Predicting Probabilistic-Based Strong Ground Motion ...

Journal of Earthquake Engineering, 13:482–499, 2009 Copyright  A.S. Elnashai & N.N. Ambraseys ISSN: 1363-2469 print / 1559-808X online DOI: 10.1080/13632460802597976

Predicting Probabilistic-Based Strong Ground Motion Time Series for Citadel of Arg-E-Bam (South-East of Iran) A. NICKNAM, A. YAZDANI, and S. YAGHMAEI SABEGH Department of Civil Engineering, Iran University of Science and Technology, Tehran, Iran The main objective of this article is to present a probabilistic-based strong motion compatible with the source-path and site soil condition given the probability of exceedence for citadel of Arg-e-Bam site bed rock (South-East of Iran). A Fourier amplitude spectral attenuation relation for bed rock beneath the site is proposed which permits the estimation of time-histories through a probabilistic seismic hazard analysis procedure. Due to lack of data, the two well-known simulation techniques, point source and finite fault models have been used for generating hundreds of strong motion as input data. Tens of model parameter values such as stress-drop nucleation points were used, in each specified magnitude-distance, to reduce the uncertainty effects inherently existing in seismological/ geological parameters. The proposed attenuation relation is validated by comparing the estimated strong motion, in the form of Fourier amplitude spectral, using the proposed attenuation relation with those of recorded ground motion data at three stations far away from the assumed source so that the results would not be influenced by the near source problems such as directivity and fling step. The results of proposed technique is assessed by comparing the estimated response spectra, with 10% probability of exceedence and 5% damping ratio, with those of traditional uniform hazard spectra. The proposed technique is supposed to be used in retrofitting procedure of international historical adobe structures in Arg-e-Bam site, which have been damaged during the destructive Bam earthquake 2003, Iran Keywords Probability of Exceedence; Stochastic Simulation; Attenuation Relation; Fourier Amplitude Spectral

1. Introduction In regions where seismic loads are predominant relative to gravity loads, estimation of ground motion level that a given site will experience in the future is of most importance. Traditionally, the design of any engineered structure is based on an estimate of ground motion, either implicitly through the use of building standard codes or explicitly by prediction of destructive ground motion in site-specific design of large or critical structures. It is often appropriate to use a probabilistic approach to characterize the ground motion in a particular site [Somerville and Moriwaki, 2003], due to the uncertainty in the timing, location, magnitude of future earthquake and the uncertainty in the level of the ground motion that a specified earthquake will generate at a particular site. A scheme of uniform hazard response spectra and PGA estimation considering local site response was described by Sokolov [2000]. Received 10 August 2007; accepted 11 August 2008. Address correspondence to A. Nicknam, Department of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran 16844, Iran; E-mail: [email protected]

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The primary advantage of probabilistic seismic hazard analysis (PSHA) is that all possible ground motion that can occur on each fault or source zone are integrated to estimate a combined probability of exceedence that incorporates the relative frequencies of occurrence earthquakes in the site of interest [Cornell, 1968]. Modern PSHA also considers multiple hypotheses on input assumption and thereby reflects the relative credibility of competing scientific hypotheses [McGuire, 1995]. In traditional PSHA, the severity of ground motion for engineering design purposes are characterized quantitatively either by a simple single-parameter PGA, or elastic response spectrum [Cornell, 1968; Somerville et al., 1997]. Engineering analyses that assess the seismic performance of structures require seismological input data that describes the amplitude, frequency content, phase angles, and duration of the expected motion. Although these parameters are implicitly included in traditional PSHA, based on the standard codes of practice such as ASCE 2005, time-history analysis of structures requires several ground motion under special requirements. The main objective of this article is to demonstrate a technique for estimating a probabilistic-based time-history complies with those of code requirements, consistent with faulting mechanism and compatible with response spectrum. Lacking the sever earthquake information, in the region under study Bam, was the most difficult problems in developing the desired probabilistic-based acceleration timehistory. Strong motion simulation models are alternatives in such regions [Silva et al., 2002]. To overcome such problem and to properly reflect the inhomogeneity of seismicity of the Bam region, hundreds of strong motion was generated incorporating range values of source-path and site soil condition seismological/geological parameters. An attenuation relation is developed for the region which reflects the attenuated Fourier amplitude spectral ordinates of the synthesized strong motion from the source up to the site of interest. The proposed attenuation relation suggests producing specific probabilisticbased strong motion for the site of interest with rock soil condition.

2. Fundamentals of Probabilistic Seismic Hazard Analysis (PSHA) The objective of probabilistic seismic hazard analysis (PSHA) is to quantify the rate of probability exceedence of various ground-motion levels at a site given all possible earthquakes. This approach was first formalized by Cornell [1968] and further discussed notably by Cornell and Merz [1975]. In particular, large application of this approach is in regions where information about seismogenic structures is poor or not available [Der Kiureghian and Ang, 1977]. Cornell and Winterstein [1988] examined a range of time and magnitude dependent earthquake occurrence models. They found that the Poisson model is adequate except where a single fault dominates the seismic hazard, the time since the last earthquake occurrence exceeds the mean recurrence interval and the fault exhibits a very regular interval of earthquake occurrence. Mathematically, based on the aggregated hazard from N sources located at different distance and capable of generating events of different magnitudes, the annual frequency of exceedence, lY(f)>y, at a specified level y, is given by: Yðf Þ>y ¼

N X

ððð i

 I½Yðf Þ > ym; r; ":fM;R:" ðm; r; "Þ:dm:dr:d";

