Seismic hazard assessment of Tehran, Iran with emphasis on near-fault rupture directivity effects

1.   Introduction

Tehran, the capital of Iran, due to its highly dense population and political and economical importance, should be capable of resisting severe earthquakes. However, the existence of active faults like North Tehran, Mosha, South and North of Rey indicates high seismicity of this region. Historical references indicate that Tehran and the old city of Rey were destroyed by catastrophic earthquakes at least six times (Amiri et al., 2003). According to JICA (2000) reports, it is estimated that in the scenarios of activation of the South of Rey and North Tehran faults, 55% and 36% of structures in Tehran will collapse, respectively. All aforementioned explanations intensify the great demand for precise seismic hazard assessment and identification of main hazard sources and scenarios in this city. To this end, applying deaggregation technique on Probabilistic Seismic Hazard Analysis (PSHA) and determining controlling earthquake lead to better understanding of seismic hazard in this region.

Most advanced seismic codes worldwide define structural design actions based on PSHA (Cornell, 1968). This method combines the probabilities of all earthquake scenarios with different magnitudes and distances with prediction of resulting ground motion (McGuire, 2004). Therefore, PSHA results are not representative of a single design earthquake. For a given site of engineering interest, the deaggregation technique extracts the combination of magnitude (m), source to site distance (r) and other parameters that contribute to hazard at a given return period. After determining relative contribution of each scenario of magnitude and distance to hazard, the lost concept of controlling earthquake in PSHA could be defined. In spite of all the advantages of conventional version of PSHA, it seems to be inadequate in capturing fault rupture characteristics in determining hazard in near field conditions. An earthquake is produced by shear dislocation which begins at a given point on a fault (asperity) and spreads with a velocity being almost as large as the shear wave velocity. Not all near fault earthquakes present the rupture directivity, because two conditions must be satisfied: the rupture front propagates towards the site and the direction of slip on the fault aligned with the site (Gioncu and Mazzolani, 2010). The main characteristic of forward rupture directivity is amplification in the horizontal and vertical components of the ground motion. Also, the presence of velocity pulse in a ground motion is related to this phenomenon, since this pulse of motion represents the cumulative effect of almost all the seismic radiation from the fault produced in earthquakes with forward rupture directivity effect.

Few attempts have been made in the past to incorporate the effects of near fault rupture directivity in PSHA. Somerville et al. (1997) proposed a model to include the amplitude and duration effects of rupture directivity on ground motion attenuation relationship. This model was then refined by Abrahamson (2000) by applying a distance and magnitude taper function to reduce effects of rupture directivity to zero for distances greater than 60 km and magnitudes less than 6, which is called directivity saturation effect. Rowshandel (2006) developed a model for overcoming restrictions in Somerville et al. (1997) model. In this model there is no need for classifying faults as purely strike-slip or dip-slip and also there is no need for imposing any delineation at the end points of a fault, as it was in Somerville et al. (1997) model. These conventional models that amplify the response spectrum monotonically are sometimes referred to as broadband models. The strong motion recordings of recent Kocaeli’Turkey (1999) and Jiji (Chi-Chi) Taiwan, China (1999) earthquakes indicated that the near fault pulse is a narrowband pulse whose period increases with magnitude (Somerville, 2002). Somerville (2003) proposed a narrowband rupture directivity model where the response spectrum is amplified in a narrow range of period close to the period of the pulse. The main difference of the broadband methods and narrowband methods could be summarized in the fact that, in broadband methods the response spectrum is adjusted monotonically over a range of periods based on empirical equations without considering period of pulse-like ground motion, on the other hand, in narrowband methods the response spectrum is amplified/de-amplified as a function of period of pulse-like ground motion. Shahi and Baker (2011) proposed a framework which is the extension of approach proposed by Tothong et al. (2007). They rotated recordings in next generation attenuation (NGA) data base and applied Baker (2007) quantitative pulse classification algorithm and categorized recordings into two groups of pulse-like and non-pulse-like ground motions. They split the main PSHA equation into two cases depending on whether or not pulse-like ground motion is observed. These two cases can then be combined to calculate the overall exceedance rate. In recent studies (Wen et al., 2015; Pacor et al., 2016) a directivity coefficient, C_d, which is primarily proposed by Ben-Menahem (1961), is adopted in order to consider the rupture directivity effects of the small-to-moderate earthquakes on ground motion parameters. Also, Wang et al. (2017) used the directivity coefficient, C_d, in order to simulate the directivity effects with two-step Empirical Green’s Function (EGF) method.

