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

Emile A. Okal

doi:10.1007/s00024-021-02804-0

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

Emile A. Okal^*

^*Corresponding author for this work

Earth and Planetary Sciences

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 language	English (US)
Pages (from-to)	4985-4999
Number of pages	15
Journal	Pure and Applied Geophysics
Volume	178
Issue number	12
DOIs	https://doi.org/10.1007/s00024-021-02804-0
State	Published - Dec 2021

Funding

Discussions with Costas Synolakis and Tony Dalrymple are gratefully acknowledged. The paper was greatly improved by the comments of an anonymous reviewer.

Keywords

Shallow water approximation
Tsunami energy
theoretical hydrodynamics

ASJC Scopus subject areas

Geophysics
Geochemistry and Petrology

Access to Document

10.1007/s00024-021-02804-0

Cite this

@article{b1cccb743c42409aa7711ef9e6930365,

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

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.",

keywords = "Shallow water approximation, Tsunami energy, theoretical hydrodynamics",

author = "Okal, {Emile A.}",

note = "Funding Information: Discussions with Costas Synolakis and Tony Dalrymple are gratefully acknowledged. The paper was greatly improved by the comments of an anonymous reviewer. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2021",

month = dec,

doi = "10.1007/s00024-021-02804-0",

language = "English (US)",

volume = "178",

pages = "4985--4999",

journal = "Pure and Applied Geophysics",

issn = "0033-4553",

publisher = "Birkhauser Verlag Basel",

number = "12",

}

TY - JOUR

T1 - The Energy of a Tsunami Generated by Dynamic Uplift of the Ocean Bottom. I. Analytical Solutions

AU - Okal, Emile A.

N1 - Funding Information: Discussions with Costas Synolakis and Tony Dalrymple are gratefully acknowledged. The paper was greatly improved by the comments of an anonymous reviewer. Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2021/12

Y1 - 2021/12

N2 - 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.

AB - 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.

KW - Shallow water approximation

KW - Tsunami energy

KW - theoretical hydrodynamics

UR - http://www.scopus.com/inward/record.url?scp=85111091110&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85111091110&partnerID=8YFLogxK

U2 - 10.1007/s00024-021-02804-0

DO - 10.1007/s00024-021-02804-0

M3 - Article

AN - SCOPUS:85111091110

SN - 0033-4553

VL - 178

SP - 4985

EP - 4999

JO - Pure and Applied Geophysics

JF - Pure and Applied Geophysics

IS - 12

ER -

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

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this