ORIGINAL ARTICLE

Strong ground motion simulation of the 2003 Bam, Iran,earthquake using the empirical Green’s function method

Hossein Sadeghi & Hiroe Miyake & Ali Riahi

Received: 4 July 2011 /Accepted: 4 June 2012 /Published online: 19 June 2012# Springer Science+Business Media B.V. 2012

Abstract The 2003 Bam, Iran, earthquake causedcatastrophic damage to the city of Bam and neighbor-ing villages. Given its magnitude (Mw) of 6.5, thedamage was remarkably large. Large-amplitudeground motions were recorded at the Bam accelero-graph station in the center of Bam city by the Buildingand Housing Research Center (BHRC) of Iran. Wesimulated the Bam earthquake acceleration records atthree BHRC strong-motion stations—Bam, Abaraq,and Mohammad-Abad—by the empirical Green’sfunction method. Three aftershocks were used as em-pirical Green’s functions. The frequency range of theempirical Green’s function simulations was 0.5–10 Hz. The size of the strong motion generation areaof the mainshock was estimated to be 11 km in lengthby 7 km in width. To estimate the parameters of thestrong motion generation area, we used 1D and 2Dvelocity structures across the fault and a combined

source model. The empirical Green’s function methodusing a combination of aftershocks produced a sourcemodel that reproduced ground motions with the bestfit to the observed waveforms. This may be attributedto the existence of two distinct rupture mechanisms inthe strong motion generation area. We found that therupture starting point for which the simulated wave-forms best fit the observed ones was near the center ofthe strong motion generation area, which reproducednear-source ground motions in a broadband frequencyrange. The estimated strong motion generation areacould explain the observed damaging ground motionat the Bam station. This suggests that estimating thesource characteristics of the Bam earthquake is veryimportant in understanding the causes of the earth-quake damage.

Keywords Bam earthquake . Aftershocks . Strongground motion . Empirical Green’s function method

1 Introduction

Bam is an ancient city located in the Kerman provinceof southeastern Iran, 900 km south–east of Tehran,Iran’s capital. Bam city covers an area of approximate-ly 5,500 ha and is surrounded by desert. This relativelysmall city is a few centuries old and is known for thehistorical fortress of the citadel Arg-e-Bam, con-structed in the 1,700 s, which encompasses an areaof 6 km2 and is the biggest mud-brick complex in the

J Seismol (2013) 17:297–312DOI 10.1007/s10950-012-9317-4

H. Sadeghi (*) :A. RiahiEarthquake Research Center,Ferdowsi University of Mashhad,Mashhad 9177948974, Irane-mail: sadeghi@um.ac.ir

A. Riahie-mail: a.riahi.seismo@gmail.com

H. MiyakeEarthquake Research Institute, University of Tokyo,Tokyo, Japane-mail: hiroe@eri.u-tokyo.ac.jp

world. In the early morning on Friday, the Iranianweekend, 26 December 2003 at 0526 local time(0156 GMT), a powerful earthquake with a magnitude(Mw) of 6.5 hit this ancient city and its surroundingarea. At the time of the earthquake, most of theregion’s inhabitants slept in their poorly constructedunreinforced mud-brick houses.

The high death toll, as well as the huge damage tobuildings, made this earthquake one of the deadliest andmost damaging earthquakes in the world that year.According to the official report by the StatisticalCenter of Iran (SCI 2004), the earthquake left 25,514people dead and 9,447 injured out of a total populationof 142,376 in the affected area. Generally, damagecaused by an earthquake depends on two principal fac-tors: (1) the construction quality of buildings in theaffected area and (2) the characteristics of the strongground motion. Although the low quality and poorlyconstructed houses were themain reason for the massivedamage, the damage was disproportionally large whencompared with that caused by other major earthquakesof similar magnitude that occurred in Iran (USGS 2011).The closest known active fault based on geomorpholog-ical and geological evidence is the Bam fault, approxi-mately 5 km southeast of Bam city, which posesa potential seismic hazard for the Bam area (e.g.,Berberian 1976). This fault passes through Baravat city;however, the most notable feature of the earthquake wasthat the amount of damage around Bavarat was consid-erably lower than that in Bam city (Fig. 1). The differ-ence between the damage levels in Bam and Baravatwas one of the main research questions, which motivat-ed several research groups to determine the causativefault. Interferometric analysis of synthetic aperture radar(InSAR) images of coseismic surface deformation(Wang et al. 2004; Fielding et al. 2005; Stramondo etal. 2005; Fielding et al. 2009), the epicentral distributionof aftershocks (Tatar et al. 2005; Nakamura et al. 2005),and the field mapping of minor surface ruptures(Fielding et al. 2005) showed that the Bam earthquakewas caused by a previously unknown buried fault. Mostof the causative fault (called the Arg-e-Bam fault byNakamura et al. 2005) lies as a north–south-trendingstrike-slip fault located approximately 4 km west of theBam fault and extending beneath Bam city toward thesouth. However, a minor effect of a secondary reversefault, which might be related to the geological Bamfault, has also been suggested (Talebian et al. 2004;Zare and Hamzehloo 2005; Jackson et al. 2006).