(1-a)

i¼1

where Y stands for strong motion characteristics at the site such as PGA or uniform response spectra. In this work, it represents the Fourier amplitudes spectral form, Y( f ), propagated from each source to the site of interest, which will be discussed later, and:

484

A. Nicknam, A. Yazdani, and S. Yaghmaei Sabegh  vi is the mean annual rate of occurrence of earthquakes generated by source i with magnitude greater than some specified lower bound.  I[Y(f) > y|m,r,e] is an indicator function for the Y( f ) of a ground motion (generated by source i) of magnitude m, and distance r. This term represents the mean values of attenuated Fourier amplitudes spectral form of strong motion, with magnitude m and distance r, at the site. Traditionally, the attenuation relation has the following form: ln½Y ðfÞ ¼ fðM; RÞ þ E;

(1-b)

where E, the variability of M and R is modeled as a normal distribution with zero mean and standard deviation slnY [Campbell, 1981; Abrahamson and Silva, 1997].  fM,R,e (m, r, e), is the joint probability density function of magnitude, M, distance R, and e for source i. Note that the standard deviation slnY depends on M and R while e is independent of M and R, then fM,R,e (m, r, e) = fM,R (m,r).fe(e) [Bazzurro and Cornell, 1999].

3. Seismotectonic of Bam Region The active tectonic environment in Iran is related to the convergence of the Eurasian and Arabic plates. Indentation of the Arabian plate into a composite system of collisionoblique transpressive fold-thrust mountain belts has resulted in lateral escape of central Iran toward the Lut Block, without a through-going high slip rate strike slip fault [Berberian, 2005]. At longitude 560 E, 25 mm/year of north-south shortening is accommodated across Iran [McClusky et al., 2003; Vernant et al., 2004]. Some of the roughly N-S right lateral shear between central Iran and Afghanestan occurs on the long N-S strike slip faults of Sistan near the Iran-Afghan border [Berberian et al., 2000, 2001; Berberian 2005], but a portion is also on right lateral faults striking N-S to NNW-SSE on the western side of the Lut block, which includes the Nayband, Gowk, Bam, and Sabzevar fault systems [Berberian, 2005]. The kuh Banan, Jorjafk, Nayband, Gowk, Bam, Sabzevaran, and Rafsanjan strike slip faults and Shahdad thrust are the main active faults of the Kerman province of southeastern Iran, west of Lut Desert (Fig. 1). Despite the active deformation feature along these faults in the Kerman plateau, there is a lack of seismicity and active deformation in the low-lying Lut Desert. The right later shear along the western margin of the Lut block is directly transmitted between the Nayband, Lakarkuh, Kuh Banan, Gowk, and Bam fault systems [Berberian, 2005].

4. Estimation of Seismotectonic Parameters The seismic assessment, at the site of interest, depends mainly upon the earthquake data which have been occurred within the last decades in the concerned region. The earthquake database, catalog of earthquakes and potential seismic sources, were compiled from available references containing historical and instrumental events in a radius of 200 km (Appendix 1). Historical earthquake were ascribed magnitudes that were computed on the basis of a simple linear relationship between intensities and magnitudes [Moinfar et al., 1994]. Due to inaccuracy in earthquake focal depths and considering that, those of the Zagros earthquakes are mostly shallow, the variation of earthquake focal depths would not have a significant impact and were neglected in this study.

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FIGURE 1 Seismo-tectonic map around Arg-e-Bam.

4.1. Seismicity Catalogs The ancient earthquakes in the region under study have been studied by Ambraseys and Melville [1982] providing a review of Iran’s historical earthquakes, and by Moinfar et al. [1994], collecting historical as well as instrumentally recorded earthquakes. Furthermore, there are other catalogs available for Bam region. These data mainly include the International Seismological Center (ISC), and the National Earthquake Information Center (NEIC). The available earthquake data in the region under study were classified into the historical earthquakes (before 1900) and the instrumentally recorded earthquakes (after 1900). The final collective catalogue in this study was prepared by eliminating the aftershocks, foreshocks [Gardner and knopoff, 1974] and the incorrect reported events from data. The cleaned and updated catalogue contains earthquake magnitudes given in several scales, therefore, the catalog of earthquakes were made uniform in surface wave magnitude form, using the relationship proposed by Iranian Committee of Large Dams [IRCOLD, 1994].

4.2. Determination of Seismicity Parameters Due to lack of sufficient recorded data, it was not possible to assign the occurrence of the earthquakes to their causative sources; as a result, estimating the seismicity parameters for individual fault was not possible and was obtained in an area with a radius of 200 km around the Arg-e-Bam site. It is notable that the scope of this article is to show how it is possible to insert inside the main equation of probabilistic seismic-hazard analysis

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(PSHA, e.g., Cornell 1968) so as the response spectra be replaced by a time-series to be used in dynamic analysis of structures. Three types of cataloged earthquakes, historical earthquakes (before 1900), instrumentally recorded earthquakes from 1900–1963 and instrumentally recorded earthquakes from 1963–2005 were used. The magnitude uncertainties of these earthquakes are estimated to be 0.3, 0.2, and 0.1, respectively. The lower magnitude 4.5, by which the structures are expected to be damaged, was chosen as the lower threshold used in Eq. (1). The new method of Kijko [2000], based on the double truncated distribution function of Gutenberg-Richter, using the probabilistic method of maximum likelihood estimation which allows the combination of historical and instrumental data [Kijko and Sellvol, 1992], was used for estimating the maximum magnitude (Mmax), activity rate (l), and regional b value (b · ln10). In this method, uncertainty in magnitude and incomplete earthquake catalog is applied. Figure 2, shows the annual rate of occurrence l, for earthquakes with magnitude greater than 4.5. The estimated seismicity parameter values in a region of 200 km radius around Bam city are shown in Table 1. In another work carried out by Tavakoli [1996], Iran has been divided into 20 seismo-tectonic provinces estimating the seismicity parameters for each province (Table 1). The time span he has used was limited from 1923–1995. This information was added to those of ours for reducing the uncertainties existing in the seismicity parameters for estimating the probability of exceedence at the bed rock beneath the Arg-e-Bam site.

