The impact of variable seabed bathymetry on tsunami wave propagation: a one-dimensional shallow water equation using Forward Time Central Space scheme

Tsunami wave dynamics are profoundly dictated by seafloor morphology, yet the specific influence of complex bathymetry on wave evolution remains a critical gap in predictive modeling. This research utilizes a finite difference approach to solve one-dimensional linearized shallow water equations (1D SWE), simulating tsunami propagation across three distinct seabed profiles: flat, sloping, and wavy. Our numerical results reveal that seafloor geometry is a primary driver of both wave amplification and velocity transformation. While flat beds maintain stable, low-hazard profiles characteristic of the deep ocean, sloping bathymetry triggers intense shoaling effects, maximizing wave height as the energy compresses in shallower coastal regions. Crucially, wavy seabed configurations induce complex energy dispersion and amplitude fluctuations, highlighting the non-linear risks posed by irregular underwater terrain. These findings underscore that precise bathymetric data is not merely a variable—it is a prerequisite for accurate early warning systems and robust coastal disaster mitigation strategies. This study provides a foundational framework for integrating high-resolution seafloor data into real-time risk assessments.