Abstract: In this study, probabilistic evaluation of seismic hazard in metropolitan Tehran, capital of Iran, is presented. The present study has been done in north part of Tehran due to the existence of high-rise buildings, important structures and the flourishing of high-rise building constructions in this zone. The objective of this study was the preparation of spectral acceleration maps with different seismic hazard levels for some specific periods. A set of historical and instrumentally recorded seismic data have been employed covering the timeline from 4 centuries BC up to 2003 and the seismic sources were modeled in a radius of 200 km around Tehran. The calculations for horizontal motion were carried out using two weighted horizontal attenuation relationships; using Logic Tree method. The calculations for vertical motion were carried out. Probabilistic seismic hazard evaluation was performed on a grid of 16x9 points in north part of Tehran using SEISRISK III. The corresponding results have been depicted by horizontal spectral acceleration maps with 2 and 10% PE (Probability of Exceedence) in 50 years and by vertical spectral acceleration maps with 10% PE in 50 years. The results show that whenever soil type changes from rocky to stiff, there is an increase in the spectral acceleration in that region. However in eastern north parts of Tehran, due to approaching to the north Tehran faults and also being situated over small or large faults of the region, there will be higher spectral accelerations than other points.
INTRODUCTION
Iran, one of the most seismic countries of the world, is situated over the Himalayan-Alpied seismic belt and is one of those few countries which have lost many human lives and a lot of money due to the occurrence of earthquakes. Tehran, capital of Iran needs a very precise investigation of seismicity and seismic hazard due to the population exceeding 10 million people and existence of major political, economical, social and cultural centers from one point of view and the high probability of occurrence of a severe earthquake from another point. Considering the history of the past severe earthquakes and the existence of major faults within metropolitan Tehran, the probability of occurrence of earthquake with magnitude over 7 is seriously high. Moreover, since the engineering principles and regulations regarding earthquake resistance design are not observed in most small and tall buildings in Tehran, the occurrence of earthquake shall be catastrophic and its consequence shall be very dire. Therefore seismic hazard analysis is very necessary for this region including strong ground motion parameters and seismic spectra.
The present study is in relation with the authors' earlier studies (Ghodrati et al., 2003) and has been performed for northern parts of Tehran due to the existence of high-rise buildings, important structures and the flourishing of high-rise building constructions. The extent of the region under study is 450 km2, which is bound from north to Alborz mountain ranges, from west to Kan canal, from east to Haraz Mountains and from south to Azadi, Enghelab and Damavand streets (Fig. 1)
To obtain an approximation of the probable losses of earthquake, it is initially necessary to find an estimation of the probable earthquakes in the region. To achieve this goal, seismic hazard spectrum analysis is required. This analysis, in essence, is a method using which it would be possible to have an estimation of impending earthquakes with regard to the geologic and tectonic conditions of the region and the past-recorded earthquakes.
| Fig. 1: | Different municipality zones of north parts of Tehran city illustrated with hector |
With this analysis, for different periods, the seismic hazard for different points of the region with regard to different seismic return periods can be estimated and afterwards, the spectral acceleration maps are obtained for each period and hazard level. This procedure can be used as an appropriate tool for obtaining uniform hazard spectra. In this paper probabilistic seismic hazard evaluation was performed on a grid of 16x9 points in north part of Tehran using SEISRISK III. The corresponding results have been depicted by horizontal spectral acceleration maps with 2 and 10% PE (Probability of Exceedence) in 50 years and by vertical spectral acceleration maps with 10% PE in 50 years. It should be mentioned that there is no recent and previous works for uniform hazard spectra in this region. Most of the existing works in this area are about PGA analysis.
SEISMOTECTONIC STRUCTURE OF TEHRAN
Tehran city is situated on the south plateau of central Alborz Mountain and over alluvium sediments. Its southern parts lie roughly on the northwest corner of Iranian large desert (with mean altitude of 1300 m). The distance of the nearest mountain to this city is less than 10 km (Tochal Mountain with altitude approaching to 3933 m).