Annual rate

1

0.1

0.01

0.001 4.5

5

5.5

6

6.5

7

Ms

7.5

FIGURE 2 Annual rates estimated by Kijko [2000] method for Bam region.

TABLE 1 Seismicity parameters of the region

Kijko method

Beta

Mmax

Lambda (Mmin = 4.5)

1.44 ± 0.09

7.28 ± 0.21

0.893 ± 0.09

Tavakoli [1996] results for below faults: Bam; 1.3 Shahdad, Golbaf-Sirch, Nayband; 1.6 Gowk, Lalezar; 1.95 Zendan Minab; 2.12 Sabzevaran, Jiroft; 2.49

± ± ± ± ±

0.27 0.16 0.15 0.05 0.13

7.2 7.6 7.5 7.2 7.0

± ± ± ± ±

0.3 0.3 0.3 0.2 0.4

0.26 0.64 0.47 1.70 0.27

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5. Attenuation Relation An attenuation relation, or ground motion model as seismologists prefer to call it, is a mathematic-based expression that relates a specific strong-motion parameter, such as PGA or response spectra and acceleration time-history in this study, at a site with respect to the source-site distance R, and earthquake magnitude M. It quantitatively characterizes the earthquake severity, source, the wave propagation path between the source and the site, and geological profile beneath the site. The attenuation relation studies have been reviewed in the past years which provide a good summary of the used techniques and the problems associated with the proposed relationships. A summary of the methods used to drive the equations is reported by Douglas [2001] and Campbell [2003] which contains the peak ground acceleration and response spectra using data processing and regression methods. Due to lack of data and poor knowledge of seismological/geotechnical information in Bam region, a significant irresolvable issue exits in estimation of strong ground motion for specified magnitude, distance, and site conditions. For this purpose, hundreds of strong motion, in the Fourier amplitude spectral (FFT) forms, consistent with the known faults was generated as input data for estimating the attenuation relation, taking into account the regional source-path influences. Among the currently used strong motion generation techniques, the two widely used stochastic point source/finite fault models were used for synthesizing the required strong motion. 5.1. Strong Motion Generation As already mentioned, poor knowledge of strong motion information in the region under study, necessitates synthesizing hundreds strong motion compatible with the source-path and site soil conditions to be used as input data in developing regional attenuation relation. The two well-known techniques, Point/Finite-fault models were used for generating the required input data. The reliability of the results was previously validated by Nicknam et al. [2006a,b]. Point-source synthesizing model is based on omega-squared approach, may be divided into three major components: source S(M0,Ds,f), path P(f,R), and site G(f) [Boore, 2003; Cramer, 2006], That is: YðM0 ;
; f ; RÞ ¼ C:SðM0 ;
; f Þ:Pðf ; RÞ:Gðf Þ;

(2)

where M0 is seismic moment, Ds is the seismic stress drop, f is frequency, and R is distance from the source to the site of interest. C is scaling factor, and S(M0, Ds, f) is the source spectrum term. The path-portion of the model represents the seismic wave propagation through the source to the site in the form of P(M0, f, R) = Z(M0, R).e–p.f.r/[Q(f).b], where Z(M0,R) is the geometrical spreading term and e–p.f.R/[Q(f).b] is the anelastic attenuation factor [Atkinson and Mereu, 1992]. The site-amplification factors were related to the shear wave velocity profiles using the frequency-dependent functions proposed by Boore and Joyner [1997]. The site-decay portion, D(f)=e-p.f.k, adjusts arriving seismic motion in rock for increased shallow crustal attenuation [Anderson and Hough, 1984] and impedance effects [Silva et al., 2002]. Four types of the path-dependent quality factor (Qðf Þ ¼ Q0 :f n ), shown in Table 2 with a shallow crustal damping kappa value 0.06 s, was used to reduce the uncertainty due to this factor [Shoja-Taheri et al., 2005]. In Finite-Fault method, the fault is subdivided into smaller elements, each of which is then treated as a point source [Hartzell, 1978; Irikura, 1983]. The fields from all sub-events are geometrically delayed and added together at the observation point [Irikura, 1983;

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TABLE 2 Parameters associated with the used quality factor Region

Q0

n

Literature References

This region This region Quebec(CENA) South eastern Canada(CENA)

350 150 755 680

1.0 0.94 0.5 0.36

[Shoja-Taheri et al., 2005] [Nicknam et al., 2007] [Boore and Atkinson, 1992] [Atkinson and Mereu, 1992]

