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Acoustic–gravity waves from multi-fault rupture

Published online by Cambridge University Press:  29 March 2021

Byron Williams Open the ORCID record for Byron Williams [Opens in a new window] ,
Usama Kadri Open the ORCID record for Usama Kadri [Opens in a new window]  and
Ali Abdolali Open the ORCID record for Ali Abdolali [Opens in a new window]
Byron Williams
Affiliation:
School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK
Usama Kadri*
Affiliation:
School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK
Ali Abdolali
Affiliation:
NWS/NCEP/Environmental Modeling Center, National Oceanic and Atmospheric Administration (NOAA), College Park, MD 20740, USA I.M. Systems Group, Inc. (IMSG), Rockville, MD 20852, USA University of Maryland, College Park, MD 20742, USA
*
†Email address for correspondence: kadriu@cardiff.ac.uk
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Abstract

The propagation of wave disturbances from a complex multi-fault submarine earthquake of slender rectangular segments in a sea of constant depth is discussed, accounting for both water compressibility and gravity effects. It is found that including gravity effects the modal envelopes of the modified two-dimensional acoustic waves and the tsunami are governed by the Schrödinger equation. An explicit solution is derived using a multi-fault approach that allows capturing the main peak of the tsunami. Moreover, a linear superposition of the solution allows solving complicated multi-fault ruptures, in particular in the absence of dissipation due to large variations in depth. Consequently, the modulations of acoustic waves due to gravity, and of tsunami due to compressibility, are governed simultaneously and accurately, which is essential for practical applications such as tsunami early warning systems. The results are validated numerically against the mild-slope equation for weakly compressible fluids.

