Structural stress perturbation in salt formations is important for salt-cavern site selection, cavern stability, and underground storage safety, but direct stress measurements are usually sparse and numerical geomechanical modeling depends strongly on model parameters and boundary conditions. This study proposes a seismic curvature-based method for estimating local structural stress perturbation in finite-thickness salt layers. The method uses interpreted top and bottom salt-layer horizons to construct the middle surface and thickness field, calculates the maximum and minimum principal curvatures, and introduces Poisson coupling and a thickness-dependent correction factor to build a normalized curvature-derived structural stress index. Synthetic model tests show that the proposed index is controlled not only by curvature anomalies, but also by principal-curvature coupling, salt-layer thickness, and finite-thickness correction. Mechanical validation indicates that the index is spatially consistent with the main stress concentration patterns obtained from theoretical and elastic solutions, while sensitivity analysis shows that the major high-value zones remain relatively stable under parameter variations. Field applications demonstrate that the proposed method can generate continuous stress concentration zoning maps from seismic salt-layer horizons. The method provides a rapid seismic–geometry-constrained tool for identifying potential stress-sensitive zones and supporting salt-cavern site evaluation, cavern layout optimization, monitoring deployment, and subsequent geomechanical modeling.