Earthquake Risk Assessment for Tehran, Iran

: The megacity of Tehran, the capital of Iran, is subjected to a high earthquake risk. Located at the central part of the Alpine–Himalayan seismic belt, Tehran is surrounded by several active faults that show some M7 + historical earthquake records. The high seismic hazard in combination with a dense population distribution and several vulnerability factors mean Tehran is one of the top 20 worldwide megacities at a high earthquake risk. This article aims to prepare an assessment of the present-day earthquake risk in Tehran. First, the earthquake risk components including hazard, exposure, and vulnerability are evaluated based on some accessible GIS-based datasets (e.g., seismicity, geology, active faults, population distribution, land use, urban fabric, buildings’ height and occupancy, structure types, and ages, as well as the vicinity to some critical infrastructures). Then, earthquake hazard maps in terms of PGA are prepared using a probabilistic approach as well as a surface rupture width map. Exposure and vulnerability maps are also provided deterministically in terms of population density and hybrid physical vulnerability, respectively. Finally, all these components are combined in a spatial framework and an earthquake risk map is provided for Tehran.


Introduction
Earthquakes are one of the most powerful natural phenomena that can impose substantial human and economic losses on societies. Since 1980, earthquakes have accounted for 12.2% of all catastrophic natural hazards worldwide, contributing to 56.2% of all casualties and 25.2% of financial losses in total [1]. More than 800,000 fatalities, 1.4 million injuries, 30 million made homeless, as well as approximately USD 950 billion in economic losses are consequences of destructive earthquakes during the same period [2]. The top five countries that have been most frequently affected by damaging earthquakes are China, Indonesia, Iran, Turkey, and Japan, with 16%, 10%, 8%, 4.5%, and 4% of all damaging earthquakes, respectively [3,4].
Over the last decades, population growth along with unplanned rapid urbanization and poor land management have been underlying disaster risk drivers, so that leading to the accumulation of life and property assets in potentially earthquake-prone areas and thus resulting in an increase in earthquake risk [5][6][7]. According to the latest global seismic risk map [8][9][10], there are currently 17 megacities around the world with a population of more than 10 million that are placed at the highest risk level, including Tokyo, Jakarta, Delhi, Beijing, Manila, Mexico City, Osaka, Los Angeles, Dhaka, Chengdu, Karachi, Tehran, Istanbul, Lahore, Nagoya, Bogota, and Lima.
One of the best efforts to address the impact of earthquakes on a region, especially in densely populated urban areas, is to conduct earthquake risk assessments. In this regard, a common practice to conceptually formulate earthquake risk is a simple convolution of three components [11][12][13][14][15][16], as below: active zone, where is under huge tectonic stresses due to the northward convergence of central Iran toward Eurasia. At the longitude of Tehran, Alborz accommodates 6-10 mm of shortening per year [50][51][52].

Active Faulting
As a result of such active tectonics, Tehran is surrounded by several major faults, also embracing some inner-city active faults (Figure 1). These faults mainly show both reverse and strike-slip mechanisms. Here is a brief description of some the most important active faults inside or in the vicinity of Tehran along with their main specific features [53,54]: • North Tehran: The most prominent active tectonic structure in Tehran; E-W strike; north-dipping fault surface; length of 175 km with a predominant thrust mechanism along its 110-km western segment, and a predominant left-lateral strike-slip mechanism along its 65-km eastern segment; average slip rate of~0.3 mm yr −1 . in Damavand (60 km northeast of Tehran) in 2020, respectively. Based on the historical/instrumental seismicity records in Alborz seismotectonic zone, where Tehran belongs to, the beginning years for completeness of earthquake magnitudes include 850, 1440, 1680, 1800, and 1955 for the magnitude ranges of 5.5 < Mw, 5.0 < Mw ≤ 5.5, 4.5 < Mw ≤ 5.0, 4.0 < Mw ≤ 4.5, and Mw ≤ 4.0, respectively [63]. The trend of historical and instrumental seismicity along with limited paleoseismic data and the regional fault map suggest that the megacity of Tehran is currently located on a seismic gap in the south of Alborz [64]. It is worth mentioning that the state-of-the-art studies e.g., [65,66] imply the importance of time-dependent models which incorporate the most basic physics of the earthquake cycles and gaps in order to calculate time-dependent conditional probabilities. Therefore, the observed seismic gap beneath Tehran will have a considerable contribution to future time-dependent seismic hazard and risk models in this region.

