Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-13T22:33:01.987Z Has data issue: false hasContentIssue false
  • English
  • Français

Noise generation in the solid Earth, oceans and atmosphere, from nonlinear interacting surface gravity waves in finite depth

Published online by Cambridge University Press:  25 January 2013

Fabrice Ardhuin  and
T. H. C. Herbers
Fabrice Ardhuin*
Affiliation:
Ifremer, Laboratoire d’Océanographie Spatiale, 29280 Plouzané, France
T. H. C. Herbers
Affiliation:
Department of Oceanography, Naval Postgraduate School, Monterey, CA 93943, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Oceanic pressure measurements, even in very deep water, and atmospheric pressure or seismic records, from anywhere on Earth, contain noise with dominant periods between 3 and 10 s, which is believed to be excited by ocean surface gravity waves. Most of this noise is explained by a nonlinear wave–wave interaction mechanism, and takes the form of surface gravity waves, acoustic or seismic waves. Previous theoretical work on seismic noise focused on surface (Rayleigh) waves, and did not consider finite-depth effects on the generating wave kinematics. These finite-depth effects are introduced here, which requires the consideration of the direct wave-induced pressure at the ocean bottom, a contribution previously overlooked in the context of seismic noise. That contribution can lead to a considerable reduction of the seismic noise source, which is particularly relevant for noise periods larger than 10 s. The theory is applied to acoustic waves in the atmosphere, extending previous theories that were limited to vertical propagation only. Finally, the noise generation theory is also extended beyond the domain of Rayleigh waves, giving the first quantitative expression for sources of seismic body waves. In the limit of slow phase speeds in the ocean wave forcing, the known and well-verified gravity wave result is obtained, which was previously derived for an incompressible ocean. The noise source of acoustic, acoustic-gravity and seismic modes are given by a mode-specific amplification of the same wave-induced pressure field near zero wavenumber.

