Attenuation of Macroseismic Intensity: A New Relation for ......In the current study we derive ground-motion prediction equations for macroseismic intensity valid for the Marmara Sea

Attenuation of Macroseismic Intensity: A New Relation

for the Marmara Sea Region, Northwest Turkey

by M. B. Sørensen, D. Stromeyer, and G. Grünthal

Abstract Prediction equations for macroseismic intensity are the backbone of seis-mic hazard assessment, of source parameter estimation, and of shake map generationin cases where an output in terms of intensity is desired. This is especially requiredwhen a direct relation to the damage associated with ground shaking is of interest or ifground shaking estimates will be used for informing nonseismologists such as emer-gency response teams or the general public. In the current study we derive ground-motion prediction equations for macroseismic intensity valid for the Marmara Searegion, northwest Turkey. The relations have a physical basis and are easy to imple-ment for the user. In one relation, the finite extent of the fault rupture is accounted forby defining distance as the Joyner–Boore distance leading to the relation

IS � 0:376Mw � 5:913 � 2:656 log

��R2JB � h2

h2

r� 0:0020

� ��R2JB � h2

q� h

�;

where Mw is the moment magnitude, RJB is the Joyner–Boore distance, and h is thehypocentral depth. Furthermore, a relation based on the epicentral distance (Repi) isderived for application in cases where the extent of the fault plane is unknown:

IS � 0:793Mw � 3:417 � 2:157 log

��R2epi � h2

h2

s� 0:0065

� ��R2epi � h2

q� h

�:

The relations are valid for the ranges 5 ≤ I ≤ 10, 5:9 ≤ Mw ≤ 7:4, and R ≤ 350 km. Itis shown that inclusion of the rupture dimensions leads to an improvement in theability of the relation to fit observations in the near field for large earthquakes. Com-parison to already existing intensity prediction equations for the region shows that thenew relations provide better estimates of the macroseismic intensity distribution, espe-cially in the region near the rupturing fault plane.

Introduction

When generating shake maps with the purpose of earth-quake early warning or rapid earthquake response, an es-sential parameter is the attenuation of seismic waves in thearea of interest. Such ground-motion prediction equations(GMPEs) are also of crucial importance for seismic hazardassessment. GMPEs are traditionally given in terms of re-corded ground-motion parameters, for example, peak groundacceleration, peak ground velocity, or response spectral ac-celeration based on recorded strong-motion data (e.g., seeJoyner and Boore [1993]; Campbell [1997] and other articlesin the same issue; Ambraseys and Douglas [2003]). An im-

portant element connected to such relations is the asso-ciated uncertainty caused by, for example, spread in thedata, assumption of the functional form of the relation or ofthe source being a point source, or lack of knowledge ofearthquake faulting parameters. When studying the damagepotential of large earthquakes, GMPEs based on recordedground motions have two drawbacks. First, the availabil-ity of strong-motion recordings is limited and thereforeone is often forced to apply GMPEs based on recordingsfrom different areas with similar tectonics. Second, thereis no straightforward way to associate the recorded ground

538

Bulletin of the Seismological Society of America, Vol. 99, No. 2A, pp. 538–553, April 2009, doi: 10.1785/0120080299

motions with damage, which is a complex function ofground-motion level, duration, local site conditions, andbuilding vulnerability.

As an alternative, to overcome these problems, ground-motion attenuation can be expressed in terms of macroseis-mic intensity. Intensities have the major advantage of muchbetter availability, as data are dependent on the availability ofpeople and a built environment rather than on instrumenta-tion and therefore can be sampled closer and as far back intime as historical records allow. Furthermore, the macroseis-mic intensity is assigned based on the observed ground shak-ing and damage, and thereby it can be directly related to thedamage potential of future earthquakes. Another advantageis that intensity data are easily understandable for nonseis-mologists and easily convertible for risk management teams.

In the present study we derive a new attenuation modelfor macroseismic intensity and apply it for the Marmara Searegion, northwest Turkey. Here, especially the city of Istan-bul is under a significant seismic hazard and potential seis-mic risk due to the likely rupture of a 100–150 km longsegment along the North Anatolian fault zone (NAFZ) justsouth of the city within the lifetime of the present city en-vironment (e.g., Parsons, 2004). The capacity of the NAFZfor generating large earthquakes was latest manifested bythe occurrence of the 1999 Mw 7:4 Izmit earthquake. Thisevent caused damage over an extended region around therupturing fault plane and lead to the loss of more than18,000 lives (Barka et al., 2002).

Macroseismic intensity prediction equations have pre-viously been derived by Erdik and Eren (1983) and Erdiket al. (1985), valid for the NAFZ in general. These relationsgive the Medvedev–Sponheuer–Kárník (MSK-64) intensityas a function of MS and the natural logarithm of the rupturedistance. More recently, Böse (2006) derived a GMPE formacroseismic intensity in the Marmara Sea region basedpurely on simulated ground motions that are converted intointensity following Sokolov (2002). Ambraseys (2001) pre-sents a relation giving MS as a function of intensity and dis-tance. This relation is based on Greek and western Turkishearthquakes and is valid for far-field conditions.

The attenuation model derived in this study takes intoaccount the finite extent of the fault plane and represents siteintensities as a function of fault distance, event depth, andmoment magnitude. Additionally, we derive a model undera point-source assumption for application in cases where theextent of faulting is not known. It is aimed at deriving simple,physically based relations that are easy to implement for theuser. We base our relations on available macroseismic infor-mation for significant earthquakes in the region.

