1 Introduction

The significance of natural hazards research has grown considerably locally and globally due to the increasing economic impact and public concern associated with these events. With the rise of urbanization in hazard-prone areas and heightened public awareness, there is a growing emphasis on mitigating and preventing natural disasters (Bastaminia et al. 2018; Mohammadi et al. 2022). Earthquakes, floods, and tsunamis, among others, result in significant financial and human losses and often dominate media attention (Azim and Islam 2016). Among these hazards, earthquakes are the most devastating, claiming an average of over 25,000 lives worldwide annually (Silva et al. 2017).

Earthquake risk assessment is pivotal in monitoring seismic activity, enhancing our understanding of earthquakes across various sectors, improving building standards in high-risk regions, and facilitating optimal crisis management programs (Paradise 2005). The demand for earthquake risk knowledge is particularly pronounced in tectonically active areas (Bernardi et al. 2015). Risk is characterized by the probability of an event and its adverse consequences. Risk assessment methods are applied to ascertain the nature and extent of hazards and assess vulnerability conditions (Erdik 2017). A common approach to conceptualizing earthquake risk involves examining its two main components: hazard and vulnerability (Jena and Pradhan 2020). Earthquake hazard, rooted in geological and geophysical sciences, denotes the likelihood of seismic events occurring in specific regions (Du et al. 2023). Vulnerability, on the other hand, signifies the potential damage inflicted by natural disasters on human communities, infrastructure, and the environment (Rashed and Weeks 2003; Rabiei-Dastjerdi et al. 2020; Karataş 2023).

Due to the destructive impacts of earthquakes, numerous studies have been conducted to assess earthquake hazards, vulnerability, and overall risk. Various methods have been introduced for this purpose, including geographic information system (GIS) methods (Nyimbili et al. 2018; Civelekler and Pekkan 2022), probabilistic approaches (Salgado-Gálvez et al. 2017), real-time approaches (Cauzzi et al. 2016), multi-criteria decision-making techniques (MCDM) (Jena and Pradhan 2020; Gulum et al. 2021) and neural network methods (Alizadeh et al. 2018a, b). Technological advances in GIS and Remote Sensing (RS) provide valuable tools for assessing earthquake hazards, vulnerability, and risk (Nyimbili et al. 2018; Rabiei-Dastjerdi and Matthews 2018; Shan et al. 2021; Sichugova and Fazilova 2024). In recent years, MCDM approaches based on RS and GIS have demonstrated highly effective performance and have become powerful tools for strategy identification and evaluation (Xiang et al. 2022). GIS-based MCDM approaches for processing spatial and non-spatial data offer a structured framework for decision-makers (Alizadeh, Hashim, et al. 2018). The combined use of multiple-criteria decision analysis (MCDA) and GIS provides comprehensive solutions for managing complex geographic issues, especially earthquake management (Shadmaan and Popy 2023). Many researchers claim that earthquake risk assessment is a multidimensional problem that can be effectively investigated using MCDM methods (Jena and Pradhan 2020; Wibowo et al. 2021; Xiang et al. 2022).