In this study, in the first step, the Gutenberg and Richter (1954) coefficients are calculated using historical earthquakes and instrumentally recorded data. For this purpose, the Kijko (2000) method is employed. This method provides numerous capabilities particularly for the data of seismic events that are not uniform, which is appropriate for the Iran region. In the second step, using in-house calculations coded in MATLAB, hazard curves and response spectrum are determined for a 2475-year return period. The resulted spectrum is validated by the results of the final report of PSHA for greater Tehran regions (Gholipour et al., 2008) and also the results obtained from SESRISKIII. In the next step, response spectrum is determined for the bed-rock of considered site in Tehran for a 10000-year return period. Afterwards, a PSHA de-aggregation analysis is carried out and relative contribution of each magnitude and distance scenario to hazard is determined. After deaggregating the seismic hazard, the dominant hazard scenario is identified and the controlling earthquake for the considered site is determined in the range of periods. After identifying the North Tehran fault as the most hazardous source affecting the considered site, forward rupture directivity effect of this fault is incorporated into the PSHA using the Somerville et al. (1997) model with broadband approach and Shahi and Baker (2011) model with narrowband approach.

2.   Seismic hazard assessment

Seismic hazard analysis involves the quantitative estimation of ground shaking hazard at a particular site (Kramer, 1996). One of the following approaches may be undertaken when conducting seismic hazard assessment. The first one is deterministic approach which relies on a worst-case earthquake size and location to estimate the ground motion. This approach is a simple framework which does not account for aleatory and epistemic uncertainties. The second approach is probabilistic which allows uncertainties in the size, location and rate of recurrence of earthquake to be explicitly considered in the evaluation of seismic hazard.

The PSHA calculates the mean annual rate of exceedance at a particular site based on the aggregated hazard from many magnitude and distance scenarios. The ground motion parameter Y exceeding a particular value y^* in a time period n at a given site of engineering interest, which follows the Poisson probability distribution, is determined by equation (1)

where λ_y* is the average exceedance rate for the considered region.

Frequency of exceedance, λ_y*, incorporates the aleatory variability in time, size and location of future earthquakes at the site and is computed using equation (2)

where ν_i is the frequency of earthquakes on seismic source i above a minimum magnitude of engineering significance M₀, $f_{M_i}$ (m) is the probability density function of magnitude on source i, $f_{R_i}$ (r) is the probability density function for distance to earthquake rupture related to source i and P[Y > y^*|m, r] is the probability that ground motion parameter from a given magnitude m at a distance r from the site exceeds value y^*.

In practice, the double integration presented in equation (2) cannot be calculated analytically and is replaced by double summation of discretized density functions. This resulted function which is suitable for programming purposes can be written as equation (3):

where N_s, N_m and N_r are numbers of seismic sources, magnitudes and distance divisions, respectively.

The third approach in determining seismic hazard is hybrid. In this approach, first of all, PSHA is conducted and then a deaggregation technique is performed for determining the controlling earthquake. A source with such a magnitude and distance is selected for conducting deterministic seismic hazard analysis (DSHA) (Ares and Fatehi, 2013).

2.1   Seismic hazard assessment of Tehran

In this study, considering the importance of Tehran and the need for a comprehensive seismic hazard assessment for different parts of Tehran, PSHA is conducted for an important site located in this city in a 2475-year and 10000-year return periods using the latest and most up-to-date data. The response spectrum for a 2475-year return period is compared to response spectrum resulted in Gholipour et al. (2008).

