Defining the Tsunamigenic Limit State Function: A Multivariate Extreme Value Theory Approach with Archimedean Copulas

Traditional tsunami prediction relies on binary classification using machine learning, which lacks physical interpretability and extrapolation capability. This study introduces a novel probabilistic framework for tsunami genesis characterization using Multivariate Extreme Value Theory (MEVT) and Archimedean copula dependence modeling. We analyse an expanded dataset of 1,002 significant earthquakes [Formula: see text] drawn from the USGS/NEIC catalog spanning 1976-2022 and supplemented with moment-magnitude conversions following Scordilis (2006), yielding 391 confirmed tsunami events (39.0%). Generalized Extreme Value and Generalized Pareto distributions are fitted to the marginal parameters; negative shape parameters [Formula: see text] confirm light-tailed magnitude behavior consistent with tectonic fault-dimension constraints. Among three competing Archimedean families, the Clayton copula provides the best fit for magnitude-significance dependence ([Formula: see text] = 2.367, AIC = -725.17, AIC weight = 98.4%) with strong lower tail dependence ([Formula: see text] = 0.746, Kendall’s [Formula: see text] = 0.542), while magnitude-depth and depth-significance pairs display near-independence best described by the Frank copula. These bivariate structures are embedded in a trivariate nested Gumbel-Hougaard copula for complete joint modelling. A closed-form limit state equation is derived via the First Order Reliability Method (FORM): [Formula: see text], where inverse depth contributes 26.4% of total variance. Cross-validation yields AUC = 0.607 ± 0.038, Brier score = 0.233, and ECE = 0.031. This framework provides engineers with a physics-based, directly calculable tool for probabilistic tsunami hazard assessment (PTHA), bridging structural reliability theory with seismological practice.