In order to evaluate the seismic hazard of a region or zone, all the probable seismic sources must be detected and their potential to produce strong ground motion must be checked.
| Table 1: | Main active faults of Tehran and its vicinity |
The major faults in Tehran region and its vicinity are Mosha fault, North Tehran thrust, Niavaran thrust, North Rey fault, South Rey fault, Kahrizak fault, Garmsar fault and Pishva fault. The list of these faults and their specifications are given in Table 1.
It must be noted that Mmax (Maximum Magnitude) in Table 1 is calculated using Nowroozi relationship (Nowroozi, 1985), which will be explained in other section. The location of these faults with respect to Tehran is shown in Fig. 2a and b. In this regard, all the probable faults (in the radius of 200 km from Tehran) which have been considered in this study are shown in Fig. 2c.
SEISMICITY OF TEHRAN
The seismicity of each region is indicated by the past earthquakes occurred in that region. To obtain the seismotectonic properties, a thorough list of each region's earthquake events must be collected and studied. The earthquakes occurred in Tehran can be categorized in two groups:
| • | Historical earthquakes (earthquakes occurred before the year 1900). |
| • | Instrumentally recorded earthquakes (earthquakes occurred from the year 1900 up to now) |
| Fig. 2: | (a) and (b) active faults of Tehran and its vicinity (Berberian et al. 1983) and (c) active faults considered in this study in the radius of 200 km from Tehran |
Our knowledge of earthquakes that occurred before the 20th century is based on data collection from historic and ancient writings; as a result, overstatements might be present in the data. The first historic seismic event that occurred in this region went back to the 4 centuries BC that destroyed the old Rey city and present Tehran.
Rey City was the largest city near Tehran and before the extension of metropolitan Tehran; it was destroyed completely by several destructive earthquakes. Due to the very short distance of current Tehran to Rey City (The two cities are nearly connected to each other due to the expansion of Tehran), the investigation of the historical earthquakes of Rey and its surroundings can improve the evaluation of the seismic potential of Tehran.
Researchers like Berberian et al. (1983), Nabavi (1978) and Ambraseys and Melville (1982) performed some investigations in this regard and submitted their report. Of all these reports concerning Iranian historic earthquakes catalogue, it appears that Ambraseys and Melville (1982) report is more comprehensive and complete than that of the others. The largest earthquake magnitude is for the earthquake occurred in the year 958 with surface wave magnitude, Ms = 7.7. Its epicenter was between Rey and Taleghan city.
Seismic data after the year 1900 are more important since instruments record them although they might possess different inaccuracies in the location of epicenter and amount of focal depth and earthquake magnitude. These inaccuracies were reduced by the installation of the worldwide seismography network after the year 1963. The list of occurred earthquakes in a radius of 200 km around Tehran is given in appendix. The method of determining and completing these data will be discussed later.
TEHRAN SEISMICITY PARAMETERS
The evaluation of seismicity parameters is carried out based on the seismic data of earthquakes occurred in the region under study and employment of probabilistic methods. The seismic catalogue has been collected in a radius of 200 km around Tehran, assuming that earthquakes follow Poisson distribution. The seismicity parameters, occurrence rates and earthquake PE were calculated using Kijko (2000) method.
SEISMICITY CATALOGUE
For the collection of seismicity data in this study, the list of earthquakes occurred in the radius of 200 km around Tehran was selected and collected. The reason for the application of probabilistic method and its advantage over other methods are for the incompleteness of our seismic data regarding magnitude and focal depth of earthquakes.
Since foreshocks and aftershocks are events that happen before and after earthquakes (main shock) respectively, therefore the complete list of earthquakes in each zone (without the elimination of foreshocks and aftershocks) usually don't follow Poisson distribution, as a result all foreshocks and aftershocks must be excluded. The method which is used to eliminate the foreshocks and aftershocks is the variable windowing method in time and space domains by Gardner and Knopoff (1974).
EARTHQUAKE MAGNITUDE
Due to incompleteness of the magnitude values in the earthquake list, it is necessary to compensate this deficiency. The most appropriate probabilistic method which has been introduced by now in this regard, is the least square method and obtaining the equation of the best fitted line from the data for which both values of MS (Surface Wave Magnitude) and mb (Body Wave Magnitude) have been reported.