Beresnev and Atkinson, 1997]. Different source orientation parameters, different hypocentral point positions, and different number of sub-faults were incorporated in this work. The empirical relation Log(A) = M-4.0 proposed by Wells and Coppersmith [1994] was used to assign areas to target earthquakes and corresponding sub-faults. In order to reduce the aleatoric uncertainty (also referred to as stochastic or irreducible uncertainty), inherently existing in the seismological/geotechnical model parameters such as, nucleation point, fault rupture area and quality factor, we incorporated the mean values of these parameters by generating tens of strong motion for specified moment magnitudes M and source-to-site distance R. Epistemic uncertainty (also referred to as reducible or subjective or model form uncertainty ), due to uncertainty in the true state of nature which results from lack of knowledge about the used model and/or model coefficients, was accommodated by averaging the results obtained from the two models, point source and finite fault in our study (Campbell, 2003; Toro et al., 1997). Note that the distances R was selected far away from source so that the generated strong motion would not be influenced by near source problems such as directivity effect and fling step. Furthermore, different values of stress drop with a 100% variation of the base stress drop value were run [Silva et al., 2002]. The single corner frequency model with f0 = 0.18 Hz, and a stress drop parameter Ds =105bar was run as the base values corresponding to the moment magnitude Mw = 6.6. These values were previously estimated from the Bam earthquake [Nicknam et al., 2006a,b]. Epistemic uncertainty was relatively reduced by getting together the results of both models, Pint source and Finite-fault approaches as input data.

5.2. Proposed Fourier Amplitude Spectral (FAS) Attenuation Relation An attenuation relation, for Arge-Bam bed rock in the Fourier amplitude spectral form, is proposed which reflects the attenuated amplitudes corresponding to each frequency at the site of interest. The functional form of the proposed attenuation relation to be used in regression analysis procedure was given as [Campbell, 2003b]: ln Y ¼ C1 þ C2 :M  C3 : ln R  C4 :R þ ":;

(3)

where ‘‘ln’’ represents the natural logarithm, Y is the strong motion parameter (frequency spectral amplitude in this study), M is earthquake magnitude, R is a measure of source-tosite distance. The distance term R was chosen as: R ¼ r þ C5 : expðC6 :MÞ. This term was used to model the widely held belief that, close to the causative fault, short-period ground motion should be smaller dependent on magnitude [Campbell, 2003a]. In order to calculate the constant coefficients C1, C2, C3, C4, C5, C6, and finally the standard deviation of lnY, tens of stations in citadel of Arge-Bam site were selected. For each station, a source on Bam fault sufficiently far (with distances from 15–200 km) was

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489

assumed. The source-to-station distances were sufficiently far so as the synthesized strong motion would not be influenced by near source effects. Note that, none of the selected sources was that of causative 2003 Bam earthquake which is located close to our stations. Twenty-four strong motions corresponding to the earthquake magnitudes of Mw 4.5 to Mw 8 were generated at each station in Arge-Bam site incorporating different values of seismological/geotechnical parameters. The coefficients of Eq. (3) were calculated for the frequency ranges of 0.2–12 Hz, using the least square approach. Table 3 shows the proposed attenuation coefficients for the bed rock of the Arge-Bam site. Figure 3 demonstrates the attenuated Fourier amplitudes spectral of earthquake M6.6 at frequencies 0.5, 1, 2, 5 Hz as a function of distance using the proposed FAS attenuation (Eq. 3). As is clearly shown, the Fourier amplitudes spectral are decreased proportional to the distances with fewer slopes for higher frequencies. TABLE 3 Regression coefficients of the proposed attenuation relation for the bed rock of Bam region Fre.(Hz) 0.2 0.5 1.0 1.5 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 12.0

C1

C2

C3

C4

C5

C6

Sigma

7.77168 5.82666 3.33763 3.13177 2.62977 2.26966 2.29123 2.09866 2.10268 2.12003 2.64027 2.54240 3.47160

2.786979 2.115710 1.397829 1.328265 1.282662 1.210415 1.191819 1.155943 1.161648 1.140246 1.156421 1.168919 1.168862

2.303363 1.519410 0.900167 0.817409 0.861771 0.853568 0.834145 0.880969 0.942846 0.938186 0.910915 0.997558 0.828566

0.013939 0.000856 0.967803 0.762636 0.675522 0.788122 0.754855 1.115160 3.275200 3.902120 4.922380 2.374980 0.292845

1.134865 1.396614 5.282250 5.519200 5.314170 5.477240 5.845350 5.567820 5.535500 5.744630 8.771900 4.926480 3.649140

0.013198 0.006683 0.001886 0.000523 0.001333 0.001192 0.000537 0.001283 0.001895 0.001526 0.002087 0.002679 0.000497

0.630 0.410 0.400 0.300 0.325 0.290 0.275 0.270 0.280 0.305 0.330 0.295 0.340

Ln (Amplitude of FFT)

10

Attenuation relations

Att.(f =0.5 Hz.) Att.(f =1.0 Hz.) Att.(f =2.0 Hz.) Att.(f =5.0 Hz.)

1

0.1 0

50

100 150 Distance (Km)

200

250

FIGURE 3 Fourier amplitudes spectra of M6.6 earthquake at frequencies 0.5, 1, 2, and 5 Hz vs. distance based on the proposed attenuation relation.

