Abstract
Based on a simple physical model, we derive a formula for the energy radiated into a tsunami by a dynamic deformation of the ocean floor. We use the analytical solutions developed by J.L. Hammack, Jr. (1972, Tsunamis – A model of their generation and propagation, Ph.D. Dissertation, 261 pp., California Institute of Technology, Pasadena) to show that, in addition to its expected dependence on the source rise time, and even in the limiting case of an instantaneous source, the energy of the tsunami is controlled by the ratio of water depth to source size. For very large earthquakes, these results have no impact on the time-honored approximation which uses the static deformation of the ocean floor as a set of initial conditions of the surface displacements for numerical simulations, but they provide insight into the theoretical limits of this practice.
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Acknowledgements
Discussions with Costas Synolakis and Tony Dalrymple are gratefully acknowledged. The paper was greatly improved by the comments of an anonymous reviewer.
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Okal, E.A. The Energy of a Tsunami Generated by Dynamic Uplift of the Ocean Bottom. I. Analytical Solutions. Pure Appl. Geophys. 178, 4985–4999 (2021). https://doi.org/10.1007/s00024-021-02804-0
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DOI: https://doi.org/10.1007/s00024-021-02804-0