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Analytical Solutions of Seismic-Generated Internal Tsunamis

Internal tsunamis induced by an instantaneous seabed deformation are theoretically analyzed in this paper. Based on Hammack’s mathematical methods and findings, an in-depth and extensive study is performed to examine tsunami waveforms, especially at the initial stage. Waveforms of surface and internal tsunamis induced by three fundamental seabed uplifts, the rectangle-, cosine-, and sine-shape deformations, are solved to constitute an important base for analyzing waves generated by arbitrary seabed movements. A closed-form solution for the rectangle-shape deformation and analytic solutions for cosine and sine cases are obtained. The effects of spatial parameters on waveforms and the contributions of two frequency modes are investigated for the Boussinesq limit. The derived wave solutions not only improve the understanding of the formation of internal tsunamis but also provide an exact initial waveform for simulating wave propagation by various wave models.