In one study, Gulum et al. (2021) used AHP (Analytical Hierarchy Process) and TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) to assess earthquake risk, identifying the most dangerous areas of Istanbul, Turkey. According to the findings, AHP and TOPSIS are reliable methods for evaluating earthquake risk. Erden and Karaman (2012) employed the AHP method to map earthquake hazards, utilizing a hierarchical structure to simulate the earthquake hazard map (EHM). Their results demonstrated the efficiency of the hierarchical method in determining the weights of parameters affecting earthquakes. Jena and Pradhan (2020) calculated earthquake risk using the AHP-TOPSIS method, taking into account both the hazard potential and the vulnerability of the area. Despite these studies, some researchers argue that the issue of earthquake risk and vulnerability involves inherent uncertainty, which is why MCDM methods can significantly impact evaluation results (Alizadeh et al. 2018b; Jena and Pradhan 2020). In other studies, the issue of uncertainty in MCDM studies has been considered and addressed. One approach to assessing uncertainty is using fuzzy logic in MCDM methods. For instance, Lyu et al. (2020) employed Fuzzy-Hierarchical Analysis (FAHP) and AHP methods to assess earthquake risk in China. The FAHP method was used to determine decision-making options, and the results of this study mitigated some biases associated with AHP. In another study, Zheng et al. (2014) developed a hybrid fuzzy neural network to classify the population at risk of earthquakes in a specific region of China. The main components of the system include a Takagi-Sugeno-type fuzzy neural network (T-S) for classifying the affected population and an optimization algorithm for fine-tuning the parameters of the main network and subnet. The results showed that the combined fuzzy neural network demonstrated better classification performance compared to some conventional fuzzy neural networks. Mirjafari et al. (2012) used the fuzzy inference system (FIS) to investigate earthquake vulnerability in Tabriz and determined the percentage of vulnerable areas based on the FIS method. Veysi and Hosseinali (2024) prepared vulnerability maps of urban building blocks in Kermanshah city using data related to faults, structure age, building block strength, and block area through a fuzzy logic inference system. Then, utilizing fuzzy analytic hierarchy process analysis, they presented spatial suitability maps for accommodating the vulnerable population in case of an earthquake.

This study uses the FIS, a Multiple-Criteria Decision-Making (MCDM) method, to develop an earthquake risk index. Among various MCDA methods, fuzzy logic approaches are highly recommended because they accommodate multiple-valued membership degrees within a fuzzy set and facilitate gradual transitions between system states. These characteristics make fuzzy logic particularly suitable for addressing the complexities inherent in earthquake risk assessment (Cárdenas et al. 2020).

Several countries, including China, Indonesia, Iran, Turkey, and Japan, consistently rank high in earthquake vulnerability, experiencing frequent and devastating seismic events (CRED 2020). Iran, in particular, holds the unfortunate distinction of leading in earthquake frequency, with numerous events exceeding a magnitude of 5.5 on the Richter scale annually (Yariyan et al. 2020). Noteworthy among these are historical earthquakes such as the 1962 event in Boyin-Zahra city, measuring 7.2 on the Richter scale, the devastating 6.6 magnitude earthquake that struck Bam city on December 26, 2003, and the 7.3 magnitude earthquake in Kermanshah on November 12, 2017s (Khoshgoftar and Saradjian 2021). These events caused extensive damage and resulted in significant loss of life. The recurrence of such catastrophic earthquakes underscores the critical importance of earthquake risk assessment in Iran and other regions facing similar seismic risks.

While numerous studies have examined earthquake risk analysis on a national scale in Iran (Motamed et al. 2019; Taherian and Kalantari 2019; Talebi et al. 2020) There remains a significant gap in achieving a detailed and comprehensive understanding of earthquake risk, including vulnerability and hazard components. Existing studies often lack a comprehensive evaluation basis. Therefore, there is an urgent need for a thorough assessment of earthquake hazard probability, vulnerability, and overall risk in the region. This study aims to address this gap by employing an innovative FIS-based approach, utilizing the latest satellite and GIS data sources to minimize uncertainty in earthquake risk mapping. The primary objectives of this study are to answer the following key questions: (1) Which cities in Iran are most susceptible to earthquake occurrence and vulnerability? (2) What percentage of Iran’s population is exposed to high earthquake risk? (3) How does earthquake risk vary across different regions of Iran? Our goal is to provide a comprehensive earthquake risk assessment in the study area, utilizing a practical and effective methodology. The subsequent sections of this paper are organized as follows: the second part describes the data sources and methodology in detail, followed by the presentation of results and discussion in the third section. Subsequently, the final risk layer is compared and validated with historical earthquake data. Finally, the conclusion section summarizes the findings and outlines avenues for future research.