Although we know that a causative fault extends be-neath Bam city, the distances of Bam and Baravat fromthe epicenter are nearly the same; therefore, it wasremarkable that the damages and casualties were con-centrated around the localized area of Bam city. Over70 % of the houses in Bam were completely destroyed.The SCI (2004) report shows that nearly 88 % of thefatalities and over 86 % of the injured were in Bam city,which had a population of 89,145. Therefore, the highdamage as well as damage distribution are the maintopics of interest and to understand them, we need tostudy the characteristics of the strong ground motionduring the Bam earthquake. The ground accelerationwas recorded at the Bam accelerograph station in thecenter of Bam city by the Building and HousingResearch Center of Iran (BHRC: http://www.bhrc.ac.ir/ismn/SHABAKEH/accelerograms/earthquake/2003/bam.htm). These records contain some interesting infor-mation that is important for understanding the physics ofthe Bam earthquake. An S–P time of about 1 s and amaximum vertical ground acceleration of approximately1 g clearly show contribution of a very shallow focal-depth earthquake with a very strong ground motion tothe destruction.

Another interesting characteristic in these records isthe existence of two horizontal velocity pulses withdominant frequencies of approximately 1 Hz in theEW component. The first velocity pulse does notappear in the NS component; on the other hand, thesecond velocity pulse provided larger amplitude in theNS component than in the EW component (Fig. 2).

Estimating source parameters and rupture character-istics could help in explaining the strong groundmotions, as well as the damage pattern, observed duringthe Bam earthquake.

Several authors have suggested a shallow slip re-gion on the fault plane with a larger slip than theaverage slip on the fault for the Bam earthquake.Miyake et al. (2004) used acceleration data recordedat the Bam station, suggested that the extremely strongmotions were localized, and proposed that the main-shock ruptured a shallow asperity. By the inversion ofthe surface deformation measured by InSAR, Fialko etal. (2005) and Funning et al. (2005) suggested a largeslip of >2 m at depths of 4–5 km on the main fault.Motagh et al. (2006) combined leveling data andInSAR images and Peyret et al. (2007) applied imagecross-correlation; both studies proposed the samelarge slip areas. By using 3D tomographic inversion,

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Sadeghi et al. (2006) introduced a shallow low-Poisson’sratio layer that coincides with the large slip zone.

Some authors tried to model the source and rupturecharacteristics to simulate the observed near-faultground motions. Bouchon et al. (2006) derived a

Rayleigh-like speed of rupture propagation and apeak-slip velocity exceeding 2 m/s over a large partof the fault. They explained the first high-amplitudepulse in the EW component by a combination of theimmense speed of rupture propagation and forward

Fig. 1 Location (Poiata et al.2009) and focal mechanism(Stramondo et al. 2005) forthe 2003Bam earthquake, thegeological Bam fault (dashedline), and the causative Bamearthquake fault (solid line).The locations of the threestrong motion stations thatrecorded the Bam earthquakeand aftershocks are alsoshown

Fig. 2 Acceleration with baseline correction and velocity groundmotions for the mainshock recorded at the Bam station. The two observedpulses are shown in the velocity ground motions

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directivity. However, their simulation model could notreproduce the second EW pulse or the ground motionsin the NS component. Miyake et al. (2004) suggestedthat the second pulse is due to the directivity effect ofthe fault rupture, which extends northeastward beneathBam city. This fault geometry, which includes a south-west–northeast striking branch and is in agreementwith the results of Wang et al. (2004) and Nakamuraet al. (2005), was also modeled by Ghayamghamianand Hisada (2007) to simulate the long-period (0.1–1.5 Hz) strong ground motions of the Bam earthquake.Their model required a second fault with dip-sliprupturing to simulate the observed pulses in the NScomponent. Talebian et al. (2004) concluded that acombination of a strike slip followed by a pure thrustsource is necessary to improve the fit to the InSARobservations. However, the other InSAR-related stud-ies did not verify the existence of the secondary thrustdislocation (e.g., Wang et al. 2004; Motagh et al.2006). The possibility of a second fault in the areasoutheast of the main fault was discussed by Sadeghiet al. (2006), but the located aftershocks were notsufficient to provide constraints on the fault geometry.