2.1.1   Earthquake catalog

In order to collect information about historical and instrumentally recorded earthquakes, a radial range of 200 km is employed around the center of considered site. To this end, updated data base of International Institute of Earthquake Engineering and Seismology (IIEES) is used for earthquakes after 1900. The distribution of the location of earthquakes with magnitudes greater than 5 after 1900 and the faults in the investigation region is presented in Figure 1. Also, the list of earthquakes prior to 1900 is chosen from the catalog collected by Amiri et al. (2003). An updated catalog usually contains earthquake magnitudes given in several scales. In this study, all the magnitude scales are converted to surface wave magnitude. In these catalogs, earthquakes with magnitudes lower than 5 are eliminated according to USNRC (2007). The method that is used for eliminating after-shocks and fore-shocks for meeting Poisson distribution assumption is the variable windowing method in time and space domains (Gardener and Knopoff, 1974). Since the majority of earthquakes in Iran are shallow and there is not enough reliable data for the depth of earthquakes, the focal depth of earthquakes is taken to be 10 km.

Figure  1.  Distribution of the faults and the earthquakes after 1900 with magnitudes greater than 5 in the investigation region (IIEES)

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2.1.2   Seismicity parameters

Seismic hazard analysis requires determination of seismicity parameters of the region such as the maximum expected magnitude, M_max, the activity rate, λ, and the b value of Gutenberg-Richter relationship. These parameters have significant effects on determining seismic hazard. Several methods are available for determining seismicity parameters and all of them are based on the relationship of Gutenberg and Richter (1954). In this study, Kijko (2000) method is employed for determining seismicity parameters of Tehran due to its numerous capabilities, especially for the seismic data that is not uniform in the span of the time. Therefore, this method has a good applicability with Iranian earthquake data. This maximum likelihood method applied in this method allows the combination of historical and instrumentally recorded earthquakes. Kijko (2000) used extreme distribution function for historical events and double truncated Gutenberg-Richter distribution for instrumentally recorded earthquakes. In order to use Kijko (2000) computer program, three input files are prepared. The first file contains data for historical earthquakes prior to 1900, the second file contains data of instrumentally recorded earthquakes from 1900 to 1963 and the third file contains data of instrumentally recorded earthquakes after 1964. Note that in the year 1964, world seismography network are installed and after this year, reliability of information is improved significantly.

Several studies are conducted for determining seismicity parameters of Tehran (Tavakoli, 1996, Amiri et al., 2003, Nezamabadi and Vayeghan, 2008). The results of these investigations and also the seismicity parameters determined in this study using Kijko (2000) method are compared in Table 1. It should be noted that in this table, the Lambda coefficient is the annual rate of occurrence for earthquakes greater than the considered minimum magnitude and Beta (b ln10) is the coefficient presented in Gutenberg-Richter relationship in which, b represents the relative number of small magnitude earthquakes to large magnitude earthquakes. Also, annual rate of occurrence for magnitudes greater than 5 is presented in Figure 2.

Figure  2.  Annual rate of occurrence estimated by Kijko (2000) method for Tehran and its vicinity

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Table  1.  Comparison of seismicity parameters of Tehran region in recent studies and that determined in this study using Kijko (2000) method

Studies	Parameters	Historical and instrumental
Tavakoli (1996)	Beta	1.41
	Lambda (MS4)	0.37
Amiri et al. (2003)	Beta	1.08
	Lambda (MS4)	0.62
Nezamabadi and Vayeghan (2008)	Beta	1.51
	Lambda (MS4)	0.655
This study using Kijko (2000) method	Beta	1.75
	Lambda (MS5)	0.32
	Mmax	7.71

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2.1.3   Attenuation relationship

An attenuation relationship, usually gives an estimate of the parameters of the probability distribution of a measure of ground motion in terms of a parameter of engineering interest, as a function of simple seismological parameters that characterize the seismic source, the seismic wave propagation path and surficial geological conditions at a site ( Committee of American Nuclear Society, 2008). Therefore, it is important to select the attenuation relationship which is compatible with the investigation region. In this study, it is decided to use Campbell and Bozorgnia (2003) attenuation relationship. The data base used for presenting this attenuation relationship is mostly consisted of Western North America earthquake recordings, but including Tabas and Manjil earthquakes happened in Iran. However, Chandra et al. (1979) showed that the attenuation of acceleration in Iran is more rapid than that in Western North America. Therefore, the use of this attenuation relationship for Iran region may be conservative (Tavakoli and Ghafory-Ashtiyani, 1999).

