Basin-scale geometric focusing: a probabilistic-geometric framework for global tsunami exposure assessment and the 2025 Kamchatka Peninsula tsunami

We present a hybrid probabilistic-geometric framework that integrates probabilistic earthquake statistics with large-scale ray-tracing simulations to efficiently map global coastal tsunami exposure. Utilizing a catalog of historical tsunamigenic events and the Gutenberg–Richter relation, we derive probabilistic weights for 9000 rays released across potential fault zones. The simulated ray pathways reveal persisting bathymetry-driven energy convergence patterns that govern far-field coastal focusing and shadowing. The geometric framework's predictive power is demonstrated using the 2025 M 8.8 Kamchatka Peninsula earthquake and the 2011 M 9.0 Tohoku-oki event. Validation against these events utilizes phase-corrected FUNWAVE-TVD simulations and in-situ DART observations. The resulting ray-based coastal focusing patterns display strong qualitative and quantitative spatial agreement (e.g., Spearman's ρ = 0.66 and ρ = 0.63, respectively) with the transoceanic maximum wave amplitudes from the high-fidelity FUNWAVE-TVD model. This agreement confirms the hybrid probabilistic-geometric approach as a scalable and computationally efficient tool for rapidly identifying transoceanic focusing potential and prioritizing coastal regions for high-resolution exposure assessment, mapping relative geometric convergence.