Regression Method

The regression for intensity prediction equations isbased on the least-squares regression method of Stromeyerand Grünthal (2009) for the well-established and physi-

cally based attenuation model for point sources (Sponheuer[1960]; later adopted by, e.g,. Kárník [1969] and Howell andSchulz [1975]):

I � I0 � a log

��R2 � h2

h2

r� b

� ��R2 � h2

p� h

�: (1)

In this expression, I0 is the epicentral intensity, R is the epi-central distance, and h is the focal depth, usually taken as thehypocenter depth. The term log refers to the decadic (base10) logarithm. The first term a log

��R2 � h2�=h2

pdescribes

the geometrical spreading (having its main effect at short dis-tances) and the second term b�

��R2 � h2

p� h� represents the

energy absorption (most significant at larger distances).The epicentral intensity can be described by a regression

model between I0, moment magnitude Mw, and depth h(Stromeyer et al., 2004):

I0 � cMw � d log�h� � e: (2)

Combining (1) and (2) leads to the following model for themacroseismic site intensity:

I � cMw � d log�h� � e � a log

��R2 � h2

h2

r

� b

� ��R2 � h2

p� h

�: (3)

This expression is in many respects comparable with thecommon type of strong-motion intensity predicting equa-tions consisting of a term giving the epicentral ground-motion level, a linear distance term, and a logarithmicdistance term (e.g., Joyner and Boore, 1993). For large earth-quakes, the point-source assumption fails and the finitenessof the fault must be accounted for. In this study, this is in-cluded by defining the distance R as the Joyner–Boore dis-tance (i.e., the shortest distance to the surface projection ofthe fault plane) instead of as the epicentral distance. Thefunctional form of our relation does not need to be adjustedas we do indeed expect the previously described decay withdistance and just extend the epicentral intensity to cover theentire surface projection of the fault plane. In this way wederive a relation that is symmetric around the rupturing faultplane. Our relation does not account for site effects explicitlyand, hence, site effects are included in the uncertainty relatedto the relation.

Input data for the regression is a collection of intensitydata points (IDP) describing the intensity at a given location.Usually intensity datasets are characterized by great varietyin the number of observations of the different intensity levels.In most cases the highest intensities are undersampled asthese are restricted to a relatively small area compared tothe lower, more distributed intensities. To avoid bias in thedata due to such effects, a weighting scheme has been ap-

Attenuation of Macroseismic Intensity: A New Relation for the Marmara Sea Region, Northwest Turkey 539

plied where each intensity class (integer intensity level) hasbeen assigned the same weight in the regression, regardlessof the number of observations within the class. Therefore, thedetermination of the regression parameters a; b;…; e leadsto the weighted least-squares problem

minx

kW�1�I � Ax�k; (4)

where I � Ii (i � 1;…; n) is a vector of n IDP, A is an(n × 5) design matrix,W is an (n × n) weighting matrix withonly diagonal entries, and x � �c; d; e;�a;�b� is the pa-rameter vector to be estimated. The values of the diagonalelements of W are chosen in such a way that (1) they areequal for all data in one intensity class and (2) the sum ofsquared inverse weights is equal for all intensity classes(classes are identically weighted). This procedure defines theweights up to an arbitrary constant scaling factor, which doesnot influence the regression solution x but is important forestimating uncertainties for a new intensity predicted by themodel. The natural way to overcome this problem is a rescal-ing of W in such a way that the mean weighted and un-weighted residuals are equal:

Wnew � WoldkWold

�1�I � Ax�kk�I � Ax�k : (5)

For a combined regression of k events I, A, and W are thestacked versions of individual terms.

The uncertainties in the estimated parameters x and inpredicting a new intensity I for given predictor values Mw,R, and h are connected with the covariance matrix C of theparameter estimates

C � �ATW�2A��1 (6)

and the mean squared regression error (making use ofequation 5)

σ2 � kW�1�I � Ax�k2n �m

� kI � Axk2n �m

; (7)

where m is the dimension of x (the number of model param-eters). For a specified level of certainty α, the confidencebounds xc for the fitted parameters x are given by

xc � x� t�1��1 � α�=2; n �m��diag�C�

p; (8)

where t�1�p; ν� is the inverse of the cumulative t distributionfor the corresponding probability p and ν degrees of free-dom. For ν ≥ 40, t�1�p; ν�≈ N�1�p�, the inverse of thecumulative standard normal distribution at p. In this case acertainty level of 68.3% (α � 0:683) corresponds to the stan-dard deviation (1σ) of normally distributed errors.

Much more interesting in this study is the error of a newintensity prediction I of the estimated model. For given pre-dictor values Mw, R, and h, this can be expressed by

Ierror � t�1��1 � α�=2; n �m��σ2 � yTCy

q; (9)

where y is the Jacobian of equation (3) with respect to themodel parameters at the predictor values:

yT � ∂I∂x

��Mw; log�h�; 1; log

��R2 � h2

h2

r;

��R2 � h2

p� h

�:

(10)

Earthquake Sources in the Marmara Sea Region

The described methodology has been applied for theMarmara Sea region of northwestern Turkey, which is a seis-mically active region having experienced many large earth-quakes in the past. The dominating tectonic feature in theregion is the NAFZ, which is an approximately 1200 km longfault zone passing through northern Turkey, accommodatingthe westward movement of the Anatolian Block with respectto the Eurasian plate as a consequence of the African–Eurasian collision. The Marmara Sea was probably devel-oped as a pull-apart basin along the NAFZ, causing anincreased complexity with the fault zone splitting into twomain branches (e.g., Sengör et al., 2005; see Fig. 1 forthe most important faults in the region).

One branch (the southern branch) continues south of theMarmara Sea whereas the other (the northern branch) ex-tends further north, under the sea. Some authors argue fora third branch striking through the eastern part of the centralMarmara Sea (e.g., Okay et al., 2000) whereas others find noevidence for this (e.g., Imren et al., 2001). Based on GlobalPositioning System displacement vectors, it has been shownthat the main part of the strain accumulation due to the 22�3 mm=yr plate motion takes place along the fault segment inthe northern Marmara Sea (Straub et al., 1997; Meade et al.,2002), and this is therefore the most likely segment to breakin a future large earthquake.