Geological Structure
In terms of geology, Tehran lays on the Quaternary alluvial deposits, which have the potential of seismic wave amplification and increase of shaking during an earthquake. These sediments are usually classified into four stratigraphic units named from A to D, as below [67] (Figure 1): • Unit A: Also known as the 'Hezardarreh' formation, this unit is the oldest deposit in Tehran   [55,56] (Figure 1).
Besides historical documents, several paleoseismological trench investigations have been carried on Tehran's adjacent faults in order to decode possible ancient earthquakes. Trench analysis and dating of fault-related sediments have revealed several important large-magnitude earthquakes around Tehran, including events related to the North Tehran [57], Mosha [58,59], Taleghan [60], Kahrizak-Rey [61], and Pishva [62] faults. For instance, the paleoseismological study on the North Tehran fault [57] has revealed seven surface-rupturing events with magnitudes between 6.1 and 7.2 and a mean recurrence interval of about 3800 years.
In the modern era of seismology (since 1900), there have been also several records of large-magnitude instrumental earthquakes around Tehran, including the 1930 Ah-Mobarakabad (M w 5.2), 1962 Buin Zahra (M w 7.1), 1990 Manjil-Rudbar (M w 7.4), and 2004 Baladeh (M w 6.3) earthquakes. Recently, two M w 5.2 and M w 5.1 events have occurred in Malard (40km west of Tehran) in 2017, and in Damavand (60 km northeast of Tehran) in 2020, respectively. Based on the historical/instrumental seismicity records in Alborz seismotectonic zone, where Tehran belongs to, the beginning years for completeness of earthquake magnitudes include 850, 1440, 1680, 1800, and 1955 for the magnitude ranges of 5.5 < M w , 5.0 < M w ≤ 5.5, 4.5 < M w ≤ 5.0, 4.0 < M w ≤ 4.5, and M w ≤ 4.0, respectively [63]. The trend of historical and instrumental seismicity along with limited paleoseismic data and the regional fault map suggest that the megacity of Tehran is currently located on a seismic gap in the south of Alborz [64]. It is worth mentioning that the state-of-the-art studies e.g., [65,66] imply the importance of time-dependent models which incorporate the most basic physics of the earthquake cycles and gaps in order to calculate time-dependent conditional probabilities. Therefore, the observed seismic gap beneath Tehran will have a considerable contribution to future time-dependent seismic hazard and risk models in this region.

Geological Structure
In terms of geology, Tehran lays on the Quaternary alluvial deposits, which have the potential of seismic wave amplification and increase of shaking during an earthquake. These sediments are usually classified into four stratigraphic units named from A to D, as below [67] (Figure 1):

•
Unit A: Also known as the 'Hezardarreh' formation, this unit is the oldest deposit in Tehran with a thickness of~1200 m, forming a long anticline throughout the northeast-east of Tehran. Having a light gray in color and an almost vertical bedding (dip~90 • ), this unit is mainly made of conglomerates with a well-developed lime carbonate cementation and is considered to be of the Pliocene-Pleistocene age.

•
Unit B: This unit, also known as the 'Kahrizak' formation, unconformably overlies on the eroded surfaces of unit A. The thickness of unit B varies from 10 to 60 m, and its bedding is generally horizontal with a maximum dip of 15 • . This deposit has a heterogeneous mechanical resistance and changeable porosity and its age is estimated to be~700,000 years.

•
Unit C: Since a considerable part of Tehran has been built on this unit, it is also called as the 'Tehran' formation, and includes conglomeratic young alluvial fan deposits. The maximum thickness of this formation is about 60 m, and its age is estimated to be~50,000 years. Its bedding indicates an almost horizontal slope. Unit C has higher cementation than its underlying and overlying stratigraphic units (B and D formations, respectively).
• Unit D: Known as the 'Recent' alluvium, this unit is the youngest stratigraphic unit within the Tehran region and its formation dates back to the Holocene epoch (11,500 years). The thickness of this unit is less than 10 m and its color is gray to dark gray. This unit has an alluvial and fluvial origin, and it composes of poorly consolidated to unconsolidated cementation.

Methodology
As mentioned in the introduction, earthquake risk can be quantified as the convolution of three elements including hazard, exposure, and vulnerability. A brief overview of the methodology we have adopted in this study and its key components are summarized by the flowchart in Figure 2. The process of risk quantification in this study starts with a time-independent probabilistic seismic hazard assessment (PSHA) for Tehran, the output of which is a Peak Ground Acceleration (PGA), accompanied by a surface rupture width map of the faults in Tehran. Then, exposure is presented as a population density map derived from the accurate population distribution in Tehran. To model vulnerability, we consider a mixture of several sub-layers and combine them in a classification framework. Both exposure and vulnerability components are evaluated using a deterministic approach. Finally, based on the concept of a GIS-based 3D matrix-the elements of which constitute the same risk elements (hazard, exposure, and vulnerability)-we will combine the classified values of the components and derive the final risk value. The details about the computational steps of this methodology are described in the following sections. bedding indicates an almost horizontal slope. Unit C has higher cementation than its underlying and overlying stratigraphic units (B and D formations, respectively). • Unit D: Known as the 'Recent' alluvium, this unit is the youngest stratigraphic unit within the Tehran region and its formation dates back to the Holocene epoch (11,500 years). The thickness of this unit is less than 10 m and its color is gray to dark gray. This unit has an alluvial and fluvial origin, and it composes of poorly consolidated to unconsolidated cementation.