JFM classification

Acoustics: Acoustics Geophysical and Geological Flows: Geophysical and Geological Flows Waves/Free-surface Flows: Surface gravity waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 716 , 10 February 2013 , pp. 316 - 348
Copyright
©2013 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramovici, F. 1968 Diagnostic diagrams and transfer functions for oceanic wave-guides. Bull. Seismol. Soc. Am. 58 (1), 426–456.Google Scholar
Aki, K. & Richards, P. G. 2002 Quantitative Seismology, 2nd edn. University Science Books.Google Scholar
Anderson, D. L. & Hart, R. S. 1978 Q of the Earth. J. Geophys. Res. 83 (B12), 5869–5882.Google Scholar
Ardhuin, F., Chapron, B. & Collard, F. 2009 Observation of swell dissipation across oceans. Geophys. Res. Lett. 36, L06607.Google Scholar
Ardhuin, F., Stutzmann, E., Schimmel, M. & Mangeney, A. 2011 Ocean wave sources of seismic noise. J. Geophys. Res. 116, C09004.Google Scholar
Arendt, S. & Fritts, D. C. 2000 Acoustic radiation by ocean surface waves. J. Fluid Mech. 415, 1–21.Google Scholar
Arrowsmith, S. J., Johnson, J. B., Drob, D. P. & Hedlin, M. A. H. 2010 The seismoacoustic wavefield: a new paradigm in studying geophysical phenomena. Rev. Geophys. 48, RG4003.CrossRefGoogle Scholar
Bonnefoy-Claudet, S., Cotton, F. & Bard, P.-Y. 2006 The nature of noise wavefield and its applications for site effects studies: a literature review. Earth Sci. Rev. 79, 205–227.Google Scholar
Cooper, R. I. B. & Longuet-Higgins, M. S. 1951 An experimental study of the pressure variations in standing water waves. Proc. R. Soc. Lond. A 206, 426–435.Google Scholar
Cox, C. S. & Jacobs, D. C. 1989 Cartesian diver observations of double frequency pressure fluctuations in the upper levels of the ocean. Geophys. Res. Lett. 16 (8), 807–810.Google Scholar
Duennebier, F. K., Lukas, R., Nosal, E.-M., Aucan, J. & Weller, R. A. 2012 Wind, waves, and acoustic background levels at Station ALOHA. J. Geophys. Res. 117, C03017.Google Scholar
Farrell, W. E. & Munk, W. 2008 What do deep sea pressure fluctuations tell about short surface waves? Geophys. Res. Lett. 35 (7), L19605.Google Scholar
Farrell, W. E. & Munk, W. 2010 Booms and busts in the deep. J. Phys. Oceanogr. 40 (9), 2159–2169.Google Scholar
Fukao, Y., Nishida, K. & Kobayashi, N. 2010 Seafloor topography, ocean infragravity waves, and background Love and Rayleigh waves. J. Geophys. Res. 112 (10), B04302.Google Scholar
Hasselmann, K. 1962 On the nonlinear energy transfer in a gravity wave spectrum, Part 1: General theory. J. Fluid Mech. 12, 481–501.Google Scholar
Hasselmann, K. 1963 A statistical analysis of the generation of microseisms. Rev. Geophys. 1 (2), 177–210.Google Scholar
Hasselmann, K. 1966 Feynman diagrams and interaction rules of wave–wave scattering processes. Rev. Geophys. 4 (1), 1–32.Google Scholar
Hasselmann, K., Barnett, T. P., Bouws, E., Carlson, H., Cartwright, D. E., Enke, K., Ewing, J. A., Gienapp, H., Hasselmann, D. E., Kruseman, P., Meerburg, A., Müller, P., Olbers, D. J., Richter, K., Sell, W. & Walden, H. 1973 Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project. Dtsch. Hydrogr. Z. 8 (12, Suppl. A), 1–95.Google Scholar
Herbers, T. H. C. & Guza, R. T. 1991 Wind-wave nonlinearity observed at the sea floor. Part I: Forced-wave energy. J. Phys. Oceanogr. 21, 1740–1761.Google Scholar
Herbers, T. H. C. & Guza, R. T. 1994 Nonlinear wave interactions and high-frequency seafloor pressure. J. Geophys. Res. 99, 10035–10048.Google Scholar
Herbers, T. H. C., Lowe, R. L. & Guza, R. T. 1992 Field observations of orbital velocities and pressure in weakly nonlinear surface gravity waves. J. Fluid Mech. 245, 413–435.CrossRefGoogle Scholar
Hillers, G., Graham, N., Campillo, M., Kedar, S., Landès, M. & Shapiro, N. 2012 Global oceanic microseism sources as seen by seismic arrays and predicted by wave action models. Geochem. Geophys. Geosyst. 115, B05302.Google Scholar
Hughes, B. 1976 Estimates of underwater sound (and infrasound) produced by nonlinearly interacting ocean waves. J. Acoust. Soc. Am. 60 (5), 1032–1039.Google Scholar
Kanamori, H. & Given, J. W. 1981 Use of long-period surface waves for rapid determination of earthquake-source parameters. Phys. Earth Planet. Inter. 27 (1), 8–31.Google Scholar
Kedar, S., Longuet-Higgins, M., Graham, F. W. N., Clayton, R. & Jones, C. 2008 The origin of deep ocean microseisms in the north Atlantic ocean. Proc. R. Soc. Lond. A 1–35.Google Scholar