JFM classification

Low-Reynolds-number flows: Slender-body theory

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JFM Papers
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Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A108
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Abdolali, A., Cecioni, C., Bellotti, G. & Kirby, J.T. 2015 a Hydro-acoustic and tsunami waves generated by the 2012 Haida Gwaii earthquake: modeling and in situ measurements. J. Geophys. Res. 120 (2), 958–971.CrossRefGoogle Scholar
Abdolali, A., Cecioni, C., Bellotti, G. & Sammarco, P. 2014 A depth-integrated equation for large scale modeling of tsunami in weakly compressible fluid. Coast. Engng Proc. 1 (34), 9.CrossRefGoogle Scholar
Abdolali, A., Kadri, U. & Kirby, J.T. 2019 Effect of water compressibility, sea-floor elasticity, and field gravitational potential on tsunami phase speed. Sci. Rep. 9, 16874.CrossRefGoogle ScholarPubMed
Abdolali, A., Kadri, U., Parsons, W. & Kirby, J.T. 2018 On the propagation of acoustic–gravity waves under elastic ice sheets. J. Fluid Mech. 837, 640–656.CrossRefGoogle Scholar
Abdolali, A. & Kirby, J.T. 2017 Role of compressibility on tsunami propagation. J. Geophys. Res. 122 (12), 9780–9794.CrossRefGoogle Scholar
Abdolali, A., Kirby, J.T. & Bellotti, G. 2015 b Depth-integrated equation for hydro-acoustic waves with bottom damping. J. Fluid Mech. 766, R1.CrossRefGoogle Scholar
Abdolali, A., Kirby, J.T., Bellotti, G., Grilli, S. & Harris, J.C. 2017 Hydro-acoustic wave generation during the Tohoku-Oki 2011 earthquake. In Coastal Structures and Solutions to Coastal Disasters 2015, pp. 24–34. American Society of Civil Engineers.CrossRefGoogle Scholar
Bernabe, G. & Usama, K. 2021 Near real-time calculation of submarine fault properties using an inverse model of acoustic signals. Appl. Ocean Res. 109, 102557.Google Scholar
Cecioni, C., Abdolali, A., Bellotti, G. & Sammarco, P. 2015 Large-scale numerical modeling of hydro-acoustic waves generated by tsunamigenic earthquakes. Nat. Hazards Earth Syst. Sci. 15 (3), 627–636.CrossRefGoogle Scholar
Cecioni, C., Bellotti, G., Romano, A., Abdolali, A., Sammarco, P. & Franco, L. 2014 Tsunami early warning system based on real-time measurements of hydro-acoustic waves. Procedia Engng 70, 311–320.CrossRefGoogle Scholar
Dziewonshi, A.M. & Anderson, D.L. 1981 Preliminary earth reference model. Phys. Earth Planet. Inter. 25, 297–356.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
Gower, J. 2005 Jason 1 detects the 26 December 2004 tsunami. EOS Trans. AGU 86 (4), 37–38.CrossRefGoogle Scholar
Grilli, S.T., Harris, J.C., Tajalli Bakhsh, T.S., Masterlark, T.L., Kyriakopoulos, C., Kirby, J.T. & Shi, F. 2013 Numerical simulation of the 2011 Tohoku tsunami based on a new transient FEM Co-seismic source: comparison to far- and near-field observations. Pure Appl. Geophys. 170 (6–8), 1333–1359.CrossRefGoogle Scholar
Grilli, S.T., Ioualalen, M., Asavanant, J., Shi, F., Kirby, J.T. & Watts, P. 2007 Source constraints and model simulation of the December 26, 2004, Indian Ocean tsunami. ASCE J. Waterway Port Coastal Ocean Engng 133 (6), 414–428.CrossRefGoogle Scholar
Hamling, I.J., et al. 2017 Complex multifault rupture during the 2016 M $_\textrm {w}$ 7.8 Kaikōura earthquake, New Zealand. Science 356 (6334), eaam7194.CrossRefGoogle Scholar
Hammack, J.L. 1973 A note on tsunamis: their generation and propagation in an ocean of uniform depth. J. Fluid Mech. 60 (4), 769–799.CrossRefGoogle Scholar
Hendin, G. & Stiassnie, M. 2013 Tsunami and acoustic-gravity waves in water of constant depth. Phys. Fluids 25 (8), 086103.CrossRefGoogle Scholar
Kadri, U. 2015 Acoustic-gravity waves interacting with a rectangular trench. Intl J. Geophys. 2015, 1–9.CrossRefGoogle Scholar
Kadri, U. 2016 Generation of hydroacoustic waves by an oscillating ice block in Arctic zones. Adv. Acoust. Vib. 2016, 1–7.Google Scholar
Kadri, U. 2019 Effect of sea-bottom elasticity on the propagation of acoustic–gravity waves from impacting objects. Sci. Rep. 9 (1), 912.CrossRefGoogle ScholarPubMed
Kadri, U. & Akylas, T.R. 2016 On resonant triad interactions of acoustic–gravity waves. J. Fluid Mech. 788, R1.CrossRefGoogle Scholar
Kadri, U. & Stiassnie, M. 2012 Acoustic-gravity waves interacting with the shelf break: interaction of acoustic-gravity waves. J. Geophys. Res. 117 (C3), C03035.Google Scholar
Kadri, U. & Stiassnie, M. 2013 a Generation of an acoustic-gravity wave by two gravity waves, and their subsequent mutual interaction. J. Fluid Mech. 735, R6.CrossRefGoogle Scholar
Kadri, U. & Stiassnie, M. 2013 b A note on the shoaling of acoustic–gravity waves. WSEAS Trans. Fluid Mech. 8 (2), 43–49.Google Scholar
Mei, C.C. & Kadri, U. 2018 Sound signals of tsunamis from a slender fault. J. Fluid Mech. 836, 352–373.CrossRefGoogle Scholar
Mei, C.C., Stiassnie, M. & Yue, D.K.-P. 2009 Theory and Applications of Ocean Surface Waves. World Scientific.Google Scholar
Michele, S. & Renzi, E. 2020 Effects of the sound speed vertical profile on the evolution of hydroacoustic waves. J. Fluid Mech. 883, A28.CrossRefGoogle Scholar
Miyoshi, H. 1954 Generation of the tsunami in compressible water (Part I). J. Oceanogr. Soc. Japan 10 (1), 1–9.CrossRefGoogle Scholar
Nosov, M.A. 1999 Tsunami generation in compressible ocean. Phys. Chem. Earth B 24 (5), 437–441.CrossRefGoogle Scholar
Okal, E.A., Reymond, D. & Hébert, H. 2014 From earthquake size to far-field tsunami amplitude: development of a simple formula and application to DART buoy data. Geophys. J. Intl 196 (1), 340–356.CrossRefGoogle Scholar
Prestininzi, P., Abdolali, A., Montessori, A., Kirby, J.T. & Rocca, M.L. 2016 Lattice Boltzmann approach for hydro-acoustic waves generated by tsunamigenic sea bottom displacement. Ocean Model. 107, 14–20.CrossRefGoogle Scholar
Renzi, E. 2017 Hydro-acoustic frequencies of the weakly compressible mild-slope equation. J. Fluid Mech. 812, 5–25.CrossRefGoogle Scholar
Renzi, E. & Dias, F. 2014 Hydro-acoustic precursors of gravity waves generated by surface pressure disturbances localised in space and time. J. Fluid Mech. 754, 250–262.CrossRefGoogle Scholar
Richards, D. 2009 Advanced Mathematical Methods with Maple 2 Part Set: Advanced Mathematical Methods with Maple 2 Part Paperback Set, 1st edn. Cambridge University Press.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.CrossRefGoogle 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 (1–2), 23–32.CrossRefGoogle Scholar
Watada, S. 2013 Tsunami speed variations in density-stratified compressible global oceans: tsunami speed in layered ocean. Geophys. Res. Lett. 40 (15), 4001–4006.CrossRefGoogle Scholar
Watada, S., Kusumoto, S. & Satake, K. 2014 Traveltime delay and initial phase reversal of distant tsunamis coupled with the self-gravitating elastic earth: delay and precursor of distant tsunami. J. Geophys. Res. 119 (5), 4287–4310.CrossRefGoogle 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

Williams et al. supplementary movie 1

Bottom pressure fields from the numerical model for a single fault (L= 100 km and b= 10 km). The parameters are given in Figure 3. the numerical domain extent and the coordinates of the virtual point observations are shown.

Download Williams et al. supplementary movie 1(Video)
Video 72.2 MB

Williams et al. supplementary movie 2

Bottom pressure fields from the current model, Eq. (5.1) (left column), numerical model for the case of constant depth of 4 km (middle column) and numerical model for the case of variable depth (right column).

Download Williams et al. supplementary movie 2(Video)
Video 28 MB
Supplementary material: PDF

Williams et al. supplementary material

Supplementary data

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