Ross S. Stein^{ 1}, Aykut A.
Barka^{ 2} and James H. Dieterich^{ 1}
SUMMARY
Ten M>=6.7 earthquakes ruptured 1,000 km of the North Anatolian fault (Turkey) during 193992, providing an unsurpassed opportunity to study how one large shock sets up the next. We use the mapped surface slip and fault geometry to infer the transfer of stress throughout the sequence. Calculations of the change in Coulomb failure stress reveal that 9 out of 10 ruptures were brought closer to failure by the preceding shocks, typically by 110 bars, equivalent to 330 years of secular stressing. We translate the calculated stress changes into earthquake probability gains using an earthquakenucleation constitutive relation, which includes both permanent and transient effects of the sudden stress changes. The transient effects of the stress changes dominate during the mean 10year period between triggering and subsequent rupturing shocks in the Anatolia sequence. The stress changes result in an average threefold gain in the net earthquake probability during the decade after each event. Stress is calculated to be high today at several isolated sites along the fault. During the next 30 years, we estimate a 15% probability of a M>=6.7 earthquake east of the major eastern center of Ercinzan, and a 12% probability for a large event south of the major western port city of Izmit. Such stressbased probability calculations may thus be useful to assess and update earthquake hazards elsewhere.
Key words: stress triggering, stress transfer, earthquake sequence, earthquake nucleation, hazard assessment, Izmit, Erzincan, Istanbul
INTRODUCTION
Like falling dominoes, four westwardmigrating earthquakes ruptured 725 km
of the North Anatolian fault during 193944, with subsequent earthquakes extending
the zone of faulting eastward and westward (Fig.
1). This classic case of progressive earthquake failure has tantalized earth
scientists (Allen, 1969; Dewey, 1976; Jackson & McKenzie, 1988; Richter,
1958; Scholz, 1990) , and terrorized insurance providers, for half a century.
Although clustering of earthquakes in space and time is common (Dieterich, 1994;
Kagan & Jackson, 1991) , and migrating earthquake sequences have occurred
elsewhere (Kasahara, 1981; Mogi, 1985) , none is as spectacular as on the North
Anatolian fault. Most recently, Roth (1988) modeled the shear stress buildup
along the western part of the North Anatolian fault using a simple fault geometry
with collinear ruptures of uniform slip, and found that the stress at future
ruptures was generally raised by the preceding events.
New observations of the North Anatolian fault, as well as new methods to calculate
how seismic stress transfer alters the probability of subsequent earthquakes,
encourage us to revisit this sequence to learn what conditions promote progressive
failure. Until recently, the fault geometry was poorly known, and there were
few measurements of the 193944 earthquake fault slip (Ambraseys, 1970; Ketin,
1969) , precluding calculation of the earthquakeinduced stresses. Nor could
the stress transferred by the steady or 'secular' stress accumulation be calculated,
since the rate of deep fault slip driving the stress buildup was uncertain by
a factor of four (Barka, 1992; Jackson & McKenzie, 1988; Le Pichon, et
al., 1993) . New findings remove these obstacles: A threefold increase in
measurements of earthquake slip, including a twelvefold increase for the largest
1939 shock (Barka, 1995) provides data essential to model the earthquake stress
changes (Fig. 1b).
New detailed fault mapping (Barka, 1992; Saroglu & Kusçu, 1992) (Fig.
1c) reduces the uncertainty in the fault location from about ±25
km to ±5 km. Finally, geodetic analyses yield the slip rate along the fault
(Oral, 1994; Straub & Kahle, 1994; Straub, 1996) .
The North Anatolian fault emerges as a close analogue of the San Andreas fault
in California, with the two continental transforms sharing similar slip rates,
total length, and straightness relative to their poles of rotation (Fig.
1a). But while the San Andreas fault produced just two M>=6.7
earthquakes in this century (in 1906 and 1989), the North Anatolian fault has
suffered ten such shocks, thus providing a superior natural laboratory to study
earthquake interaction (Fig.
1bc). Ruptures from Parkfield to the Salton Sea within 5 yr would,
for example, be a comparable sequence on the San Andreas fault. We find that
all but one earthquake increased the stress toward failure at the site of the
subsequent shocks, and inhibited failure on most fault segments which did not
rupture. We argue that the calculated severalbar stress increases raised the
earthquake probability threefold during the ensuing decade, and we suggest
why migrating earthquake sequences are prevalent on the North Anatolian fault.
Bolstered by recent findings that aftershocks and background seismicity concentrate
where the stress has risen (Harris & Simpson, 1992; Harris, et al.,
1995; Jaumé & Sykes, 1992; King, et al., 1994; Stein, et
al., 1994; Jaumé & Sykes, 1996) , these results offer a new approach
to updatable forecasts of earthquake hazard.
COULOMB FAILURE STRESS CHANGE
We calculate the static Coulomb stress changes resulting from North Anatolian
ruptures since 1939, with stress calculated in an elastic halfspace at all points
(as shown in Figs. 3b,
4 and 5)
or resolved on the fault plane (as listed in the tables and shown in Fig.
3a). Since we lack hypocentral depths for the Anatolian main shocks,
we sample stress in the central part of the seismogenic crust at a depth of
8 km. Failure is facilitated on a plane when the Coulomb failure stress sf
rises
,  (1) 
where is the shear stress on the failure plane b (positive in the direction
of fault slip) and sb' is the effective normal stress (positive in compression);
ms'b ª m'sb, where m' is the apparent coefficient of friction with range
0.00.75. The confining stress can be related to fluid pore pressure by Skempton's
coefficient, B, the ratio of the change in pore pressure in a cavity
to the change in applied stress, where m' = m(1B) (Roeloffs, 1988) .
Immediately after the earthquake, B ª 2/3, but could fall to zero
if fluids were to drain fully from the fault zone (Scholz, 1990) . We set m'=0.4;
equivalent to laboratory values of friction (m~0.75) and moderate pore pressure
if fluids are not fully expelled (B~0.5), or to a low value of friction
as inferred for the San Andreas fault (Zoback et al., 1987) . A m' of
0.4 also minimizes the calculation error caused by the uncertainty in m' to
±25% (King, et al., 1994) ; compare, for example, col. 2 (for m'
= 0.75) and col. 3 (for m' = 0.40) in Table 2.
Secular stress change
In addition to earthquakes, steady slip beneath the North Anatolia fault system
transfers stress to the seismogenic portion of the fault. This we model with
slip tapering from 0 at 12.5km depth to the full rate below 24 km (Fig.