Kibblewhite, A. C. & Ewans, K. C. 1985 Wave–wave interactions, microseisms, and infrasonic ambient noise in the ocean. J. Acoust. Soc. Am. 76 (3), 981–994.Google Scholar
Knudsen, V. O., Alford, R. S. & Emling, J. W. 1948 Underwater ambient noise. J. Mar. Res. 7, 410–429.Google Scholar
Koper, K. D., Seats, K. & Benz, H. 2010 On the composition of Earth’s short-period seismic noise field. Bull. Seismol. Soc. Am. 100 (2), 606–617.Google Scholar
Kurrle, D. & Widmer-Schnidrig, R. 2008 The horizontal hum of the Earth: a global background of spheroidal and toroidal modes. Geophys. Res. Lett. 35 (2), L06304.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.Google Scholar
Landès, M., Hubans, F., Shapiro, N. M., Paul, A. & Campillo, M. 2010 Origin of deep ocean microseisms by using teleseismic body waves. J. Geophys. Res. 115, B05302.Google Scholar
de Laplace, P. S. 1776 Mem. Présentés par Divers Savants Acad. Sci. Inst. Fr. 542–552.Google Scholar
Latham, G. V. & Sutton, G. H. 1966 Seismic measurements on the ocean floor. J. Geophys. Res. 71 (10), 2545–2573.Google Scholar
Lighthill, J. 1978 Waves in Fluids. Cambridge University Press.Google Scholar
Lighthill, J. M. 1952 On sound generated aerodynamically. Proc. R. Soc. Lond. A 211, 564–587.Google Scholar
Lloyd, S. P. 1981 Underwater sound from surface waves according to the Lighthill–Ribner theory. J. Acoust. Soc. Am. 69 (2), 425–435.Google Scholar
Longuet-Higgins, M. S. 1950 A theory of the origin of microseisms. Phil. Trans. R. Soc. Lond. A 243, 1–35.Google Scholar
Longuet-Higgins, M. S. 1970 Mass transport in the boundary layer at a free oscillating surface. J. Fluid Mech. 8, 293–306.Google Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1962 Radiation stresses and mass transport in surface gravity waves with application to ‘surf beats’. J. Fluid Mech. 13, 481–504.Google Scholar
Miller, G. F. & Pursey, H. 1955 On the partition of energy between elastic waves in a semi-infinite solid. Proc. R. Soc. Lond. A 233 (1192), 55–69.Google Scholar
Nishida, K. & Fukao, Y. 2006 Source distribution of Earth’s background free oscillations. J. Geophys. Res. 112 (10), B06306.Google Scholar
Nishida, K., Kawakatsu, H., Fukao, Y. & Obara, K. 2008 Background Love and Rayleigh waves simultaneously generated at the Pacific ocean floors. Geophys. Res. Lett. 35 (2), L16307.Google Scholar
Obrebski, M., Ardhuin, F., Stutzmann, E. & Schimmel, M. 2012 How moderate sea states can generate loud seismic noise in the deep ocean. Geophys. Res. Lett. 39, L11601.Google Scholar
Okal, E. A. 1988 Seismic parameters controlling far-field tsunami amplitudes: a review. Nat. Hazards 1, 67–96.Google Scholar
Pasyanos, M. E., Walter, W. R. & Matzel, E. M. 2009 A simultaneous multiphase approach to determine $P$ -wave and $S$ -wave attenuation of the crust and upper mantle. Bull. Seismol. Soc. Am. 99, 3314–3325.Google Scholar
Peregrine, D. H. 1976 Interaction of water waves and currents. Adv. Appl. Mech. 16, 9–117.Google Scholar
Posmentier, E. 1967 A theory of microbaroms. Geophys. J. R. Astron. Soc. 13, 487–501.Google Scholar
Rhie, J. & Romanowicz, B. 2006 A study of the relation between ocean storms and the Earth’s hum. Geochem. Geophys. Geosyst. 7 (10), Q10004.Google Scholar
Shapiro, N. M., Campillo, M., Stehly, L. & Ritzwoller, M. H. 2005 High-resolution surface-wave tomography from ambient seismic noise. Science 307, 1615–1617.Google Scholar
Snoke, J. A. 2009 Traveltime tables for iasp91 and ak135. Seismol. Res. Lett. 88 (2), 260–262.Google Scholar
Stoneley, R. 1926 The effect of the ocean on Rayleigh waves. Mon. Not. R. Astron. Soc. Geophys. (Suppl. 1), 349–356.Google Scholar
Tanimoto, T. 2007 Excitation of normal modes by nonlinear interaction of ocean waves. Geophys. J. Intl 168, 571–582.Google Scholar
Tyler, G. L., Teague, C. C., Stewart, R. H., Peterson, A. M., Munk, W. H. & Joy, J. W. 1974 Wave directional spectra from synthetic aperture observations of radio scatter. Deep-Sea Res. 21, 989–1016.Google Scholar
Vinnik, L. P. 1973 Sources of microseismic $P$ waves. Pure Appl. Geophys. 103 (1), 282–289.Google Scholar
Waxler, R. & Gilbert, K. E. 2006 The radiation of atmospheric microbaroms by ocean waves. J. Acoust. Soc. Am. 119, 2651–2664.Google Scholar
Webb, S. C. 1998 Broadband seismology and noise under the ocean. Rev. Geophys. 36, 105–142.Google Scholar
Webb, S. C. 2007 The Earth’s ‘hum’ is driven by ocean waves over the continental shelves. Nature 445, 754–756.Google Scholar