Since few numbers of earthquakes with both magnitudes, MS and mb, are reported, in this study the relationship presented by IROCLD (1994), is applied. The form of this relationship is:
MS = 1.2mb
- 1.29 |
(1) |
Therefore the usage of the relationship (1) completed the MS magnitude of the data in the catalogue.
EVALUATION OF SEISMIC PARAMETERS
The calculations for the evaluation of seismic parameters are performed based on the occurrence of earthquakes and their magnitude-frequency relationship. Up to now several methods have been presented for the evaluation of this relationship and calculation of its constant coefficients which specify the seismic parameters. Almost all of them are based on Gutenberg-Richter (1954) relationship. Due to the very high importance of these parameters in seismic hazard evaluation, in this study the new Kijko (2000) method has been employed which is based on doubly truncated Gutenberg-Richter relationship and the maximum likelihood estimation method. The assumptions of Kijko (2000) method are as follows:
| • | Earthquakes must follow Poisson distribution, which implies they must be independent in both time and space domain. |
| • | Seismicity must be homogenous in the extent under study and this extent must have specific seismic properties. |
EVALUATION OF SEISMIC PARAMETERS BY KIJKO METHOD
The maximum likelihood estimation is the proper method for the evaluation of seismicity parameters of Iran due to the fact that the amount of Iranian seismic data inaccuracy is not equal in different times. Considering the lack of existence of proper seismic data and the low precision of the existing data, it would be impossible to relate the occurrence of earthquakes to their causative source. Therefore, the seismicity parameters of each seismic source cannot be obtained. As a result, in this study the seismic parameters have been obtained for Tehran city in a radius of 200 km for whole faults, which uniform seismicity has been assumed for the unit length of all faults.
In the maximum likelihood estimation method, it is possible to use historical and instrumentally recorded data at the same time. The bases of Kijko computer program (Kijko, 2000) are the utilization of maximum value distribution function for historical data with low precision and large magnitude, doubly truncated Gutenberg- Richter function for instrumentally recorded earthquakes and maximum likelihood estimation method.
In this method, mainly 3 groups of earthquakes are considered:
| • | Historical earthquakes (prior to the year 1900) for which the magnitude inaccuracy is considered between 0.3 and 0.5 (Case 1) |
| • | Instrumentally recorded earthquakes between the years 1900 and 1963 (The time of worldwide seismography network installation) with magnitude inaccuracy of 0.2 and the threshold magnitude of Ms = 4.5 (Case 2) |
| • | Instrumentally recorded earthquakes from 1964 up to now, with magnitude inaccuracy of 0.1 and threshold magnitude of Ms = 4.5 (Case 3) |
In order to investigate the seismicity of this region and the effect of historical and instrumentally recorded data over seismicity parameters, the Kijko method (Kijko, 2000) is applied in three cases and the results are presented in Table 2.
| Fig. 3: | Annual rates estimated by Kijko method for Tehran and its vicinity |
| Table 2: | Seismicity parameters in different cases for Tehran |
In case 1, only the instrumentally recorded earthquakes have been used for evaluating the seismicity parameters. In case 2, only the historical earthquakes have been employed and in case 3, the combination of historical earthquakes (with maximum value distribution) and instrumentally recorded earthquakes (with doubly truncated distribution) has been applied. The annual average occurrence rate of earthquake versus magnitude for earthquakes with magnitude greater than MS = 4.5 in the extent of 200 km around Tehran is shown in Fig. 3 based on these investigations and the performed calculations with Kijko method (Kijko, 2000).
The maximum expected magnitude for Tehran based on this method is 7.8±0.5.
It must be noted that annual average occurrence rate is the most important seismicity parameter for the calculations of maximum spectral acceleration values in the computer program SEISRISK III (Bender and Perkins, 1987).
Furthermore, the utilization of historical earthquakes (for extending the time domain of earthquake occurrence list and increasing the authenticity of the obtained results) and the instrumentally recorded earthquake list (for their better preciseness and completeness) improve the authenticity of the results. Therefore in this study, the main emphasis is on the simultaneous usage of these two catalogues (Case 3) and all the calculations are based on the seismicity parameters (β: Seismicity Coefficient, λ: Annual Rate) obtained from the case 3 (Fig. 3).