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5.3. Validation of the Proposed FAS Attenuation Relation As already mentioned, hundreds of ground motion were synthesized to be used as input data in developing the FAS attenuation relation for the buildings in citadel of Arge-Bam. The strong motion was generated in the form of Fourier amplitude spectral ordinates. For this purpose, the attenuated amplitude, for each frequency (from 0.2–12 Hz), was calculated on the basis of FSAA relation using the corresponding equation coefficients from Table 3. The proposed technique was validated against the recorded data at three stations No. 3155-2 (M6.6, R = 111 km, Bam 2003), 1544 (M6.4, R = 57 km, Golbaf 1998), and 3168 (M6.6, R = 43, Bam 2003). For avoiding confusion it is notable that, the records of Bam station located at an office in down town have not been used in any parts of this study and the word Bam in the above mentioned stations is used to show that the record is due to the main shock of 2003 Bam earthquake. The strong motion at these three stations, in the form of Fourier amplitude spectral, was estimated using the proposed FSAA relation. The effect of site amplification was also considered based on frequency-dependent functions proposed by Boore and Joyner [1997]. Figure 4 shows the comparison of estimated strong motion, in the form of Fourier amplitude spectral ordinates, with those of observed data reported by the Building and Housing Research Center (BHRC) strong-motion database. In these figures, the estimated strong motion is those at the bed rock beneath the three above-mentioned stations.

6. Probabilistic Seismic Hazard Analysis (PSHA) The well-known software SEISRISK III [Bender and Perkins, 1987] was used for probabilistic seismic hazard analyzing procedure to estimating the Fourier amplitudes spectral of strong motion given a probability of exceedence (PE). For this purpose, Eq. (1) was used for estimating spectral Fourier amplitudes in a frequency range 0.2–12 Hz, for bed rock of Arg-e-Bam site This site contains to many buildings which are one of the most famous historical adobe-structures which were seriously damaged during the 2003 Bam earthquake. Since there are various types of structures in the site, different PE values from 2–50% were estimated. Figure 5 demonstrates the uniform hazard curves concerning probability of exceedence from 2–50%, using the proposed FAS attenuation relation and classical PSHA technique. Each plot represents the uniform Fourier amplitudes spectral of estimated strong motion with specified probability of exceedence versus frequency. A FORTRAN computer program originally written by Beresnev and Atkinson [1998] was modified to invert the estimated probabilistic-based Fourier amplitude spectra to time-series. Inverting procedure is briefly summarized as follows: (i) Generation of Gaussian band limited white noise. (ii) Windowing the white noise using the window function in the Jenning form [Vanmarcke, 1977] to shape the accelerogram to resemble a real accelerogram. (iii) Derivation of the frequency filters taking into account the produced seismological moel. (iv) Generation of the synthetic accelerograms based on filtered frequency amplitudes and random phase angles in the last step. Traces in Fig. 6 show estimated time-histories with different probability of exceedence. It is worth mentioning that, the estimated probabilistic-based time-histories are based upon the mean value spectral amplitudes of the strong motion frequencies [McGuire et al., 2005].

Predicting Probabilistic-Based Strong Ground Motion Time Series 100

491

Record No. 1944 (M=6.4 & R=57; Golbaf 1998)

Amplitude of FFT

10 1 0.1 FFT of Obs. Earth.

0.01

Att (Mean) Att (Mean +/– Sigma)

0.001 0.1

1

10

100 Frequency (Hz)

Amplitude of FFT

100

Record No. 3155-2 (M=6.6 & R=111; Bam 2003)

10 1 0.1 FFT of Obs. Earth. Att (Mean) Att (Mean +/– Sigma) 0.01 0.1

1

10

100

Frequency (Hz)

Amplitude of FFT

1000

Record No. 3168 (M=6.6 & R=11; Bam 2003)

100

10 FFT of Obs. Earth.

1

Att (Mean) Att (Mean +/– Sigma)

0.1 0.1

1

10

100

Frequency (Hz)

FIGURE 4 Comparison of the simulated Fourier amplitudes spectral of strong motion with those of observed data.

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A. Nicknam, A. Yazdani, and S. Yaghmaei Sabegh FFT(2% in 50) FFT(8%in 50) FFT(12%in 50) FFT(50% in 50)

1000

FFT(5% in 50) FFT(10%in 50) FFT(20% in 50)

Amp. of FFT

100

10

1 0

2

4

6

8

10

12

14

Fre.(Hz)

500 300

Time (Se c)

100 –100 0

2

4

6

8

10

12

700

P.E.=5%

500 300

Time (S ec)

100

14

–100 0

2

4

6

8

10

12

14

–500

–500

–500

–700

–700

–700

300

700

P.E.=10%

500 300

Time (sec)

100 –100 0

2

4

6

8

10

12

Acc(Cm/sec^2)

–300

Acc (cm/sec^2)

–300

500

700

P.E.=12%

500 300

100 –100 0

14

Time(S ec) 2

4

6

8

10

12

14

–300

–500

–500

–500

–700

–700

–700

300

Acc(Cm/sec^2)

–300

500

4

6

8

10

12

10

12

14

P.E.=20%

Time (S ec) 2

4

6

8

14

P.E.=50%

Time (S ec)

100 –100 0

Time(S ec) 2

100

–100 0

–300

700

P.E.=8%

100 –100 0

–300

700

Acc(Cm/sec^2)

300

700

P.E.=2%

Acc(Cm/sec^2)

500

Acc (Cm/sec^2)

700

Acc (Cm/sec^2)

FIGURE 5 Illustration of different levels of uniform probability of exceedence in spectral Fourier amplitude forms at Arg-e-Bam site.

2

4

6

8

10

12

14

–300 –500 –700

FIGURE 6 Earthquake ground motions corresponding to the probability of exceedence 2%, 5%, 8%, 10%, 12%, 20%, and 50% in bed rock of Arg-e-Bam site.

