During the twentieth century, about 75% of the earthquake casualties were caused by buildings destruction and people trapped in collapsed buildings (Coburn & Spence, 2003); if the secondary phenomena are excluded, this amount would be almost 90% of earthquake-related deaths (Coburn & Spence, 2003). Earthquakes cause a wide range of crises. One way to overcome this crisis is to rescue the injured and transport them to the nearest medical center. Indeed, delays in rescue efforts, absence of medical facilities, and secondary disasters can lead to unavoidable loss of life in an earthquake-stricken area. The existence and implementation of proper crisis management strategies play a key role in avoiding these problems. One of the main components of crisis management is the management of rescue operations. After an earthquake, crisis management squads need to properly allocate the available manpower, facilities and resources to the affected areas to minimize the number of casualties. The majority of earthquake-prone countries have a range of pre-determined plans to deal with such crises (Zhou & Liu, 2003). The lack of such plans in those countries has caused huge damage to even the smallest earthquake. Earthquake damage in countries such as Iran and Turkey proves this claim. The average earthquake damage in these two countries is much higher than the leading countries in earthquake management such as China and Japan (Wang, 2021).

In general, rapid implementation of rescue operations in an earthquake-stricken area can prevent many post-earthquake casualties. Research has shown that time plays a key role in post-earthquake mortality. Since most earthquake victims cannot survive more than 72 under the rubble, the first 72 hours after an earthquake is called the golden time (Godschalk et al., 1999). Therefore, developing an effective method for optimized allocation of victims to medical centers can greatly help reduce earthquake casualties. In this operation, issues such as the number of rescue squads and their distribution, the capacity of medical centers, and determining the fastest routes to transport the injured to medical centers should be considered. The rescue operation can be more effective by considering these issue. This operation is well carried out when there is a proper estimate of the people trapped in the rubble.

On the other hand, there needs to be a criterion for measuring the extent of earthquake damage to structures. Over the years, researchers have proposed two measures for this purpose: the magnitude of the earthquake, and the intensity of the earthquake (Walker et al., 2014). Given the definition of earthquake magnitude and intensity, the former is proportional to the amount of energy released in the earth, but the latter is related to the amount of damage caused by the seismic effect. In other words, an earthquake of a certain magnitude can have different intensities depending on its depths, and can even induce different intensities at different distances from the epicenter. The magnitude of an earthquake, denoted by M, indicates the total amount of energy released. Basically, the magnitude of an earthquake is measured by its seismic waves, which are divided into surface waves and volumetric waves (Elnashai & Di Sarno, 2008). Several scales have been proposed for measuring earthquake magnitude, the best known among which is the Richter scale. The intensity of an earthquake, which is perfectly proportional to its destructive power, can be measured by the Mercalli scale (Duzgun et al., 2011).

In general, research on the modeling of earthquake impacts with Geographic Information System (GIS) can be divided into two categories: 1- pre-earthquake zoning and hazard assessment, 2- post-earthquake survivability modeling. Among the studies of the first category, one can mention the research carried out by Zhang et al., who stressed the importance of the demographic characteristics of the disaster-stricken area. They developed a general model based on fuzzy multi-attribute decision-making that takes characteristics such as age and education into account. After presenting their method for assessing vulnerability against natural disasters based on demographic characteristics, they implemented the model for the city of Helsinki (Zhang et al., 2014). In another study, Aghamohammadi et al. (2013), developed a vulnerability assessment model based on the artificial neural network using the data collected in the aftermath of the Bam earthquake in Iran. In this study, the number of casualties was used in each urban area as the model input. After training the neural network with Tehran city data, they used the model to predict the casualty rate of a hypothetical earthquake in Tehran. One of the strengths of this model is the use of real seismic data, which increases the accuracy of the results (Aghamohammadi et al., 2013).

Hashemi and Alesheikh (2011), developed a GIS-based model for earthquake damage assessment and implemented it also in Tehran. In their research, the earthquake simulation was carried out based on the parameters of the Masha fault near Tehran. Damage estimation was modeled based on ground shaking, attenuation, local geological amplification, earthquake intensity, and fragility curves of buildings. Damage assessment was divided into two categories: casualty and street assessments. In assessing the casualties, criteria such as the time of the earthquake, population, the amount of damage to buildings, and the mortality ratio were considered. In assessing street damage, criteria such as street width and building materials were considered. The simulation showed that the assumed earthquake would severely damage 64% of the district’s buildings, kill 33% of all residents, injure 27% of the population, and block 22% of the streets (Hashemi & Alesheikh, 2011).

Karimzadeh et al. (2014), also developed a model for the vulnerability assessment of buildings and people in the city of Tabriz (Iran) and implemented it in an earthquake simulation scenario. In this study, the maps of effective parameters including geological, geodetic, geotechnical, and geophysical factors were prepared in the GIS environment. Weights were then determined for the maps using the Analytical Hierarchy Process (AHP). In this study, a magnitude 7 earthquake in the fault north of Tabriz was used for simulation. The developed model was used to assess the vulnerability of buildings, people, and infrastructure of the city in two main areas. The results of this study showed if the assumed earthquake occurred at night, it would completely destroy 69.5% of the buildings and kill 33% of residents (Karimzadeh et al., 2014).

Ranjbar and Nekooei (2018) used the fuzzy TOPSIS method to identify the buildings vulnerable to earthquake damage in two scenarios day and night in Tehran city. Buildings and roads were the main criteria of this research. The results of the simulation showed that the Tehran Grand Bazaar has the highest level of vulnerability and the lowest level of accessibility for rescue operation (Ranjbar & Nekooie, 2018).

