# Tsunami modeling with dynamic seafloors: a high-order solver validated with shallow water benchmarks

## TL;DR

This paper presents a high-order spectral solver for nonlinear shallow water equations that incorporates dynamic seafloor motion, improving tsunami modeling accuracy and efficiency, validated through benchmarks and a novel seismological study.

## Contribution

It introduces a Fourier continuation-based pseudo-spectral algorithm for modeling tsunamis with time-dependent seafloor displacement, enabling high accuracy and efficiency.

## Key findings

- High-order convergence in space and time.
- Effective removal of numerical dispersion errors.
- Demonstrated importance of dynamic seafloor modeling in hazard assessment.

## Abstract

Recent scientific studies have suggested that, in certain physical configurations, the time-dependent behavior of earthquake rupture and seafloor (bathymetry) motion can leave observable near-field signatures in tsunami wave generation and propagation. However, dynamic ground movement is often neglected in conventional tsunami models, which commonly assume instantaneous ground displacement (sourcing). This work introduces a pseudo-spectral algorithm for the solution of the nonlinear shallow water equations with timedependent seafloor displacement and velocity. Based on a Fourier continuation (FC) methodology for the accurate trigonometric interpolation of a non-periodic function, the solver provides high-order convergence in space and time; mild (linear) Courant-Friedrichs-Lewy (CFL) constraints for explicit time integration; and results that are effectively free of numerical dispersion (or ''pollution'') errors. Such properties enable the efficient and robust resolution of the different space-time scales involved modeling tsunamis generated by dynamic earthquake ground motion (including over long distances). Numerical experiments attesting to accuracy and computational performance are presented with direct comparisons to high-order finite difference methodologies. The solver is physically validated by a number of classical and semi-classical benchmark cases based on simulated or experimental data. Additionally, a seismologically realistic, first-of-its-kind parametric study based on earthquake speed is introduced, whose results-easily facilitated by the FC-based approach proposed herein, with minimal numerical tuning-further demonstrate the potential importance of (and the motivation herein for) incorporating time-dependent seafloor behavior in quantitative tsunami hazard assessment.

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Source: https://tomesphere.com/paper/2508.20596