order to compute the total interseismic stress
di (t) acting on a fault i after an earthquake at ti ,
we assume that this stress corresponds to the sum
of a secular stress accumulation c, a local stress
relaxation after the earthquake, and the sum of
stress changes coming from N31 other faults. di is
therefore given by:
…7†
The total stress di increases with time until the
yield stress dyield . Earthquake motion then occurs
on fault i. The coseismic stress drop vdco is set to
50 bar which is compatible with seismic estimates
[25]. Since the stress interaction is already known
from vCFSCO and vCFSPOST , the free parameters
in Eq. 7 remain vdrel and R. We choose a relaxation time of 30 years as proposed by Thatcher
[33] for the San Andreas Fault. According to Eq.
3 we choose three values of 5, 10, and 20 bar to
encompass possible values of vdrel . We suppose a
mean recurrence time T of 4000 years for individual faults [12,13]. The loading rate c is given by
the ratio vdrel /T, which leads to secular loading
rates ranging from 0.00125 to 0.005 bar/yr. A
random variation is introduced in the system
with varying dbase in order to encompass the probable scatter of event magnitude on a fault along
the seismic cycle. The scalar seismic moment for
each fault therefore varies by þ 10% with respect
to the value associated to the 1905, 1931 and 1957
events. Integrating Eq. 7 using a ¢nite di¡erence
method, we compute the stress evolution of this
three-fault system and predict the time of earthquake occurrence on each fault. Using a series of
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J. Chëry et al. / Earth and Planetary Science Letters 194 (2001) 277^286
283
10 000 earthquakes, we illustrate (Fig. 4) the repartition of elapsed times Telapsed between successive earthquakes on this three-fault system.
Elapsed times between two successive earthquakes
range from 0 to 6000 years, but only short values
are displayed. We ¢rst tested whether any abnormal recurrence times occur when only the coseismic stress vCFSCO (Eq. 4) is used (Fig. 4a). Adding the postseismic stress change (Eqs. 5 and 6
leads to a dramatic increase of short recurrence
time. The disturbance is especially marked for
small vdrel values (Fig. 4b). The decay of the histogram towards the plateau value occurs for recurrence times between 70 and 100 years, three
times as large as the relaxation time R.
5. Discussion
Given the geometrical and mechanical simpli¢cations made in our modeling, we do not claim
that this analysis may be used in a predictive way.
Also, Quaternary seismic activity in Mongolia
probably involve tens of faults (Fig. 1), suggesting
that various faults can be involved in a clustering
process. The interest of the model is rather to
reveal that the Bolnay, Fuyun, and Gobi^Altay
faults, which are practically uncoupled when considering coseismic motion only, can su¡er signi¢cant interaction due to postseismic relaxation. As
a consequence, a large earthquake may signi¢cantly a¡ect the earthquake probability on distant
faults for several decades. This time-dependent
stress change process is two-fold. First, it reduces
the local stress drop where the earthquake took
place, bringing the stress level closer to yield limit
in only a few decades. This local relaxation favors
a possible instability due to a distant trigger. Secondly, it magni¢es the CFS change on distant
faults.
The di¡erence between coseismic stress transfer
and relaxed stress transfer can be better illustrated
using the concept of clock advance (Eq. 2) and
the example of the stress transfer from Fuyun to
Gobi^Altay (Figs. 2c and 3c). If we consider only
coseismic stress change, vdco is in the order of 50
bar [25,26], and vCFSCO coming from the Fuyun
Fault to the Gobi^Altay Fault is in the order of
Fig. 4. Histogram of elapsed time Telapsed between successive
earthquakes based on 10 000 earthquake series. Only short
values smaller than 200 years are shown. (a) Coseismic stress
transfer leads to a £at histogram. This means that the low
interfault stress transfer does not promote earthquake triggering between the Bolnay, Fuyun and Gobi^Altay faults.
(b) Postseimic stress transfer increases by 10 the abundance
of short elapsed times. This time clustering e¡ect is controlled by the relaxation time R. A normal abundance is recovered for elapsed times larger than 100 years (c). (d) Larger values of relaxed stress drop lead to a progressive
decrease of the clustering e¡ect.
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J. Chëry et al. / Earth and Planetary Science Letters 194 (2001) 277^286
0.001 bar. Clock advance is therefore approximately 1 month when considering a recurrence
time of 4000 years. Clock advance computations
cannot be done directly if postseismic relaxation is
being taken into account, since interseismic stress
accumulation is no longer linear with time (Fig.
3a,b). However, if we consider periods that display a complete postseismic relaxation, stress accumulation recovery is linear. If the relaxation
time is far smaller than the mean recurrence
time for individual faults, such as in Mongolia,
the relaxed phase lasts most of the interseismic
period. During this phase, the loading stress rate
is given by scaling vdrel by T, and the CFS stress
change is given by vCFSREL . Using vdrel = 5 bar
and vCFSREL = 0.15 bar, we ¢nd a clock advance
vt of 120 years. This clock advance is now quite
signi¢cant, and corresponds to a marked clustering as demonstrated by our seismic cycle model.
Our modeling predicts clusters having a maximum duration of 100 years, i.e. about three times
the postseismic relaxation time R. Because this
factor of three may also be controlled by the fault
number of the tectonic system, we have performed
other experiments and have computed this factor
using fault systems having lower (two) and higher
(six) numbers of faults. Within this fault number
range, the cluster duration remains unchanged,
which indicates that this duration is mainly controlled by the postseismic relaxation time. According to Eq. 6, such a duration corresponds
to an almost complete (95%) postseismic stress
e¡ect. In nature, the assessment of this relaxation
time relies on a few long-term geodetic measurements after large earthquakes. Because proposed
values range between 5 and 30 years [33,48], temporal cluster sizes should be between 15 and 90
years. Due to the low precision of historical and
paleoseismic observations, it may be hard to extract reliable earthquake clusters from data sets.
Also, local rheological variations may cause scattering of the relaxation time in the lithosphere.
However, speci¢c examples indicate cluster durations of approximately 50 years: 52 years for the
1905^1957 Mongolian sequence, 60 years for the
1939^1999 North Anatolian Fault sequence, and
V50 years for the earthquake storm of Nur and
Cline [5]. A new cluster may also be the pair 1992
Landers^1999 Hector Mine, which occurred in a
slowly deforming area, as attested by the long
recurrence time (5^15 years) on the Landers Fault
[49]. Therefore, revealing postseismic strain by
satellite geodesy [50,31] and modeling earthquake
clusters in actively deforming areas could improve
our understanding of earthquake occurrence,
above all in zones where large earthquakes have
already struck in the past decades.
Acknowledgements
This work has been supported by the research
program `ACI Prëvention des catastrophes naturelles' of the French Ministry of Research. We
thank Bettine van Vuuren who greatly enhanced
the quality of the English text. We also thank
Hugo Perfettini and Ruth Harris for their careful
reviews leading to an improved paper.[AC]
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