Methodology
As mentioned in the introduction, earthquake risk can be quantified as the convolution of three elements including hazard, exposure, and vulnerability. A brief overview of the methodology we have adopted in this study and its key components are summarized by the flowchart in Figure 2. The process of risk quantification in this study starts with a time-independent probabilistic seismic hazard assessment (PSHA) for Tehran, the output of which is a Peak Ground Acceleration (PGA), accompanied by a surface rupture width map of the faults in Tehran. Then, exposure is presented as a population density map derived from the accurate population distribution in Tehran. To model vulnerability, we consider a mixture of several sub-layers and combine them in a classification framework. Both exposure and vulnerability components are evaluated using a deterministic approach. Finally, based on the concept of a GIS-based 3D matrix-the elements of which constitute the same risk elements (hazard, exposure, and vulnerability)-we will combine the classified values of the components and derive the final risk value. The details about the computational steps of this methodology are described in the following sections.

Hazard
Earthquake hazard in a region is usually defined as the level of ground shaking with a certain chance of being exceeded over a given period of time (typically, 475-year return period, which is associated with a probability exceeding 10% in 50 years). In this study, we prepare two maps as the hazard component to feed the risk calculations: (1) surface PGA map which provides the level of

Hazard
Earthquake hazard in a region is usually defined as the level of ground shaking with a certain chance of being exceeded over a given period of time (typically, 475-year return period, which is associated with a probability exceeding 10% in 50 years). In this study, we prepare two maps as the hazard component to feed the risk calculations: (1) surface PGA map which provides the level of ground motion considering the local site response in Tehran, and (2) surface rupture width map which indicates the potential rupture areas around active faults in Tehran.

Surface PGA
To develop a seismic hazard map for the megacity of Tehran, we use the time-independent probabilistic seismic hazard analysis (PSHA). PSHA is one of the most widely used approaches that quantifies the rate or probability of exceeding various ground motion levels given all possible earthquakes. This method explicitly considers uncertainties in earthquake size, location, and time of occurrence [68,69].
As the first step of the PSHA study, it is necessary to determine seismogenic sources which impose seismic hazard to a region. In general, a seismogenic source model within an area consists of several individual seismic sources, which have experienced, or expected to potentially have, seismic activities. Each source has its own specific characteristics in terms of geometry, seismicity behavior, and geological features. This model can be prepared based on area sources, linear sources (faults), or a mixture of them. To determine seismic sources, we have considered area sources within a region with a 150-km radius from the center of the megacity of Tehran. Our primary data consists of the faults [53,54] and an updated version of the historical and instrumental earthquake catalog (400 B.C.-2020) [63]. On the basis of the standard criteria mentioned in the EMME project [70], area source boundaries are delineated around Tehran ( Figure 3). ISPRS Int. J. Geo-Inf. 2020, 9, x FOR PEER REVIEW 6 of 19 ground motion considering the local site response in Tehran, and (2) surface rupture width map which indicates the potential rupture areas around active faults in Tehran.