Throughout the historical record, there are several exam-ples of significant earthquakes in the Marmara Sea, some ofwhich have caused great damage in Istanbul. The most recentruptures of the northern strand of the NAFZ in the MarmaraSea are the 1509 MS 7:2 and the 1766 MS 7:1 and MS 7:4earthquakes. More recently, a smaller (MS 6:4) earthquakeruptured in the eastern part of the Marmara Sea in 1963. Eastand west of the Marmara Sea, recent large ruptures have oc-curred with the 1912 MS 7:3 Ganos earthquake to the westand the 1999 MS 7:4 Izmit earthquake to the east (Ambra-seys and Jackson, 2000). The general style of faulting alongthe NAFZ is right-lateral strike-slip faulting, but deviations

540 M. B. Sørensen, D. Stromeyer, and G. Grünthal

from this occur in connection with changes in fault orienta-tion. For example, earthquakes in the eastern Marmara Seasuch as the 1963 event usually have normal or oblique nor-mal mechanisms (e.g., Sato et al., 2004).

During the last century there has been a westward mi-gration of large, destructive earthquakes along the NAFZ withthe most recent events occurring in Izmit and Duzce in 1999(e.g., Barka et al., 2002). Following these large events, therehas been an increase in the Coulomb stress along the Mar-mara Sea segment (Hubert-Ferrari et al., 2000), bringing thissegment closer to rupture. From this observation, combinedwith recurrence relationships based on the earthquake historyin the Marmara Sea, the probability of an M 7� earthquakein the Marmara Sea within the next 30 yr has been calculatedto be in the range of 35%–70% (Parsons, 2004).

Macroseismic Intensity Data

We have collected a dataset of macroseismic intensitiesfor the study area based on available sources. A general prob-lem when working with macroseismic intensity data is thatintensities are assigned relative to various scales and with, incertain cases, a considerable portion of personal judgment.The personal judgment has generally a much greater impacton the assigned intensity than the use of the different 12 de-grees scales (Musson et al., 2006). The European Macroseis-mic Scale (EMS-98; Grünthal, 1998), which provides detailedguidelines for the assignment of macroseismic intensitiestaking into account building vulnerability, was developed inan attempt to overcome this problem. The EMS-98 has beenin use since it was first introduced as an update to the MSK-64scale in 1993. The EMS-98 was developed to avoid at all coststhat conversions between MSK-64 and Modified Mercalli

(MM) intensities would have to be applied. In this study,we follow Musson et al. (2006) and can therefore assumethat the three intensity scales are consistent in the intensityrange used here.

The macroseismic intensity data available for the Mar-mara Sea region consist of a number of isoseismal mapsfor selected large earthquakes. Most of these are collectedby Eyidogan et al. (1991) in terms of MM intensity, cover-ing the time interval 1900–1988. In addition, an isoseismalmap for the 1999 Izmit earthquake is available from Özmen(2000). We include data for earthquakes in the MarmaraSea region (26°–31° E, 39.5°–41.5° N) for which a minimumof four intensity levels are available as isoseismal contours,which is the case for seven events in the time period 1912–1999. An event just east (but outside) of the study area on26 May 1957 has not been included. The intensity distribu-tion of this event is significantly different from what is ob-served for the remaining events in the Marmara Sea area, andas the event is furthermore located so far east that tectonicdifferences may be the explanation for this discrepancy,the event has been left out.

Unfortunately, none of the original datasets that haveformed the basis for the isoseismal maps used are availabletoday. The only available information for the region in termsof IDP is a collection of 61 observations for the 1999 Izmitearthquake, which has been published by Mucciarelli et al.(2002). A comparison between the IDP of Muciarelli et al.(2002) and the intensity map of Özmen (2000), as shown inFigure 2, indicates a much stronger attenuation of the inten-sity in the dataset of Muciarelli et al. (2002). There can beseveral reasons for this discrepancy. Firstly, we expect theintensity assignments to be associated with a natural varia-bility as well as uncertainties in the intensity assignments (for

Figure 1. Surface projections of the fault planes used for the studied earthquakes. Faults in the region are shown as gray lines (redrawnfrom Okay et al. [2000] and Saroglu et al. [1992]).


Italian earthquakes we have estimated this variability to be ofthe order of 1 intensity unit [M. B. Sørensen, D. Stromeyer,G. Grünthal, unpublished manuscript, 2008] and we expect asimilar value here). Secondly, within a given intensity con-tour we expect also to see subregions with damage less thanthe class of the intensity contour. In this respect, a single lo-cal intensity assignment may not represent the picture on aregional scale. As the dataset of Muciarelli et al. (2002) cov-ers only 61 locations and because all other macroseismic in-formation is available as isoseismal maps, it has been chosento derive the attenuation relation based only on the isoseismalmap of Özmen et al. (2000) in order to have a uniform data-set. An overview of the studied earthquakes and the macro-seismic data is given in Table 1.

The problem of lacking intensity assignments is wellknown and arises when working with macroseismic infor-mation in most regions in the world. Following a largeearthquake it has been, and in some places still is, commonpractice to use intensity assignments for drawing isoseis-mal maps and then discard the originally assigned intensityvalues. Our recommendation is to always publish the rawintensity data and to preferably use IDP when studying suchdata in retrospect. However, the vast amount of data availablefor longer time spans only in terms of isoseismal maps callsfor a method to treat such data causing the minimum amountof bias. In the following we give our suggestion for how toconvert isoseismal contours into IDP.

We convert the digitized isoseismal maps into IDP bycovering the map area with a fine grid (2 km grid spacing).Each grid point is assigned the intensity value of the contourcontaining the point. Grid points located offshore or outsidethe intensity contours of the isoseismal map are not includedin the study as we do not expect that any intensity observa-tions have been available in these regions for drawing themap. In this approach we maintain the discrete nature of theintensity assignments, which we find important because as-signing noninteger intensity values through some interpola-tion procedure would lead to data points that do not makesense in relation to the definition of macroseismic intensityand furthermore indicate a nonexisting level of precision inthe data. We are aware that there is currently an increased useof so-called instrumental intensities that are converted fromrecorded ground shaking and can take noninteger values, butthese are not to be confused with macroseismic intensities,which are assigned based on felt reports and damage obser-vations. We assume only that observation points are homo-geneously distributed over the study area and, furthermore,apply a weighting scheme reducing the influence of largecontours (low intensities) with respect to the smaller ones.In comparison to the true observations this approach is ex-pected to smooth the data rather than to bias it, as we wouldexpect the contours to be drawn in such a way that there isa comparable number of too low and too high intensitieswithin a given contour.

