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Sound signals of tsunamis from a slender fault

Published online by Cambridge University Press:  11 December 2017

Chiang C. Mei Open the ORCID record for Chiang C. Mei [Opens in a new window]  and
Usama Kadri
Chiang C. Mei*
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Usama Kadri
Affiliation:
School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: ccmei@mit.edu
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Abstract

Since the speed of sound in water is much greater than that of the surface gravity waves, acoustic signals can be used for early warning of tsunamis. We simplify existing works by treating the sound wave alone without the much slower gravity wave, and derive a two-dimensional theory for signals emanating from a fault of finite length. Under the assumptions of a slender fault and constant sea depth, the asymptotic technique of multiple scales is applied to obtain analytical results. The modal envelopes of the two-dimensional sound waves are found to be governed by the Schrödinger equation and are solved explicitly. An approximate method is described for the inverse estimation of fault properties from the pressure record at a distant hydrophone.

JFM classification

Acoustics: Acoustics Geophysical and Geological Flows: Coastal engineering Acoustics: Hydrodynamic noise
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 836 , 10 February 2018 , pp. 352 - 373
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Copyright
© 2017 Cambridge University Press 

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References

Abdolali, A., Kirby, J. T. & Bellotti, G. 2015 Depth-integrated equation for hydro-acoustic waves with bottom damping. J. Fluid Mech. 766, R1.Google Scholar
Abramowitz, M. & Stegun, A. A. 1964 Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, vol. 55. Courier Corporation.Google Scholar
Brekhovskikh, L. M. & Lysanov, Y. P. 1991 Fundamentals of Ocean Acoustics. Springer.Google Scholar
Chierici, F., Pignagnoli, L. & Embriaco, D. 2010 Modeling of the hydroacoustic signal and tsunami wave generated by seafloor motion including a porous seabed. J. Geophys. Res. 115 (C3), C03015.Google Scholar
Denny, M. W. 1993 Air and Water. Princeton University Press.CrossRefGoogle Scholar
Erdélyi, A. 1956 Asymptotic expansions of Fourier integrals involving logarithmic singularities. J. Soc. Ind. Appl. Maths 4 (1), 38–47.CrossRefGoogle Scholar
Eyov, E., Klar, A., Kadri, U. & Stiassnie, M. 2013 Progressive waves in a compressible-ocean with an elastic bottom. Wave Motion 50 (5), 929–939.CrossRefGoogle Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 2014 Table of Integrals, Series, and Products. Academic Press.Google Scholar
Hamling, I. J., Hreinsdóttir, S., Clark, K., Elliott, J., Liang, C., Fielding, E., Litchfield, N., Villamor, P., Wallace, L., Wright, T. J. et al. 2017 Complex multifault rupture during the 2016 M W 7.8 Kaikōura earthquake, New Zealand. Science 356 (6334), eaam7194.Google Scholar
Hendin, G. & Stiassnie, M. 2013 Tsunami and acoustic–gravity waves in water of constant depth. Phys. Fluids 25 (8), 086103.Google Scholar
Kadri, U. 2015 Acoustic–gravity waves interacting with a rectangular trench. Intl J. Geophys. 2015, 8036834.CrossRefGoogle Scholar
Kadri, U. & Akylas, T. R. 2016 On resonant triad interactions of acoustic–gravity waves. J. Fluid Mech. 788, R1.CrossRefGoogle Scholar
Kadri, U., Crivelli, D., Parsons, W., Colbourne, B. & Ryan, A. 2017 Rewinding the waves: tracking underwater signals to their source. Scientific Reports 7, 13949.Google Scholar
Kadri, U. & Stiassnie, M. 2012 Acoustic–gravity waves interacting with the shelf break. J. Geophys. Res. 117 (C3), C03035.Google Scholar
Kadri, U. & Stiassnie, M. 2013 Generation of an acoustic–gravity wave by two gravity waves, and their subsequent mutual interaction. J. Fluid Mech. 735, R6.Google Scholar
Kajiura, K. 1970 Tsunami source, energy and the directivity of wave radiation. Bull. Earthq. Res. Inst. 48, 835–869.Google Scholar
Miyoshi, H. 1954 Generation of the tsunami in compressible water. Part I. J. Oceanogr. Soc. Japan 10 (1), 1–9.Google Scholar
Nosov, M. A. 1999 Tsunami generation in compressible ocean. Phys. Chem. Earth B 24 (5), 437–441.Google Scholar
Nosov, M. A. & Kolesov, S. V. 2007 Elastic oscillations of water column in the 2003 Tokachi-oki tsunami source: in-situ measurements and 3-D numerical modelling. Nat. Hazards Earth Syst. Sci. 7 (2), 243–249.Google Scholar
Sammarco, P., Cecioni, C., Bellotti, G. & Abdolali, A. 2013 Depth-integrated equation for large-scale modelling of low-frequency hydroacoustic waves. J. Fluid Mech. 722, R6–1.Google Scholar
Sells, C. C. L. 1965 The effect of a sudden change of shape of the bottom of a slightly compressible ocean. Phil. Trans. R. Soc. Lond. A 258 (1092), 495–528.Google Scholar
Stiassnie, M. 2010 Tsunamis and acoustic–gravity waves from underwater earthquakes. J. Engng Maths 67 (1), 23–32.Google Scholar
Stoll, R. D. 1977 Acoustic waves in ocean sediments. Geophysics 42 (4), 715–725.Google Scholar
Wu, N. & Wei, Y.-Q. 2013 Research on wavelet energy entropy and its application to harmonic detection in power system. Intl J. Appl. Phys. Maths 3 (1), 31–33.Google Scholar
Yamamoto, T. 1982 Gravity waves and acoustic waves generated by submarine earthquakes. Intl J. Soil Dyn. Earthq. Engng 1 (2), 75–82.Google Scholar