EVALUATION OF SEISMIC HAZARD
In order to evaluate the strong ground motion parameters (in this study, the values of maximum spectral acceleration), probabilistic seismic hazard analysis method has been used. In this method, seismicity parameters (β, λ) are assigned to the seismic sources (which were modeled as line sources) based on the seismicity investigations in the extent under consideration. λ is divided to the total length of all faults to obtain the seismicity of the unit length of each fault and β for the unit length of each fault is the same as β for the total length of all faults. Then based on earthquake magnitude, distance of epicenter or hypocenter from site and application of an appropriate attenuation relationship, maximum values of seismic strong ground motion parameters at the corresponding site will be evaluated. It is very important to pay special attention to the following items for properly evaluating the interested parameter (spectral acceleration) and performing seismic hazard analysis:
| • | Selection of an appropriate attenuation relationship |
| • | Modeling of seismic sources |
| • | Evaluation of seismic potential of each source |
| • | Determination of the site soil type |
ATTENUATION RELATIONSHIP
One of the most important steps of probabilistic seismic hazard analysis is the selection of attenuation relationship. These relationships express the relation of ground motion parameters with magnitude, distance and in some cases other parameters; moreover, they are affected by many factors, the most important of which are as follows:
| • | Source specifications, magnitude, fault rupture type and distance to the seismogenic sources. |
| • | Wave path, reflection, refraction and energy absorption due to the properties of materials through which the waves pass. |
| • | Geology and topology of site. |
Selection of appropriate attenuation relationship is very important in validity and reliability of the analysis results therefore, there are some important notes that must be paid attention for the selection of attenuation relationship. For instance, in this study, our relationship must be spectral, must relate to the region under study as much as possible, must observe the requirements of magnitude domain and type, must cover an extent of 200 km from distance point of view and it must consider the different soil classifications of the region from the soil type and classification point of view.
Based on the mentioned remarks, two horizontal and ones vertical attenuation relationships were found from the existing attenuation relationship list to satisfy our demands. The horizontal relationships are Ambraseys et al. (1996) and Berge-Thierry et al. (2003). The vertical relationship is Ambraseys and Simpson (1996). Horizontal relationships were applied using the logic tree method with the weight of 0.5.
In Ambraseys et al. (1996) and Ambraseys and Simpson (1996), a large set of seismic data pertaining to Europe zone and its vicinity (Middle East) has been used for the development of mentioned equations to calculate maximum horizontal and vertical spectral accelerations. For the development of horizontal attenuation relationship, Iranian seismic records including Naghan, Tabbas and Manjil were used which is one of its advantages. In this relationship, the magnitude scale is Ms and magnitude range is assumed to be 4≤Ms≤7.5. The focal depth of 81% of the applied records in this relationship is between 5 and 15 km. The site soil types considered in this relationship are in the form of 4 categories of soil based on the average velocity of shear wave in the depth of 30 meters, similar to the Iranian Code of Practice for Sciesmic Resistant Design of Buildings (2005). The general form of these horizontal and vertical attenuation relationships is:
Log Y = C1(T)+C2(T)MS+C4(T)
Log(r)+CASa+CSSS+σP |
(2) |
| Y | = | The maximum spectral acceleration, |
| Ms | = | Surface wave magnitude, |
| r | = | |
| Sa and Ss | = | Site effects, |
| T | = | Period, |
| σ | = | standard deviation. |
The values of coefficients: C1 (T), C2 (T), h0, C4 (T), CA, CS and σ are calculated for periods from 0.1 to 2 sec.
