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.

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.