2 Material and methodology

2.1 Study area

This research focuses on Iran, located between 44 and 64 degrees east longitude and 25 to 40 degrees north latitude. Iran’s climate is predominantly dry and semi-arid, with an average annual rainfall of about 250 mm. In 1966, Iran’s population was approximately 25.8 million, and twelve cities—Tehran, Isfahan, Mashhad, Tabriz, Abadan, Shiraz, Ahvaz, Kermanshah, Rasht, Qom, Hamedan, and Urmia—each had populations exceeding 100,000. Over the next 50 years, the country’s population nearly tripled to 86.5 million, while the urban population increased sixfold, resulting in 98 cities having populations over 100,000 by 2016. Additionally, over the past five decades, Iran has undergone significant environmental, political, and socioeconomic changes, which have shaped its urban landscape (Rabiei-Dastjerdi 2023; Mohammadi et al. 2021). Moreover, Iran is on a seismic belt, making it highly susceptible to earthquakes. The Iranian Plateau experiences active crustal deformation and seismic activity due to its location between the Arabian and Eurasian plates. As a result, the region remains tectonically active, with ongoing seismic movements to achieve isostatic equilibrium (Berberian 2014). According to data from the US Geological Survey earthquake database, Iran has experienced approximately 6,900 earthquakes with a magnitude greater than 2.5 on the Richter scale between 1950 and 2023. Among these, 733 earthquakes exceeded a magnitude of 5 on the Richter scale (Fig. 1).

Fig. 1
figure 1

Location of the study area, including DEM, city centers (2016), megacities, and province borders of Iran

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2.2 Datasets

This study conducted a comprehensive earthquake risk assessment using data from multiple sources. The datasets included information from the United States Geological Survey (USGS), the Census Bureau of Iran, the GEM database, the National Mapping and Geological Survey, the OSM database, the WorldPop database, and the Global Human Settlement Layer (GHSL) (Pesaresi and Politis 2023). Table 1 provides details about the sources and characteristics of the data used, while Fig. 2 illustrates the primary input layers.

We utilized datasets from the American Geological Survey, including a 250-meter Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM). Geological maps and fault data from the National Mapping and Geological Organization were also employed to calculate fault density, a crucial indicator for assessing earthquake risk. Additionally, information sourced from the OSM and Joint Research Centre (JRC) databases provided data on road networks, building density, and proximity to infrastructure. Table 2 presents a comprehensive list of all input datasets used in this study.

Table 1 Overview of the data used in this study
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2.3 Fuzzy inference system (FIS)

Various methods are available for evaluating earthquakes, including deterministic, probabilistic, heuristic, geostatistical, inventory-based, and knowledge-based approaches, categorized as quantitative or qualitative. In our study, we focus on quantitative methods to achieve precise assessments, emphasizing computational intelligence techniques for their capability to mitigate analytical uncertainties (Azarafza and Ghazifard 2016). Recently, knowledge-based methods like the FIS have gained prominence (Chen et al. 2017). These methods improve upon traditional approaches by addressing uncertainties through linguistic variables, scaled numerically based on available data. The FIS model, applied across diverse fields, excels in handling problems with imprecise data, thereby reducing uncertainty compared to conventional methods (Mangir 2023). Fuzzy logic, introduced by Zadeh in 1965 as a departure from binary Boolean systems, finds broad application (Zadeh 1965; Pathak and Bhandary 2020). ‘Fuzzy’ signifies a multi-valued nature that offers a spectrum of answers instead of binary choices, aligning well with complex real-world phenomena and providing flexibility in decision-making (Cherkassky 1998; Kazeminezhad et al. 2005; Kaloop et al. 2021). One significant advantage of fuzzy sets lies in their ability to model linguistic variables, facilitating the integration of expert knowledge into various applications. Furthermore, fuzzy methods capture uncertain and ambiguous phenomena effectively, making them invaluable tools in diverse problem-solving contexts (Cherkassky 1998).