2.1.4   Conducting PSHA for Tehran

In this study, in order to conduct a PSHA for considered site located in Tehran, 26 sources of seismicity and their relative coordinates are identified in 200 km radial vicinity of this site. The formulations for PSHA procedure is coded in MATLAB. In order to verify the validity of in-house MATLAB code, the Mosha fault is selected and is assumed to be the only source of seismicity in the region. Hazard curve is determined for the considered site using MATLAB code and SEISRISKIII. The resulted hazard curves for peak ground acceleration (PGA) are compared in Figure 3. Comparing resulted hazard curves in Figure 3 and considering the maximum 6% error in calculating ground motion parameter using MATLAB code, validates the written code for conducting PSHA.

Figure  3.  Comparison of the resulted hazard curves for PGA using in-house MATLAB code and SEISRISKIII software, while the Mosha fault is considered as the only source of seismicity

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A key part of probabilistic seismic hazard analysis is the quantitative target performance goal that corresponds to an estimate of the mean probability failure of the structure to perform its safety function. These probabilistic goals lead to selecting the return period for design basis earthquake (DBE). In this study, a 2475-year return period DBE is selected for verification purposes and because of the importance of the considered site, a 10000-year return period DBE is selected for the main seismic hazard assessment.

The response spectrum for the bedrock of considered site in a 2475-year return period is presented in Figure 4 and is compared to the response spectrum presented in Gholipour et al. (2008) PSHA reports for Tehran. According to this figure, PGA for the bedrock of the considered site in Tehran in a 2475-year return period is estimated to be 0.83 g which was 0.78 g in Gholipour et al. (2008) reports.

Figure  4.  Comparison of a 2475-year return period response spectrum resulted in this study with response spectrum presented in Gholipour et al. (2008) final PSHA reports for Tehran

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The response spectrum for the bedrock of the considered site in a 10000-year return period is presented in Figure 5. According to this figure, PGA for considered hazard level is estimated to be 1.06 g. It should be noted that in this study, for conservatism, PSHA is conducted in one standard deviation above the mean.

Figure  5.  Response spectrum for the bedrock of considered site in a 10000-year return period

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3.   De-aggregation and determining controlling earthquake

PSHA aggregates hazard from many earthquake scenarios of different magnitude and distance pairs. De-aggregation is undertaken as a way to better understand the earthquake that most contributes to hazard at the site of interest and also is used to assess the reasonability of PSHA results (USNRC, 2007). The deaggregation technique is used for physical interpretation of PSHA and taking important engineering decisions like selecting an appropriate set of earthquake recordings for time history analysis. The method used to calculate the seismic deaggregation in terms of magnitude and distance is proposed by Bernreuter (1992). The equation for deaggregation can be expressed as equation 4:

For calculating the fractional contribution to hazard from each magnitude and distance scenario, annual rate of exceedance for each magnitude and distance bin, ${\lambda _{{{\rm{y}}^{\rm{*}}}}}$ [m_j, r_k], is divided by total annual rate of exceedence, ${\lambda _{{{{y}}^*}}}$ .

After extracting relative contribution to hazard from different magnitudes at different distances, concepts of the so-called controlling earthquake (Bernreuter, 1992), the design earthquake (McGuire, 1995), the modal event (Chapman, 1995) and the dominant event (Bazzurro and Cornell, 1999) could be defined.