In Berge-Thierry et al. (2003) also, a large set of European strong motion records and American records has been used for the development of mentioned equation to calculate maximum horizontal spectral accelerations. For the development of horizontal attenuation relationship, 37 of Iranian seismic records including Tabbas and Manjil were used which is one of its advantages. In this relationship, the magnitude scale is MS and its range is 4≤Ms≤7.9. The site soil types considered in this relationship are in the form of 2 categories of soil based on the average velocity of shear wave in the depth of 30 m. The general form of this horizontal attenuation relationship is:
LogPSA(f) = a(f)M + b(f)d - Logd
+ C1,2(f) |
(3) |
| PSA | = | The maximum spectral acceleration, |
| M | = | Surface wave magnitude, |
| d | = | Hypocentral distance, |
| C1 and C2 | = | Site effects and the values of coefficients: a(f) and b(f) are calculated for frequencies (f) from 0.1 to 34 Hz. |
RELATIONSHIP BETWEEN EARTHQUAKE MAXIMUM MAGNITUDE AND FAULT RUPTURE LENGTH
Several empirical relationships have been presented to express the relation between fault rupture and the earthquake magnitude, an example of which is Nowroozi relationship (Nowroozi, 1985). Nowroozi presented the following empirical relationship after the study of 10 severe earthquakes in Iran and the investigation of ruptures of active faults like Zagros, North Alborz, North Tabriz, Zafre in Isfahan, Dehshir in south west of Isfahan, Shahre Babak in Kerman and Dorouneh in Makran (Eq. 4):
MS = 1.259 + 1.244Log
(L) |
(4) |
| Ms | = | Surface wave magnitude, |
| L | = | Half of rupture length in meter. |
SITE SOIL TYPE
For characterizing the soil type of north part of Tehran, the average shear wave velocity (Vs) distribution map with depth between 0 and 30 m conforming to Iranian Code of Practice for Sciesmic Resistant Design of Buildings (2005), which was developed in the seismic macrozonation complementary research project for Tehran by Jafari (2002), has been used. Based on this map, there are 2 soil types in northern parts of Tehran. One is Rocky (vs >750 m sec–1) and another one is Stiff (360 m sec–1 < vs <750 m sec–1). The different municipality zones of north parts of Tehran city with the corresponding soil conditions (Table 3 and Fig. 4)
| Fig. 4: | Soil type of north part of Tehran based on 30 m averaged shear wave velocity (vs) (Jafari, 2002) |
| Table 3: | Different municipality zones of north parts of Tehran city with this soil condition |
PROBABILISTIC SEISMIC HAZARD ANALYSIS
For the seismic hazard probabilistic evaluation, the software SEISRISK III (Bender and Perkins, 1987) was utilized to calculate the maximum spectral acceleration in the structure lifetime. The calculated values can be shown in the form of iso-acceleration lines for each period with a specific hazard level in the structure lifetime.
In probabilistic seismic hazard analysis, the strong ground motion values are generally considered for different seismic hazard levels (different PE). In this study, based on the Seismic rehabilitation code for existing buildings in Iran (IIEES, 2002), for horizontal acceleration, 2 hazard levels were considered.
Hazard level 1: This hazard level is based on 10% PE in 50 years which is equivalent to the return period of 475 years. Earthquake with this hazard level is called Design Basis Earthquake (DBE) in Iranian Code of Practice for Sciesmic Resistant Design of Buildings (2005).
Hazard level 2: This hazard level is based on 2% PE in 50 years which is equivalent to the return period of 2475 years. Earthquake with this hazard level is called Maximum Probable Earthquake (MPE).
| Fig. 5: | 0.3 s horizontal spectral acceleration (g) with 10% PE in 50 years |
| Fig. 6: | 1.5 s horizontal spectral acceleration (g) with 10% PE in 50 years |
| Fig. 7: | 0.3 s horizontal spectral acceleration (g) with 2% PE in 50 years |
| Fig. 8: | 1.5 s horizontal spectral acceleration (g) with 2% PE in 50 years |
| Fig. 9: | 0.3 s vertical spectral acceleration (g) with 10% PE in 50 years |
| Fig. 10: | 1.5 s vertical spectral acceleration (g) with 10% PE in 50 years |
For vertical accelerations, only hazard level 1 has been used. Before the calculations, a grid of sites must be considered in the region where seismic hazard analysis will be performed. For this purpose a grid of 16x9 or 144 sites shall be considered. The longitude distance of these sites to each other is 2.2 km and the latitude distance is 1.8 km. Seismic hazard analysis shall be performed for each of these sites.