In this study, we simulated strong motion records ofthe Bam earthquake by estimating the source model bythe empirical Green’s function method using its after-shocks record. The complexity of the source and siteeffects makes it very difficult to synthesize groundmotion in the simulation. The advantage of the empir-ical Green’s function method is that the effects of thepropagation path and the local site amplification areincluded in the aftershocks, which are used as empir-ical Green’s functions. In general, the broad frequencyband motions could be estimated as long as the after-shock records are sufficiently accurate in the broadband (Kamae and Irikura 1998). We searched for thebest source model parameters that provided the best fitbetween the observed and synthetic waveforms. Thestrong motion generation area and the rupture startingpoint are key parameters.

2 Strong ground motions of the Bam earthquake

The mainshock of the Bam earthquake was recordedby 27 accelerograph stations of the Iranian StrongMotion Network maintained by BHRC. All instru-ments are of the SSA-2 type with a trigger thresholdof 10 gals and the pre-event memory of 15 s. While 78

stations of the Iranian Strong Motion Network weredeployed at an equal triggering level within a 300-kmradius of Bam city, all triggered stations except onewere located on the west side of the causative fault(Fig. 3). This could be attributed to local installationconditions, the different tectonic regime, different at-tenuation properties, or the source rupture mechanism,but as of now, there is no clear explanation.

The Bam station, located very close to the causativefault, recorded important near-fault strong groundmotions. The Abaraq and Mohammad-Abad stationsare located approximately 50 km northwest and south-west of Bam, respectively. After Bam station, they arethe two triggered stations closest to the epicenter(Fig. 1). Among the triggered stations, these two andthe Bam station are the only stations that recorded theaftershocks. On the same day of the earthquake, twomoderate aftershocks of magnitude 5.3 and 4.6 wererecorded at 0306 and 1408, respectively. The Abaraqstation recorded the M 5.3 aftershock with a PGA of19 cm/s2 on the horizontal component. The M 4.6aftershock was recorded by both the Abaraq andMohammad-Abad stations with PGA values of ap-proximately 18.5 and 16 cm/s2, respectively. AsBHRC reported, the Bam accelerograph did not recordthese aftershocks, because the disk space of its digitalinstruments had run out after recording nine after-shocks during the first 1.5 h following the mainshock.The Bam governor’s office building, where the Bamrecording instrument was located, experienced signif-icant damage during the earthquake. Therefore, ap-proximately 30 h after the mainshock, BHRC installedanother instrument in Bam city, 0.5 km from the oldlocation. A number of aftershocks were recorded by thenewly installed instrument.

Since the Abaraq and Mohammad-Abad stationswere sufficiently far from the mainshock, the accuracyof the hypocenter location did not affect ground-motion simulations of these stations. Therefore, as-suming a hypocenter location, we first examined thebest fit source model for the mainshock using theaftershocks recorded by the Abaraq and Mohammad-Abad stations. Then, we used the obtained model asthe initial source model for the Bam station. Thesource model was adjusted to synthesize the strongmotions of the mainshock using an aftershock that wasrecorded at the Bam station. The key factor in obtain-ing a good simulation of the near-fault strong motioncomplexity is to use an aftershock, which is likely to

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be a good approximation of the empirical Green’sfunction over the entire source area. All eventsrecorded by Bam stations were examined in order tofind the most suitable event for the empirical Green’sfunction analyses. Table 1 shows the list of selectedevents along with their details at the recorded stations.Owing to the insufficient data, it was difficult to in-clude estimations of all source parameters in the sim-ulation. In the next section, we explain why someparameters are fixed during forward simulations ofthe ground motion data.