2a). GPS data give 24±4 mm/yr along the North Anatolian fault
(Oral, 1994) ; near its western end, slip is partitioned with 16 mm/yr along
the KaramürselSapanca faults and 9 mm/yr along the IznikGeyve faults (Straub
& Kahle, 1994; Straub, 1996) . GPS data also resolve leftlateral slip of
18±6 mm/yr on the East Anatolian fault and ~5 mm/yr on the Northeast Anatolian
fault (Bennett, et al., 1996; Oral, 1994) (Fig. 1c and Fig.
2). During a complete earthquake cycle in this model, coseismic slip would
take place over 012.5 km and secular slip over 12.5100 km. Such a model will
not produce uniform stress even when averaged over many earthquake cycles, since
the fault strike and coseismic slip are both variable (Fig.
1b). In addition, we neglect postseismic slip beneath 12.5 km, so
we likely underestimate the total stress transfer during the cycle.
Shear stress builds in this model at 0.15 bar/yr along most of the North
Anatolian fault (Fig.
2b). Because uniform rightlateral slip is imposed beneath a relatively
straight North Anatolian fault at depth, appreciable normal stress is transferred
to the fault at seismogenic depths only at fault bends (such as at km = 350
to 400, or km 500550). A uniform stress increase of 0.01 bar/yr is added at
all points to account for the small residual stressing on faults more than 100
km from Anatolia fault system. (Fig.
1a). This small addition stress keeps the secular stress buildup
positive at all sites in the model.
Resolved and optimallyoriented stress changes
The Coulomb stress change caused by the 1939 earthquake is resolved on major
faults in Fig. 3a.
Shear and normal stress is resolved on the fault surface, (projected in UTM
coordinates) at a depth of 8 km. Faults are assumed to be vertical and to slip
in the sense indicated by the arrows, except for the west end of the 1939 rupture,
which dips 50°N and has oblique reverse slip. The apparent coefficient
of friction, m', is assumed to be 0.4; no information about the regional stress
is needed for this calculation. The Coulomb stress is seen to drop by 50100
bars along most of the 1939 rupture, with increases of several bars along the
west end, beyond the east end, and along most of the succeeding 1942 fault rupture
zone. The resolved stress changes are sensitive both to position and fault strike.
Note that a rightlateral Coulomb stress of 100 bars is not equivalent to a
leftlateral Coulomb stress of 100 bars on the same fault unless m'=0, because
unlike the shear stress change, the sign of the normal stress change is the
same for right or leftlateral slip (e.g., faultnormal tension always favors
failure). Thus the resolved stresses depends on inferring the sense of slip
on each fault correctly. This result for the 1939 rupture, and for all succeeding
events, is summarized in Tables 14.
The Coulomb stress change on optimally oriented vertical strikeslip faults
(King, et al., 1994) is plotted in Fig.
3b at a depth of 8 km. To create such a map, one must impose an orientation,
and to a lesser extent, magnitude, of the regional (or tectonic) stress, sr.
Here we assume a 100bar uniaxial compression oriented 55° clockwise from
the fault as shown by the white opposed arrows in Figs. 2b
and 4a. About
a dozen sites along the North Anatolian fault exhibit geologic indicators of
the orientation of the principal compression axis (Andrieux, et al.,
1995; Neugebauer, 1995; Suzanne, et al., 1990); they average 58°
relative to the local strike of the North Anatolian fault. The principal strainrate
axes (Oral, 1994) measured geodetically from the Marmara Sea to the central
1939 rupture zone indicate an axis oriented 48° clockwise from the fault.
We use a weighted average of these observations. Dynamic models (Gülen,
et al., 1987; Kasapoglu & Toksöz, 1983), which consider the
stresses imparted to the North Anatolian fault by remote plate tractions, yield
a similar orientation.
The principal stresses are calculated from the tensor addition of the 100bar
regional stress, the earthquake stress change, and the secular stress, at every
calculation point. Optimal planes are then calculated relative to the local
principal stress axes. The internal angle between the right and left plane is
a function of the apparent friction coefficient; the planes are orthogonal for
m' = 0. Once the optimal planes are obtained, the earthquake plus secular stress
changes are resolved on them. We thus calculate the change in Coulomb stress
on planes that are optimally oriented after the earthquake. At any given point,
the Coulomb stress change along the optimum right and leftlateral planes is
the same (the black and gray planes, respectively, in Figs. 2b
and 3b).
The earthquake stress change causes the optimum planes to rotate from the
orientation imposed by the regional stress. In the limiting case that the regional
stress is zero, all stress changes are positive and large rotations occur far
from the source, regardless of whether such slip directions are possible in
that environment. For an infinitely large regional stress, no rotations of the
optimal planes occur, and the areas of the positive and negative fields exactly
balance. For realistic assumptions about the regional stress (e.g., that
the regional stress is 110 times the earthquake stress drop), large rotations
are restricted close to the fault rupture, where the earthquake stress change
is significant relative to the regional stress. Positive optimallyoriented
stress changes are seen along the fault in Fig.
3b where the fault slip exceeded 6 m (as seen in Fig.
1b), but such positive changes apply to planes which strike at high
angle to the North Anatolia fault. Far from the 1939 rupture, rotation of the
optimal planes is negligible. For an apparent coefficient of friction m' of
0.4 in this stress field, it is seen that rightlateral faults striking eastwest,
such as the North Anatolian, are optimally oriented (Figs. 2b
and 3b). Coulomb
stress changes on optimally oriented planes are also plotted for a decade of
secular stress buildup in Fig.
2b. Here the rotations are negligible because the stress per decade,
about 1.5 bars, is small relative to the 100bar regional stress. A complete
description of this method, and its dependence on friction and the regional
stress, is given in King, et al. (1994) .
To sum, we use the optimallyoriented Coulomb stress changes to visualize
stress transfer, because the patterns are simpler, and because they do not depend
on knowledge of the faults surrounding the source. Such figures also show the
correspondence between regions of calculated stress change and background seismicity
or aftershocks (Figs. 4g
and 5), because small
shocks can occur on small faults, which could take any orientation consistent
with the regional stress. But for calculations of triggering, time advance,
and earthquake probability, we use the resolved stress changes as shown in Fig.
3a and as listed in the tables.