In this study, the expression proposed by Bernreuter (1992) is used for determining controlling event's relative magnitude ( $\bar M$ ) and distance ( $\bar R$ ) as expressed in equations (5) and (6), respectively

where, m is the magnitude, r is the distance from rupture and P(m, r) is the fractional contribution to the seismic hazard of magnitude m [representative value of $m \pm \left( {\frac{{\Delta m}}{2}} \right)$ range] at distance r [representative value of $r \pm \left( {\frac{{\Delta r}}{2}} \right)$ range]. Bernreuter (1992) and SSHAC (1997) recommended magnitude intervals of 0.5 (Δm=0.5) and linear distance increment of 10 km (Δr=10 km) for performing de-aggregation and determining controlling earthquake.

3.1   Deaggregation and controlling earthquake results for Tehran

The PSHA deaggregation analysis is carried out for the site of interest in Tehran in a 10000-year return period. This procedure is done using in-house MATLAB code. The results of deaggregation for 0.1, 1, 2 and 3 s periods are shown in Figure 6. This figure illustrated that the main contribution to hazard for 0.1 s period in a 10000-year return period is related to small magnitudes at close distances and as the period becomes longer, large magnitudes from far distances become more important. For 0.1 s period, most of the contribution to hazard is related to 0 to 5 km distance and 5.15 to 5.25 magnitudes, while, for 3 s periods this range is 15 to 20 km and 7.05 to 7.15 magnitudes. It is evident from the figure that for all periods, distances lower than 20 km have the most contribution to hazard, which matches the distance range of North Tehran fault. Therefore, conducting seismic hazard assessment for northern Tehran regions requires comprehensive attention about the effects of the North Tehran fault.

Figure  6.  Deaggregation of hazard for the site of interest in Tehran in a 10000-year return period for different vibration periods, T

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As it is obvious from Figures 7 and 8, for 0.1 s to 3 s periods, controlling magnitude for the considered site varies from 5.9 to 7.1 and controlling distance varies from 7 to 15.5 km. According to controlling distance values, lower distances have more contribution weight to hazard.

Figure  7.  Variation of controlling magnitude with period for the site of interest in a 10000-year return period

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Figure  8.  Variation of controlling distance with period for the site of interest in a 10000-year return period

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4.   Incorporating near fault directivity effects into PSHA

Near fault ground motions are defined as those recorded within a distance about 20 km from hypocenter. These ground motions have inherent differences with those recorded further away from the hypocenter. Near field ground motions often contain strong dynamic long period pulses and permanent ground displacements caused by rupture directivity and fling step effects, respectively. Estimation of ground motion for a site of engineering interest close to active faults should account for these aspects. In this study, because of the limited inertial demands of fling step effects on structures, only forward rupture directivity effects are incorporated into PSHA. The directivity effects are observed at a site when the fault ruptures towards the site at a speed close to the propagation velocity of shear wave (Somerville et al. 1997). When this condition is met, a large portion of energy arrives at the site in a small time interval causing a distinct pulse in the velocity of time history of ground motion. Therefore, it is important to incorporate the effects of pulse-like ground motions in seismic hazard assessment. Several attempts have been made in recent years for taking into account the pulse-like ground motions in PSHA. All these attempts could be classified into two basic models known as broadband models and narrowband models. In broadband models response spectrum is amplified either by monotonically increasing or decreasing over a range of periods. Near fault ground motions cannot be adequately described by uniform scaling of a fixed response spectrum shape, as it is in broadband models. In narrowband models, response spectrum is amplified in a narrow range of periods close to the period of pulse. The response spectra for near-fault ground motions become richer in longer periods as a result of a magnitude increase which lengthens the pulse period. Earthquakes with higher magnitude result in pulses with longer periods. Consequently, longer period pulses increase the level of response spectra for longer periods. This shifts the peak response spectral acceleration of the strike-normal component to longer periods (Sehhati, 2008). In this study, the Somerville et al. (1997) model with broadband approach and the Shahi and Baker (2011) model with narrowband approach are selected for incorporating rupture directivity effects of the North Tehran fault, as the most hazardous faults affecting the site of interest, into seismic hazard assessment of the considered site in Tehran. Relative contributions to hazard from main sources of seismicity in a 10000-year return period are reported in Table 2.

