**T. Parsons, S. Toda, R. S. Stein, A. Barka and J. H. Dieterich,**

- Heightened odds of large earthquakes near Istanbul: An interaction-based
probability calculation,
*Science, 288, pp. 661-665, 2000.* - [Printable article (213kb)]

**Heightened odds of large earthquakes near
Istanbul: **

**An interaction-based probability calculation**

Tom Parsons, Shinji Toda, Ross S. Stein,

Aykut Barka, James H. Dieterich

We calculate the probability of strong shaking in Istanbul–an
urban center of 10 million people–from the description of earthquakes
on the North Anatolian fault system in the Marmara Sea during the past 500
years, and test the resulting catalog against the frequency of damage in
Istanbul during the preceding millennium. Departing from current practice,
we include the time-dependent effect of stress transferred by the 1999 moment
magnitude** M**=7.4 Izmit earthquake to faults nearer to Istanbul. We
find a 62±15% probability (one standard deviation) of strong shaking during
the next 30 years and 32±12% during the next decade.

The 17 August 1999 **M**=7.4 Izmit and 12 November 1999
**M**=7.1 Düzce earthquakes killed 18,000 people, destroyed 15,400 buildings,
and caused $10-25 billion in damage. But the Izmit event is only the most recent
in a largely westward progression of seven large earthquakes along the North
Anatolian fault since 1939. Just northwest of the region strongly shaken in
1999 lies Istanbul, a rapidly growing city that has been heavily damaged by
earthquakes twelve times during the past 15 centuries. Here we calculate
the probability of future earthquake shaking in Istanbul using new concepts
of earthquake interaction, in which the long-term renewal of stress on faults
is perturbed by transfer of stress from nearby events.

Stress triggering has been invoked to explain the 60-year sequence
of earthquakes rupturing toward Istanbul [Toksoz et al ref](1-3), in which all
but one event promoted the next (4). Although an earthquake drops the average
stress on the fault that slipped, it also changes the stress elsewhere. The
seismicity rate has been observed to rise in regions of stress increase and
fall where the off-fault stress decreases (5,6). The **M**=7.4 Izmit earthquake,
as well as most background seismicity (7), occurred where the failure stress
is calculated to have increased 1-2 bars (0.1-0.2 MPa) by **M**³6.5 earthquakes
since 1939 (Fig. 1A)
(8). The Izmit event, in turn, increased the stress beyond the east end of the
rupture by 1-2 bars, where the **M**=7.2 Düzce earthquake struck, and
by 0.5-5.0 bars beyond the west end of the 17 August rupture, where a cluster
of aftershocks occurred (Fig
1B). The correspondence seen here between calculated stress changes and
the occurrence of large and small earthquakes, also reported in (9), strengthens
the rationale for incorporating stress transfer into a seismic hazard assessment.

A probabilistic hazard analysis is no better than the earthquake
catalog on which it is based. Global observations support an earthquake renewal
process in which the probability of a future event grows as the time from the
previous event increases . To calculate such a renewal probability, ideally
one wants an earthquake catalog containing several large events on each fault
to deduce earthquake magnitudes, the mean inter-event time of similar events,
and the elapsed time since the last shock on each fault . Although such catalogs
are rarely, if ever, available, Ambraseys and Finkel compiled a wealth of earthquake
damage descriptions for events since AD 1500 in the Marmara Sea region (12-15).
We assigned modified Mercalli intensities (MMI) to 200 damage descriptions (available
online), and used the method of Bakun and Wentworth (16) to infer **M** and
epicentral location from MMI through an empirical attenuation relation (17).
We calibrated the relation against Marmara Sea events that have both intensity
and instrumental data (18). Uncertainties in earthquake location were explicitly
calculated from MMI inconsistencies and inadequacies.