Fig. 2
figure 2

Primary input layers for the study: (a) historic earthquakes of magnitudes greater than 5 Richter from 1950 to 2023; (b) Faults in Iran; (c) Road layer; (d) Residential and Construction Area layer in 2023

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Table 2 Probability hazard and vulnerability indicators for constructing the earthquake risk map
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The advantages of fuzzy logic methods have motivated researchers to integrate them with traditional approaches in various fields, including risk management (Hu et al. 2018; Beiranvand and Rajaee 2023). Three types of FIS models have been proposed: Mamdani, Takagi-Sugeno, and Tsukamoto, each distinguished by its fuzzification scheme (Lee 1990). The Mamdani type formulates fuzzy rules in an IF-THEN structure and presents the output as fuzzy sets. These sets are transformed into the final fuzzy output using fuzzy operators. Takagi-Sugeno defines rules in IF-THEN format with weighted linear functions, calculating the output as a linear function of the inputs. Tsukamoto, similar to Mamdani, uses increasing and decreasing functions to determine output values, although it is less favored in research due to its lower transparency compared to the Mamdani and Takagi-Sugeno models (Chaudhari et al. 2014); Murnawan and Lestari, 2021).

For this study, the Mamdani inference system was selected due to its successful application in various industrial contexts (Pourjavad and Mayorga 2019). Fuzzy rules within the control system are developed in collaboration with domain experts (Mamdani and Assilian 1975). The FIS function involves converting crisp inputs into fuzzy inputs using a fuzzifier (Kazeminezhad et al. 2005). The fuzzy inference engine then processes the set of fuzzy rules stored in the inference system to make decisions based on these rules. The system’s behavior is defined by employing a set of rules in the “IF-THEN” format. To illustrate the model, consider Eq. 1, which presents a simple problem with two inputs and one output consisting of three rules (Iancu 2012):

$$\begin{array}{l}Rule\begin{array}{*{20}{c}}{}\end{array}1:{\rm{ }}If\begin{array}{*{20}{c}}{}\end{array}x\begin{array}{*{20}{c}}{}\end{array}is\begin{array}{*{20}{c}}{}\end{array}A3,\begin{array}{*{20}{c}}{}\end{array}Or\begin{array}{*{20}{c}}{}\end{array}y\begin{array}{*{20}{c}}{}\end{array}is\begin{array}{*{20}{c}}{}\end{array}B1,\begin{array}{*{20}{c}}{}\end{array}Then\begin{array}{*{20}{c}}{}\end{array}z\begin{array}{*{20}{c}}{}\end{array}is\begin{array}{*{20}{c}}{}\end{array}C1\\Rule\begin{array}{*{20}{c}}{}\end{array}2:{\rm{ }}If\begin{array}{*{20}{c}}{}\end{array}x\begin{array}{*{20}{c}}{}\end{array}is\begin{array}{*{20}{c}}{}\end{array}A2,\begin{array}{*{20}{c}}{}\end{array}And\begin{array}{*{20}{c}}{}\end{array}y\begin{array}{*{20}{c}}{}\end{array}is\begin{array}{*{20}{c}}{}\end{array}B2,\begin{array}{*{20}{c}}{}\end{array}Then\begin{array}{*{20}{c}}{}\end{array}z\begin{array}{*{20}{c}}{}\end{array}is\begin{array}{*{20}{c}}{}\end{array}C2\\Rule\begin{array}{*{20}{c}}{}\end{array}3:{\rm{ }}If\begin{array}{*{20}{c}}{}\end{array}x\begin{array}{*{20}{c}}{}\end{array}is\begin{array}{*{20}{c}}{}\end{array}A1,\begin{array}{*{20}{c}}{}&{}\end{array}Then\begin{array}{*{20}{c}}{}\end{array}z\begin{array}{*{20}{c}}{}\end{array}is\begin{array}{*{20}{c}}{}\end{array}C3\end{array}$$
(1)

In the inference engine part of FIS, a set of rules is defined to encompass layers, establishing conditions for combining them within the knowledge base. Subsequently, in the final stage of FIS output, the linguistic variable is transformed from its fuzzy state into a crisp value (output) using a defuzzification method (Chaudhari et al. 2014; Kaloop et al. 2021). Defuzzification is the process of converting the fuzzy output into a crisp set or crisp output. Among various defuzzification methods, the Center of Area (CoA) method is widely used (Pourjavad and Shahin 2018). In this research, the CoA method is employed for defuzzification, marking the final stage of the FIS.