3 Empirical Green’s function simulations

We used the empirical Green’s function method(Irikura 1986; Irikura and Kamae 1994) to reproduce

broadband ground motions for a large event (main-shock) using recordings of small events (aftershocks).The empirical Green’s function method assumes thatthe record of the small event represents the Green’sfunction for all points of the mainshock asperity areaat the same site. It is also assumed that source spectraof both events follow the omega-squared scaling law(Aki 1967; Brune 1970, 1971) under the same con-ditions of stress drop. Additionally, the focal mecha-nism of the earthquake to be simulated is considered tobe equivalent to that of the Green’s functions. A cor-rection function adjusts the slip-velocity differencebetween large and small events. The parameter N,which is the number of subfaults, is obtained fromthe moment ratio of the large and small events. Thestress drop ratio C for the large and small events canbe derived from the flat levels of their displacement

Fig. 3 BHRC accelerograph stations (triangles) within a 300-kmradius of the Bam earthquake epicenter. The Bam, Abaraq, andMohammad-Abad stations are shown in red triangles. The other

recorded stations triggered by the Bam earthquake are shown asgreen triangles

Table 1 Stations, locations, and component orientations for the events used as EGFs

Station Longitude(degree East)

Latitude(degree North)

Component orientationL/T Azimuth (degree)

Event ID Date Time (GMT) Magnitude

Abaraq 57.94 29.34 72/162 3176/02 26/12/2003 03:06 5.3

Abaraq 57.94 29.34 72/162 3176/03 26/12/2003 14:08 4.6

Mohammad-Abad 57.89 28.90 350/80 3162/02 26/12/2003 14:08 4.6

Bam 58.35 29.07 283/13 3182/11 27/12/2003 20:38 3.4

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and acceleration amplitude spectra. The records of theaftershocks listed in Table 1 were selected for theempirical Green’s functions. The aftershocks at 0306and at 1408 are the largest ones that can be expectedwith a high signal-to-noise ratio in a wider frequencyranges. The strong motion generation area reproduc-ing near-source ground motions in a broadband fre-quency range is a key outcome of the empiricalGreen’s function method. The strong motion genera-tion area, almost equivalent to the asperity area(Miyake et al. 2003), is assumed to be homogenouswith large and uniform slip velocities. The correctionfunction provides the rupture growth referred to as theKostrov (1964) slip-velocity time function, which hasa sharp rise and a relatively smooth decay. We haveused the available frequency range from 0.5 to 10 Hz.The minimum frequency limit originates from thesignal-to-noise level of the aftershocks.

The fault-plane solution of the mainshock is veryimportant to achieve the best possible simulation.InSAR and teleseismic focal mechanisms were pro-posed by several groups. All of them believe that alarge majority (more than 80 %) of the seismic mo-ment was released at an almost vertical north–south-oriented strike-slip fault. The main differences amongtheir models are in the fault-dip direction. The tele-seimic models (e.g., Yamanaka 2003) introduce awestward dip, while some InSAR models (e.g.,Wang et al. 2004; Funning et al. 2005) support aneastward dip of the fault. The InSAR-based modelby Stramondo et al. (2005) suggests a fault plane witha strike of 177°, dip of 88°, and rake of 166°. Thestrike and dip angles are in accord with the trends ofthe epicenter and hypocenter distribution of after-shocks (Nakamura et al. 2005) and the inversion ofteleseismic and strong motion datasets (Poiata et al.2009; Poiata 2010). For the simulation in this study,we considered the fault-plane model determined byStramondo et al. (2005).

The accurate location of the mainshock is anotherimportant factor necessary to achieve reasonable sim-ulation results. We used the teleseismic waveforminversion of Poiata (2010) for the mainshock locationat 29.052°N, 58.365°E, 7.5 km in depth. This locationis in good agreement with the low-aftershock activity(Suzuki et al. 2004; Nakamura et al. 2005) and wouldbe sufficiently accurate for the Abaraq andMohammad-Abad stations. These stations are located sufficiently far(about 50 km) from the epicenter; hence, a shift of a few

kilometers in the hypocenter will not affect ground-motion simulations.

We considered the 1D crustal velocity model byTatar et al. (2005) and rupture velocity of 0.92 Vs byBouchon et al. (2006).

In the present study, we focused on estimating therupture starting point, strong motion generation areaand its location related to the Bam station, and the risetime by applying a trial-and-error forward modelingthat produces a good match between the observed andsimulated ground motions. The rupture starting pointwas tested for all subfaults. Our data are limited toonly three stations; we used size estimates taken fromprevious studies in our trial-and-error approach. Thefault-slip distribution models by Wang et al. (2004),Funning et al. (2005), and Poiata (2010) were used toestimate the strong motion generation area.