In the GMPE in equation (3), distance (R), event depth(h), and moment magnitude (Mw) must be input for eachevent/IDP pair. It has therefore been necessary to collect ba-sic source parameters for the studied earthquakes. For mostof the events, the information is limited, and different ap-proaches have been followed depending on the available in-formation. A summary of the source parameters is given inTable 2 and fault locations are shown in Figure 1. The detailsof assigning the parameters are described in the follow-ing text.

In general, the events of this study can be separated intotwo groups where the fault plane has been determined basedon either (1) surface rupture or (2) magnitude and eventstrike/dip. The largest events of this study, the 1912 Ganosearthquake and the 1999 Izmit earthquake belong to thegroup 1. The offshore extent of the 1912 earthquake rupture

0 50 100 150 2004

5

6

7

8

9

10

11

Joyner−Boore distance [km]

Inte

nsity

Özmen, 2000Muciarelli et al., 2002

Figure 2. Comparison of the intensity versus distance distribu-tion of the datasets of Özmen (2000) and Muciarelli et al. (2002) forthe 1999 Izmit earthquake. The intensity map of Özmen (2000) isrepresented by data (gray circles) extracted from a regular grid cov-ering the map (see text for details). The IDP of Muciarelli et al.(2002) are shown as black circles.

Table 1Macroseismic Data Included in This Study

Year Date (mm/dd) I0 Imin Imax Number of IDP

1912 08/09 10–11 5 9 27,0151935 01/04 9 5 8 43751953 03/18 9–10 5 8 21,7201963 09/18 8 5 8 14,9851964 10/06 8–9 5 9 16,3081967 07/22 10 5 9 22,3021999 08/17 10–11* 5 10 14,490

I0 is the epicentral intensity as given by Eyidogan et al. (1991)(in most cases the presence of two values is due to results ofvarious authors being presented). Imin and Imax are the mini-mum and maximum intensity contour levels in the isoseismalmaps. Number of IDP is the number of intensity points avail-able on a regular grid (see text).


has been debated (e.g., Ambraseys and Finkel, 1987; Altinoket al., 2003; Altunel et al., 2004; Armijo et al., 2005), butthere is increasing evidence for a significant offshore rup-ture in the Marmara Sea. We adopt the fault rupture mappedby Armijo et al. (2005). The 1999 event is well studied andwe represent the fault by a number of segments as mappedby Gülen et al. (2002). For both these events we assume avertically dipping fault. We have no exact knowledge aboutthe hypocentral depth of the 1912 event, which occurredat shallow depth and therefore assume a depth of 10 kmas is also suggested by Ambraseys and Finkel (1987). Forthe 1999 event, Li et al. (2002) present depth estimatesfrom four agencies from which we use an average valueof 17 km.

For the remaining five earthquakes, the location of thefault plane has been determined based on the hypocenterlocation, the strike and dip of the fault plane, and the earth-quake magnitude. The hypocenters have mostly been takenfrom the published literature (see Table 2). For the event in1935, no depth estimate has been published and the depthwas fixed at 5 km, assuming a shallow depth due to its smallmagnitude. For the 1964 event, the published epicenter lo-cation (40.30° N, 28.23° E, Taymaz et al., 1991) is shifted tothe northeast relative to the maximum intensities. As we areseeking a symmetric relation around the fault plane and thelocation is furthermore associated with significant uncer-tainty at this time where seismic networks were limited, ithas been chosen to move the epicenter to the location of max-imum intensity, maintaining depth and fault orientation givenby Taymaz et al. (1991). Strike and dip estimates have beenpublished by Taymaz et al. (1991) for all events except the1935 earthquake. This event is described by Altinok andAlpar (2006) as occurring along the northern margin of theMarmara Island. Magnitude estimates have been based on

the information of Ambraseys (2001). He gives estimates ofMS and log�M0� (from which Mw is calculated) for all theevents and it has been chosen to use this information, even ifmore detailed studies are available, to have a consistent mag-nitude estimate. For a given event, the hypocenter is locatedin the middle of the fault plane with orientation as given bythe strike and the dip. The extent of the fault plane is calcu-lated based on Wells and Coppersmith’s (1994) relations be-tween rupture length or width and magnitude for a generalfocal mechanism, which are based on a global dataset. Hereit should be mentioned that Ambraseys and Jackson (1998)have presented regional relations between magnitude andrupture length for the eastern Mediterranean region. Unfor-tunately their relations provide only information about faultlength whereas we need also to derive the fault width. Byusing Wells and Coppersmith’s (1994) relations we obtainconsistent values for length and width that are based onthe same dataset. As Ambraseys and Jackson (1998) further-more find their relations to be very similar to the ones ofWells and Coppersmith (1994), we prefer to use their rela-tions in this study.

It is evident that the source parameters in Table 2 are as-sociated with some uncertainties, which may influence theregression result. This issue has been studied in detail byM. B. Sørensen, D. Stromeyer and G. Grünthal (unpublishedmanuscript, 2008) through a Monte Carlo approach where1 million regressions were performed with source parameterssampled from within given uncertainty ranges of the param-eters. The results of this study showed that the effect of suchuncertainties on the derived relation and its prediction errorfor a new intensity estimate is negligible and that the predic-tion error is mainly controlled by the uncertainties in the IDPthemselves. In this respect, the prediction error is mainly de-termined by the mean prediction error σ (see equation 9),

Table 2Source Parameters of the Studied Earthquakes

Year* Date* (mm/dd) Time* (UTC) Longitude (°) Latitude (°) h (km) Mw* MS

* Strike (°) Dip (°)

1912 08/09 01.28 27.10† 40.67† 10‡ 7.3 7.3 — —1935 01/04 14.41 27.51§ 40.64§ 5‡‡ 6.4 6.4 45∥ 45∥