STRESS EVOLUTION DURING THE SEQUENCE
The buildup of stress at successive rupture sites, as well as the competition
between secular stress accumulation and earthquake stress drop, are illustrated
by sequential plots of the Coulomb stress change (Fig.
4). The stress increase along the North Anatolian fault, most evident outside
the rupture zones (yellow), is a product of the secular fault slip at depth.
Earthquakes generally relieve stress along the ruptures (purple zones), and
typically transfer stress at some sites beyond the rupture tips and off the
fault (red). Large earthquakes in 1939, 1943, and 1944 (Fig. 4ad)
profoundly decreased the stress over a distance of ~50 km normal to the fault;
with time, this zone of diminished stress narrows. Compare, for example, the
purple zone of the 1943 shock in Fig.
4c with the same region an halfcentury later in Fig.
4g. Moderate earthquakes in 1957 and 1967 (Fig.
4ef) extended the earthquake sequence 100 km westward, but these
shocks redistributed rather than diminished the stress within 50 km of the fault,
and thus the western North Anatolian fault could rerupture long before its
central segments. The calculated stress reduction near the 1942 shock is likewise
modest, suggesting that this section could also rerupture. Though imperfect,
the correlation between sites of calculated stress increase and seismicity (Fig.
4g) suggests that stress remains high at several sites along the
North Anatolian fault, such as the Yedisu segment (km 450500 in Fig.
4g).
The occurrence of a large earthquake off the North Anatolian fault in 1971
lends additional evidence for the stresstriggering hypothesis (Fig.
5). Of the four zones brought closer to failure after the 1949 shock, two
sustained M>=6.7 earthquakes (beyond the end of the 1949 rupture in 1966,
and in an offfault lobe in 1971). A third site sustained an M=5.6 shock
(in 1967) beyond the 1949 rupture at the east end of the Yedisu segment (Fig.
5b). The leftlateral East Anatolian fault ruptured 50 km south of
where it joins the North Anatolian fault (Seymen & Aydin, 1972) . The preceding
North Anatolian earthquakes increased stress on the East Anatolian fault by
0.6 bars, with the stress maxima centered on the future 1971 rupture zone.
Note that stress resolved on the East Anatolian fault reaches its maxima near
the future 1971 epicenter, and remains above 0.5 bars for most of the 1971 rupture
zone (Fig. 5a).
In addition, most fault segments that have not ruptured were brought farther
from failure by the 193949 shocks (Fig.
5a). Finally, most small earthquakes occurred where the stress on
optimallyoriented faults is calculated to have risen (Fig.
5b).
STRESS AT FUTURE RUPTURE SITES
Nine out of 10 shocks occurred where the mean stress over the entire
future rupture had increased, typically by 24 bars (Table 2, col. 4).
Similarly, 9 of 10 epicenters struck where the stress had been increased by
the preceding earthquakes, typically by 3 bars (Table 2, col. 3). This
calculation is independent of the regional or tectonic stress, and depends only
on the fault slip, geometry, and the friction, m'. The stress transfer averages
about 20% of the stress released by the earthquakes (Table 1, col. 7),
a substantial trigger.
Although it is unknown whether the stress change along the future rupture,
or at the future epicenter, is most important to triggering, the results for
both assumptions are quite similar (Table 2). Faults are inherently complex,
en echelon, and multistranded on many scales. Thus it is also unknown whether
the stress change resolved on the fault plane as defined by its surface trace
(as listed in the tables), or the stress change on optimallyoriented planes
(as shown in Fig. 4)
is most important to earthquake triggering. The optimallyoriented stress increases
are about 25% larger than the resolved stress changes. Thus despite uncertainty
in identifying the stress component that is most effective in triggering or
advancing future earthquakes, the results lead to a consistent finding that
the transfer of stress by one earthquake to another promoted the Anatolia sequence.
Scholz (1990) argued that the 1943 epicenter lies at the 'wrong' end of the
1943 rupture, because the epicenter locates at the end of the rupture farthest
from the preceding 1942 shock. However, the calculated stress change at the
end of the 1943 rupture closest to the 1942 shock inhibited failure (Fig.
3), and the 1943 epicenter lies within 40 km of where the stress change
is most positive (Fig. 3ab). Only the 1949 earthquake struck farther
from the stress maxima associated with the preceding shocks (Fig. 2d),
which is surprising because the intervening Yedisu segment last ruptured in
1784, and so the accumulated stress should have been high. Seismicity is now
concentrated along this segment (Fig. 3g). The much better located
aftershocks of the 1992 earthquake lie in regions of calculated failure stress
increase (Nablant, et al., 1996) .
Most fault segments that sustained stress decreases have not ruptured,
a further indication that stress changes influence earthquake
occurrence. The typical stress change for the dozen unruptured
segments since 1939 is 0.1 to 0.6 bars (Table 3, col.
2), in comparison with a 2 to 4bar increase for those that
have ruptured (Table 2, col. 3). Even when the secular
stress accumulation during 193995 is included, the stress changes
on the unruptured segments facilitated failure by only 1.21.6
bars (Table 3, col. 4), in comparison with a 3.6 to 6.1bar
increase for the segments that ruptured (Table 2, col. 5).
EARTHQUAKE PROBABILITIES
The effect of the stress change on times of earthquake recurrence can be cast
as a change in the probability of future events. The times of future earthquakes
along a fault segment are uncertain because of intrinsic variability of the
earthquake faulting process and uncertainty of the observations used to estimate
recurrence time. Estimations of the probability of future events over a given
time interval provide the means to account for these uncertainties. Departing
from previous studies, which consider only a permanent effect of stresses on
segment probabilities (Cornell, et al., 1993; Working Group on California Earthquake
Probabilities, 1990; Working Group on the Probabilities of Future Large Earthquakes
in Southern California, 1992), we consider both permanent and transient effects
of the stress changes on earthquake probabilities.
Segment Probability Prior to a Stress Step
Two models for estimation of earthquake probabilities are in general use,
the stationary Poisson model and the conditional probability model (Cornell,
1968; Hagiwara, 1974). The conditional probability model can be tailored to
find the effects elapsed time and stress changes on earthquake probabilities.
We first present results from the simple Poisson model for comparative purposes
and for later use in addressing transient effects of stress changes on probabilities.
The stationary Poisson model, assumes the probability of an earthquake in a
time interval is independent of the elapsed time from previous events. The probability
of at least one event in the interval Dt is
,  (2) 
where r is a constant occurrence rate for earthquakes that rupture
the segment of interest and N is the expected number of such events in
the interval Dt.