Surface PGA
To develop a seismic hazard map for the megacity of Tehran, we use the time-independent probabilistic seismic hazard analysis (PSHA). PSHA is one of the most widely used approaches that quantifies the rate or probability of exceeding various ground motion levels given all possible earthquakes. This method explicitly considers uncertainties in earthquake size, location, and time of occurrence [68,69].
As the first step of the PSHA study, it is necessary to determine seismogenic sources which impose seismic hazard to a region. In general, a seismogenic source model within an area consists of several individual seismic sources, which have experienced, or expected to potentially have, seismic activities. Each source has its own specific characteristics in terms of geometry, seismicity behavior, and geological features. This model can be prepared based on area sources, linear sources (faults), or a mixture of them. To determine seismic sources, we have considered area sources within a region with a 150-km radius from the center of the megacity of Tehran. Our primary data consists of the faults [53,54] and an updated version of the historical and instrumental earthquake catalog (400 B.C.-2020) [63]. On the basis of the standard criteria mentioned in the EMME project [70], area source boundaries are delineated around Tehran ( Figure 3). Then, the characteristics of these seismic sources are modeled using recurrence relationships. By application of the algorithms mentioned in [71][72][73], seismicity parameters including the b-value of the Gutenberg-Richter relation [74], annual mean occurrence rate (λ), and maximum possible magnitude, (Mmax) are evaluated for each area source (Table 1). It should be noted that the Mmax is estimated based on the maximum observed historical/instrumental earthquake and the assessment of maximum probable earthquake for a seismic source using empirical relationships between the magnitude and fault length. In this study, two empirical relationships were used to calculate the probable Mmax of each area source as follows [75,76]: Then, the characteristics of these seismic sources are modeled using recurrence relationships. By application of the algorithms mentioned in [71][72][73], seismicity parameters including the b-value of the Gutenberg-Richter relation [74], annual mean occurrence rate (λ), and maximum possible magnitude, (M max ) are evaluated for each area source (Table 1). It should be noted that the M max is estimated based on the maximum observed historical/instrumental earthquake and the assessment of maximum probable earthquake for a seismic source using empirical relationships between the magnitude and fault length. In this study, two empirical relationships were used to calculate the probable M max of each area source as follows [75,76]: where L R is the rupture length and equals to 37% of the fault length (L F ) based on the records of the Iranian fault ruptures [75].
The next step of a PSHA approach is the selection of suitable Ground Motion Prediction Equations (GMPEs). GMPEs are proper models to predict the level of ground shaking at a site, which is correlated with other parameters such as magnitude, site-to-source distance, fault mechanism, local site conditions, etc. It is a common practice to use several ranked GMPEs-which are appropriate to regional geology of an area-in order to reduce the level of uncertainty associated with the parameters of PSHA. In this respect, we select three GMPEs [77][78][79] which are consistent with the geological conditions of the study area.
Once the two previous steps have been carried out, they are combined in a probability framework to quantify the earthquake hazard in terms of a ground motion parameter-usually peak ground acceleration (PGA) or spectral accelerations (Sa)-for a specified time period. Here, we avoid mentioning the computational approach of PSHA analysis as it can be found in detail in the main references [68,69]. Subsequently, the hazard model in terms of PGA is produced on the bedrock level considering a 475-year return period ( Figure 4). This map shows a maximum PGA of 0.45-0.5 g in the northern and southern parts of Tehran where are in the vicinity of Mosha, North Tehran and Rey-Kahrizak faults.
On the ground surface level, the PGA might be different, as local soil deposits in an area may amplify the seismic wave field, and considerably change its characteristics. Therefore, to calculate the surface PGA, local soil effects should be taken into account. To do so, we used the classification of V S30 (shear wave velocity in the upper 30 m depth) in Tehran [80], and prepared the hazard model in terms of surface PGA for 475-year return period. The surface hazard map ( Figure 5) shows a maximum PGA of about 0.7 g in the southwest of Tehran. Comparing the two hazard maps on bedrock and surface confirms that the thick soil deposits in different parts of Tehran are able to amplify ground motions during an earthquake. Therefore, central and southern areas of the city are assigned as the highest hazardous zones which are exposed to amplified strong ground motions due to large earthquakes. cracks may occur within active fault zones, leading to large ground-surface displacements and extensive damages to structures.  In this regard, we decided to consider potential areas prone to near-field effects and surface ruptures within fault zones as another aspect of earthquake hazard in Tehran. For this purpose, the main active faults in Tehran ( Figure 6) are classified into three groups, including 'major', 'medium', and 'minor' faults, with a length of more than 15 km, 5-15 km, and less than 5 km, respectively. According to the records of seismic faults of the Iranian Plateau, surface rupture width best fits with the rupture length as the following empirical regression [81]: cracks may occur within active fault zones, leading to large ground-surface displacements and extensive damages to structures.  In this regard, we decided to consider potential areas prone to near-field effects and surface ruptures within fault zones as another aspect of earthquake hazard in Tehran. For this purpose, the main active faults in Tehran ( Figure 6) are classified into three groups, including 'major', 'medium', and 'minor' faults, with a length of more than 15 km, 5-15 km, and less than 5 km, respectively. According to the records of seismic faults of the Iranian Plateau, surface rupture width best fits with the rupture length as the following empirical regression [81]:

Surface Rupture Width
Besides the estimation of ground shaking acceleration, it is necessary to consider that some earthquakes may significantly produce near-field effects on the ground which can be permanent or temporary. For instance, forward/backward directivity, fling step, fault scarps, large ruptures, and cracks may occur within active fault zones, leading to large ground-surface displacements and extensive damages to structures.
In this regard, we decided to consider potential areas prone to near-field effects and surface ruptures within fault zones as another aspect of earthquake hazard in Tehran. For this purpose, the main active faults in Tehran ( Figure 6) are classified into three groups, including 'major', 'medium', and 'minor' faults, with a length of more than 15 km, 5-15 km, and less than 5 km, respectively. According to the records of seismic faults of the Iranian Plateau, surface rupture width best fits with the rupture length as the following empirical regression [81]: where L R is the rupture length and is calcualted as 37% of the total fault length [75]. The coefficient a = −0.45, b = 0.48 with standard deviation of σ = 0.7. Therefore, the surface rupture width of each group is estimated according to the above formula ( Table 2).
thirds of the calculated rupture width on each fault is allocated to the hanging walls, and one-third is assigned to the footwalls of the faults. The rupture widths are shown in pink in Figure 6. It is also noteworthy to mention that detailed geological/neotectonic mapping might better determine the fault rupture width zones. This is because there are sometimes some splays highly localized, or faultpropagating folds which can be ignored under the current computational methodology. These structures are sometimes rather complex in terms of geology and geometry.