1953 03/18 19.06 27.40# 40.00# 10§§ 7.0 7.0 60# 90#

1963 09/18 16.58 28.95* 40.70* 15* 5.9 6.4 304# 56#

1964 10/06 14.31 27.90** 40.05** 14# 6.3 6.8 100# 40#

1967 07/22 16.57 30.69# 40.67# 12# 7.2 7.2 275# 88#

1999 08/17 00.01 29.97†† 40.76†† 17∥∥ 7.4 7.4 — —

*After Ambraseys (2001). Mw is calculated from log�M0� using Kanamori’s (1977) definition.†Central point of fault plane digitized after Armijo et al. (2005).‡Estimated, shallow event in standard depth of 10 km.§Altinok and Alpar (2006).∥Estimated based on descriptions in Altinok and Alpar (2006).#Taymaz et al. (1991).**Estimated from isoseismal lines (see text).††Gülen et al. (2002).‡‡Estimated, very shallow event (see text).§§Eyidogan (1988).∥∥Li et al. (2002).


which for reliable models can be understood as a first esti-mate of the uncertainty of the used IDP and should have avalue between 0.5 and 1 intensity units. Based on this experi-ence, we choose not to include errors in the earthquake-source parameters in this study.

The final dataset consists of 121,195 IDP covering theintensity range 5–10, the magnitude range Mw 5:9–7:4,and a distance range of R ≤ 350 km. These values also rep-resent the limitations of the derived GMPEs as it cannot be

assumed that simple extrapolation outside these bounds willbe successful.

Derived Intensity Prediction Equation

Regressions were performed first for each earthquakeindividually to see how well the individual events could befit by relation (3). For the case of one single earthquake, the

Figure 3. Comparison of observed intensities for the 1912 event with theoretical predictions from relations (13) (left-hand panels) and(14) (right-hand panels). Upper panels: predicted intensity contours (black) in a map view compared to the observed isoseismal lines (grayscale). The intensity contours are drawn for the midpoint value between two integer intensities (e.g., for half intensities). The surface trace ofthe fault plane is shown as a white line. Lower panels: intensity versus distance plots comparing the grided intensities based on the isoseismalmap (circles) with the predicted intensities (solid curve) together with the 68.3% confidence bounds (dashed curves) corresponding to onestandard deviation of normally distributed errors.


terms cMw � d log10�h� � e describing the source are insep-arable and only their sum cMw can be resolved. In this case,regressions can be performed for the relation (IS indicatingsite intensity):

IS � x1Mw � x2 log

��R2 � h2

h2

r� x3

� ��R2 � h2

p� h

�:

(11)

As this test showed that a relatively good fit couldbe obtained for all earthquakes, a joint regression was per-formed based on the seven events. As can be seen in Table 2,the depth variation among the individual events is small, and

as some event depths are furthermore associated with signifi-cant uncertainty, it was chosen to exclude the d log�h� ex-pression in the source term from the regression model to keepthe problem as simple as possible. This in practice means thatan average depth effect on the epicentral intensity is includedin the constant term e. The regression is then performed for arelation of the form:

IS � x1Mw � x2 � x3 log

��R2 � h2

h2

r

� x4

� ��R2 � h2

p� h

�: (12)

Figure 4. Comparison of observed intensities for the 1935 event with theoretical predictions from relations (13) (left-hand panels) and(14) (right-hand panels). Upper panels: predicted intensity contours (black) in a map view compared to the observed isoseismal lines (grayscale). The intensity contours are drawn for the midpoint value between two integer intensities (e.g., for half intensities). The surface projec-tion of the fault is shown as a gray rectangle. Lower panels: intensity versus distance plots comparing the grided intensities based on theisoseismal map (circles) with the predicted intensities (solid curve) together with the 68.3% confidence bounds (dashed curves) correspond-ing to one standard deviation of normally distributed errors.


When introducing the Joyner–Boore distance (RJB), the fol-lowing intensity prediction equation in the Marmara Sea re-gion was obtained:

IS � 0:376Mw � 5:913 � 2:656 log

��R2JB � h2

h2

r

� 0:0020

� ��R2JB � h2

q� h

�: (13)

The mean regression error is relatively small, σ � 0:672, andthe dependency of the prediction error Ierror on the predictorvaluesMw, RJB, and h, as listed in the covariance matrixC, isnegligible in comparison to the regression error. Therefore,Ierror is approximately equal to σ; Ierror ≈ 0:7.

In some applications (e.g., in shake map generation forearly warning purposes or when studying extensive earth-quake catalogs), the extent of the fault plane is not known.In such cases it is better to use a less precise GMPE derivedfor epicentral distance (Repi) than to simply enter the epicen-tral distance in an RJB-based relation. For this reason, and to



be able to quantify the improvement obtained by accountingfor rupture dimensions, we derive an additional relation forepicentral intensity:

IS � 0:793Mw � 3:417 � 2:157 log

��R2epi � h2

h2

s

� 0:0065

� ��R2epi � h2

q� h

�: (14)

The mean regression error for this relation is 0.742 indi-cating, as expected, that a worse fit is obtained for the epi-central distance than for the Joyner–Boore distance, butalso that reasonable intensity estimates can be obtained withthis relation.

Figures 3–9 show the performance of the relations incomparison with the observed intensity data. For each eventand relation the intensity contours are shown in a map viewcompared to the observed isoseismal lines. Intensity versusdistance plots comparing the grided intensities based on the



isoseismal map (circles) with the intensities predicted fromequation (13) or (14) (solid curve) together with the 68.3%confidence bounds (dotted curves) corresponding to onestandard deviation of normally distributed errors are alsoshown. It is seen that for all events, the predicted intensitiesare within the range of the observed data. The intensity mapsin Figures 3–9 show that an important reason for the misfitbetween the observed and predicted intensity is due to thesymmetric distribution of the predicted intensities aroundeither the epicenter or the fault plane. In reality, intensitiesdo not follow such isotropic distributions. It is, though, evi-

dent that the inclusion of the dimensions of the rupturingfault plane by using the Joyner–Boore distance instead ofthe epicentral distance provides an improvement in the shapeof the intensity curves, especially for the larger events. Thisis most evident for the near-field intensities, whereas the twodistance measures seem to be equally appropriate at somedistance from the fault plane. It is also clear from Figures 3–9 that the average trend of the intensity decay is well repro-duced by our relations.