With the conditional probability model, probability can increase with time
to represent increasing stress on a fault segment toward an uncertain stress
threshold. We estimate the probability for recurrence of an earthquake on a
fault segment prior to the stress step, given an elapsed time t from
the previous earthquake, following the method of the Working Group on California
Earthquake Probabilities (1990). The probability for recurrence of slip in any
time interval (t, t+Dt) is
,  (3) 
where f(t) is the probability density function for
the uncertain recurrence time T for a segment rupturing
earthquake. The probability, conditional on the earthquake not
occurring prior to t, is
,  (4) 
We assume a lognormal probability distribution of recurrence times
,  (5) 
where m is the median and s is the standard deviation
of the natural logarithm of the random recurrence time.
To estimate probabilities, we require values for m and s, as
well as the time elapsed t during the 193967 sequence. Because the observations
are sparse and uncertain, we do not distinguish different repeat times along
the North Anatolian fault; instead we use the portions of the fault for which
the record is longest to estimate a generic repeat time (Fig.
7). Although segment probabilities are sensitive to m, s and
t, we show that probability gains associated with the stress steps (the
ratios of probability after the steps to the probability before the steps) are
insensitive to parameter choices. In the west (at about km = 200 in Fig. 7),
earthquakes struck in A.D. 1035 , 1668, and 1944. For the central region, at
km = 50, events occurred in A.D. 1050 , 1668, and 1943. For the eastern region
near Erzincan at km = 350, earthquake took place in 1043 A.D., 1254, and 1939
(Ambraseys, 1970; Ikeda, et al., 1991; Ambraseys & Finkel, 1995). Together
these yield m=450 yr, with s = 220 yr. The derived coefficient
of variation of 0.5 is in accord with observations for faults with longer paleoseismic
records, such as the southern San Andreas (Working Group on California Earthquake
Probabilities, 1995). The time t elapsed between the 193967 sequence
and the previous events in 12541668 is taken to be ~425 yr (a weighted average)
in a 450± 220year cycle. For the Poisson calculation (eq 2) the earthquake
rate r is taken as 1/m. The stressing rate in our model is 0.15
bar yr1 along most of the North Anatolian fault system (Fig.
2b).
The fault slip rate of 24 mm/yr, an average secular stressing rate of 0.15
bar/yr, and repeat time of 450 years, give a mean slip of 11 m per event and
mean stress drop of 68 bars. During the twentieth century, the slip and stress
drops are lower than this estimate except for the 1939 earthquake, suggesting
that we may have overestimated the repeat time and thus underestimated the earthquake
probability. This could arise if some large earthquakes are missing from the
historical record. To examine the impact of overestimating the repeat time,
and to define a range of probabilities appropriate to the observations, we also
calculate probabilities a using an alternate set of parameters with repeat time.
We arbitrarily halve the repeat time, leaving the coefficient of variation at
0.5. Thus m=225 yr, s=110 yr. For these calculations, for the
elapsed time we use the time since the great 1668 earthquake (Fig.
7), so t=271 yr. The mean recurrence time of 225 years gives a mean
event slip of 5.4 m per event and mean stress drop of 34 bars.
For the time interval used in this study, Dt=10 years, the first
set of parameters (m=450 yr, s=220 yr, t=450 yr) give generic
segment probabilities of 0.022 and 0.036 for the Poisson and conditional probability
models, respectively, and the second set of parameters (m=225 yr, s=110
yr, t=271 yr) give generic segment probabilities of 0.044 and 0.130 for
the Poisson and conditional probability models, respectively. Because the elapsed
times are close to the mean recurrence times, the conditional probabilities
are larger than the Poisson probabilities for both parameter sets.
Permanent effect of Stress Change
Increasing (or decreasing) the Coulomb stress on a fault segment permanently shortens (or lengthens) the time required for tectonic stressing to bring a segment to failure (Fig. 6a), and thus causes a permanent change in conditional probability. The conditional probability model can be adapted to estimate the effect of stress changes by equating a stress change with the time required to accumulate stress through secular stressing.
Two very similar methods have been proposed to estimate the effect of a stress
increase on the conditional probability. The first method advances the elapsed
time in the conditional probability calculation (eqs 35) from t to
t' by the equivalent time required to accumulate the stress step Ds
through the secular stressing process (Dieterich, 1988)
,  (6) 
where is tectonic stressing rate. The second approach reduces
the expected median recurrence time from m to m'
by the equivalent time required to accumulate the stress step
through the secular stressing process (Working Group on California
Earthquake Probabilities, 1990)
,
,  (7) 
Reducing m or increasing t for a positive step in stress increases
the conditional probability of an earthquake (Fig.
6b, dotted to dashed lines). We have employed eq (7) in computing
conditional probabilities following a stress step, because it is consistent
with the concept that recurrence time is reduced by a step increase in stress.
Both methods yield similar results, though eq (7) yields larger changes of probability
for a given stress step. Segment probabilities following the stress step are
given in Table 4 (col. 5) for the first parameter set, and in Table 5
(col. 5) for the second parameter set.
Transient effect of Stress Change
The existence of foreshocks and aftershocks demonstrate that when
an earthquake occurs there is a large transient increase in the
probability of additional earthquakes in the surrounding area.
Similarly, global statistics of earthquake pairs reveal strong
clustering in space and time, in which the occurrence of one earthquake
increases the probability of a second earthquake, with the probability
decaying with time and distance from the first event (Kagan and
Jackson, 1991). These transient increases of earthquake probabilities
are among the most prominent of statistical features of earthquake
occurrence. A quantitative and unified explanation of aftershock
distributions and decay, global clustering statistics, and foreshock
statistics, is given by a single model in which the rate of earthquake
occurrence is perturbed by the local stress increase caused by
a prior earthquake (Dieterich, 1994; Dieterich & Kilgore,
1996). We employ this model to calculate this transient change
of the segment earthquake probabilities.
The model is based on the constitutive formulation for rate of earthquake
activity proposed by Dieterich (1994), derived from laboratory observations
of rate and statedependent fault properties. Rate and statedependence of
fault properties has been observed for a diverse variety of materials over the
range of conditions for crustal earthquakes. Numerical simulations using these
fault constitutive properties reproduce the full range of observed fault slip
phenomena, including laboratory observations of spontaneous timedependent nucleation
of slip instabilities over a range of stresses above some minimum critical stress
level, and healing following slip (Dieterich and Kilgore, 1996). A consequence
of clustering statistics and timedependent nucleation is that earthquake rates
at all magnitudes undergo a strong transient amplification at the time of a
step increase of stress, followed by 1/t decay to their background rate
(Fig. 6b).