First, we chose the aftershock at 0306 (M 5.3), whichwas the largest event that was recorded only by theAbaraq station, as the Green’s function to simulate theobserved strong motions of the Bam earthquake.Second, we chose the aftershock at 14:08 (M 4.6), whichwas recorded by both the Abaraq andMohammad Abadstations. A rectangular-shaped strong motion generationarea for the mainshock was estimated to be 11 km inlength by 7 km in width. The rupture starting point,which produces the best fit between the simulated andobserved waveforms, was found to be near the center ofthe strong motion generation area. Finally, the estimatedsource model was used to synthesize ground motions atthe Bam station using the aftershock, which occurred at2038, the day after the mainshock (M 3.4). Table 2 liststhe parameters for the empirical Green’s function meth-od that successfully reproduced the ground motion dur-ing the Bam earthquake. Initially, although a rise timegreater than 0.1 s for each empirical Green’s functionwas considered on the basis of the magnitude relationscale of Miyake et al. (2003), a rise time of 0.05 wasfound to produce the best fit to the waveforms. The bestfit location for the rupture point was found to be at anepicentral distance of 5 km from the Bam station and adepth of 7 km. Figure 4 shows a comparison of thestrong motion generation area, the large slip area byPoiata (2010) and Funning et al. (2005), and the seismicgap by Sadeghi et al. (2006). The strong motion gener-ation area estimated in this study is in good agreementwith the asperity area defined by Funning et al. (2005),but displays a southward shift related to the large sliparea inverted by Poiata (2010).

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4 Results

The theory of the empirical Green’s function methodis based on S-waves, and only S-wave pulses could begenerated from the strong motion generation area onthe fault plane. Therefore, without the P-wave compo-nent, it might be expected to reproduce the S-wavepulses on the vertical components as well. Since thelargest PGA appears on the vertical component of theBam record (Fig. 2), we tried to examine the ground-motion simulations on the vertical components, inaddition to the horizontal components.

Figure 5 shows the waveform and spectral fitting ofthe mainshock using the M 5.3 aftershock at theAbaraq station in terms of acceleration, velocity, anddisplacement in the frequency range 0.5–10 Hz.Although the omega-squared model and a smooth,homogenous faulting model are the empirical tools

for simulating strong ground motion, in reality,observational and numerical results have shownthat earthquake source processes are highly hetero-geneous. To present more realistic near-sourcestrong ground motions at broadband frequencies,Hisada (2000, 2001) suggested considering spatialvariations in slip and rupture velocities. To observethe effect of the variation in the slip velocity andrupture time, we also examined the simulations byusing the 2D fault velocity model of Sadeghi et al.(2006). The waveform and spectral fitting pro-duced by the 2D model is shown in Fig. 5.Although we would expect the 2D fault model tolead to an improvement in simulation accuracy, thecomparison shows that the simulations using 2Dfault structures have a close fit with some pulses,but have made no significant improvement in gen-eral. We found three main reasons why such animprovement did not occur. First, there are fewsimulations to verify any improvement due to the2D model. Second, the heterogeneous rupture ve-locities over the fault may enhance mainly thehigh-frequency content of the synthetic waveform.Third, if we assumed that the 2D fault model isdifferent from the true structure, the results mightbe ambiguous and not always lead to the desiredoutcome. The sensitivity to uncertainties in the 3Dvelocity structure in the source inversions usingGreen’s functions was studied by Graves and Wald(2001). They showed that to improve seismic-source imaging, the 3D velocity model requires acareful examination of validity against the true 3Dstructure.

Since a similar result was also obtained for othersimulations, we discuss only the results obtained bythe 1D homogenous model. Figure 6 shows the wave-form and spectral fitting of the mainshock usingthe M 4.6 aftershock at the Abaraq and Mohammad-Abad stations.

Table 2 Event source parame-ters obtained for the EGFsimulations

Event C N Vs (km/s) Starting point (alongstrike, along dip)

Range ofanalysis (Hz)

ID Magnitude

3176/02 5.3 1.12 5 3.06 (3, 4) 0.5–10.0

3176/03 4.6 2.0 7 3.06 (4, 5) 0.5–10.0

3162/02 4.6 2.3 7 3.06 (3, 6) 0.5–10.0

3182/11 3.4 45 8 3.06 (4, 6) 0.5–5.0

Fig. 4 Comparison of the strong motion generation area (solidrectangular), the area with a slip larger than 2 m of the main-shock (bold dashed line) by Funning et al. (2005), and theseismic gap (dotted line) by Sadeghi et al. (2006), superimposedon the slip inversion by Poiata (2010). The star shows theassumed initial rupture starting point from Poiata (2010), andthe cross shows the rupture starting point assumed in this study