Because of the limited distance range represented by thedataset, there is a strong trade-off between the parameters x3



and x4 in equation (12). This trade-off is represented by thecorresponding correlation coefficient r34 and similarly forthe parameters x1 and x2, r12, where the magnitude rangelimits the resolution. For the Joyner–Boore distance, the cor-relation coefficients are (similar values are obtained for theepicentral distance)

r12 �C12��C11C22

p � �0:991 and

r34 �C34��C33C44

p � �0:887:(15)

For our application this trade-off is not a problem as long asthe relations are only applied within the distance and mag-nitude ranges specified previoulsy. Extrapolating to othermagnitudes or distances, however, can lead to increased un-certainties in the estimated intensities.

Discussion

The GMPEs derived in the previous section can be usedfor estimating ground shaking either in seismic hazard as-sessment or for early warning purposes. In this respect, how-ever, it is important to keep in mind that equation (12)provides a continuous representation of a discrete parameter.Based on the definitions of intensity scales it only makessense to represent intensities as integer values. Our sugges-tion for dealing with situations where integer values areneeded is to apply a simple rounding scheme to the assignedintensities such that, for example, intensities in the interval4:50 ≤ I ≤ 5:49 are all assigned an intensity value of I � 5.This approach has also been followed in Figures 3–9. Hereit is important to keep in mind the difference between cal-culated and assigned intensities. When assigning intensityvalues based on macroseismic observations, uncertain obser-vations that can be associated with either of two integer in-



tensity values (e.g., 5 and 6) will usually be assigned thelower intensity value (5) or both values (5–6) (Grün-thal, 1998).

The error in a new intensity estimate using our relationsis of the order of 0.7 intensity units. This relatively large er-ror level is to a large extent due to the nature of intensityassignments that have some associated variability, but is alsocaused by variations in, for example, local site effects. The

advantages of good data availability also for historical earth-quakes and the direct relation to earthquake damage, how-ever, makes macroseismic intensity a useful ground-motionmeasure despite the associated uncertainties.

We compare our relations (13) and (14) to the alreadyexisting intensity prediction equations for the North Anato-lian fault. These relations are listed in Table 3. The relationsof Erdik and Eren (1983) and Erdik et al. (1985) are simple

Figure 9. Comparison of observed intensities for the 1999 event with theoretical predictions from relations (13) (left-hand panels) and(14) (right-hand panels). Upper panels: predicted intensity contours (black) in a map view compared to the observed isoseismal lines (grayscale). The intensity contours are drawn for the midpoint value between two integer intensities (e.g., for half intensities). The surface trace ofthe fault plane is shown as a white line. Lower panels: intensity versus. distance plots comparing the grided intensities based on the isoseismalmap (circles) with the predicted intensities (solid curve) together with the 68.3% confidence bounds (dashed curves) corresponding to onestandard deviation of normally distributed errors.

Table 3Previously Published Prediction Equations for Macroseismic Intensity for the North Anatolian Fault

Author Relation

Erdik and Eren (1983) IMSK � 0:34� 1:54MS � 1:24 ln�R�Erdik et al. (1985) IMSK � �3:92� 2:08MS � 0:98 ln�R�Böse (2006) ln�I� � 0:8089� 0:2317Mw � 0:1073 ln�RJB � 0:6Mw� � 0:0052RJB � cB


functions of surface wave magnitude and the natural loga-rithm of rupture distance. The relation of Böse (2006) is amore complex function of Joyner–Boore distance, momentmagnitude, and a correction factor cB, which depends on siteclass and magnitude. The correction factor (with values lessthan 0.06) has not been included in this comparison. As theAmbraseys (2001) relation is valid only for far-field condi-tions, we make no comparison to this relation.

The comparison is based on the mean regression error(equation 7) with different design matrices A and number ofparameters m. The results for our relations and the relationsin Table 3, when applying the relations to the earthquakesincluded in this study, are presented in Table 4.

Table 4 confirms the observation that a similar fit is ob-tained with our two relations for the small events, whereasthe Joyner–Boore distance-based relation can fit the obser-vations for the larger events better. As was observed inFigures 3–9, this is especially important in the region nearthe fault plane where the strongest ground shaking occurs.Therefore, we recommend the use of the Joyner–Boore-based relation in all applications and especially when esti-mating near-field ground shaking. It is, however, alwaysbetter to use an epicentral distance-based relation than tosimply enter the epicentral distance in a relation derived fromanother distance measure.

In comparison to the previously published relations, it isseen that for most events our relations provide a better fit tothe observations. This is partly to expect as our relations arederived based on the data to which we compare; however, theimprovement is expected to also originate from the appropri-ate functional form used. Our functional form is more com-plex than for the relations of Erdik and Eren (1983) and Erdiket al. (1985), taking into account anelastic attenuation andgeometrical spreading in separate terms and also includingthe event depth. Especially problematic are the predictionsof the Erdik and Eren (1983) and Erdik et al. (1985) relationsnear the epicenter where the ln�R� term increases toward in-finity. This leads to highly overestimated epicentral intensi-ties. As most damage is associated with the highest intensitylevels, this is problematic and makes these relations less suit-able for ground-motion estimation in the near field of anearthquake. The relation of Böse (2006) is much more com-plex but based on simulated data. This relation performs well

for the 1999 earthquake but has problems reproducing themacroseismic fields of the other earthquakes consideredhere. Furthermore, it is more complicated to implement dueto the constant cB for which the soil class must be known. Inconclusion, even though the performance of the previous re-lations at some distance from the fault may be relatively goodand will lead to realistic estimates of the ground motion, ourrelations provide an improved estimate of the macroseismicfield due to a strong earthquake in the Marmara Sea area.

