1. Introduction
Rapid urbanization and persistent dilapidated fabric in seismically active cities require risk and spatial resilience to be evaluated jointly, since disaster severity depends on the interaction between built-environment vulnerability, population distribution, and urban response capacity. Seismic vulnerability assessment, urban risk analysis, shelter siting, and resilience measurement have nonetheless developed largely as separate research streams. Consequently, no integrated framework has quantified both the potential demand generated by earthquake-induced displacement and a city’s spatial response capacity in a single measure. This gap is especially consequential for historic Iranian cities with dense cores and narrow street networks. Kerman, located in a high seismic-hazard zone with an extensive dilapidated historic core, exemplifies this category, yet no prior study has jointly analyzed its vulnerability, exposure, and response capacity within a unified spatial framework.

2. Research Questions
1. What is the spatial pattern of seismic vulnerability, spatial risk, and spatial resilience in Kerman city?
2. How does the relationship between the spatial distribution of risk and emergency shelter capacity shape Kerman’s spatial resilience?
2. Literature Review
Contemporary scholarship frames risk as the interaction of vulnerability, exposure, and response capacity (Alexander, 2012; Blaikie et al., 2014; UNDRR, 2017, 2022), rooted in the Pressure-and-Release model, although this framework translates poorly into measurable neighborhood-scale spatial patterns (Wilder, 2018). Composite indices also frequently rely on arbitrarily weighted variables without sensitivity testing (Beccari, 2016; Wehbe & Baroud, 2024). Shelter-accessibility studies commonly assume an intact post-earthquake road network despite evidence that seismic events can disable access routes (Hosseini et al., 2024; Liu & Guo, 2025). The closest precedent is Wei et al.’s (2024) identification of a “spatial incongruity between disaster resilience and risk” in Chengdu. Iranian studies confirm concentrated vulnerability in historic cores but continue to treat risk analysis and shelter siting as separate research streams (Amrei et al., 2024; Kamranzad et al., 2020). These gaps motivate the integrated Spatial Resilience Index (SRI) developed in this study.

3. Methodology
This applied study used spatial multi-criteria analysis in a GIS environment on a 30×30 m raster grid covering Kerman (population 527,650; 2016 census), with population dasymetrically mapped onto cells. Dilapidated fabric was identified using structural instability, parcel fragmentation, and street impermeability. Seismic vulnerability was assessed through the Karmania Hazard Model (KHM), combining six criteria weighted by AHP (15 experts; consistency ratio = 0.04), and applied to an MMI-IX scenario using JICA (2000) fragility curves. Validation against an independent dilapidated-fabric layer yielded AUC = 0.83 and Cohen’s κ = 0.62. Population exposure combined vulnerability and population layers into a Population Exposure Index (PEI = Ph/Pt). Shelter capacity was assessed for immediate shelter (500 m buffer, 2 m²/person) and transitional shelter (>10,000 m², 9.5 m²/person), yielding a Shelter Capacity Index (SCI = Cs/Ds) and Spatial Resilience Gap (Ds − Cs). Spatial risk was calculated as R = V × E. Fuzzy AHP weighted spatial risk and shelter capacity to parameterize the SRI: SRI = Wr(1−R) + Wc(C), classified into five levels. Robustness was tested through OAT weight perturbation, alternative normalization/aggregation methods, and 1,000-iteration Monte Carlo simulation.

4. Results
The KHM identified vulnerability hotspots in the central, eastern, northern, southeastern, and southwestern districts, coinciding with the historic core; high-to-complete damage classes covered 31.7 km² (24.4% of the city). Population exposure analysis showed that 257,780 residents (48.9%) lived in high-to-complete vulnerability zones (PEI = 0.489), indicating the importance of population concentration in shaping risk. The highest spatial risk occurred in the central core and eastern/southeastern districts, where vulnerability and population density reinforced one another. Shelter assessment identified 483 immediate-shelter sites and 497 transitional-shelter candidates. Twelve principal transitional sites (2,057,467 m²) provided potential capacity for 216,576 people against a demand of 257,780 (SCI = 0.84), producing a citywide Spatial Resilience Gap of 41,204 people. Fuzzy AHP assigned weights of 0.62 to spatial risk and 0.38 to shelter capacity. The SRI showed a clear center–periphery structure: 30.8% of the city fell within very low/low resilience, concentrated in the historic core; 45.6% fell within high/very high resilience in peripheral areas; and 23.6% showed medium resilience. Sensitivity analysis confirmed robustness: ±20% OAT weight perturbations shifted critical low-resilience areas by no more than ±7.2 percentage points; alternative methods correlated above 0.94 with the baseline; and Monte Carlo results showed CV < 0.15 in 85% of cells, with the center–periphery pattern stable across all iterations.

5. Discussion
The findings situate Kerman within a broader pattern of structural risk accumulation in historic Iranian urban cores, consistent with Tehran’s historic fabric (Amrei et al., 2024). Critically, spatial resilience is not simply risk’s inverse: adequate shelter access can elevate resilience even under moderate risk, demonstrating that response infrastructure independently moderates the risk–resilience relationship. This parallels Wei et al.’s (2024) Chengdu findings and suggests that such spatial incongruities may be characteristic of historic-core cities. A key limitation is the assumption of an intact road network. Because shelter-access shortfalls concentrate in fine-grained, dilapidated fabric prone to post-earthquake blockage, the actual supply–demand gap may exceed the static estimate of 41,204 people. The SRI’s stability under weight perturbation, a validation step often absent from composite-index studies (Beccari, 2016), strengthens confidence that the observed spatial structure reflects underlying conditions rather than expert judgment alone.

6. Conclusion
Kerman’s spatial resilience follows a pronounced center–periphery pattern: the historic core, characterized by dilapidated fabric, high seismic vulnerability, dense population, and limited shelter access, occupies the lowest resilience tiers, whereas peripheral areas perform comparatively well. The main theoretical contribution is demonstrating that spatial resilience emerges from the balance between risk and response capacity rather than constituting risk’s simple inverse. Methodologically, the integrated, sensitivity-tested SRI provides a decision-support tool for prioritizing risk-reduction interventions, urban regeneration, and emergency resource allocation in historic, seismically active cities. Its limitations include the static road-network assumption, exclusion of social and institutional resilience dimensions, and the cross-sectional nature of the data.