2.4 Implementation of FIS for earthquake risk analysis

To implement the fuzzy inference model, the input layers were adjusted by resampling all layers to a uniform cell size of 250 m. This step ensured detailed representation of urban areas and maintained consistent spatial resolution across all layers, minimizing spatial discrepancies during overlay operations (Mayfield 2016). Subsequently, a Geodatabase was established in ArcGIS. Integrating layers for mapping earthquake hazard probability within the FIS involved two main criteria: earthquake indicators (proximity to the epicenter, epicenter density, depth density, and magnitude density) and environmental indicators (slope, elevation, fault density, and PGA). Generating the earthquake occurrence probability hazard entailed integrating four environmental layers using 81 rules (each layer with three membership functions: low, medium, and high, totaling 81 rules). Similarly, four earthquake layers were combined under the same 81 rules. Finally, overlaying the environmental and earthquake layers yielded the earthquake hazard probability layer for the entire country.

Conversely, the vulnerability layer was generated by integrating four predefined indicators using 81 rules. The earthquake risk layer was also derived by combining the probability of earthquake occurrence map with the vulnerability layer according to a specified risk formula. This research involved a three-step process for preparing the risk layer. Initially, the hazard of occurrence and vulnerability layers were multiplied using the linear multiplication method, resulting in a preliminary risk layer (Jena and Pradhan 2020). Subsequently, the resulting risk layers were integrated using the FIS with 25 rules. Finally, the combined earthquake risk layers underwent fusion using nine rules to produce the final integrated layer using both multiplication and FIS methods, as shown in Eq. 2.

$$\begin{array}{l}Ris{k_m} = Multiplication\left( {Hazard*Vulnerability} \right)\left( {model1} \right)\\Ris{k_f} = FIS\left( {Hazard\begin{array}{*{20}{c}}{}\end{array}\& \begin{array}{*{20}{c}}{}\end{array}Vulnerability} \right)\left( {Hazard\begin{array}{*{20}{c}}{}\end{array}and\begin{array}{*{20}{c}}{}\end{array}Vulnerability} \right)\left( {model2} \right)\\Ris{k_c} = FIS\left( {Ris{k_m}\begin{array}{*{20}{c}}{}\end{array}\& \begin{array}{*{20}{c}}{}\end{array}Ris{k_f}} \right)\left( {model3} \right)\end{array}$$
(2)

The study employed expert knowledge to reduce uncertainty, thereby improving the performance of composite indicators (Alimohammadi et al. 2004; Libório et al. 2023). Additionally, Fig. 3 illustrates the stages of the research process.

Fig. 3
figure 3

Flowchart of the proposed methodology

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3 Result and discussion

This section presents the results and information derived from the earthquake and vulnerability risk assessments and discusses the earthquake risk layer obtained through their integration.

3.1 Risk of earthquake

Eight layers were integrated using the FIS method to assess earthquake risk probability. These layers included elevation, slope, fault density, PGA, magnitude density, epicenter density, proximity to the epicenter, and depth density. Among these inputs, the elevation ranges and the extent of the Zagros and Alborz Mountain ranges are closely associated with areas exhibiting higher PGA, epicenter density, magnitude density, and depth density. Additionally, fault density emerged as a significant factor in earthquake analysis.