Conclusions

GMPEs for macroseismic intensity are useful for shakemap generation and seismic hazard assessment when an out-put is required that is directly associated with the damagecaused by an earthquake. In the present study, such relationshave been derived for the Marmara Sea region, northwestTurkey, which is under a significant seismic hazard due toan expected large earthquake along the North Anatolianfault. The derived GMPEs are based on intensity maps fromseven large earthquakes, which occurred during the last cen-tury. One relation takes into account the finite extent of thefault plane whereas another is derived based on a point-source assumption for application in cases where fault di-mensions are not known. The relations can be used to predictthe distribution of macroseismic intensity based on momentmagnitude, event depth, and fault distance. Uncertaintieshave been estimated based on the regression error, and anew intensity value for an earthquake in the Marmara Searegion can be given with an uncertainty of ca. 0.7. In thisrespect, the relations can be used to obtain reliable estimatesof the intensity distribution due to large earthquakes in theMarmara Sea region, which is important for seismic hazardassessment and risk mitigation measures.

Data and Resources

All data used in this article came from published sourceslisted in the references. Figure 1 was drawn using the Ge-neric Mapping Tools (GMT; Wessel and Smith, 1998).

Table 4Comparison of Mean Squared Prediction Error for Relations (13), (14), and Previously Published Intensity

Prediction Equations

Earthquake This Study (Joyner–Boore) This Study (Epicentral) Erdik and Eren (1983) Erdik et al. (1985) Böse (2006)

1912 0.646 0.606 0.615 0.971 2.1231935 0.369 0.345 0.497 0.354 1.0361953 0.600 0.747 0.635 0.759 2.0791963 0.642 0.617 1.016 0.656 2.3501964 0.563 0.570 0.577 0.462 2.0921967 0.673 0.901 0.566 1.105 1.9341999 0.970 1.017 0.744 1.412 1.113


Acknowledgments

The presented work was carried out as part of the European Com-mission funded project Seismic eArly warning For EuRope (SAFER; www.saferproject.net). Macroseismic information for the Marmara Sea area waskindly provided by Eser Dukukal and Zehra Cagnan, Kandilli Observatory,Istanbul.

References

Altinok, Y., and B. Alpar (2006). Marmara Island earthquakes, of 1265 and1935; Turkey, Nat. Hazards Earth Syst. Sci. 6, 999–1006.

Altinok, Y., B. Alpar, and C. Yaltirak (2003). Sarköy-Mürefte 1912 earth-quake’s tsunami, extension of the associated faulting in the MarmaraSea, Turkey, J. Seism. 7, 329–346.

Altunel, E., M. Meghraoui, H. S. Akyüz, and A. Dikbas (2004). Character-istics of the 1912 co-seismic rupture along the North Anatolian faultzone (Turkey): implications for the expected Marmara earthquake,Terra Nova 16, 198–204.

Ambraseys, N. N. (2001). Reassessment of earthquakes, 1900–1999, in theEastern Mediterranean and the Middle East, Geophys. J. Int. 145,471–485.

Ambraseys, N. N., and J. Douglas (2003). Near-field horizontal and verticalearthquake ground motions, Soil Dyn. Earthq. Eng. 23, 1–18.

Ambraseys, N. N., and C. F. Finkel (1987). The Saros-Marmara earthquakeof 9 August 1912, Earthq. Eng. Struct. Dyn. 15, 189–211.

Ambraseys, N. N., and J. A. Jackson (1998). Faulting associated with his-torical and recent earthquakes in the Eastern Mediterranean region,Geophys. J. Int. 133, 390–406.

Ambraseys, N. N., and J. A. Jackson (2000). Seismicity of the sea ofMarmara (Turkey) since 1500, Geophys. J. Int. 141, F1–F6.

Armijo, R., N. Pondard, B. Meyer, G. Ucarkus, B. M. de Lepinay, J.Malavieille, S. Dominguez, M.-A. Gustcher, S. Schmidt, C. Beck,N. Cagatay, Z. Cakir, C. Imren, K. Eris, B. Natalin, S. Özalaybey,L. Tolun, I. Lefevre, L. Seeber, L. Gasperini, C. Rangin, O. Emre,and K. Sarikavak (2005). Submarine fault scarps in the sea of Marmarapull-apart (North Anatolian fault): implications for seismic hazardin Istanbul, Geochem. Geophys. Geosyst. 6, Q06009, doi 10.1029/2004GC000896.

Barka, A., H. S. Akyüz, E. Altunel, G. Sunal, Z. Cakir, A. Dikbas, B. Yerli,R. Armijo, B. Meyer, J. B. de Chabalier, T. Rockwell, J. R. Dolan,R. Hartleb, T. Dawson, S. Christofferson, A. Tucker, T. Fumal, R.Langridge, H. Stenner, W. Lettis, J. Bachhuber, and W. Page (2002).The surface rupture and slip distribution of the 17 August 1999 Izmitearthquake (M 7.4), North Anatolian fault, Bull. Seismol. Soc. Am. 92,43–60.

Böse, M. (2006). Earthquake early warning for Istanbul using artificialneural networks, Ph.D. Thesis, University of Karlsruhe, availableat http://digbib.ubka.uni‑karlsruhe.de/volltexte/1000005845 (last ac-cessed September 2008), 181 pp.

Campbell, K. W. (1997). Empirical near-source attenuation relationships forhorizontal and vertical components of peak ground acceleration, peakground velocity, and pseudo-absolute acceleration response spectra,Seism. Res. Lett. 68, 154–179.

Erdik, M., and K. Eren (1983). Attenuation of Intensities for EarthquakeAssociated with the North Anatolian Fault, Middle East TechnicalUniversity Earthquake Engineering Research Center, Ankara.

Erdik, M., V. Doyoran, N. Akkas, and P. Gulkan (1985). A probabilisticassessment of the seismic hazard in Turkey, Tectonophysics 117,295–344.

Eyidogan, H. (1988). Rates of crustal deformation in western Turkey as de-duced from major earthquakes, Tectonophysics 148, 83–92.

Eyidogan, H., U. Güclü, Z. Utku, and E. Degirmenci (1991). Türkiye büyükdepremleri makro-sismik rehberi (1900–1988), Istanbul Teknik Üni-versitesi, Maden Fakültesi, Jeofizik Mühendisligi Bölümü, 198 pp.

