Earthquakes in marine settings may trigger long chains of secondary hazards. These chains propagate from the seafloor to coastal infrastructure and on to society, yet they have rarely been quantified as a whole. To address this gap, this study proposes a quantitative model of marine seismic hazard chains that combines a catastrophe-dynamics formulation with directed-graph analysis. This network draws on documented secondary hazards from dozens of major tsunamis and includes 39 nodes. This study characterises its topology through degree centrality, network density, centralisation, mean path length, and a layer-resolved net-flow measure. The result is a single-source, dual-hub, multi-sink cascade that is shallow, with most hazards reachable within about two steps. Submarine and coastal earthquakes drive the whole chain, while tsunamis and critical infrastructure failure act as the two high-throughput hubs that amplify and route the flow. Critical network failure is the principal convergence node, where these losses accumulate. The model reveals a monotonic cascade from geological triggers to socioeconomic losses, in which the engineering layer is the gateway through which natural hazards convert into technological failures. A comparison with a mainland earthquake chain at a common taxonomic resolution shows that the two systems share the same four-layer architecture. The mainland earthquake chain exhibits stronger centralisation while the marine tsunami chain presents a more distributed structure. These findings suggest that the controllable engineering hubs, rather than the uncontrollable seismic sources, are the most effective targets for disaster mitigation.