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Fig. 5 Comparison of the observed (blue) and simulated (red)waveforms and the Fourier amplitude spectra of acceleration atthe Abaraq station for the aftershock 3176/02 with the 1Dhomogenous fault model (upper) and the 2D fault velocity

model (lower). Seismograms are band-pass filtered between0.5 and 10 Hz. The maximum amplitude values and the absolutevalue of the linear correlation coefficient, r, between the wave-forms are also given

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Fig. 6 Comparison of the observed (blue) and simulated (red)waveforms and the Fourier amplitude spectra of acceleration at theAbaraq station for the aftershock 3176/03 (upper), and at the

Mohammad-Abad station for the aftershock 3162/02 (lower).Seismograms are band-pass filtered between 0.5 and 10 Hz

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Waveform comparison in the time domain involvesa comparison of acceleration and velocity as well asdisplacement. High frequencies dominate accelera-tion, while low frequencies dominate displacement.Therefore, the velocity component includes an impor-tant range of frequencies for the evaluation of the fitbetween the simulated and observed waveforms.Hence, we compared the velocity and concluded witha glimpse into the acceleration and displacement. Thequality of the fit can be judged by visual inspection orquantitative evaluation such as the RMS of the resid-uals. Der et al. (1991) showed that the quality of thewaveform fit varies strongly with frequency, becom-ing progressively worse toward higher frequencies.Their study indicated that the correlation coefficientin the time domain often decreased significantly above0.15 Hz. We calculated linear correlation coefficient, r,to quantify the goodness of fit between each pair ofobserved and simulated waveforms. The r valuescorresponding to the simulated velocity time series atfrequencies up to 10 Hz, range between 0.17 and 0.38(in absolute value). Here it is found that even thecorrelations, as small as 0.17, show a reasonable visualmatch between the observations and the simulations.Therefore, we visually evaluated the fit between thesimulated and observed waveforms.

The simulated strong motions at the Mohammad-Abad station show a good fit for the EW component,but in the NS component, the amplitude of the seismo-grams, except some pulses around 22 s, is generallyunderestimated. The simulations at the Abaraq stationshow a better fit of the NS component, but in both theEW and NS components, the seismograms are gener-ally overestimated. On the other hand, Fig. 5 showsthat the simulated strong motion at the Abaraq stationusing the M 5.3 aftershock presents a good fit in theEW component, but the amplitude of the accelerationand velocity seismograms are underestimated in theNS component. One of the reasons for these under-and over-estimations could be the different focalmechanism that controls the effect of the radiationpattern. No solution for the focal mechanism of theseaftershocks is available. We attempted to compute thefocal mechanism from the polarity of the P-wave firstmotions, reported by ISC (International SeismologicalCentre 2012). The fault plane solutions are shown inFig. 7a. A strike of 157, dip of 77, and rake of 153°, isdetermined for the M 5.3 aftershock. This solution isroughly similar to the mainshock solution. Since there

is lower number of polarities for the M 4.6 aftershock,many acceptable solutions exist. However, the plot ofpolarities on the fault plane solution of the mainshockshows a good agreement, except one polarity, with thesolution. Therefore we can consider same focal mech-anism for EGFs and the mainshock. Another way toassess the nature of the mechanism is to observe theratio of the maximum amplitude EW component to theNS component, although Liu and Helmberger (1985)and Takemura et al. (2009) have pointed out distortionof radiation pattern for high-frequencies (e.g., above2 Hz). So we also checked relative amplitude amongthe components to support the similar focal mecha-nisms of the mainshock and the aftershocks.Figure 7b, c shows rose diagrams for the maximumEW/NS ratios of the mainshock and aftershocks forthe Mohammad-Abad and Abaraq stations, respective-ly. It is interesting to note that the ratios for the M 4.6aftershock and the mainshock are similar at theMohammad-Abad station but different at the Abaraqstation. Moreover, the Abaraq mainshock has an EW/NS ratio similar to that of the M 5.3 aftershock. Thisencouraged us to examine the empirical Green’s func-tion method through various combinations of the M5.3 and M 4.6 aftershocks to improve the simulationresults for the Abaraq station. The combined faultmodel consisting of two fault surfaces using two dif-ferent aftershocks as empirical Green’s function wasintroduced by Fukuyama and Irikura (1986). Theystudied the rupture process of the 1983 Japan Seaearthquake by considering a faulting model consistingof two fault surfaces—northern and southern faults.They had good knowledge of the strikes and locationsof the faults, whereas for the causative fault of theBam earthquake, there is no available information offault surfaces. Therefore, we assumed two faults—southern and northern or shallow and deeper faultareas. After testing different fault combinations, wefinally obtained a combined model as the best fitmodel for the source, as shown in Fig. 8. Figure 9shows the waveform and spectral fitting of the com-bined source model using both the M 5.3 and M 4.6aftershocks at the Abaraq station. Comparing the sim-ulations in Figs. 5 and 9, the combined model couldreproduce a better fit to the observed waveforms of theground motion in the NS and UD components.

