## 1 Introduction  
With rapid urbanization, it has been estimated that around 68 percent of the population will be living in cities by 2050. The concerns around human health issues regarding urban settings has shaped a large body of research. However, these attempts are yet to provide measurable standards for healthy cities' policy targets [1], and more research is required to understand the full extent of the impacts of urban settings on various health dimensions [2]. Particularly, the influence of urban green space (UGS) on individuals' overall well-being and quality of life has been highlighted by numerous studies [3, 4, 5, 6]. Research has shown a stronger association of UGS with improved physical health metrics, while the mental health impacts remain less clear [7]. Similar to other urban amenities, UGS can be distributed inequitably and in favor of communities with higher socioeconomic status (SES) [8]. Similarto other OECD countries, Australian cities have arguably failed to provide equitable access to health-supportive amenities and infrastructure [9]. Numerous studies have shown a positive relationship between UGS, physical health, and well-being in general [5; 10; 11; 12; 13; 14]. Alongside personal and behavioral factors, environmental factors significantly contribute to decreased cardiovascular disease (CVD) rates [15; 16; 17; 18]. Research has found that living in areas with higher and more variable UGS forms can decrease the CVD hospitalization rate by 37% [19]. An extensive study on over 100,000 Australians shows that living within 1.6 km of areas with at least 30% tree canopy significantly reduces the risk of CVD [20]. A longitudinal population-based cohort study in Canada showed that a 1.2% increase in Normalized Difference Vegetation Index (NDVI) exposure is associated with a 3% reduction in stroke risk [20]. These studies suggest a strong theoretical basis for a positive association between higher vegetation density and lower CVD rates, but the type of vegetation (if it is a large natural reserve that is accessible to the public or a sidewalk tree line or a gated golf course) and exposure is not clear. A systematic review of the UGS and CVD shows that a considerable body of literature is mainly focused on measures like the UGS area per inhabitant, or UGS area/count/percent within a certain buffer zone or urban area [21]. The findings have confirmed the positive relationship but have not further suggested practical tools for urban planning and UGS policy making purposes. Despite being essential for the primary stages of identifying potential associations, from an urban planning view, these approaches may disregard the spatial nature of UGS. For example, by drawing unrealistic boundaries like buffer zones or even official urban boundaries, some significant aspects can be neglected in the study, like accessibility through an existing network, and the impacts of neighboring UGSs. From an environmental justice perspective, UGS should be equitably distributed throughout a city [5], but even in developed countries, UGS availability is limited or distributed unevenly [8; 22]. The uneven UGS disparity can be associated with several factors, namely central versus suburban city areas. For instance, a comparative analysis shows that every kilometer farther from the city center contributes an average increase of 73 and 67 m to trips to the most frequently used UGS in Luxembourg and Brussels, respectively [23]. Similarly, [PERSON] and [PERSON] [24] revealed that although the majority of sub-districts in Berlin meet the 6 m\({}^{2}\) per person UGS threshold, inner-city areas with high immigrant rates and population density face disproportionate UGS shortages, confirming distributive injustice. Therefore, another factor associated with UGS distribution can be the socioeconomic status (SES) of the area, meaning that socioeconomically disadvantaged communities may be less exposed to UGS in their living environment than more affluent communities [25; 26]. For example, [PERSON] et al.