Exposure
Exposure is simply defined as the number of people or amounts of assets (e.g., physical, economic, social, environmental, historical, cultural, etc.) exposed to a hazard. Exposure can be evaluated based on observed (census) or estimated data. There are some exposure databases at a global scale such as GPW [85], GRUMP [86], and LandScan [87]. In case of lack of observed records,  It should be noted that the sizes of up-and down-dip rupture widths are constrained by type of faulting, fault geology and geometry, stress distribution, soil thickness above bedrock, etc. [82,83]. In general, a down-dip rupture width on a fault occupies a larger area than an up-dip rupture width. For example, width of the rupture zone on the hanging wall (HW) is almost twice that of the footwall (FW), presenting a HW/ FW ratio of about 2 for simple thrust faults [84]. Therefore, in this study, two-thirds of the calculated rupture width on each fault is allocated to the hanging walls, and one-third is assigned to the footwalls of the faults. The rupture widths are shown in pink in Figure 6. It is also noteworthy to mention that detailed geological/neotectonic mapping might better determine the fault rupture width zones. This is because there are sometimes some splays highly localized, or fault-propagating folds which can be ignored under the current computational methodology. These structures are sometimes rather complex in terms of geology and geometry.

Exposure
Exposure is simply defined as the number of people or amounts of assets (e.g., physical, economic, social, environmental, historical, cultural, etc.) exposed to a hazard. Exposure can be evaluated based on observed (census) or estimated data. There are some exposure databases at a global scale such as GPW [85], GRUMP [86], and LandScan [87]. In case of lack of observed records, exposure databases can be generated using techniques such as high-resolution satellite imagery, LidAR data and building footprint maps e.g., ( [88]).
Over the past 65 years, the population of Tehran province has increased from about 1.5 million to 15 million people (approximately 10 times). It should be considered that exposure is in fact a dynamic concept in urban areas, as it may vary during day and night times. This is the case for large cities such as the Tehran megacity, where there is a floating population of about 4 million people between the night (permanent residents) and the day time (permanent residents and people who come to Tehran from the surrounding cities for daily work).
To investigate exposure in Tehran, we used the 2016 population distribution based on the formal census data [89]. Our dataset includes GIS-based urban building parcels along with the accurate number of inhabitants in each parcel. For the purposes of the study, we first normalized the population distribution by area of parcels and prepared a density map (number of inhabitants per square kilometers). The GIS layer of the population density in Figure  exposure databases can be generated using techniques such as high-resolution satellite imagery, LidAR data and building footprint maps e.g., ( [88]). Over the past 65 years, the population of Tehran province has increased from about 1.5 million to 15 million people (approximately 10 times). It should be considered that exposure is in fact a dynamic concept in urban areas, as it may vary during day and night times. This is the case for large cities such as the Tehran megacity, where there is a floating population of about 4 million people between the night (permanent residents) and the day time (permanent residents and people who come to Tehran from the surrounding cities for daily work).
To investigate exposure in Tehran, we used the 2016 population distribution based on the formal census data [89]. Our dataset includes GIS-based urban building parcels along with the accurate number of inhabitants in each parcel. For the purposes of the study, we first normalized the population distribution by area of parcels and prepared a density map (number of inhabitants per square kilometers). The GIS layer of the population density in Figure

Vulnerability
Seismic risk depends not only on the severity of an earthquake (hazard) or the number of people exposed (exposure), but also on the susceptibility of those people to suffer damages and losses (vulnerability). In this respect, vulnerability analysis plays an important, challenging role as the third part of the risk assessment procedure.
Vulnerability is a complex multi-dimensional concept that can cover a wide range of different components (e.g., physical, economic, social, psychological, environmental, cultural, institutional, political, etc.). In reality, given that the protection of human lives is the top priority in disaster risk assessments, physical vulnerability (vulnerability of the built environment) is usually considered as the main key factor among others.
Over the past few decades, population growth in Tehran has not only led to rapid urban