Our catalog thus consists of nine **M**³7 earthquakes in
the Marmara Sea region since 1500. For the six events that occurred before instrumental
recording began in 1900, we selected the minimum magnitude falling within the
95% confidence bounds at locations associated with faults of sufficient length
(19) to generate the event (Fig.
2). We estimated rupture lengths and the mean slip from empirical relations
on **M** for continental strike-slip faults (20). The locations and geometry
of faults in the Marmara Sea are under debate; we follow (19), which is based
on seismic reflection profiles (Fig
2), and find four faults capable of producing strong shaking in Istanbul:
the Yalova, Izmit, Prince's Islands, and central Marmara. Our catalog suggests
two earthquakes on the Izmit fault (1719,1999), yielding an inter-event time
of ~280 yr, and three on the Yalova fault (1509, 1719, 1894), permitting an
estimate of ~190 yr (21). We infer one earthquake (May 1766) on the Prince's
Islands fault and one (1509) on the central Marmara fault (Fig. 2).
For these, we gauge inter-event times by dividing the seismic slip estimated
from the catalog by the GPS-derived slip rate (22,23), yielding a ~210 yr inter-event
time for the Prince's Islands fault and ~540 yr for the central Marmara fault.
Thus at least two of the four faults are likely late in their earthquake cycles.

One way to validate the catalog magnitudes, locations, and
segment inter-event times is to compare the relative abundance of small to large
shocks through the *b*-value; another is to see if the seismic strain release
from the catalog is consistent with the measured strain accumulation from GPS.
The frequency-magnitude relation for our catalog yields* b*=1.1 by maximum
likelihood (24), close to the global average (25). Over a sufficiently long
time period, the moment release by earthquakes must balance the moment accumulation
by elastic strain if aseismic creep is negligible. We compared the seismic slip
rate represented by the catalog (23.5±8 mm/yr) to the observed slip rate measured
by GPS across the North Anatolian fault system in the Marmara region (22±3 mm/yr)
(quoted uncertainties are one standard deviation here and elsewhere) (26) (Fig.
3). For *b*~1, most of the moment is conferred by the largest shocks,
so the consistency between GPS and catalog strain means that the size and location
of the three **M**~7.6 events, as well as the number of smaller earthquakes,
are plausible.

Perhaps the strongest test of the 500-yr catalog can be made by calculating the combined Poisson, or time-independent, probability predicted from the inter-event times for the three faults we regard as capable of producing MMIVIII shaking in Istanbul. This is the probability averaged over several earthquake cycles on each fault, and yields 29±15% in 30 yr. This can be compared to the Poisson probability calculated directly from the longer record of MMIVIII shaking in Istanbul during the preceding ~1000 years (AD447-1508). The older record gives the long-term frequency of shaking used in a Poisson calculation without knowledge of the earthquake locations. At least 8 earthquakes (27) caused severe damage in Istanbul between AD 447 and 1508 (12-14), translating into a 20±10% 30-yr probability, roughly comparable to that derived from our catalog. Thus the fault inter-event times estimated from the 500-yr catalog are consistent with the independent record of shaking in Istanbul during the preceding millennium.

We combined earthquake renewal and stress transfer into the
probability calculation on the basis that faults with increased stress will
fail sooner than unperturbed faults. Because two out of the three faults within
50 km of Istanbul are interpreted to be late in their earthquake cycles, the
renewal probability is higher than the Poisson probability. Additionally, the
permanent probability gain caused by stress increase is amplified by a transient
gain that decays with time. The transient gain is an effect of rate- and state-dependent
friction (28-30), which describes behavior seen in laboratory experiments and
in natural seismic phenomena, such as earthquake sequences, clustering, and
the occurrence of aftershocks. We estimated the duration of the transient decay
directly from the times between triggering and rupturing earthquakes on the
North Anatolian fault (Fig.
4A). Because parameter assignments used in the calculation are approximate,
we perform a Monte Carlo simulation to explore the uncertainties (31). The resulting
probability functions (Fig.
4B) exhibit a gradual rise as the mean time since the last shock on each
fault grows, and a sharp jump in August 1999 followed by a decay. We find a
62±15% probability of strong shaking (MMIVIII; equivalent to a peak ground acceleration
of 0.34-0.65*g *(32)) in greater Istanbul over the next 30 yr (May 2000-2030),
50±13% over the next 22 yr, and 32±12% over the next 10 yr (Table
1). Inclusion of renewal doubles the time-averaged probability; interaction
further increases the probability by a factor of 1.3.

