Modelling tsunami initial conditions due to rapid coseismic seafloor displacement: efficient numerical integration and a tool to build unit source databases

Abstract

This paper, published in Natural Hazards and Earth System Sciences by researchers from INGV (Italy), UMA (Spain), and GFZ (Germany), presents a novel method for calculating the initial conditions of tsunamis generated by rapid coseismic seafloor displacements. The authors propose an efficient numerical integration of the Kajiura filter, which translates seafloor deformation into sea surface displacement by filtering out short wavelengths that are damped by the water column. The method discretizes the seafloor deformation into rectangular "unit sources" and computes the sea surface response as a linear combination of these elementary contributions.

Key contributions include:

- Efficient Numerical Integration: An optimized adaptive quadrature scheme (Gauss-Legendre) is developed to solve the Kajiura integral, significantly reducing computational time compared to standard methods while maintaining high accuracy. - Unit Source Database: The study introduces a tool to generate databases of pre-computed, filtered unit sources for specific regions (based on local bathymetry). This allows for rapid construction of tsunami initial conditions by simply summing pre-calculated effects, ideal for real-time early warning systems and probabilistic hazard assessment. - Horizontal Displacements: The model explicitly accounts for the contribution of horizontal seafloor displacements to the vertical uplift, which is critical in areas with steep bathymetry like trenches. - Validation: The approach is validated using the 2006-2007 Kuril Islands earthquake doublet (a megathrust and an outer-rise event), demonstrating that the proposed method produces initial conditions that match or improve upon existing analytical solutions, with greater computational efficiency.

The resulting algorithm and database tool facilitate the rapid simulation of thousands of tsunami scenarios, supporting both source inversion studies and operational tsunami hazard planning.