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1.4 1.2

Sa(g)

1 Sa (mean)

0.8

Sa (ground motion)

0.6 0.4 0.2 0 0

1

2 3 Period (Sec)

4

5

FIGURE 7 Schematically comparison of the proposed technique with traditional approach in estimating 10% probability of exceedence for bed rock of Arg-e-Bam site. The smoothed plot shows the %5 damping response spectra while the other plot demonstrates that of the proposed approach. A comparison between the results of traditional approach and this study is also performed to assess the performance of the proposed attenuation relation used in hazard analysis procedure. For this purpose, the response spectra with 5% damping ratio corresponding to 10% probability of exceedence (PE = 10%) in the bed rock of Arg-e-Bam site is estimated using the traditional approach and that of this study. A logic tree method with the same weight consisting the attenuation relations proposed by Ambraseys et al. [1996], Sedigh et al. [1997], and Abrahamson and Silva [1997] were employed in traditional technique. The proposed attenuation relationship was employed in estimating the acceleration time history at the same point. Figure 7 shows such comparison. It is not claimed that good agreement of these two approaches confirm the accuracy/reliability of the proposed relation, since there are many uncertainties which could influence on the results. However, since the proposed attenuation relation ends with acceleration time history compatible with source-path and site, it can be regarded as a merit compared to the traditional approach by which the results are either the probable PGA or response spectra.

7. Discussion and Conclusion A Fourier amplitude spectral based hazard analysis for the existing buildings of Arg-eBam site, where were destroyed during the 2003 earthquake is presented. The proposed technique can be used to predict the probabilistic/deterministic strong motion time history given the probability of exceedence, in the bed rock beneath the site of the existing structures. Due to lack of data, the two widely used stochastic techniques, point source/ finite fault models, were used to generate the strong motion time histories as input data for developing the attenuation relation of this site. In developing attenuation relation, the aleatoric uncertainties inherently existing in the seismological/geotechnical parameters such as; stress drop, nucleation point, rupture area and quality factor were reduced by generating hundreds of data incorporating a range of these values in the model. The proposed attenuation relation was validated against observed data at three stations. For comparison purpose, the records at three stations far from the site, No. 3155-2 (M6.6, R=111 km, Bam 2003), 1544 (M6.4, R=57 km, Golbaf 1998), and 3168 (M6.6, R=43, Bam 2003), were selected. The strong motion at these stations, in the form of spectral Fourier amplitude, were estimated and compared with those of the recorded

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data (see Fig. 4). Acceptable agreement of the plots confirms the reliability of the proposed attenuation relation. The attenuated strong motion corresponding to the probability of exceedence 2%, 5%, 8%, 10%, 12%, 20%, and 50% in bed rock of Arg-e-Bam site were calculated and shown. The acceleration time history corresponding to 10% probability of exceedence in bed rock of Arg-e-Bam site, in the form of elastic response spectrum, was calculated and compared with that of traditional approach. Figure 7 demonstrates such comparison qualitatively, however, the quantitative comparison of generated strong motion has been previously performed by Nicknam et al. [2007, 2008]. Although these two plots shows a good agreement, it not claimed that our proposed approach and/or model parameters are free from uncertainties, rather, it confirms the merit of the model in estimating a strong motion in the form of time history, compatible with source-path and site soil condition, to be used instead of those compatible time histories necessary for dynamic analysis of important structures as recommended by credible codes [ASCE, 2005]. Physically, we believe that the derived PSHA doesn’t represent a comprehensible event, because there is no single event (by a magnitude and distance) that represents the earthquake threat at the site of interest [NRC, 1988]. It is worth mentioning that future additional data is required for improving the results and developing the substantial coefficient of spectral attenuation relation for the region under study, Kerman (Iran).

Acknowledgments The authors appreciate comment from Dr. Ghoraishi that was helpful in predicting strong motion of Bam region and appreciate the reviewers whose their comments improves this manuscript.

References Abrahamson, N. A. and Silva, W. J. [1997] ‘‘Empirical response spectral attenuation relations for shallow crustal earthquakes,’’ Seismological Research Letters 68(1), 94–127. Ambraseys, N. N. and Melville, C. P. [1982] A History of Persian Earthquakes, Cambridge University Press, Cambridge. Ambraseys, N. N., Simpson, K. A., and Bommer, J. J. [1996] ‘‘Prediction of horizontal response spectra in Europe,’’ Earthquake Engineering and Structural Dynamics 25(4), 371–400. Anderson, J. G. and Hough, S. [1984] ‘‘A model for the Fourier amplitude spectrum of acceleration at high frequency,’’ Bulletin of the Seismological Society of America 74, 1969–1993. ASCE (American Society of Civil Engineers). [2005] SEI/ASCE 7-05 (ASCE Standard No. 7-05): Minimum Design Loads for Buildings and Other Structures. American Society of Civil Engineers, Reston, VA. Atkinson, G. M. and Mereu, R. F. [1992] ‘‘The shape of ground motion attenuation curves in Southeastern Canada,’’ Bulletin of the Seismological Society of America 82(5), 2014–2031. Atkinson, G. M. and Boore, D. M. [1995] ‘‘Ground – motion relations for Eastern North America,’’ Bulletin of the Seismological Society of America 85, 17–30. Bazzurro P. and Cornell, C. A. [1999] ‘‘Disaggregation of seismic hazard,’’ Bulletin of the Seismological Society of America 89(2), 501–520. Bender, B. and Perkins, D. M. [1987] ‘‘SEISRISK III, a computer program for seismic hazard estimation,’’ US Geological Survey, Bulletin 1772. Berberian, M., Jackson, J. A., Qorashi, M., Talebian, M., Khatib, M., and Priestley, K. [2000] ‘‘The 1994 Sefidabeh earthquakes in eastern Iran: Blind thrusting and bedding-plane slip on a growing anticline, and active tectonics of the Sistan suture zone,’’ Geophysical Journal International 142(2), 283–299.