Fig. 4
figure 4

Hazard indicators of the probability of occurrence: (a) DEM; (b) Slope; (c) PGA; (d) Fault Density; (e) Epicentre Density; (f) Magnitude Density; (g) Depth Density; (h) Proximity to Epicentre

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Regions with higher fault numbers, longer lengths, and greater densities corresponded to increased probabilities of significant earthquakes. The Zagros and Alborz Mountains exhibited elevated slope, elevation, fault density, and PGA values, directly influencing earthquake occurrence (see Fig. 4). A comprehensive study of these factors provides valuable insights into earthquake hazards.

The depth of earthquake epicenters is crucial for seismological analysis. Figure 4 illustrates the distribution of earthquake depths, showing the deepest earthquakes along the southeastern coast of Iran. In contrast, the Zagros high-risk belt experiences earthquakes at shallower depths. Regions within the Zagros belt, like Sarpol-e Zahab, have seen significant human and economic losses due to earthquakes.

Figure 5 presents the frequency of earthquakes in Iran from 1963 to 1976, revealing a cyclical pattern. This trend, observed over 73 years, demonstrates a seismic frequency cycle lasting approximately 10–15 years. Earthquake frequency increases with energy release within the Earth and decreases until equilibrium is reached. The cyclical pattern is evident in the continuous rise in earthquakes from the 1960s to the 1970s, followed by a gradual decline from 1970 to 1972.

Figure 6 depicts earthquake magnitudes across different provinces of Iran from 1950 to 2023. Tehran and Zanjan provinces did not record earthquakes above 5 on the Richter scale during this period. However, Hormozgan Province, situated along the southern coasts of the Persian Gulf and the Sea of Oman, experienced the highest number of earthquakes (140) over 73 years. Other provinces, including Fars (133 earthquakes), Khuzestan (42 earthquakes), Ilam (33 earthquakes), Bushehr (31 earthquakes) on the Zagros faults, central Iran’s Kerman province (76 earthquakes), South Khorasan (37 earthquakes), and Sistan and Baluchestan (35 earthquakes), also witnessed significant seismic activity along their respective fault lines.

Fig. 5
figure 5

Frequency of earthquakes with magnitudes greater than 5 Richter in Iran from 1950 to 2023

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Table 3 lists the ten cities with the highest earthquake hazard probabilities, including Faryab, Nurabad Mamasani, Savadkuh, Kahnuj, Koohrang, Kazerun, Shemiranat, Savadkuh-e-Shomali, and Rudan. These areas are characterized by proximity to earthquake epicenters and high PGA values.

Fig. 6
figure 6

Frequency of earthquakes greater than 5 Richter in different provinces from 1950 to 2023

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3.2 Earthquake vulnerability

Given the paramount importance of human safety in vulnerability assessments, this indicator primarily focuses on urban areas. Four key factors were selected and integrated into the Mamdani inference system to evaluate vulnerability. These critical factors include population density, building density, proximity to roads, and distance from buildings. The integration of these layers provides valuable insights into vulnerability assessment.

Building density and population density are particularly influential factors affecting vulnerability levels. Areas with low building density, indicating more open land available for vertical construction, coupled with high population density, can significantly mitigate earthquake vulnerability.

Figure 7 illustrates that provincial centers exhibit the highest concentrations of population and buildings. However, during earthquakes, the heightened density of these indicators leads to substantial financial and human losses, highlighting the lack of available open space for temporary accommodations (Liu et al. 2023). Furthermore, the accessibility of communication routes emerges as a critical factor in post-earthquake crisis management. Increasing the number of road intersections and ensuring wide streets facilitates faster access and emergency response, especially during peak traffic hours. In contrast, narrow roads often become blocked after earthquakes, hindering emergency efforts.

Demographic data analysis reveals an uneven distribution of population across Iran. As the capital, Tehran province has the highest population concentration, comprising 16.59% of the total population. Subsequent rankings prioritize provinces like Khorasan Razavi, Isfahan, and Khuzestan, each with populations exceeding four million. Conversely, the central region of Iran, which includes desert areas, exhibits lower building and population densities.