Because the transient effect of the stress change is expressed as a change in expected rate of segment events, it is convenient to formulate the probability analysis as a nonstationary Poisson process. Generalizing eq (2) gives
,  (8) 
where, Pn is the net probability, which combines the transient and
permanent effects of the stress change on earthquake probability and R(t)
is now a nonconstant (decaying) earthquake rate following a stress step. Dt
is measured from the time of the stress step; we use 10 years for these computations.
To evaluate eq (8), we obtain N, by integrating the solution for
R(t) following a stress step (Dieterich, 1994; his eq 12). For
the interval 0 to Dt, this yields
,  (9) 
where r is the permanent background component of the earthquake rate
following the stress step (Fig.
6b), ta is the characteristic duration of the transient effect,
and Dsf is the calculated Coulomb stress change. A is a dimensionless
fault constitutive parameter and s is the effective normal stress. Since
ta and As are unknown for the Anatolia sequence, we set ta
= 10.2 yr, the value derived from pair clusters in the Harvard CMT global catalog
for M>5 earthquakes at depths<70 km, and As=1 bar from analyses
of aftershocks and foreshocks (Dieterich, 1994). Note that the transient effect
disappears if Dsf = 0, that is N = r Dt.
In eq (9) r is the rate of activity implicit to the conditional
probability following the stress step (Tables 4 and 5, col.
6). Hence, to evaluate r we equate the value of the
conditional probability to a stationary Poisson probability and
solve for r. From eq (2),
(10) 
where, P is the previously obtained conditional probability for the
fault segment following the stress step.
In summary, the net probability of events rupturing each fault
segment (Tables 4 and 5, col. 7) combines both the permanent
and transient effects of a stress step. Net probability is obtained
by first computing the permanent effect of a stress change on
the conditional probability using the approach of eq (7). Then
the equivalent Poisson rate r for the permanent effect
is obtained using eq (10) to evaluate eqs (8) and (9) for the
net probability.
For completeness we noted that eq (9) assumes the background rate r
after the stress step, is constant over the interval Dt, which it is
not. Conditional probability grows slowly with elapsed time, requiring an increase
of r with time (Fig.
6b). However, for the Anatolian computations the change of r
over Dt=10 years is small relative to the magnitude of r, and
the resulting error introduced by this approximation is slight. In cases where
Dt is large relative to the repeat time T, and where higher accuracy
in the application of eq (9) is sought, the time interval can be broken into
n subintervals, . The conditional probabilities Pi, and expected
number of events Ni are computed as before, for each subinterval i.
Pn for the entire interval is then given by
,  (11) 
where Pn1 etc. are the net probabilities obtained for each subinterval.
Using the definition Pni=1exp(Ni), eq (11) can be written as
,  (12) 
where N=N1+N2+ .. Nn .
Net Probability Gain
The probability gain associated with the stress step is the net
probability for some period after a stress increase, divided by
the conditional probability prior to the step (Aki, 1981). The
probability gains for the two sets of parameters are listed in
Tables 4 and 5 (col. 8). Note that although net probabilities
are very different for the two assumed repeat times, each set
of recurrence parameters yields similar probability gains. It
is also apparent that about 95% of the 10yr gain is caused by
the transient effect. In other words, both aftershocks and subsequent
mainshocks are more likely in the stressed areas during the first
decade after each large shock. We find an average threefold gain
in the probability of an M>=6.7 earthquake during the
decade after each triggering event, with a wide range for individual
triggers of 119.
LIMITATIONS OF THE ANALYSIS
Although we incorporate stress changes caused by earthquakes and secular fault
slip, we make several assumptions that influence our results. Earthquake slip
measured at the surface may underrepresent the net slip at depth, and thus
the stress change, by as much as 50%. Surface slip occasionally exceeds the
slip at depth, as at the north end of the 1992 M=7.4 Landers, California,
earthquake (Wald & Heaton, 1994) , so the calculated stress beyond the fault
ends can also be too large. Our assumed 12.5km depth of coseismic slip is consistent
with the 1992 Erzincan earthquake (Barka & Eyidogan, 1993; Bennett, et al.,
1996; Nablant, et al., 1996), but it is unknown for the preceding events.
The deep slip rate used for the secular model is also uncertain by ±8 mm/yr
(95% confidence) (Oral, 1994). In addition, we neglect two timedependent effects:
Porefluid flow could raise m' with time, as suggested by Harris & Simpson
(1992), Jaumé & Sykes (1992), and Scholz (1990) , which would increase
the stress changes by up to 25% (Table 2, col. 2). Postseismic asthenospheric
relaxation also transfers stress to the upper crust. An 12.5kmthick elastic
plate overlying an inviscid fluid approximates complete relaxation of the lower
crust; this yields stresses twice as high and twice as broad as those calculated
here (Stein, et al., 1992). Thus most processes we omit would, if included,
increase the calculated stress transfer and associated probability gains.
Several assumptions introduce uncertainty into our probability
calculations. To estimate the permanent stress effects, we used
a common repeat and elapsed time for large earthquakes on the
Anatolian fault, whereas repeat times for the better studied San
Andreas fault differ by nearly a factor of two between the northern
and southern segments. For the transient probability effects,
we relied upon global average values for the key parameters because
we lacked local information for Anatolia. Based on analyses of
earthquakes elsewhere, these parameters could differ by ±50%.
Fortunately, the probability gains listed in Tables 4 and 5 (col.
8) are less sensitive to these assumptions than the probabilities,
particularly during the first decade after each triggering earthquake
when transient effects are large.
IMPLICATIONS FOR EARTHQUAKE FORECASTING
We identify several faults with an heightened probability of failure. The
port city of Izmit is most vulnerable to an earthquake on the Sapanca fault
(Fig. 4g).
Stress increases of 1.32.5 bars are found for the Geyve and Sapanca faults,
which pose the greatest threat to Istanbul, particularly if the faults ruptured
from east to west. The Sapanca fault last ruptured in 1878. We calculate a 30yr
probability during 19962026 for M>=6.7 shocks on the Geyve and Sapanca
fault segments to be 12%; this probability is higher by a factor of 1.07 than
the rate before the these segments were stressed by the 1967 earthquake. The
Yedisu (last rupture in 1784), Ovacik, and Göynük (last event in 1866)
faults near Erzincan have been stressed toward failure by 1.79.2 bars. Erzincan,
badly damaged during the 1939 and 1992 earthquakes, would be most affected if
these faults ruptured toward the city (Fig.
