Depth-Dependent Rigidity and Stress Drop Control on Near- and Far-Field Tsunami Hazard from Mediterranean Subduction Earthquakes and Site-Specific PTHA

In this study, we present a physics-based framework for generating stochastic earthquake source models that jointly account for depth-dependent rigidity and stress-drop variability. This formulation extends previous approaches by explicitly linking the co-evolution of mechanical properties with depth to rupture geometry, slip concentration, and rupture duration, providing a consistent representation of subduction earthquake sources from shallow to deeper domains. The methodology is designed for ensemble-based Seismic Probabilistic Tsunami Hazard Assessment (S-PTHA) and ensures consistency between individual-event rupture characteristics, seismic moment release, and tsunami hazard estimates.

We systematically explore three depth-dependent rigidity–stress-drop models characterised by different rigidity gradients, spanning the range between a constant stress-drop end-member case, (Bilek & Lay, 1999) and the Preliminary Reference Earth Model (PREM). For a fixed seismic moment, rupture size and propagation velocity are calibrated to reproduce observed rupture durations, allowing stress-drop variability with depth to emerge naturally. Results show that steeper rigidity gradients lead to more spatially compact rupture areas with higher shallow slip amplitudes, whereas smoother gradients promote larger rupture extents and more distributed lower slip. These differences are most pronounced for shallow events and progressively diminish at greater depths, where mechanical properties converge, and rupture behaviour becomes less sensitive to parameter variability.

To reconcile stochastic shallow slip amplification with long-term tectonic convergence, we modified the balancing procedure, which was introduced by Scala et al., 2020, to a depth-based approach that enforces long-term slip consistency across the ensemble according to the depth-dependent contribution of individual ruptures. This approach removes the artificial overrepresentation of shallow events while preserving physically motivated shallow slip amplification at the single-event scale, enabling meaningful comparisons of hazard outcomes across models.

Applying this framework in the Mediterranean basin to the Calabrian, Hellenic, and Cyprus subduction zones using three-dimensional slab geometries, we perform S-PTHA calculations to offshore points of interest (POIs). We use as the hazard metric the maximum offshore wave height. Results for the regional models indicate a clear depth and distance-dependent control on tsunami hazard, with near-field hazard outcomes particularly sensitive to the joint treatment of depth-dependent rigidity and stress-drop variability. Indeed, steeper stress-drop gradients with depth significantly reduce slip amplitudes for large shallow events by promoting larger rupture areas, hence leading to lower probabilities of exceedance for a given tsunami height level. In contrast, far-field tsunami hazard is primarily governed by rigidity, as the effect of the extended-source features associated with stress drop variability diminishes with distance. Consequently, peak slip amplitude, mainly controlled by rigidity, emerges as the dominant factor for far-field hazard. 

To further assess the implications of these depth-dependent source effects at the coastal scale, the same rupture ensembles are implemented within a high-resolution local PTHA framework for Catania and Siracusa, two test sites along eastern Sicily, for which we will provide preliminary results. This application enables a site-specific investigation of how alternative rigidity-stress-drop formulations translate into differences in nearshore wave amplification and inundation potential, providing a physically consistent basis for comparison with more conventional earthquake source representations.