###### Abstract  
The multi-modal two-step floating catchment area (MM-2 SFCA) method is an extension of the two-step floating catchment area (2 SFCA) method that incorporates the impact of different transportation modes, thereby facilitating more accurate calculations of the spatial accessibility of public facilities in urban areas. However, the MM-2 SFCA method does not account for the impact of distance within the search radius on supply-demand capacities, and it assumes an idealized supply-demand relationship. This paper introduces the gravity model into the MM-2 SFCA method, proposing a multi-modal gravity-based 2 SFCA (MM-2 SFCA) method to better account for distance decay and supply-demand relationships. Furthermore, a standardized gravity model is proposed based on the traditional gravity model. This model imposes constraints on upper and lower limits for distance decay weights without compromising the fundamental curve characteristics of the gravity model, thereby avoiding extreme weight scenarios. The accessibility of public hospitals in Shenzhen is evaluated through the integration of basic geographic information data, resident travel data, and official statistical data. The findings demonstrate that the standardized gravity model effectively addresses the issue of excessively high local distance weights in the traditional gravity model, making it more suitable as a distance decay function. The MM-2 SFCA method improves the consideration of distance and supply-demand relationships, thereby facilitating a more rational distribution of accessibility on a global scale. This study discovers differences in the spatial allocation of public hospital resources across the Shenzhen's districts. Accessibility within the metropolitan core is significantly higher than that outside the core. Additionally, there is a notable difference in the level of accessibility among the districts. Accessibility is found to be better in district centers and along the main traffic arteries. 2 SFCA; spatial accessibility; gravity model; spatial layout; medical facilities; Shenzhen 40.0.0000-0001-5000-0001-5000-0001-5000-0001-5000  
two-step floating catchment area (2 SFCA) method [7; 8] have garnered significant attention due to their similar theoretical foundations, broad application scenarios, and relatively comprehensive considerations. The gravity model, also known as the gravitational or potential model, is one of the most classic spatial interaction models that calculates the reachable area by setting a continuous scale of travel impedance. The 2 SFCA method determines the accessible facilities within the search radius of the demand points by sequentially searching for supply points and demand points. The 2 SFCA method is easy to understand, simple to operate, and highly interpretable, making it a foundational framework for various extended forms of research [9]. The 2 SFCA method has been extensively employed to quantify the spatial accessibility of diverse facilities. Researchers have applied it to assess spatial disparities in residents' access to medical resources, informing rational resource allocation [10; 11; 12; 13]; to explore the accessibility of urban park green spaces, advancing urban ecological restoration and green space functionality [14; 15]; and to measure the scarcity of elderly care facilities, leading to policy recommendations for optimized facility placement [16]. As the research scope broadens and methodological advancements occur, scholars have addressed the limitations of the traditional 2 SFCA method, leading to the development of a robust 2 SFCA methodology cluster. For instance, [PERSON] [17] introduced the concept of distance decay functions to refine accessibility estimates based on spatial distance relationships, addressing inaccuracies stemming from simple distance dichotomies. [PERSON] [18] integrated the classical Huff model [19] with the 2 SFCA method, considering both travel costs and facility service capabilities to enhance the method's rationality.