4g). We calculate a 30yr probability during 19962026 for M³6.7
shocks on the Yedisu segment to be 15%; this is a factor of 1.35 higher than
the rate before the these segments were stressed by the 1992 Erzincan earthquake.
The Anatolian findings complement studies of the triggering of
main shocks, aftershocks, and fault creep in California. The 1992
M=7.4 Landers earthquake was calculated to have increased
the stress by 1.53.0 bars where the M=6.5 Big Bear shock
struck 3.5 h after the Landers main shock, and 65% of the Landers
M³1 aftershocks occurred where the stress rose by >0.3
bars (King, et al., 1994) . The Landers earthquake increased the
stress 40 km away on the San Andreas fault by an estimated 26
bars (Harris & Simpson, 1992; Jaumé & Sykes, 1992;
Stein, et al., 1992) , with ~150 mm slip needed to relieve the
imposed stress (King, et al., 1994) . Subsequent GPS (Shen, et
al., 1994) and continuous strain (Wyatt, et al., 1994)
measurements indicate that deep slip on the San Andreas fault
of 115±47 mm occurred where the stress was calculated to
have risen, and slip of 39±33 mm where the stress was calculated
to have dropped, in close accord with the calculation. Stress
changes associated with several other California earthquakes influenced
subsequent seismicity (Jaumé & Sykes, 1996; Harris
& Simpson, 1996; Harris, et al., 1995; Simpson & Reasenberg,
1994; Stein, et al., 1994) . Together, these results attest that
faults are sensitive to small but sustained stress changes transmitted
over tens to hundreds of kilometers.
The North Anatolia fault has experienced several historical episodes of migrating
earthquake sequences (Fig.
7). Large earthquakes progressed ~250 km eastward during 967, 1035, and
1050 A.D. (Ambraseys, 1970). A sequence ruptured perhaps 700 km of the fault
during 1650±20 to 1668 (Ikeda, et al., 1991; Ambraseys & Finkel, 1995).
We suggest that the propensity of the fault zone toward progressive failure
is a product of its simple, straight geometry, which, as seen in Fig.
4, makes for efficient transfer of stress; its isolation from other faults,
which minimizes stress transferred between the North Anatolian and competing
faults; and its en echelon character (Wesnousky, 1988) , which tends to keep
the entire fault from rupturing at once (Fig. 1c). By contrast, the San
Andreas fault, which lacks an historical record of progressive shocks, produces
larger earthquakes along its smoother trace, and generally lies close to other
major faults, making the stress transfer more irregular and complex.
CONCLUSIONS
We find that earthquakeinduced stress increases of several bars
promoted the North Anatolia earthquake sequence, each shock raising
the probability of future earthquakes at the site of the next
to strike. Our analysis is least successful in explaining the
occurrence of the 1943 earthquake and the absence of a Yedisu
segment earthquake. Nor do we account for the time lag between
individual triggers and ruptures, which varied from months to
decades.
Our results suggest that earthquakes interact: When a large shocks
occurs, it changes the conditions for failure in its vicinity,
altering the probabilities for future events. In contrast, current
approaches to earthquake hazard generally assume a stationary
Poisson process where the past behavior of large faults is unknown,
in which earthquakes are assumed to occur randomly over time on
a fault. Where more information is available, the timepredictable
model (Shimazaki & Nakata, 1980) is employed, in which the
probability of an earthquake of specified size and location drops
after the rupture but does not change elsewhere. Ward (1996)
considered the permanent effects of stress transfer in a synthetic
seismicity model for southern California, finding significant
fault interactions, as we do here. Two seismic hazard analysis
for the San Andreas system (Working Group on California Earthquake
Probabilities, 1990; Working Group on the Probabilities of future
large earthquakes in southern California, 1992) considered Coulomb
stress changes, but only for the permanent effect associated with
the most recent large earthquake in the region. In contrast, we
find that the transient effect dominates during the first decade
after the triggering event, contributing both to the production
of aftershocks and to the higher likelihood of subsequent mainshocks.
This result may help to explain a stresstriggering paradox in
southern California: For smallmoderate southern California earthquakes
since 1932, the influence of Coulomb stress changes were discernible
for <5 yr (Harris, et al., 1995) , but persisted for 50 yr
following the great 1857 M=7.8 earthquake in the same region
(Harris & Simpson, 1996) . The transient effect decays within
510 years for large and small shocks alike, but only large shocks
substantially perturb the permanent probabilities, and so their
influence persists long after the transient effect subsides.
Clustering of strong shocks is the outstanding feature of seismicity over
historical (Kagan & Jackson, 1991) and paleoseismic (Wallace, 1987) time
periods. Clustering implies that the prospect of a large earthquake rises after
a large event. Stress transfer offers a physical explanation for earthquake
clustering and migration: stress drops on the slipped fault but rises at other
sites nearby, bringing faults in these regions closer to failure. Coulomb stress
calculations thus capture the most salient feature of earthquake distributions,
and gives insight as to where the next event is more likely to strike
.
ACKNOWLEDGMENTS.
We thank Nicholas Ambraseys, Christopher Scholz, John Vidale, Robert Simpson,
and Steven Ward for reviews of the manuscript, Pierre Briole for initial assistance,
and the Institut de Physique du Globe de Paris for a visiting professorship
(R.S.).
FIGURES and TABLES
Fig. 1. (a)
Active faults in Turkey (Barka, 1992; Saroglu & Kusçu, 1992;
Sengor, et al., 1985), with the North Anatolian fault in bold. GPS
observations establish a 24±4 mm/yr (1s confid.) deep slip rate on
the North Anatolian fault and reveal that the rightlateral transform describes
a small circle about a (33.4±0.5°E, 31.1±1.3°N) AnatoliaEurasia
rotation pole, which lies at the intersection of the dashed red lines (Oral,
1994) . (b) Cumulative rightlateral slip associated with M>=6.7
earthquakes (Barka, 1995; Barka & Eyidogan, 1993; Bennett, et al., 1996)
; the sequence ruptured from warm to cool colors. Slip in the 1949, 1966,
and 1971 shocks is approximate, and the reverseslip component for the Ezine
and Kursunlu faults is not shown. (c) The region inscribed by the
solid red line in a is projected relative to the AnatoliaEurasia
rotation pole, so that a transform fault would strike due eastwest; the
North Anatolian fault is seen to deviate less than 40 km from being a simple
rightlateral transform.

