INTRODUCTION
Iran, one of the most seismic countries of the world, is situated over
the HimalayanAlpied 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 highrise buildings, important structures and
the flourishing of highrise building constructions. The extent of the
region under study is 450 km^{2}, 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 pastrecorded
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 M_{max} (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 M_{S} (Surface Wave Magnitude) and m_{b}
(Body Wave Magnitude) have been reported.
Since few numbers of earthquakes with both magnitudes, M_{S}
and m_{b}, are reported, in this study the relationship presented
by IROCLD (1994), is applied. The form of this relationship is:
M_{S} = 1.2m_{b}
 1.29 
(1) 
Therefore the usage of the relationship (1) completed the M_{S}
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 magnitudefrequency 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 GutenbergRichter
(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 GutenbergRichter
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 M_{S} = 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 BergeThierry 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 M_{s} and magnitude
range is assumed to be 4≤M_{s}≤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 = C_{1}(T)+C_{2}(T)M_{S}+C_{4}(T)
Log(r)+C_{A}S_{a}+C_{S}S_{S}+σP 
(2) 
Where:
Y 
= 
The maximum spectral acceleration, 
M_{s} 
= 
Surface wave magnitude, 
r 
= 
in
which D is the shortest horizontal distance from site to the epicenter
and h0 is the focal depth, 
S_{a} and S_{s} 
= 
Site effects, 
T 
= 
Period, 
σ 
= 
standard deviation. 
The values of coefficients: C_{1} (T), C_{2} (T), h_{0},
C_{4} (T), C_{A}, C_{S} and σ are calculated
for periods from 0.1 to 2 sec.
In BergeThierry 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 M_{S}
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
+ C_{1,2}(f) 
(3) 
Where:
PSA 
= 
The maximum spectral acceleration, 
M 
= 
Surface wave magnitude, 
d 
= 
Hypocentral distance, 
C_{1} and C_{2} 
= 
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):
M_{S} = 1.259 + 1.244Log
(L) 
(4) 
Where:
M_{s} 
= 
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 isoacceleration 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. 510.
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
(S_{A}) 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 
Where:
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 isoratio
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. 2730.
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. 
C_{1},_{2} (f) 
= 
Site effects coefficients. 
C_{1} (T) 
= 
Constant. 
C_{ 2} (T) 
= 
Constant 
C_{4} (T) 
= 
Constant. 
C_{A} 
= 
Constant. 
C_{S} 
= 
Constant. 
d 
= 
Hypocentral distance. 
D 
= 
Shortest horizontal distance from site to the. epicenter. 
f 
= 
Frequency. 
h_{0} 
= 
Focal depth. 
H 
= 
Horizontal component of earthquake. 
L 
= 
Half of rupture length. 
Lat. 
= 
Latitude. 
Long. 
= 
Longitude. 
m_{b} 
= 
Body wave magnitude. 
M_{max} 
= 
Maximum magnitude. 
M_{S} 
= 
Surface wave magnitude. 
PE 
= 
Probability of Exceedence. 
PSA 
= 
Maximum spectral acceleration. 
S_{a} 
= 
Site effect. 
S_{A} 
= 
Horizontal spectral acceleration. 
S_{AH} 
= 
Horizontal uniform hazard spectral acceleration. 
S_{AV} 
= 
Vertical uniform hazard spectral acceleration. 
S_{s} 
= 
Site effect. 
T 
= 
Period. 
V 
= 
Vertical component of earthquake. 
V_{s} 
= 
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 GeophysicsTehran University; USGS: United State Geological Survey