As a result, our outputs are maximum horizontal spectral acceleration with 2% and 10% PE and maximum vertical spectral acceleration with 10% PE in 50 years lifetime of structure considering the mentioned periods. Some instead of Instances of horizontal and vertical spectral accelerations are presented in Fig. 5-10.
UNIFORM HAZARD SPECTRA
As the name implies, uniform hazard spectrum is a response spectrum whose amplitudes represent a uniform level of probabilistic seismic hazard at all periods or frequencies. The method is that for each point of the grid with a specific hazard level, there is a spectral acceleration. If for each point and specific hazard level, a graph is drawn with these periods and the corresponding spectral accelerations as its abscissa and ordinates, respectively, then the resulting graph is a uniform hazard spectrum for that point. Instances of uniform hazard mean and mean plus one standard deviation spectra for horizontal and vertical components with different seismic hazard levels as well as Iranian Code of Practice for Sciesmic Resistant Design of Buildings (2005) spectrum are presented in Fis. 11 to 26 for different municipality zones of north Tehran and regions with the same soil type.
Iranian Code of Practice for Sciesmic Resistant Design of Buildings (2005) uses the equation below for obtaining horizontal spectral acceleration (SA) with 10% PE in 50 years lifetime of structure considering the mentioned periods:
| Fig. 11: | Uniform hazard spectrum for municipality zones 1 with rock soil |
| Fig. 12: | Uniform hazard spectrum for municipality zones 2 with rock soil |
| Fig. 13: | Uniform hazard spectrum for municipality zones 2 with stiff soil |
| Fig. 14: | Uniform hazard spectrum for municipality zones 3 with rock soil |
| Fig. 15: | Uniform hazard spectrum for municipality zones 3 with stiff soil |
| Fig. 16: | Uniform hazard spectrum for municipality zones 4 with rock soil |
| Fig. 17: | Uniform hazard spectrum for municipality zones 4 with stiff soil |
| Fig. 18: | Uniform hazard spectrum for municipality zones 5 with rock soil |
| Fig. 19: | Uniform hazard spectrum for municipality zones 5 with stiff soil |
| Fig. 20: | Uniform hazard spectrum for municipality zones 6 with rock soil |
| Fig. 21: | Uniform hazard spectrum for municipality zones 7 with rock soil |
| Fig. 22: | Uniform hazard spectrum for municipality zones 8 with rock soil |
| Fig. 23: | Uniform hazard spectrum for municipality zones 13 with rock soil |
| Fig. 24: | Uniform hazard spectrum for municipality zones 22 with stiff soil |
| Fig. 25: | Uniform hazard spectrum for north of Tehran with rock soil |
| Fig. 26: | Uniform hazard spectrum for north of Tehran with stiff soil |
SA = A x B |
(5) |
| A | = | The design basis acceleration over bedrock (a suggested value for that is A = 0.35 g for the entire Tehran region) |
| B | = | The response factor calculated by the simultaneous consideration of the amplifying effects of soil deposit and the structural response with respect to earthquake accelerogram. |
DETERMINATION OF RATIO AMONG UNIFORM HAZARD SPECTRA
As 2 and 10% horizontal and 10% vertical uniform hazard spectra have been obtained for different parts of north Tehran, it would be a good idea to determine the ratio between them. As a result, it would be possible to obtain 2% horizontal and 10% vertical uniform hazard spectra for any point of north Tehran by multiplying these ratios and the 10% horizontal uniform hazard spectrum. Initially, an investigation must be performed over the maps of 2 and 10% horizontal and 10% vertical uniform hazard spectra with the considered periods and then check to see whether the spatial location of points with high acceleration and also those with low acceleration at different hazard levels for each period is the same or not. If it is the same, then these ratios can be determined otherwise; it would not be possible to determine them. It was made clear after investigating 2 and 10% horizontal and 10% vertical uniform hazard spectra that at each period, the spatial location of the mentioned points are approximately the same and it has an acceptable correlation, therefore the ratio between 2% horizontal to 10% horizontal and also between 10% vertical to 10% horizontal can be obtained.
| Fig. 27: | Ratio of 2% (H) to 10% (H) uniform hazard spectrums for 0.3 s |
| Fig. 28: | Ratio of 2% (H) to 10% (H) uniform hazard spectrums for 1.5 s |
| Fig. 29: | Ratio of 10% (V) to 10% (H) uniform hazard spectrums for 0.3 s |
| Fig. 30: | Ratio of 10% (V) to 10% (H) uniform hazard spectrums for 1.5 s |
The calculated values of this ratio can be shown in the form of iso-ratio lines for each period with their specification. Some instances of the ratio between 2% horizontal to 10% horizontal and also between 10% vertical to 10% horizontal are presented in Fig. 27-30.