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Berberian, M., Jackson, J. A., Fielding, E., Parsons, B. E., Priestley, K., Ghorashi, M., Talebian, M., Walker, R., Wright, T. J., and Baker, C. [2001] ‘‘The 1998 March 14 Fandoqa earthquake (Mw 6.6) in Kerman province, southeast Iran: re-rupture of the 1981 Sirch earthquake fault, triggering of slip on adjacent thrusts and the active tectonics of the Gowk fault zone, RAS, GJI 146,’’ 371–398. Berberian, M. [2005] ‘‘The 2003 Bam urban earthquake: A predictable seismotectonic pattern along the Western margin of the Rigid Lut Block, Southeast Iran,’’ Earthquake Spectra 21(S1), S35–S99. Beresnev, I. A. and Atkinson, G. M. [1997] ‘‘Modeling finite–fault radiation from the on spectrum,’’ Bulletin of the Seismological Society of America 87, 67–84. Beresnev, I. A. and Atkinson, G. M. [1998] ‘‘Stochastic Finite Fault Modeling of Ground Motion from 1994 Northridge Acceleration California earthquake: I- validation on Rock Sites,’’ Bulletin of the Seismological Society of America 88, 1392–1401. Boore, D. M. [2003] ‘‘Prediction of ground motion using the stochastic method,’’ Pure and Applied Geophysics 160, 635–676. Boore, D. M. and Atkinson, G. M. [1992] ‘‘Source spectra for the 1988 Saguenay, Quebec, earthquake,’’ Bulletin of the Seismological Society of America 82(2), 683–719. Boore, D. M. and Joyner, W. B. [1997] ‘‘Site amplification for generic rock sites,’’ Bulletin of the Seismological Society of America 87, 327–341. Campbell, K. W. [2003a] ‘‘Prediction of string ground motion using the hybrid empirical method and its use in the development of ground motion (attenuation) relations in eastern north America,’’ Bulletin of the Seismological Society of America 93, 1012–1033. Campbell, K. W. [2003b] ‘‘A Contemporary Guide to Strong-Motion Attenuation Relations,’’ In: International Handbook of Earthquake and Engineering Seismology, Supplement to Chapter 60, Vol. 2, Part B, Academic Press, London. Cornell, C. A. [1968] ‘‘Engineering seismic risk analysis,’’ Bulletin of the Seismological Society of America 58, 1583–1606. Cornell, C. A. and Merz, H. A. [1975] ‘‘Seismic risk analysis of Boston,’’ Journal of Structural Division ASCE 101, 2027–2043. Cornell, C. A. and Winterstein S. R. [1988] ‘‘Temporal and magnitude dependence in earthquake recurrence models,’’ Bulletin of the Seismological Society of America 28(4), 1522–1537. Cramer, C. [2006] ‘‘An assessment of the impact of the 2003 EPRI ground-motion prediction models on the USGS national seismic-hazard maps,’’ Bulletin of the Seismological Society of America 96, 1159–1169. Der Kiureghian, A. and Ang, A.H.-S. [1977] ‘‘A fault rupture model for seismic risk analysis,’’ Bulletin of the Seismological Society of America 67, 1173–1194. Douglas, J. [2001] ‘‘A comprehensive worldwide summary of strong-motion attenuation relationships for peak ground acceleration and spectral ordinates (1969 to 2000),’’ ESEE Report No. 011, Civil Engineering Department, Imperial College of Science,Technology and Medicine, London. Gardner, J. K. and Knopof, L. [1974] ‘‘Is the sequence of earthquake in southern California, with aftershocks removed, Poissonian?’’ Bulletin of the Seismological Society of America 64(5), 1363–1367. Hartzell, S. H. [1978] Earthquake Aftershocks as Green’s Functions, Geophysical Research Letters 5, 1–4. IRCOLD, Iranian Committee of Large Dams [1994] Relationship between MS and mb, Internal Report (in Persian). Irikura, K. [1983] ‘‘Semi-empirical estimation of strong acceleration motion during large earthquake,’’ Bulletin of Disaster Prevention Res. Ins. Kyoto University 33, 63–104. Kijko, A. and Sellevoll, M. A. [1992] ‘‘Estimation of earthquake hazard parameters from incomplete data files. Part II, Incorporation of magnitude heterogeneity,’’ Bulletin of the Seismological Society of America 82(1), 120–134. Kijko, A. [2000] ‘‘Statistical estimation of maximum regional earthquake magnitude mmax,’’ Workshop of Seismicity Modeling in Seismic Hazard Mapping, Poljce, Slovenia, May 22–24. McClusky, S., Reilinger, R., Mahmoud, S., Ben Sari, D., and Tealeb, B. [2003] ‘‘GPS constraints on Africa (Nubia) and Arabian plate motions,’’ Geophysical Journal International 1, 126–138.

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Appendix TABLE A.1 Earthquake catalog Date No.

Year

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

1497 1833 1854 1864 1877 1905 1910 1923 1925 1934 1937 1942 1948 1962 1963 1963 1964 1967 1969 1969 1970 1970 1970 1971 1971 1972 1973 1975 1976 1976 1979 1980 1980 1980 1981 1981 1981 1982 1982 1982

Month

10 11 9 7 1 5 7 7 9 10 11 5 9 7 9 3 9 11 9 12 10 5 12 3 11 3 2 5 9 4 6 7 2 2 6

Epicenter

Magnitude

Day

Lat.

