### Casualty Assessment Method Based on Building Vulnerability  
Casualty assessment methods that consider the seismic vulnerability of structures can not only predict regional earthquake hazards and rapidly assess casualties post-earthquake, but also, by limiting the number of casualties to socially acceptable levels, infer building vulnerability to provide a scientific basis for establishing reasonable seismic design standards [14; 15]. The common assessments of building vulnerability primarily include two approaches: the damage matrix method (based on historical data and expert experience) and the analytical method (based on structural performance calculations) [16]. By analyzing the probability of different types of buildings collapsing (or experiencing varying degrees of damage) during an earthquake, the number of people potentially trapped within these buildings, and the corresponding earthquake death and injury rates, the total number of casualties can be estimated. Japanese scholars analyzed the relationship between the number of completely destroyed houses \(H\) and the number of deaths \(D\), establishing the concise Kawakatsu formula, as shown in Equation (3). Subsequently, they further investigated the relationship between death rates, seismic motion intensity, and the rate of complete house damage, while also selecting data from the Great Kanto Earthquake for urban and rural areas where no house burning or loss occurred, analyzing the relationship between the number of completely destroyed houses and the number of deaths [17]. \[D=0.01\times H^{1.3} \tag{3}\]  
In the 1980s, the U.S. Federal Emergency Management Agency (FEMA) commissioned the Applied Technology Council (ATC) to classify and study building types in California [18], introducing the ATC-13 seismic damage matrix method to systematically investigate expected future earthquake losses in California. [PERSON] et al. [19] and [PERSON] et al. [20] refined casualty rates based on actual earthquake data. The probability \(P(C_{k}I_{j})\) of casualty state \(C_{k}\) (five levels) due to building damage under earthquake intensity \(I_{j}\) is given by Equation (4), where \(D_{i}\) represents building damage levels (\(D_{0}\) for no damage; \(D_{1}\) for slight damage; \(D_{2}\) for moderate damage; \(D_{3}\) for severe damage; \(D_{4}\) for very severe damage; \(D_{5}\) for collapse); \(P(D_{i}C_{k})\) is the probability of casualty state \(C_{k}\) given building damage level \(D_{i}\); and \(P(D_{i}I_{j})\) is the probability of building damage levels \(D_{1}\) to \(D_{3}\) under earthquake intensity \(I_{j}\). \[P(C_{k}I_{j})=\sum_{i=1}^{3}P(D_{i}I_{j})P(D_{i}C_{k})+\sum_{j=1}^{n}\left[P(D_ {NC}I_{j})P(D_{NC}C_{k})+P(D_{C}I_{j})P(D_{C}C_{k})\right] \tag{4}\]  
[PERSON] and [PERSON] [21] developed a post-earthquake casualty assessment model by considering five influencing factors: average indoor population, occupancy time, number of trapped individuals, building collapse mortality rate, and rescue efficiency. [PERSON] et al. [22] analyzed the relationships among population, GDP, and earthquake fatalities across different intensity zones, deriving a mortality rate function classified by per capita GDP through regression. [PERSON] et al. [23] refined [PERSON]'s assessment model by accounting for regional differences in building vulnerability matrices and dynamic changes in population data. In summary, the impact of building vulnerability on earthquake casualties cannot be overlooked, with each of its two expression methods having distinct advantages and limitations. The seismic damage matrix method is simple and practical, but is constrained by historical earthquake data, limiting its applicability. The vulnerability analysis method comprehensively considers parameters such as structural type, building height, construction age, and seismic fortification level.