Vulnerability
Seismic risk depends not only on the severity of an earthquake (hazard) or the number of people exposed (exposure), but also on the susceptibility of those people to suffer damages and losses (vulnerability). In this respect, vulnerability analysis plays an important, challenging role as the third part of the risk assessment procedure.
Vulnerability is a complex multi-dimensional concept that can cover a wide range of different components (e.g., physical, economic, social, psychological, environmental, cultural, institutional, political, etc.). In reality, given that the protection of human lives is the top priority in disaster risk assessments, physical vulnerability (vulnerability of the built environment) is usually considered as the main key factor among others.
Over the past few decades, population growth in Tehran has not only led to rapid urban development, but also simultaneously to various levels of vulnerability. To assess the seismic risk for Tehran, we selected seven spatial datasets which we had access to as the components of urban physical vulnerability. These GIS-based datasets include "land use", "urban fabric", "building height", "occupancy", "structure type", "construction age', and "vicinity to critical infrastructures".
Taking into account the scale of our study, we had limited access to some datasets in terms of homogeneity. For example, for the two factors "structure type" and "construction age", we had only access to data from the high-rise buildings (with more than 10 storeys), not all the buildings of the Tehran megacity. However, these high-rise buildings still constitute an important part of the urban area in terms of the built-environment vulnerability.
After the preparation of datasets, each of the seven spatial data layers is divided into three classes depending on its own characteristics. Each class (sublayer) is then assigned a weight. To avoid any complication, the weights are simply selected as 1, 2, and 3 which correspond to low, medium, and high vulnerability, respectively (Table 3). It is worth mentioning that in order to classify the "urban fabric" factor, we have used the classification criteria of urban areas defined by Iran's Council of Urban Planning and Architecture [90]. Accordingly, to identify the weariness of urban fabric, three criteria must be considered: (1) Instability: At least 50% of the buildings within a defined urban block are unstable and lack appropriate structural systems, (2) Micro-residency: At least 50% of the buildings within a defined urban block possess an area of less than 200 m 2 , and (3) Inscrutability: At least 50% of the passing routes within a defined urban block are narrow and less than six meters wide. Now, if the urban fabric in a region lacks the above criteria, it would be marked as "normal". But in case it meets one of the above criteria, or all the three above criteria, it would be characterized as the "unstable" and "worn-out", respectively.
Eventually, to assess the overall vulnerability in Tehran, all the classified layers should be overlapped and aggregated in a spatial framework. To do so, we adopted a simple strategy in which the raster maps of the seven vulnerability sublayers are first provided. All the raster maps consist of pixels (cells) of the same size (10 × 10 m). The coordinates at the center of pixels are considered as (x i , y i ), where i refers to the number of the row and column of the grid. Each pixel of the grid obviously contains seven attribute values that represent the weights (W) of the vulnerability sublayers at the center of that pixel. The value of total vulnerability (Z) at each pixel is then calculated based on the sum of the weights of vulnerability sublayers (W) at the center of that pixel as follows: For example, a pixel that constitutes of a new, commercial, reinforced concrete tower that locates in a high urban density with normal fabric, and medium access to critical infrastructures, receives sublayer scores of 1, 2, 1, 3, 3, 1, and 2 for its age, occupancy, structure type, height, land use, urban fabric, and vicinity to infrastructures, respectively, the total vulnerability values of which equals 13. The result of the aggregation of the vulnerability sublayers for all the pixels has led to Figure 8 as the total vulnerability in Tehran. This figure shows that 10 out of 22 districts in the megacity of Tehran including districts no. 7, 8,10,11,12,14,15,16,17, and 20 embrace a higher vulnerability than other districts. The expansion of vulnerability is almost consistent with the evolution of urban development in Tehran, as the old Tehran mainly included the central and southern parts of the present-day Tehran. Therefore, the southern half of the current city actually consists of older structures and more vulnerable factors than the northern half which is a newer built environment.