The twelve earthquakes that damaged Istanbul during the past
1500 yr attest to a significant hazard, and form the basis for a 30-yr Poisson,
or time-averaged, probability of 15-25%. Because the major faults near Istanbul
are likely late in their earthquake cycles (with no major shocks since 1894),
the renewal probability climbs to 49±15%. We calculate that stress changes altered
the rate of seismicity after the 1999 Izmit earthquake, promoting the **M**=7.2
Düzce shock and the Yalova cluster. Because the 1999 Izmit shock is calculated
to have similarly increased stress on faults beneath the Marmara Sea, the interaction-based
probability we advocate climbs still higher, to 62±15%.

**References and Notes**

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calculations. No catalog is adequate to estimate the coefficient of variation
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on a 5x5 km-spaced grid. We excluded felt reports (MMI<IV) and MMI>VIII
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18. We calibrated with the 1912 Ms=7.4 Saros-Marmara
(360 intensities; (42)), 1963 Ms=6.4 Yalova (11 intensities; (43)), and 1999
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we randomly selected 50 sets of 25 intensities (the mean number for the historical
shocks) to calculate epicentral and magnitude errors. This yields intensity
centers within ±50 km (at 95% confid.) of the instrumental epicenters, and
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site geology was available

19. J. R. Parke, et al., *Terra Nova* , in press.

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26. Includes earthquakes in 1509, 1556, 1719, 1754, 1766, 1855, 1857, 1863, 1877, 1894, 1953, and 1964 from (12-14) and (35).

27. AD 447, 478, 542, 557, 740, 869, 989, 1323.

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31. The transient change in expected earthquake rate *R*(*t*)
after a stress change, can be related
to the probability of an earthquake of a given size over the time interval
D*t* through a nonstationary Poisson process as .
Here *r* is the background seismicity rate, Dt is the Coulomb stress
change, *a* is a state/rate constitutive parameter, s the total normal
stress, *t* is time, and *t**a* is the transient decay duration.
The transient probability change is superimposed on the permanent change,
which results from an advance or delay in the expected time until failure
caused by the stress change. Integrating for is the expected number of earthquakes
in the interval D*t,* *N*(*t*) yields ,
where *r**p* is the expected rate of earthquakes associated with
the permanent probability change. This rate can be determined by again applying
a stationary Poisson probability expression as ,
where *P**c* is a conditional probability, which can be calculated
using any distribution. In addition to the inter-event time and elapsed time
on each fault, this technique requires values for the stress change on each
fault (we use the average calculated stress change resolved on each fault
surface), the transient decay (shown in Fig. 4A from data in (4)), and a stressing
rate on each fault derived from the fault geometry and the observed strain
rate (0.1 bar/yr) (4). We performed 1000 Monte Carlo trials to establish error
bounds (44). The four parameters for the Monte Carlo simulations are drawn
at random from a normal distribution with a shape factor of 0.25 about each
estimate, except for the inter-event time for which the shape factor is 0.5.
Alternating Monte Carlo trials were run with a Brownian passage time and lognormal
distribution.

32. D. J. Wald, V. Quitoriano, T. H. Heaton, H. Kanamori,
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33. Y. Okada, *Bull. Seismol. Soc. Am.* **82**,
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34. T. J. Wright, P. C. England, E. J. Fielding, M. Haynes,
B. E. Parsons, *Eos Trans.* **80, F671 ** (1999).