Long.

MS

16 1 14 11 2 11 29 5 29 16 18 11 14 20 2 6 8 9 8 20 9 24 19 10 13 4 13 28 10 24 11 28 25 28 14

27.4 29.6 30.5 30.6 30.1 29.89 30.09 28.97 29.5 30.08 29.5 29.5 29.88 28.2 28.8 29.3 28.13 28.4 28.2 30.2 28.2 28.6 29.5 29.2 28.323 30.06 28.1 28.62 28.37 28.18 28.302 28.195 28.353 28.032 29.036 29.895 29.988 29.878 28.575 30.145

56.3 59.9 57.3 57 57.6 59.98 57.58 59.33 59.5 57.56 57.5 57.5 57.73 57.4 58 57 57.38 57.04 57.3 57.7 57.5 58.9 56.9 60 57.188 57.72 57.82 56.98 57.38 57.4 57.259 57.42 57.561 57.73 56.981 57.718 57.77 57.795 57.16 57.734

6.5 7 5.8 6 5.6 6 5 6

Mb

MW

6.8

4.5 6

6

4.5 5 5.9 5.5 4.8 5 5.3 4.7 4.9 5.3 4.7 4.8 5.5 5.4 5 4.8 4.4 4.7 4.7 5

5 4

7 7

4.6 4.7 4.6 4.5 6 5.9 4.8 4.5 4.6

6.6 7.1

Reference AMB AMB AMB AMB AMB AMB AMB AMB ISS ISS ISS ISS ISS USGS USGS NEIC ISC ISC USGS USGS USGS USGS USGS USGS ISC ISC ISC USGS USGS USGS USGS ISC ISC USGS ISC ISC ISC USGS USGS ISC (Continued)

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TABLE A.1 (Continued) Date

Epicenter

Magnitude

No.

Year

Month

Day

Lat.

Long.

MS

41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83

1982 1982 1983 1983 1984 1984 1984 1985 1986 1986 1987 1987 1988 1988 1988 1989 1989 1990 1990 1990 1990 1990 1991 1991 1992 1992 1993 1993 1995 1995 1996 1996 1996 1997 1997 1997 1998 1998 1998 1998 1999 1999 2001

10 12 1 10 4 10 11 4 3 7 6 8 4 7 12 4 11 2 4 6 7 10 7 12 2 7 4 11 2 8 2 2 9 1 7 10 3 6 7 11 3 10 11

15 25 31 29 25 11 15 23 27 25 16 1 13 26 3 2 20 4 20 26 16 9 4 19 10 27 12 1 6 25 10 26 28 24 21 20 14 10 24 18 4 19 1

28.088 29.9 28.888 28.494 28.227 29.539 28.389 28.14 30.106 28.085 28.443 29.989 30.227 28.2 30.248 28.166 29.881 28.202 29.695 28.449 28.475 30.115 28.149 28.072 30.193 28.037 28.268 28.244 28.426 28.42 30.31 28.305 28.48 28.23 28.37 28.5 30.161 28.27 28.132 30.35 28.34 30.11 28.103

57.309 57.772 57.29 57.029 57.778 58.03 57.136 57.63 57.904 57.287 57.285 57.672 57.55 57.36 57.542 57.288 57.722 57.685 57.427 59.105 57.039 57.427 57.303 57.261 57.478 57.921 57.134 57.569 57.063 57.12 59.01 57.075 57.56 57.53 57.19 57.28 57.612 58.54 57.302 57.61 57.19 57.63 57.397

5.2

5 6 5 5

4 5

4

5

7 4 5 6.7 4 3

Mb 4.5 5.1 4.8 4.1 5.1 4.8 4.4 4.6 5.2 4.8 4.7 4.5 4.6 5.2 5.2 5.5 4.8 4.6 4.9 4.4 4.4 4.8 5.3 4.6 4.4 5.2 4.7 4.5 4.9 3.8 5.4 4.8 4.5 4.6 5.6 5.8 5.1 4.4 4.8 4.4 4.6

MW

5.8

6.6

Reference USGS USGS USGS ISC USGS ISC ISC USGS USGS USGS USGS USGS USGS USGS USGS ISC ISC ISC USGS ISC ISC USGS ISC ISC USGS USGS ISC USGS ISC USGS USGS ISC USGS USGS USGS USGS ISC USGS ISC ISC USGS ISC ISC (Continued)

Predicting Probabilistic-Based Strong Ground Motion Time Series

499

TABLE A.1 (Continued) Date

Epicenter

Magnitude

No.

Year

Month

Day

Lat.

Long.

MS

Mb

84 85 86 87 88 89 90 91

2001 2002 2003 2003 2003 2003 2003 2005

11 6 3 7 8 8 12 2

25 2 1 6 4 21 26 28

28.218 27.917 28.75 28.052 29.08 29.053 29.08 28.18

57.269 57.672 57.419 57.661 59.74 59.773 58.38 56.76

4 4

5 4.7 4.5 4.9 5.3 5.5

5 6 6.5 5.9

Table notification: AMB: Ambraseys, N. N., Melville, C. P. ISC: International Seismological Center, UK. ISS: International Seismological Summary, UK. NEIC: National Earthquake Information Center, USA. USGS: United States Geological Survey. IIEES: International Institute of Earthquake Engineering and Seismology.

MW

Reference ISC NEIC NEIC NEIC NEIC NEIC IIEES IIEES