Tsunami propagation kernel and its applications

Abstract

Tsunamis rarely occur in a specific area, and their occurrence is highly uncertain. Suddenly generated from their sources in deep water, they occasionally undergo tremendous amplification in shallow water to devastate low-lying coastal areas. Despite the advancement of computational power and simulation algorithms, there is a need for novel and rigorous approaches to efficiently predict coastal amplification of tsunamis during different disaster management phases, such as tsunami risk assessment and real-time forecast. This study presents convolution kernels that can instantly predict onshore waveforms of water surface elevation and flow velocity from observed/simulated wave data away from the shore. Kernel convolution involves isolating an incident-wave component from the offshore wave data and transforming it into the onshore waveform. Moreover, unlike previously derived ones, the present kernels are based on shallow-water equations with a damping term and can account for tsunami attenuation on its path to the shore with a damping parameter. Kernel convolution can be implemented at a low computational cost compared to conventional numerical models that discretise the spatial domain. The prediction capability of the kernel method was demonstrated through application to real-world tsunami cases.