Risk
After the preparation of the maps of all the risk components, including hazard, exposure, and vulnerability, we need to classify these maps based on their values, and then combine them in order to derive the final earthquake risk map.
As we have mentioned before, we have considered two maps for the hazard component: surface PGA ( Figure 5) and surface rupture width ( Figure 6). The surface rupture width map clearly includes two zones inside and outside of the rupture area, having the weights of 1 and 0, respectively. The surface PGA values are also classified into five equal classes of 0.35-0.42, 0.42-0.49, 0.49-0.56, 0.56-0.63, and 0.63-0.7 g. The value ranges are then reclassified into five classes having new values of 1, 2, 3, 4, and 5 proportional to very low, low, medium, high, and very high hazard, respectively. Then, the two classified maps are aggregated in order to prepare a unified hazard map which consists of both ground shaking (PGA) and surface rupture width. Similarly to that applied to the surface PGA map, the exposure ( Figure 7) and total vulnerability (Figure 8) maps are also reclassified into five classes of 1, 2, 3, 4, and 5, proportional to very low, low, medium, high, and very high exposure/vulnerability.
The combination of the above risk components can be conceptually represented using a 3D computation matrix ( Figure 9). The elements of this matrix correspond to the five classes of each risk component. For example, a combination of the hazard class 5, exposure class 5 and vulnerability class 5 leads to the maximum risk value in the matrix. As we have modeled the hazard, exposure, and vulnerability components in a spatial framework, we combine them pixel by pixel using GIS, and eventually produce the final map which presents the current status of the earthquake risk in Tehran ( Figure 10).
The final risk map indicates that the southern half of the megacity of Tehran is mostly at higher risk than the northern half. Looking at individual maps of the surface PGA, population density and vulnerability distribution, and comparison of them with the final risk map reveals that the nature of high-risk areas in central and southern parts of the city originates from the high hazard, high exposure, and high vulnerability that all together are surprisingly focused in these areas. This has important implications for future urban development plans and risk reduction efforts in order to make a more resilient Tehran.
ISPRS Int. J. Geo-Inf. 2020, 9, x FOR PEER REVIEW 13 of 19 After the preparation of the maps of all the risk components, including hazard, exposure, and vulnerability, we need to classify these maps based on their values, and then combine them in order to derive the final earthquake risk map.
As we have mentioned before, we have considered two maps for the hazard component: surface PGA ( Figure 5) and surface rupture width ( Figure 6). The surface rupture width map clearly includes two zones inside and outside of the rupture area, having the weights of 1 and 0, respectively. The surface PGA values are also classified into five equal classes of 0.35-0.42, 0.42-0.49, 0.49-0.56, 0.56-0.63, and 0.63-0.7 g. The value ranges are then reclassified into five classes having new values of 1, 2, 3, 4, and 5 proportional to very low, low, medium, high, and very high hazard, respectively. Then, the two classified maps are aggregated in order to prepare a unified hazard map which consists of both ground shaking (PGA) and surface rupture width. Similarly to that applied to the surface PGA map, the exposure (Figure 7) and total vulnerability (Figure 8) maps are also reclassified into five classes of 1, 2, 3, 4, and 5, proportional to very low, low, medium, high, and very high exposure/vulnerability.
The combination of the above risk components can be conceptually represented using a 3D computation matrix (Figure 9). The elements of this matrix correspond to the five classes of each risk component. For example, a combination of the hazard class 5, exposure class 5 and vulnerability class 5 leads to the maximum risk value in the matrix. As we have modeled the hazard, exposure, and vulnerability components in a spatial framework, we combine them pixel by pixel using GIS, and eventually produce the final map which presents the current status of the earthquake risk in Tehran ( Figure 10).
The final risk map indicates that the southern half of the megacity of Tehran is mostly at higher risk than the northern half. Looking at individual maps of the surface PGA, population density and vulnerability distribution, and comparison of them with the final risk map reveals that the nature of high-risk areas in central and southern parts of the city originates from the high hazard, high exposure, and high vulnerability that all together are surprisingly focused in these areas. This has important implications for future urban development plans and risk reduction efforts in order to make a more resilient Tehran.

Discussion and Conclusions
In this study, an earthquake risk assessment for Tehran is performed in order to provide an insight into the status of relative risk between different districts in Tehran and the possibility of relative comparison between them. At the first step, we used the most recent datasets (e.g., historical and instrumental catalog, active fault map, geology, etc.) and the best practices of the PSHA approach in order to assess the earthquake hazard in Tehran. The hazard is represented in terms of PGA maps for a 475-year return period, as well as a fault rupture width map. Exposure is then evaluated based on the distribution of population density. Besides the analysis of hazard and exposure, vulnerability to the built environment is also evaluated using seven GIS-based vulnerability datasets (land use, urban fabric, buildings' height, occupancy, structure types and ages, as well as the vicinity to some critical infrastructures). Consequently, the seismic risk is computed by spatial combination of the three above factors in a 3D matrix, and a seismic risk map is derived for Tehran. The main findings of this study can be summarized as follows: • Based on the hazard maps, northern and southern parts of Tehran are subjected to a high PGA of about 0.5 g on a bedrock level; however, regarding the local site response, the soft, thick soil layers in southern parts of Tehran have the potential of amplifying seismic waves up to twice of the calculated values on the rock. For example, this amount is estimated to be 0.7 g for the southwestern parts of Tehran. • Experiences of previous earthquakes indicate that some specific phenomena related to nearfield earthquakes may also result in large damages especially in urban areas. Such phenomena can occur in the form of surface fault rupture, large cracks, and directivity effects, fling step, fault scarps, etc. With respect to the fact that the northern and southern parts of Tehran embrace several active faults, these regions should be taken into account as high-potential areas for hosting the mentioned phenomena. Therefore, a surface rupture widths map was also prepared for the surrounding and inner-city faults of Tehran using the faults' geometry.
Results indicate that we should expect surface rupture widths of about 2-3, 1.5, and 1 km for the major, medium, and minor faults in Tehran, respectively. • As mentioned in Section 2-3, Tehran currently lays on a seismic gap. Regarding that we have applied a time-independent hazard assessment in this study, the duration since the last event is not considered here, so this seismic gap observation in Tehran is not taken into account in Figure 10. Earthquake risk map of Tehran.