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36. P. A. Reasenberg, R. W. Simpson, *Science* **255**,
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37. T. Parsons, R. S. Stein, R. W. Simpson, P. A. Reasenberg,
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38. C. Gürbüz, et al., *Tectonophysics*
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39. M. V. Matthews, *J. Geophys. Res.* in press.

40. Working Group Calif. Earthquake Probabilities, *U.S.
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41. Working Group Calif. Earthquake Probabilities, *U.
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44. J. C. Savage, *Bull. Seismol. Soc. Am.* **81**,
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45. The combined probability expression *P*=1-(1-*P*a)(1-*P*b)(1-*P*c)
for faults a-c assumes independent sources of hazard, since we cannot include
future interactions and for all but the most recent earthquakes, we cannot
include past interactions.

46. G. C. P. King, R. S. Stein, J. Lin, *Bull. Seismol.
Soc. Amer.* **84**, 935 (1994).

47. We thank N. Ambraseys, T. Wright, E. Fielding, A.
Ito, J. Parke, and C. Finkel for sharing their insights and preliminary results
with us, W. Bakun for his code and his review, and J. C. Savage, and W. Thatcher,
C. Straub, and S. Kriesch for incisive reviews. Support from *SwissRe*
is gratefully acknowledged.

Fig. 1. (A) Stress change caused by earthquakes since 1900. Shown are the maximum Coulomb stress changes between 0 and 20 km depth on optimally-oriented vertical strike-slip faults (8,46). Seismicity recorded since installation of IZINET (1993-July 1999 (7)) has uniform coverage over the region shown. Calculated stress increases are associated with heightened seismicity rates and with the future epicenter of the 17 August 1999 Izmit earthquake; sites of decreased stress exhibit low seismicity. Before the 1999 event, two studies (4, 35) identified this site as having increased stress and thus hazard. (B) Izmit aftershocks are associated with stress increases caused by the main rupture (first 12 days from IZINET (7)), such as the Yalova cluster southeast of "Y," and the occurrence of the 12 November Düzce earthquake. Faults: Y-Yalova, P-Prince's Islands, M-Marmara, I-Izmit.

Fig.
2. Large historical earthquakes since 1500. Intensities (dots) were assigned
from damage descriptions compiled by (12-15). Red dashed contours give the
moment magnitude **M** needed to satisfy the observations for a given location
(16), because the farther the epicenter is from the observations, the larger
the **M** required to satisfy them. The confidence on location is governed
by the relative intensities; magnitude is a function of absolute intensities.
We assigned earthquakes to faults by minimizing **M** within the 95% confidence
region (17,18). Faults labeled in lower panels: I-Izmit, Y-Yalova, P-Prince's
Islands, M-Marmara, G-Ganos, NAF-North Anatolia fault.

Fig.
3. Seismic slip from the 500-yr-long catalog of Fig. 2 is summed in four
transects across the North Anatolia fault system in the Marmara Sea. All known
or estimated **M**7 sources are included (26). The mean seismic strain
release rate balances the strain accumulation rate observed from GPS geodesy
(23). Whether earthquakes in parentheses extend to a given transect is uncertain.
'1766a' is May; '1766b' is August.

Fig.
4. **A**. Transient response to stress transfer. The thirteen **M**³6.8
North Anatolian earthquakes for which the stress at the future epicenter was
increased by ³0.5 bars are plotted as a function of time. The earthquake rate
decays as *t *^{-1} in a manner identical to aftershocks, as
predicted by (28-31). **B**. Calculated probability of a **M**³7 earthquake
(equivalent to MMIVIII shaking in greater Istanbul) as a function of time.
The probability on each of three faults is summed (45). The large but decaying
probability increase is caused by the 17 August 1999 Izmit earthquake. ‘Background’
tracks the probability from earthquake renewal; 'interaction' includes renewal
and stress transfer. Light blue curve gives the probability had the Izmit
earthquake not occurred.