The obtained source model was adjusted by repro-ducing the ground motion at Bam station during theBam earthquake using the M 3.4 aftershock. Figure 10

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shows a good fit for the waveform and spectrum in thefrequency range 0.5–5.0 Hz of this empirical Green’sfunction.

Miyake et al. (2003) constructed a self-similar scal-ing relationship between the seismic moment and both

the size of the strong motion generation area andthe rise time for a moderate-size crustal earthquakein Japan. The scaling is compatible with the self-similar scaling of the seismic moment to the com-bined area of asperities and the rise time obtainedby Somerville et al. (1999) for larger crustal earth-quakes that occurred in western North America,and the 1978 Tabas, Iran, and 1995 Kobe, Japan,earthquakes. Figure 11 shows the relationships be-tween the seismic moment and the strong motiongeneration area and between the seismic momentand the rise time for the Bam earthquake and thoseobtained by Miyake et al. (2003). For the Bam earth-quake, an average rise time of 0.34 s was estimated.Although the strong motion generation area is in goodagreement with the scale, the estimated rise time isconsiderably smaller compared to the scale.

5 Discussion and conclusions

The notable features of the Bam earthquake such asthe damage localization in the small city of Bam andthe characteristics of the ground motion record at theBam station have drawn significant attention. The

a

b c

Fig. 7 a Focal mechanism solutions computed from P wavefirst motions for the M 5.3 aftershocks, and distribution of Pwave first motions of the M 4.6 aftershock on the mainshocksolution. Rose diagrams showing the maximum amplitude ratio

of EW component to NS component by 0° to 360° rotation forthe mainshock and aftershocks at the (b) Mohamad-Abad and(c) Abaraq stations

Fig. 8 Combination of strong motion generation areas from theaftershocks 3176/2 and 3176/3. The star shows the rupturestarting point. The empirical Green’s function method uses theaftershock 3176/3 for the deeper fault elements and the after-shock 3176/2 for the shallower fault elements

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Fig. 9 Comparison of the observed (blue) and simulated (red) waveforms and the Fourier amplitude spectra of acceleration at the Abaraqstation using the combined source model of Fig. 8. Seismograms are band-pass filtered between 0.5 and 10 Hz

Fig. 10 Comparison of the observed (blue) and simulated (red) waveforms and the Fourier amplitude spectra of acceleration at the Bamstation. Seismograms are band-pass filtered between 0.5 and 5.0 Hz

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Bam station recorded the mainshock strong motionnear the causative fault and in the heavily damagedarea. Studying the characteristics of the near-sourceground motion could reveal important informationrelated to the source. The main characteristic of therecorded ground motion is the existence of two pulsesin the EW component (Fig. 2). Ghayanghamian andHisada (2007) have discussed the pulses as the theo-retically expected (Aki 1968) near-fault forward-

directivity pulses. The Bam station recorded themainshock at the northern part of the NS-trendingcausative fault (e.g., Nakamura et al. 2005) in thedirection of the rupture propagation, where thestrong seismic energy arrives due to the rupturedirectivity. However, since there was no such in-strument in the southern part of the fault, we wereunsure about the forward-rupture directivity pulsedue to a unilateral rupture. In addition, we areunsure about the assumption that the high damagein Bam is due to the effect of the forward rupturedirectivity because the damage levels are signifi-cantly lower in some areas of the city than inothers. The map provided by the National CartographicCenter of Iran (NCCI 2004), displaying the distri-bution of building damage, shows that the damagerates decreased significantly in the southern andwestern sides of Bam city relative to the northernand eastern sides. Hisada et al. (2004) reportedMSK intensities up to XI at the northern and easternsides, and only up to VIII at the south and west sides.Mostafaei and Kabeyasawa (2004) evaluated 624buildings in different parts of Bam city. Theyshowed that although the main reason for the highlevel of damage was the low earthquake resistanceof buildings, the damage rates decreased remarkably inthe eastern and southern of the city. Therefore, theysuggested that the damage distribution might be affectedby other factors. For example, Nakamura et al. (2005)found a correlation between the areas of heavy damageand the three fault branches in the northern part of theArg-e-Bam fault.