Fig. 2. Secular
slip model used to calculate the loading of the North Anatolian fault system.
(a) Steady deep slip below 12.5 km, as inferred from GPS observations
(Le Pichon, et al., 1993; Oral, 1994; Oral, et al., 1997; Straub
& Kahle, 1994; Straub, 1996) transfers stress to the seismogenic portion
of the fault. The model shown, projected relative to the pole of rotation
as in Fig. 1c,
is used for the Coulomb stress changes on optimally oriented faults (Fig.
3. Fig. 4,
and Fig. 5); an
identical model projected in UTM coordinates, as in Fig.
1a, is used for the stress changes resolved on specific faults
(Tables 13). (b) The secular stress rate is resolved on the fault
at the indicated points, and also calculated for optimally oriented vertical
strikeslip faults (color gradients). Deep slip and stress is distributed
between two strands at the west end of the fault. 
Fig. 3. Stress
changes associated with the 1939 earthquake. (a) Coulomb stress change on
major faults caused by the 1939 earthquake. Stress is resolved on the fault
surface, projected in UTM coordinates, at a depth of 8 km. Faults are assumed
to be vertical, except for the west end of the 1939 rupture, which dips
50° N. No information about the regional stress is needed for this
calculation. The mean stress change along the future 1942 rupture is +1.4
bars. (b) Color gradients show the Coulomb stress change on optimally oriented
vertical strikeslip faults at a depth of 8 km. The calculation assumes
that the regional stress is 100 bars compression oriented 55° clockwise
from the local Anatolian fault strike. Large rotations of the optimal planes
are restricted close to the fault rupture, where the earthquake stress change
is significant relative to the regional stress. Far from the 1939 rupture,
rotation of the optimal planes is negligible. 
Fig. 4. Cumulative
stress changes caused by large earthquakes and steady deep slip on the North
Anatolian fault since 1939. In each panel, the epicenter of the next earthquake
to rupture is circled. All but the 1943 epicenter lie in regions where the
stress rose significantly, typically by 25 bars, owing to the foregoing
shocks and deep fault slip. Relocated ISC earthquakes (Engdahl, et al.,
1996) are shown in g, with the 1992 Erzincan aftershock sequence
removed. Calculations are made in an elastic halfspace with a shear modulus
of 3.15 x 1011 dynecm2 and Poisson's ratio of 0.25. Earthquake slip is
assigned as in Fig.
1b, assumed to be uniform over 012.5km depth. The fault was
digitized and stress was sampled at 5km increments, and is projected as
in Fig. 1c so that the regional stress maintains nearly a fixed angle
to the fault. 
Fig.
5. Stress changes at the east end of the North Anatolian fault caused
by 1939 and 1949 earthquakes (Ambraseys, 1988) . To emphasize the earthquake
stress transfer, secular stress accumulation is not included in this plot;
its inclusion would simply raise the stress along the North and East Anatolian
faults by 11.4 bars. Projection as in Fig.
4. (a) The 1939 and 1949 earthquakes highly stress the sites of the
future 1966 and 1971 earthquakes. Most segments that did not subsequently
rupture were brought farther from failure except for the Yedisu segment.
(b) Most aftershocks or small earthquakes occur in regions where the stress
change on optimallyoriented strike slip faults was raised by the 193949
earthquakes. The optimal orientations for right and leftlateral faults
off the 1949 rupture zone is shown with the assumed regional stress direction,
sr. Earthquakes from 1964 from Engdahl, et al. (1996) are shown, rather
than from 1949, because of the poor network quality before 1964. 
Fig. 6. Schematic
illustration of a sudden stress increase Dsf on a fault at point
x near an earthquake rupture at time to (inset). (a)
The stress increase advances the time to the next rupture. If the stress
were closer to failure at the time of the stress step, the trigger might
have triggered an earthquake immediately. (b) The associated shortterm
(transient) and longterm (permanent) probability gain (Dieterich
& Kilgore, 1996) . The transient gain (curved portion of solid line)
scales with the rate of aftershock decay, and the permanent gain (dashed
to solid line) is typically a factor of 1.12 higher than the probability
before the triggers the Anatolian sequence. 
Fig. 7. Rupture
zones for large historical earthquakes along the North and East Anatolian
faults (Ambraseys & Finkel, 1988; Ambraseys & Finkel, 1995; Barka,
1992; Ikeda et al., 1991) . Zones for earthquakes before 1939 are based
largely on isoseismals, and are thus approximate. Earthquake progressions,
indicated by arrows, occurred during three sequences but in different directions
and rates. 
Earthquake  mag. M  (10 ^{26} dyncm)^{**}  Dt^{*} (bar)  trigger‡ (bar)  ratio§ (%)  advance (yr)¶  
1939  26 Dec  7.9  52.0  60       
1942  20 Dec  6.9  1.7  42  4.7  11  8.4 
1943  26 Nov  7.7  29.0  48  0.6  1  0.0 
1944  01 Feb  7.5  15.0  34  5.8  17  31.4 
1949  17 Aug  7.1  3.5  40  1.3  3  2.1 
1951  13 Aug  6.8  1.4  25  1.7  7  11.0 
1957  26 May  6.8  1.4  22  5.4  25  28.6 
1966  19 Aug  6.6  0.6  15  8.2  55  30.0 
1967  22 Jul  7.0  2.7  18  4.4  24  12.3 
1971  22 May  6.8  1.2  11  3.5  32  4.6 
1992  13 Mar  6.5  0.4  27  16.0  59  125.0 
Average (all values)  31  5.2  24  25.3  
Average (min/max excluded)  34  4.4  22  18.1  
 
** Seismic moment calculated from surface slip (Fig. 1), assuming a 0 to 12.5km width of faulting, and a shear modulus G of 3.15 x 1011 dynecm2.  
* Mean static shear stress drop of all 5kmlong rupture patches.  
‡ Mean earthquakeinduced plus secular stress change along future ruptures.  
§ Stress trigger (col. 6) divided by succeeding earthquake stress drop (col. 5).  
¶ Mean earthquakeinduced stress change (for m=0.4) along the future rupture zone divided by the modeled secular stressing rate along that rupture. 