Fig. 7
figure 7

Vulnerability indicators used in this study: (a) Proximity to Roads; (b) Population Density; (c) Building Density; (d) Proximity to Building

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The vulnerability map reveals that regions with high population density and extensive construction exhibit heightened vulnerability to earthquakes. Specifically, the Tehran metropolitan area shows a vulnerability level of 80%. This vast urban region spans 1,334 square kilometers and houses over 9 million people as per the 2021 census, exacerbating its susceptibility to seismic events. In recent years, Tehran has experienced several earthquakes ranging from 3.8 to 4.9 on the Richter scale. Further analysis detailed in Table 3 identifies Tehran, Karaj, Islamshahr, Shahriyar, Mashhad, Tabriz, Isfahan, Ray, Khomeyni Shahr, and Qaem Shahr as the top ten cities with the highest vulnerability levels.

3.3 Earthquake risk map

In continuation of previous stages, the two layers depicting hazard probability of occurrence and vulnerability, as shown in earlier phases (Fig. 8), were integrated using the FIS method to create a unified risk layer.

Fig. 8
figure 8

Earthquake Indicator Maps: (a) Hazard Probability Map at Pixel Level; (b) Hazard Probability Map at County Level; (c) Vulnerability Map at Pixel Level; (d) Vulnerability Map at County Level; (e) Risk Map at Pixel Level; (f) Risk Map at County Level

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Figure 8 illustrates the concentrated high earthquake risk zones in southern, northern, and along the Zagros Mountain range in western Iran, where approximately 31.7 million people reside, constituting 39.7% of Iran’s population. Another notable high-risk region is the Caspian Sea coast cities in northern Iran, encompassing 9.61% of Iran’s total population, approximately 7,683,097 people. According to Table 3, the ten cities most at risk of earthquakes include Karaj, Tehran, Islamshahr, Shahriyar, Tabriz, Faryab, Nurabad Mamasani, Hajiabad, Kazerun, and Savadkuh.

A box plot diagram (Fig. 9) was generated to analyze risk information across different provinces. This graphical representation highlights key statistical parameters such as the mean, minimum, maximum, and range of variations between the first and third quartiles, enabling effective comparison of multiple data groups. The graph notably shows significant differences around the 50% point, representing the median. It’s important to clarify that the middle line of the box represents the median, which differs from the calculated average.

Mazandaran Province is identified with an average risk value exceeding 50. Semnan Province exhibits the minimum values for statistical parameters, including the minimum, maximum, and average among the surveyed provinces. The highest variance is observed in Kerman Province, while East Azerbaijan, Yazd, and Zanjan display the lowest variance. Provinces with the highest earthquake risks include Mazandaran, Tehran, and Kerman. Moreover, analysis of outliers reveals critical points in the provinces of Kurdistan, Markazi, East Azerbaijan, Yazd, and Zanjan.

Fig. 9
figure 9

Box plot analysis of earthquake risk in Iran at county level

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Table 3 Ranking the top ten most hazard-prone cities for earthquakes
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In Fig. 10, a comprehensive evaluation of three hazard indicators—probability of occurrence, vulnerability, and earthquake risk across the provinces of Iran—is presented. Disparities among these indicators are evident, with the lowest values observed in Semnan and South Khorasan provinces. Conversely, Tehran, Alborz, and Mazandaran provinces exhibit the highest values across all three factors. Interestingly, while showing high vulnerability, provinces like Qom and Khuzestan display a relatively low likelihood of occurrence, resulting in comparatively lower overall risk. This underscores the importance of mitigating influential variables in either occurrence likelihood or vulnerability to reduce overall risk. Therefore, ensuring the safety of residential areas against earthquake risk necessitates consideration of diverse factors, including building density, population density, road networks, and urban design, all of which demand attention from planners.