Table  2.  Relative contribution of considered faults to hazard for T=0 in 10000-year return period

Fault name	North Tehran	Rey	Eyvanekey	Kahrizak	Mosha	Kandovan	Taleghan	Other 19 faults
Relative contribution to hazard (%)	23.1	13.2	8.2	7.7	5.8	5.1	4.5	32.4

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4.1   Somerville et al. (1997) model

In this pioneer model, an empirical base modification is proposed to account for rupture directivity effects on strong motion amplitude and duration. First of all, fault rupture mechanism should be categorized as purely strike-slip or dip-slip. Variation of ground motion parameter due to fault rupture directivity effects depends on two geometrical parameters. The first one is the angle between the direction of the fault rupture and the direction of wave propagation (θ for strike-slip fault and φ for dip-slip fault) and the second is the fraction of ruptured length (s/L). Therefore directivity parameter for strike-slip fault is defined as X and expressed by equation 7:

Somerville et al. (1997) calculated the difference between the logarithm of the recorded and of the calculated spectral accelerations for strike-slip fault using equation (8):

In this equation, C₁ is considered for reflecting database bias and is combined to the second term which represents the directivity effect. The C₁ and C₂ coefficients are both period dependant.

In written in-house MATLAB code, in order to calculate the X and W values, the North Tehran fault with overall length of 91.3 km within a distance range of 4.1 to 46.1 km from the site of interest and θ range of 7 to 174 degrees is divided to 913 segments (100-meter segments). Afterwards, the above-mentioned values are calculated for each of segments, as initial points of rupture propagation (hypocenter), and different lengths of rupture attributed to different magnitudes. The values for X as a function of magnitude for the worst scenario of initial point of rupture are illustrated in Figure 9.

Figure  9.  Variation of values for X with magnitude for the site of interest at the worst scenario for the location of hypocenter

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For incorporating directivity effects into PSHA, the conventional PSHA equation (2) is rewritten as equation (9):

In this equation, z represents the information for the source to site geometry. This equation gives the rate of exceedance of y^* at a site of engineering interest accounting for pulse-like ground motions.

4.2   Shahi and Baker (2011) model

In Shahi and Baker (2011) narrowband model, P^* [Y>y^*|m, r, z] is separated into two cases, depending on whether or not pulse-like ground motion is occurred. The probability of exceeding y^* can be expressed as equation (10) when pulse-like ground motion is observed:

where, the pulse-like ground motion has mean and standard deviation values equal to μ_{lny*, pulse} and σ_{lny*, pulse}, respectively. On the other hand, when no pulse-like ground motion is observed, the probability of exceeding y^* can be expressed as equation (11):

where non-pulse-like ground motion has mean and standard deviation values equal to μ_{lny^*, no pulse} and σ_{lny^*, no pulse}, respectively. The Φ() represents the standard normal distribution function.

The equations (10) and (11) can then be combined using the total probability theorem and the overall exceeding probability can be obtained from equation (12):

Shahi and Baker (2011) used a logistic regression model for proposing equation (13) in order to predict the probability of observing pulse-like ground motion in strike-slip fault, given the source-site geometry.

In this study, for calculating the ruptured length parameter, s, attributed to different magnitudes, equations proposed by Wells and Coppersmith (1994) are adopted. Also, the distance to rupture, r, values are calculated for different segments of North Tehran fault as different scenarios of initial point of rupture propagation. The maximum probability of pulse occurrence at the site of interest for different magnitudes of earthquakes is illustrated in Figure 10.

Figure  10.  Maximum probability of pulse occurrence at the site of interest in Tehran for earthquakes with different magnitudes on North Tehran fault

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Shahi and Baker (2011) proposed amplification and de-amplification equations for calculating $\mu_{{\rm {ln}}\;y^*,\; pulse}$ and $\mu_{{\rm {ln}}\;y^*,\;no\; pulse}$ , respectively. In these equations, the amplification factor is a function of period of the pulse. For more information about this model referring to Shahi and Baker (2011) and Shahi (2013) is recommended.

