The Energy of a Tsunami Generated by Dynamic Uplift of the Ocean Bottom. I. Analytical Solutions

Emile A. Okal*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
JournalPure and Applied Geophysics
DOIs
StateAccepted/In press - 2021

Keywords

  • Shallow water approximation
  • theoretical hydrodynamics
  • Tsunami energy

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology

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