Fig. 10
figure 10

Comprehensive assessment of three risk indicators: probability of occurrence, vulnerability, and earthquake risk across Iranian provinces

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3.4 Validation of the results

In this study, we utilized the FIS method to assess earthquake hazard and vulnerability, creating an earthquake risk map. To validate our model, we mapped four historically significant earthquakes - Manjil, Sarpol-e Zahab, Bam, and Bushehr - onto our final risk map as benchmarks (Fig. 11). The devastating earthquake in Manjil on June 21, 1990, measuring 7.4 on the Richter scale, resulted in over 40,000 fatalities and displaced nearly 500,000 people (Badri et al. 2006). As depicted in Fig. 11, our risk map identifies this region as high-risk. Another notable event was the 6.6 Richter earthquake in Bam in 2003, which claimed over 40,000 lives, injured around 30,000 individuals, and destroyed nearly 20,000 homes (Abolhadi et al. 2022). Similarly, the 2013 Bushehr earthquake, registering 4.6 Richter, caused 37 deaths and 850 injuries. The figure illustrates this area as a high-risk epicenter. The most recent earthquake studied is the 7.3 Richter earthquake in Sarpol-e Zahab, western Iran, which claimed 396 lives and injured approximately 7,000 people (Mahdi 2021). These earthquakes closely align with our research’s identified risk points. Despite lower magnitudes, such as in Bam, casualties were significantly higher, underscoring the critical need for vulnerability assessment. Moreover, it underscores the importance of evaluating soil properties to ensure safe construction in earthquake-prone residential areas, which is an essential consideration (Kurnaz 2017; Civelekler and Pekkan 2022).

Fig. 11
figure 11

Validation of the earthquake risk map modeling in Iran (Source: Wikipedia)

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In this study, we encountered several challenges, including the extensive geographical scope of the study area and limited access to data, which necessitated the consideration of general sub-criteria for vulnerability assessment. Consequently, not all sensitive sub-criteria, such as building quality, building type, and household density, could be incorporated due to these constraints. The availability of data on building quality and type, particularly in the border and southern regions of the country, could have improved the accuracy of vulnerability indicators.

Furthermore, socio-spatial inequalities are crucial in determining earthquake vulnerability and risk. Addressing these inequalities is essential for developing comprehensive strategies to reduce earthquake risk (Waly et al. 2021). By recognizing and mitigating these inequalities, the resilience of communities and regions can be enhanced, thereby minimizing the adverse impact of earthquakes on society (Carnelli and Frigerio 2016).

4 Conclusion

This study utilized data from multiple sources to analyze earthquake risk. Initially, we investigated earthquake probability and vulnerability, creating a spatial distribution layer representing earthquake risk in the study area. Our findings indicate higher earthquake risks in southern, western, and parts of northern Iran compared to other regions. While vulnerability does not exhibit a specific geographical pattern, it is notably higher in megacities and urban centers. Furthermore, our earthquake risk analysis identified cities with varying degrees of risk. Cities like Abu Musa, Abadan, and Khorramshahr showed lower earthquake risks, whereas Karaj, Tehran, and Islamshahr faced higher risks.

Based on insights from this research and an understanding of earthquake risk across different regions, proactive measures can be implemented to enhance earthquake crisis management. These measures include preventive actions, structural reinforcement, relocation of facilities from seismic zones, dispersion of residential areas away from high-risk zones, and redirection of demographic activities to safer regions. Integrating FIS with GIS proved effective in identifying earthquake risk centers and assisting policymakers in strategic planning to address earthquake-related challenges. However, challenges arose due to the vast study area and limited access to specific data, such as building materials and textures, impacting the accuracy of earthquake vulnerability and risk assessment, particularly in regions like Bam. The success of the modeling process underscores its utility as a valuable tool for enhancing urban infrastructure and designing new cities. Future research should address these aspects and incorporate social factors into vulnerability assessments. Additionally, exploring the integration and comparison of different artificial intelligence and machine learning methods presents a valuable opportunity for future investigation.