We tried to simulate the broadband ground-motiontime histories of the earthquake by the empiricalGreen’s function method. A successful simulation es-sentially depends on the accurate consideration of site,path, and source effects. The key point of the empiricalGreen’s function method is that it considers the pathand site effects by using recordings of aftershocks asempirical Green’s functions. Therefore, simulationsare controlled only by source factors describing themechanics of the rupture process, such as the asperityarea, location of the initial rupture, rise time, and thevelocity of rupture propagation.

The rupture velocity is an important source param-eter. The results obtained by Somerville et al. (1999)in a study based on 15 slip models show that therupture velocities were within a limited range—2.4–3.0 km/s—independent of the seismic moment. In our

Fig. 11 Broadband source characteristics of the Bam earth-quake (crosses). Squares are (a) strong motion generation areaand (b) rise time estimated in this study superimposed on theseismic moment scalings for crustal earthquakes by Miyake etal. (2003)

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simulation, we used the value of 0.92 times the S-wave velocity. This Rayleigh-like value, which isclose to the upper limit of rupture propagation veloc-ities, was discussed by Bouchon et al. (2006) as themain reason for the strong ground shaking that oc-curred during the Bam earthquake.

All studies of the Bam earthquake indicate that thefault asperity motion was a strike-slip motion along anearly vertical fault plane. We constructed a strong-motion generation area that was almost equivalent tothe asperity area. The location of the strong motiongeneration area, the location of the initial rupture, andthe rise time were adjusted to give an acceptable matchbetween the observed and simulated waveforms byforward modeling.

The rectangular-shaped strong motion generationarea for the mainshock was estimated to be 11 km inlength by 7 km in width. The rupture starting pointwas observed to be close to the center of the strongmotion generation area at an epicentral distance of 5 kmfrom the Bam station 7 km in depth.

The rise time or slip duration is the time taken byindividual points on the fault to reach their final val-ues. The estimated rise time in the strong motiongeneration area for the Bam earthquake is significantlyshorter than the average rise time given by Somervilleet al. (1999; Fig. 11). Moreover, a high rupture velocityof 0.92 Vs was obtained by Bouchon et al. (2006). Thecombination of fast rupture velocity and short rise timeresults in strong seismic shear waves of short duration inthe near-field region.

Despite the advantages of using aftershock record-ings as empirical Green’s functions to simulate themainshock records, in practice, there is an obviousproblem with the empirical Green’s function method.In the case of rupturing in a branched fault or withdifferent faulting mechanisms, this method is notexpected to approximate well the radiation patternfrom different points of the finite source based on onlyone recording. Since fault branching (e.g., Nakamuraet al. 2005) and even a dip-slip fault motion (e.g.,Ghayanghamian and Hisada 2007) were proposed for

Fig. 12 The acceleration and velocity ground motions of theaftershock 3182/11 that were used as the empirical Green’sfunctions for simulating the mainshock waveforms at the Bam

station. Two pulses can be identified in the velocity time histo-ries. Seismograms are band-pass filtered between 0.5 and 5.0 Hz

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the Bam earthquake causative fault, we also studied acombined model using two aftershock records for theAbaraq station. Although these are the only availablerecords, they show an obvious difference in themaximum amplitude ratio of EW to NS component(Fig. 7). The simulated waveforms produced by thecombined model provide a better fit to the observedwaveforms (Figs. 8 and 9). On the other hand, thesimulation results for the Bam station depicted inFig. 10 show a good agreement between the simulatedand observed waveforms for all three components.Both pulses in the mainshock waveforms were simu-lated using only the aftershock 3182/11 records. Thepulses were reproduced well because two pulses canalso be seen in the waveforms of the aftershock record(Fig. 12).

Based on the above discussion, we now introducethe possibility that there are two distinct mechanismsin the strong motion generation area and that thedouble pulse at the Bam station. This may supportthe findings of Poiata et al. (2009), whose results ofthe analysis of the teleseismic and strong motion data-sets show a single fault model with single asperityincluding a dip-slip component.

Acknowledgments The authors acknowledge the Editor inChief T. Dahm and the two anonymous reviewers for theirvaluable comments and suggestions that improved the manu-script. We are grateful to the Building and Housing ResearchCenter, Iran, for providing the strong motion data. We sincerelythank Kazuki Koketsu, Sadaomi Suzuki, Hiroshi Takenaka,Takeshi Nakamura, Natalia Poiata, John G. Anderson, and S.Keivan Hosseini for their fruitful discussions and comments.Some figures were made using the Generic Mapping Toolssoftware (Wessel and Smith 1998).

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