4.3   Incorporating rupture directivity effects into PSHA of Tehran

In this study, near fault rupture directivity effects of the North Tehran fault is incorporated into the (PSHA) of the site of the interest in Tehran and is compared to conventional PSHA results for a 10000-year return period. The Azad et al. (2011) investigations illustrated that the North Tehran traces of activity do not follow the older traces corresponding to dip-slip thrusting movements and there is clear evidence for left-lateral strike-slip movements. Therefore, in this study the new strike-slip dominant mechanism of this fault is considered in calculations. For this purpose, all above-mentioned procedure and formulations of the Shahi and Baker (2011) and the Somerville et al. (1997) models, are coded in MATLAB. The hazard curves for the site of interest, with and without considering directivity effects are illustrated in Figure 11. According to this figure, the Shahi and Baker (2011) model for 0.1 s period under-predicts accelerations when rupture directivity effect is considered in PSHA, but over-predicts ground accelerations for longer periods. This over-prediction becomes significant as period becomes longer. It is worth noting that Somerville et al. (1997) model does not amplify ground motion values for periods lower than 0.6 s.

Figure  11.  Hazard curves for the site of interest in Tehran in a 10000-year return period for different vibration periods, (a) T=0.1 s (b) T=1 s (c) T=2 s (d) T=4 s

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Figures 12 and 13 show the response spectrums for the site of interest in a 10000-year and a 2475-year return period, with and without considering rupture directivity effects of the North Tehran fault.

Figure  12.  Response spectrum for the site of interest in Tehran in a 2475-year return period with and without considering rupture directivity effects

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Figure  13.  Response spectrum for the site of interest in Tehran in a 10000-year return period with and without considering rupture directivity effects

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According to these figures, considering rupture directivity effects using the Shahi and Baker (2011) model, affected the response spectrum significantly, while, the difference between the response spectrum resulted from the Somerville et al. (1997) model and conventional PSHA model is little. The Shahi and Baker (2011) model for a 10000-year return period shifted the peak of response spectrum to longer periods and raised it about 27%. According to response spectrums for two different hazard levels presented in Figures 12 and 13, it is obvious that the effects of Shahi and Baker (2011) model on higher levels of hazard assessment is more significant compared with lower levels. Therefore, for higher levels of seismic hazard assessment attributed to important sites, it is necessary to incorporate near fault rupture directivity effects into PSHA using the most updated methods.

5.   Conclusions

In this paper, PSHA is conducted for an important site located in Tehran in a 10000-year return period, using the latest and most up-to-date data. After deaggregating the PSHA and determining controlling earthquakes for a range of periods, it is observed that distances lower than 20 km are the most hazardous scenarios affecting the site of interest in a 10000-year return period. It is concluded that for a period range of 0.1 s to 3 s, controlling distance and controlling magnitude varies from 7 km to 15 km and M_S 5.9 to M_S 7.1, respectively. After it was identified that lower distances have more contribution to hazard, near fault directivity effects of the North Tehran fault, as the nearest seismicity source to site of interest, is incorporated into PSHA using the Somerville et al. (1997) model with broadband approach and the Shahi and Baker (2011) model with narrowband approach. It is worth noting that in this paper new strike-slip dominant mechanism of the North Tehran fault is considered in the calculations. Considering forward rupture directivity effects in PSHA, using the Shahi and Baker (2011) model affected the 10000-year return period response spectrum significantly. In this model, the peak of response spectrum is raised about 27% and is shifted to longer periods, while the difference between the Somerville et al. (1997) model and the response spectrum resulted from the conventional PSHA model, is little. According to response spectrums resulted using the Shahi and Baker (2011) model for a 2475-year and a 10000-year return period, it is obvious that for higher levels of seismic hazard assessment attributed to important sites, it is necessary to incorporate near fault rupture directivity effects into PSHA using the most updated methods.