Discussion and Conclusions
In this study, an earthquake risk assessment for Tehran is performed in order to provide an insight into the status of relative risk between different districts in Tehran and the possibility of relative comparison between them. At the first step, we used the most recent datasets (e.g., historical and instrumental catalog, active fault map, geology, etc.) and the best practices of the PSHA approach in order to assess the earthquake hazard in Tehran. The hazard is represented in terms of PGA maps for a 475-year return period, as well as a fault rupture width map. Exposure is then evaluated based on the distribution of population density. Besides the analysis of hazard and exposure, vulnerability to the built environment is also evaluated using seven GIS-based vulnerability datasets (land use, urban fabric, buildings' height, occupancy, structure types and ages, as well as the vicinity to some critical infrastructures). Consequently, the seismic risk is computed by spatial combination of the three above factors in a 3D matrix, and a seismic risk map is derived for Tehran. The main findings of this study can be summarized as follows: • Based on the hazard maps, northern and southern parts of Tehran are subjected to a high PGA of about 0.5 g on a bedrock level; however, regarding the local site response, the soft, thick soil layers in southern parts of Tehran have the potential of amplifying seismic waves up to twice of the calculated values on the rock. For example, this amount is estimated to be 0.7 g for the southwestern parts of Tehran.

•
Experiences of previous earthquakes indicate that some specific phenomena related to near-field earthquakes may also result in large damages especially in urban areas. Such phenomena can occur in the form of surface fault rupture, large cracks, and directivity effects, fling step, fault scarps, etc. With respect to the fact that the northern and southern parts of Tehran embrace several active faults, these regions should be taken into account as high-potential areas for hosting the mentioned phenomena. Therefore, a surface rupture widths map was also prepared for the surrounding and inner-city faults of Tehran using the faults' geometry. Results indicate that we should expect surface rupture widths of about 2-3, 1.5, and 1 km for the major, medium, and minor faults in Tehran, respectively.

•
As mentioned in Sections 2 and 3, Tehran currently lays on a seismic gap. Regarding that we have applied a time-independent hazard assessment in this study, the duration since the last event is not considered here, so this seismic gap observation in Tehran is not taken into account in our model. Therefore, a future perspective for this study would be an assessment of time-dependent hazard, which considers possible seismic gaps in order to calculate time-dependent conditional probabilities. This would be helpful to arrive at a better understanding of the potential hazard associated with this seismic gap in order to adopt appropriate strategies for earthquake risk reduction.

•
The population density map (Figure 7) clearly indicates that, of 22 municipality districts of Tehran, eight districts are the most densely populated areas in Tehran. A comparison of this human exposure with the overall physical vulnerability map ( Figure 8) reveals that, in some areas, the population is exactly focused at the highest vulnerable places, which should be considered as an urgent issue in future urban development efforts.

•
According to the overall physical vulnerability map (Figure 8), 10 out of 22 districts in the megacity of Tehran including districts no. 7, 8,10,11,12,14,15,16,17, and 20 show a higher vulnerability than other districts. These results are in a good general agreement with some previous studies on the vulnerability of urban fabrics and building loss models in Tehran [91][92][93].

•
The overall risk map, which is depicted as a result of the combination of hazard, exposure and vulnerability maps, represents an estimate of risk distribution in Tehran. It generally indicates that the southern half of the city has a higher risk than the northern half. Yet the amount of risk should not be underestimated in other areas, especially the northwest parts (such as district no. 5 and 22) where are home to the North Tehran fault and also under rapid urban expansion and development.
A comparison between our study with a previous physical-socioeconomic risk assessment study in Tehran [94] indicates that the previous study [94] ranks districts no. 15,20,12,16,18, and 11 of Tehran as the top regions in terms of physical risk, while our results suggest that districts no. 10,17,20,16,15, and 11 contain the highest risk. In general, the results show some similarities, and the discrepancies originate from the difference in input data and the adopted methodologies. For example, in the previous study [94], a scenario-based seismic hazard only corresponding to earthquake occurrence on the Ray fault in south Tehran is considered, while in this study, we have adopted a PSHA analysis considering all surrounding major faults, site response considerations, as well as rupture width zones. Consequently, the results of our study provide a useful basis not only for understanding earthquake risk in Tehran, but also for prioritizing seismic risk reduction measures and increasing resilience in this megacity.