Grünthal, G. (Editor) (1998). European Macroceismic Scale 1998(EMS-98), Vol. 15, Cahiers du Centre Européen de Géodynamiqueet de Séismologie, Luxembourg, 99 pp.

Gülen, L., A. Pinar, D. Kalafat, N. Özel, G. Horasan, M. Yilmazer, andA. M. Isikara (2002). Surface fault breaks, aftershock distribution,and rupture process of the 17 August 1999 Izmit, Turkey, earthquake,Bull. Seismol. Soc. Am. 92, 230–244.

Howell, B. F., and T. R. Schulz (1975). Attenuation of modified Mercalliintensity with distance from the epicenter, Bull. Seismol. Soc. Am.65, 651–665.

Hubert-Ferrari, A., A. Barka, E. Jacques, S. S. Nalbant, B. Meyer, R. Ar-mijo, P. Tapponnier, and G. C. P. King (2000). Seismic hazard in theMarmara Sea region following the 17 August 1999 Izmit earthquake,Nature 404, 269–273.

Imren, C., X. Le Pichon, C. Rangin, E. Demirbag, B. Ecevitoglu, and N.Görür (2001). The North Anatolian fault within the sea of Marmara:a new interpretation based on multi-channel seismic and multi-beambathymetry data, Earth Planet. Sci. Lett. 186, 143–158.

Joyner, W. B., and D. M. Boore (1993). Methods for regression analysis ofstrong-motion data, Bull. Seismol. Soc. Am. 83, 469–487.

Kanamori, H. (1977). The energy release in great earthquakes, J. Geophys.Res. 82, 2981–2987.

Kárník, V. (1969). Seismicity of the European Area, Part 1, Reidel,Dordrecht.

Li, X., V. F. Cormier, and M. N. Toksöz (2002). Complex source process ofthe 17 August 1999 Izmit, Turkey, earthquake, Bull. Seismol. Soc. Am.92, 267–277.

Meade, B. J., B. H. Hager, S. C. McClusky, R. E. Reilinger, S. Ergintav,O. Lenk, A. Barka, and H. Özener (2002). Estimates of seismic po-tential in the Marmara Sea region from block models of secular defor-mation constrained by global positioning system measurements, Bull.Seismol. Soc. Am. 92, 208–215.

Mucciarelli, M., R. Camassi, and M. R. Gallipoli (2002). Collection ofmacroseismic data in a digital age: lessons from the 1999 Koceali, Tur-key earthquake, Seism. Res. Lett. 73, 325–331.

Musson, R. M., G. Grünthal, and M. Stucchi (2006). Conversions betweenolder intensity scales and EMS-98, (Abstract 542) in 1st EuropeanConf. on Earthquake Engineering and Seismiology, Geneva, Switzer-land, 3–8 September 2006, 542.

Okay, A. I., A. Kaslilar-Özcan, C. Imren, A. Boztepe-Güney, E. Demirbag,and I. Kuscu (2000). Active faults and evolving strike-slip basins in theMarmara Sea, northwest Turkey: a multichannel seismic reflectionstudy, Tectonophysics 321, 189–218.

Özmen, B. (2000). Eşşiddet Haritasi, in 17 Ağustos 1999 İzmit KörfeziDepremi Raporu, Bayındırlık ve İskan Bakanlığı Afet İşleri GenelMüdürlüğü Deprem Araştırma Dairesi, 209–221.

Parsons, T. (2004). Recalculated probability of a M ≥7 earthquake beneaththe Sea of Marmara, Turkey, J. Geophys. Res. 109, B05304, doi10.1029/2003JB002667.

Saroglu, F., Ö. Emre, and I. Kuscu (1992). Active Fault Map of Turkey,General Directorate of Mineral Research and Exploration (MTA),available at http://www.mta.gov.tr/english/harita/dirifay.html (last ac-cessed September 2007), scale 1:2,000,000.

Sato, T., J. Kasahara, T. Taymaz, M. Ito, A. Kamimura, T. Hayakawa, andO. Tan (2004). A study of microearthquake seismicity and focalmechanisms within the Sea of Marmara (NW Turkey) using oceanbottom seismometers (OBSs), Tectonophysics 391, 303–314.

Sengör, A. M. C., O. Tüysüz, C. Imren, M. Sakinc, H. Eyidogan, N. Görür,X. Le Pichon, and C. Rangin (2005). The North Anatolian fault: a newlook, Annu. Rev. Earth Planet. Sci. 33, 37–112.

Sokolov, V. Y. (2002). Seismic intensity and Fourier Acceleration Spectra:Revised Relationship, Earthquake Spectra 18, 161–187.

Sponheuer, W. (1960). Metoden zur Herdtiefenbestimmung in der Makro-seismik, Freib. Forschungsh. C88, 120 pp.

Straub, C., H.-G. Kahle, and C. Schindler (1997). GPS and geologic esti-mates of the tectonic activity in the Marmara Sea region, NWAnatolia,J. Geophys. Res. 102, no. B12, 27587–27601.


Stromeyer, D., and G. Grünthal (2009). Attenuation relationship of macro-seismic intensities in Central Europe, Bull. Seismol. Soc. Am. 99,554–565.

Stromeyer, D., G. Grünthal, and R. Wahlström (2004). Chi-square regressionfor seismic strength parameter relations, and their uncertainties, withapplications to anMw based earthquake catalogue for central, northernand northwestern Europe, J. Seism. 8, 143–153.

Taymaz, T., J. Jackson, and D. McKenzie (1991). Active tectonics of thenorth and central Aegean Sea, Geophys. J. Int. 106, 433–490.

Wells, D. L., and L. J. Coppersmith (1994). New empirical relationshipsamong magnitude, rupture length, rupture width, rupture area, and sur-face displacement, Bull. Seismol. Soc. Am. 84, 974–1002.

Wessel, P., and W. H. F. Smith (1998). New improved version of GenericMapping Tools released, EOS 79, 579.

GFZ German Research Center for GeosciencesSection 5.3 Engineering SeismologyTelegrafenberg14473 Potsdam, Germanysorensen@gfz‑potsdam.de

Manuscript received 29 November 2007


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