Kamranzad et al. (2020), assessed the earthquake hazard in Tehran. In this study, the effects of criteria such as geology, active faults, population distribution, land use, height and type of buildings were evaluated on the earthquake using GIS. The hazard, exposure and vulnerability maps were then obtained based on these criteria in terms of Peak Ground Acceleration (PGA) (Kamranzad et al., 2020).

Sen and Ekinci (2016), analyzed the level of post-earthquake vulnerability in Istanbul. In this study, fault line, geological structure, building structure, and the number of building floors were considered in post-earthquake vulnerability assessment. The building damage distribution map was then obtained by combining fuzzy logic and GIS (Şen & Ekinci, 2016).

Meshkini et al. (2013), used 11 spatial and physical criterion to assess the potential earthquake damage in the city of Zanjan (Iran) using fuzzy logic Inverse Hierarchy Process Weight (IHPW) (Meshkini et al., 2013). Fallah-zazuli et al. (2019) used GIS and Remote Sensing (RS) techniques to analyze explicit models of landslide in the Zagros Mountains, Iran. Logistic Regression (LR) and Multi-Criteria Decision Analysis (MCDM) were used to estimate the likelihood of landslide occurrences (Fallah-Zazuli et al., 2019). Mesbahi et al. (2020) prepared an earthquake vulnerability zoning map for the city of Tabriz with 10 environmental-geological criterion using fuzzy logic. The results showed a high level of risk in the northern and central parts of Tabriz, which have a high population density (Mesbahi et al., 2020).

Modeling of resource allocation and survivability in crisis management has also been the subject of several studies, like the one conducted by Dodo et al. in 2005 (Dodo et al., 2005). In another study, Aghamohammadi et al. (2013) focused on resource allocation after earthquake. They developed a heuristic method based on two nested genetic algorithms for allocating treatment centers to minimize post-earthquake relief time. In their method, the outer genetic algorithm is used to solve the location problem and the inner one is used to optimize the location-allocation of medical centers. The results showed that new places are needed for medical centers. The results also showed the good performance of the model in allocating the capacity of medical centers to individuals (Aghamohammadi et al., 2013).

Ren et al. (2016), studied the emergency planning to improve post-earthquake rescue operations. They selected 30 spatial and non-spatial criterion for evaluation of earthquake relief plans. They then used the Hesitant Analytic Hierarchy Process (HAHP) method and fuzzy logic to develop the earthquake. The results showed that HAHP is much more effective than AHP in terms of the effectiveness of earthquake rescue planning (Ren et al., 2016).

Ranjbar et al. (2017), examined the buildings damaged caused by an earthquake by using satellite images to determine the number of victims. In this study, criteria such as earthquake time, building materials, land-use, buildings age, and rough texture of the images were used. The introduced model reasonably predicted the number of casualties (Ranjbar et al., 2017).

Liu (2020), developed a new GIS-based model for quick rescue of affected people by an earthquake. This system seeks to reduce the cost and distance of transferring the injured to medical centers. In this model, seismic susceptibility map was prepared based on slope, altitude, lithology, fault, river, and road data. The result demonstrated the ability of the hierarchical model to reduce rescue time as well as casualties after the earthquake (Liu, 2020).

Yariyan, et al. (2020) developed a new hybrid learning model for seismic vulnerability mapping in Sanandaj City based on 15 factors (Yariyan et al., 2020). In addition to all these researches, various other studies were taken on resource allocation for optimum survivability in earthquake.

Various methods are used to estimate the number of injuries and casualties, including the methods developed by the US Federal Emergency Management Agency (FEMA), Shiono Coburn and Spence. The FEMA model provides a methodology for estimating the number of casualties due to the collapse of buildings and bridges, which is based on information about earthquakes and structures within the US (Molina et al., 2010). The models of Murakami and Shiono only estimate the number of casualties based on building failures (Shiono et al., 1991). The Coburn model is a fundamentally statistical method based on information about the number of casualties caused by the collapse of buildings in major earthquakes in different countries. This method can clearly estimate the casualties from the number of collapsed building and lethality ratio. Lethality ratio depends on different parameters, most of which are mechanism of collapse, building type, the time of earthquake occurrence, and rescue operations effectiveness (Coburn & Spence, 2003). Various studies have shown that the Coburn model can provide a relatively accurate estimate of casualties and injuries.

Japan International Cooperation Agency (JICA) has conducted a study to estimate the number of casualties in a potential earthquake scenario based on the Coburn method (JICA, 2000). However, the information and analyses need to be updated regularly to have a better rescue operation. This information includes: number of victims, number of rescue squads, capacity of medical centers, fastest routes to send the injured to medical centers, roads blocked by earthquake rubble and speed on the roads.

Relief for earthquake victims is very important in post-earthquake management, which has been mentioned in previous research. The most important difference between the present study and similar ones is the timeliness of the model. The studies that have been done estimate the casualties in general, while in this study, the survival expectancy of the injured is calculated in 72 hours after the earthquake for different structures according to the fuzzy function. This model provides the possibility of appropriate relief according to the chances of the injured being alive. On the other hand, studies conducted in Iran and neighboring countries are based on models used in the United States and East Asia, which are not compatible with the type materials and earthquake in these areas.

In this study, the survival rate of affected people is estimated using spatial analysis methods be optimally allocated to medical centers. Since the nature of the factors influencing the estimation of survivability is vague and uncertain, fuzzy logic is used for modeling. Therefore, this study provides a model for estimating the survivability of victims by combining the spatial information systems with fuzzy logic.