Three modes to weigh the effect of the stress changes at the sites of future
earthquakes. The trigger ratio is the Coulomb stress increase divided by the
subsequent earthquake stress drop (col. 6/col. 5); the time advance
gives the Coulomb stress increase divided by the local secular stressing rate.
Coulomb failure stress change (bars)  
Triggered Event 
Epicentre m '= 0.75 
Epicentre m ' = 0.4 
Mean m ' = 0.4 
Epicentre m ' = 0.4 
Mean m ' = 0.4 
1942  11.75  4.63  1.3  4.7  1.5 
1943  0.00  0.01  0.0  0.6  0.6 
1944  6.56  6.39  4.8  7.3  5.6 
1949  0.61  0.53  0.3  1.3  1.4 
1951  1.49  1.71  1.7  1.7  1.7 
1957  3.47  3.45  4.0  5.4  5.9 
1966  3.85  4.03  3.0  8.2  5.4 
1967  1.70  1.47  1.4  4.4  4.3 
1971  0.71  0.58  0.5  3.5  3.2 
1992  9.60  8.00  19.0  16.0  31.6 
Average  4.0  3.1  3.7  5.2  6.1 
min/max excluded  3.5  2.9  2.0  4.4  3.6 
Cumulative stress transferred by M>=6.7 earthquakes and by secular
stress accumulation since 1939, resolved onto future ruptures at 8 km depth.
Faults were digitized at 5km increments, with calculations performed with the
fault projected in UTM coordinates, as in Fig.
1a. The stress change shown for the 1942 earthquake assumes that
the Ezine fault (Fig.
1c) has a 50°N dip and a 1:1 rightreverseslip component (if
the Ezine is treated as a vertical strikeslip fault, the mean change on the
1942 rupture zone is 6.0 bars and the epicentral change is 3.0 bars). The
stress transferred by the 1951 earthquake is calculated for the 60°Ndipping
Kursunlu thrust fault (Pinar, 1953) , although the epicenter could lie on the
North Anatolian fault. The epicentral stress for m'=0.75 gives results for low
pore fluid pressure.
Coulomb stress change (bars)  
Earthquakes  Earthq.+secular  
Fault  Max  Mean  Max  Mean 
Yalova  0.03  0.02  1.3  1.3 
Sapanca  0.5  0.2  1.6  1.3 
Geyve  2.6  1.6  6.7  2.5 
Hendek  1.6  0.8  1.8  1.0 
Düzce  2.3  2.5  4.1  0.7 
Merzifon  0.3  1.4  0.4  0.7 
Alaca  3.0  0.2  3.0  0.2 
Esençay  3.7  9.8  3.6  2.5 
Ovacik  8.0  1.8  7.6  1.7 
NE Anat.  0.9  0.3  0.1  0.8 
Yedisu  2.3  1.4  10.1  9.2 
Göynük  5.4  3.5  8.1  6.2 
Average  1.9  0.6  4.0  1.6 
min/max excluded  1.8  0.1  3.8  1.2 
Calculated stress transferred by M>=6.7 earthquakes and secular accumulation
during 193995, for m'=0.4, resolved onto unruptured faults, listed from west
to east (see Figs. 1c
& 3g).
Probability before the stress step 
recurrence* time change (yr) 
Conditional probability after the stress step‡ 
Probability gain (col. 7÷ col. 4) 

Triggered Year 
Shock Date 
Poisson  Conditional †  Permanent effect 
Transient + perm. effect 

1942  20 Dec  0.022  0.036  8.4  0.038  0.074  2.0 
1943  26 Nov  0.022  0.036  0.0  0.036  0.036  1.0 
1944  1 Feb  0.022  0.036  31.4  0.041  0.204  5.6 
1949  17 Aug  0.022  0.036  2.1  0.037  0.044  1.2 
1951  13 Aug  0.022  0.036  11.0  0.038  0.087  2.4 
1957  26 May  0.022  0.036  28.6  0.041  0.174  4.8 
1966  19 Aug  0.022  0.036  30.0  0.041  0.140  3.9 
1967  22 Jul  0.022  0.036  12.3  0.038  0.078  2.1 
1971  22 May  0.022  0.036  4.6  0.037  0.050  1.4 
1992  13 Mar  0.022  0.036  125.0  0.059  0.704  19.4 
Average  25.3  0.041  0.159  4.9  
Average (min/max values excluded)  16.1  0.039  0.105  2.9 
† Elapsed time is assumed to be 425 yr (weighted average time since complete rupture of the North Anatolian fault in earthquakes during 1254 and 1668; see Fig. 7).
* From eq (7), using the stress transfer in Table 2 (col. 4) divided by the secular stressing rate for each rupture zone (0.100.15 bar/yr) as shown in Fig. 2b.
‡ This uses the stressmodified recurrence time to compute the conditional
probability for the ten years after the stress step.
Probability before the stress step 
recurrence* time change (yr) 
Probability after the stress step‡ 
Probability gain (col. 7÷ col. 4) 

Triggered Year 
Shock Date 
Poisson  Conditional †  Permanent effect 
Transient + perm. effect 

1942  20 Dec  0.043  0.130  8.4  0.136  0.254  2.0 
1943  26 Nov  0.043  0.130  0.0  0.130  0.130  1.0 
1944  1 Feb  0.043  0.130  31.4  0.155  0.599  4.6 
1949  17 Aug  0.043  0.130  2.1  0.131  0156  1.2 
1951  13 Aug  0.043  0.130  11.0  0.138  0.296  2.3 
1957  26 May  0.043  0.130  28.6  0.152  0.533  4.1 
1966  19 Aug  0.043  0.130  30.0  0.154  0.453  3.5 
1967  22 Jul  0.043  0.130  12.3  0.139  0.296  2.1 
1971  22 May  0.043  0.130  4.6  0.133  0.175  1.3 
1992  13 Mar  0.043  0.130  125.0  0.252  0.996  7.7 
Average  25.3  0.152  0.386  3.0  
Average (min/max values excluded)  16.1  0.142  0.342  2.6 
† Elapsed time is assumed to be 271 yr (time since the great 1668 earthquake in Fig. 7).
* From eq (7), using the stress transfer in Table 2 (col. 4) divided by the secular stressing rate for each rupture zone (0.100.15 bar/yr) as shown in Fig. 2b.
‡ This uses the stressmodified recurrence time to compute the conditional probability for the ten years after the stress step.
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