CONCLUSIONS
In this study, probabilistic seismic hazard evaluation was performed on a grid of 16*9 points in north part of Tehran using SEISRISK III. The corresponding results have been depicted by horizontal spectral acceleration maps with 2 and 10% PE (Probability of Exceedence) in 50 years and by vertical spectral acceleration maps with 10% PE in 50 years. By paying attention to the uniform hazard spectra curves for different periods, it can be noticed that whenever soil type changes from rocky to stiff (Fig. 4), there is an increase in the spectral acceleration in that region. However in eastern north parts of Tehran, due to approaching to the North Tehran faults and also being situated over small or large faults of the region (Fig. 2c), there will be higher spectral accelerations than other points. Moreover, by viewing the uniform hazard spectra, it can be noticed that the horizontal spectral acceleration has the highest value for periods 0.2 and 0.3 sec. The acceleration increases up to the period 0.3 sec and then it gradually decreases.
One of the most important results of this research is obtaining equation of ratios for 2% over 10% horizontal uniform spectra in 50 years lifetime of structure and also 10% vertical over 10% horizontal spectra in 50 years lifetime of structure. Accordingly, the 2% horizontal and 10% vertical uniform hazard spectra can be obtained by multiplying these ratios to the 10% horizontal uniform hazard spectrum for each point of north Tehran.
NOTATION
| a(f) | = | Values of coefficients. |
| A | = | Design basis acceleration over bedrock. |
| ave | = | Average. |
| ave + sigma | = | Average + one standard deviation. |
| b(f) | = | Values of coefficients. |
| B | = | Response factor. |
| C1,2 (f) | = | Site effects coefficients. |
| C1 (T) | = | Constant. |
| C 2 (T) | = | Constant |
| C4 (T) | = | Constant. |
| CA | = | Constant. |
| CS | = | Constant. |
| d | = | Hypocentral distance. |
| D | = | Shortest horizontal distance from site to the. epicenter. |
| f | = | Frequency. |
| h0 | = | Focal depth. |
| H | = | Horizontal component of earthquake. |
| L | = | Half of rupture length. |
| Lat. | = | Latitude. |
| Long. | = | Longitude. |
| mb | = | Body wave magnitude. |
| Mmax | = | Maximum magnitude. |
| MS | = | Surface wave magnitude. |
| PE | = | Probability of Exceedence. |
| PSA | = | Maximum spectral acceleration. |
| Sa | = | Site effect. |
| SA | = | Horizontal spectral acceleration. |
| SAH | = | Horizontal uniform hazard spectral acceleration. |
| SAV | = | Vertical uniform hazard spectral acceleration. |
| Ss | = | Site effect. |
| T | = | Period. |
| V | = | Vertical component of earthquake. |
| Vs | = | Average shear wave velocity. |
| Y | = | Maximum spectral acceleration. |
| β | = | Seismicity coefficient. |
| λ | = | Annual rate. |
| σ | = | Standard deviation. |
APPENDIX
| Earthquake catalogue |
AMB: Ambraseys, N. N., Melville, CP; BCIS: Bureau Centrel International de Seismologie, Strasburg, France, BER, M: Berberian, Geological and Mining Survey of Iran; BHRC: Building and Housing Research Center, CCP: Atlas USSR Earthquake; CGS: U.S. Coast and Geodetic Survey, USA; FS (BAN): Fisher; HFSI: Hagfors, Sweden; ISC: International Seismological Center, UK; MOS: Moscow, USSR; NOW: Nowroozi; NEIC: National Earthquake Information Center, USA; NEIS: National Earthquake Information Service, USA; PT: Publication of Institute of Geophysics-Tehran University; USGS: United State Geological Survey
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