China Ocean Engineering

, Volume 30, Issue 4, pp 591–601 | Cite as

Model of shipping noise in the deep water: Directional density and spatial coherence functions

  • Peng Xiao (肖 鹏)
  • Kun-de Yang (杨坤德)Email author
  • Bo Lei (雷 波)


The shipping noise properties in the deep ocean are studied. Shipping noise exhibits the strong dual-horned directionality features in the flat-seabed ocean, and its directional density can be modeled by a Von Mises distribution. With the explicit expression for the directional density function, the spatial coherence functions of shipping noise are also derived, and the relative features are studied. The research result shows that the properties of shipping noise are different from the ambient noise of other sources, and it can be used for the sonar array design. The model is well matched with the experimental result, and it can be extended to the situations when the ambient noise exhibits the dual-horned structure.

Key words

shipping noise dual-horned structure Von Mises distribution directional density spatial coherence 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Buckingham, M. J., 2013. Theory of the directionality and spatial coherence of wind-driven ambient noise in a deep ocean with attenuation, J. Acoust. Soc. Am., 134(2): 950–958.CrossRefGoogle Scholar
  2. Carey, W. M., Evans, R. B., Davis, J. A. and Botseas, G., 1990. Deep-ocean vertical noise directionality, IEEE J. Oceanic Eng., 15(4): 324–334.CrossRefGoogle Scholar
  3. Carey, W. M. and Evans, R. B., 2011. Ocean Ambient Noise Measurement and Theory, Springer-Verlag New York Press, New York.CrossRefGoogle Scholar
  4. Cron, B. F. and Sherman, C. H., 1962. Spatial-correlation function for various noise models, J. Acoust. Soc. Am., 34(11): 1732–1736.CrossRefGoogle Scholar
  5. Cron, B. F. and Sherman, C. H., 1965. Spatial-correlation function for various noise models, J. Acoust. Soc. Am., 38, 885.CrossRefGoogle Scholar
  6. Cox, H., 1973. Spatial correlation in arbitrary noise field with application to ambient sea noise, J. Acoust. Soc. Am., 54(5): 1289–1301.CrossRefGoogle Scholar
  7. Duan, R., Yang, K., Ma, Y., Yang, Q. and Li, H., 2014a. Moving source localization with a single hydrophone using multipath time delays in the deep ocean, J. Acoust. Soc. Am., 136(2): 159–165.CrossRefGoogle Scholar
  8. Duan, R., Yang, K. and Ma, Y., 2014b. Narrowband source localization in the deep ocean using a near-surface array, Acoust. Aust., 42(1): 36–42.Google Scholar
  9. Evans, M., Hastings, N. and Peacock, B., 2000. Statistical Distributions, 3rd edition, Wiley, New York.zbMATHGoogle Scholar
  10. Harrison, C. H., 1997. Formulas for ambient noise level and coherence, J. Acoust. Soc. Am., 99(4): 2055–2066.CrossRefGoogle Scholar
  11. Kuperman, W. A. and Ingenito, F., 1980. Spatial correlation of surface generated noise in a stratified ocean, J. Acoust. Soc. Am., 67(6): 1988–1996.CrossRefzbMATHGoogle Scholar
  12. Liggett, W. S. and Jacobson, M. J., 1966. Noise covariance and vertical directivity in a deep ocean, J. Acoust. Soc. Am., 39(2): 280–288.CrossRefGoogle Scholar
  13. Munk, W. H., 1974. Sound channel in an exponentially stratified ocean with applications to SOFAR, J. Acoust. Soc. Am., 55(2): 220–226.CrossRefGoogle Scholar
  14. Porter, M., 1991. The KRAKEN Normal Mode Program, SACLANT Undersea Res. Ctr., Memo. SM–245.Google Scholar
  15. Walker, S. C. and Buckingham, M. J., 2012. Spatial coherence and cross correlation of three-dimensional ambient noise fields in the ocean, J. Acoust. Soc. Am., 131(2): 1079–1086.CrossRefGoogle Scholar
  16. Wagstaff, R. A., 1981. Low-frequency ambient noise in the deep sound channel–the missing component, J. Acoust. Soc. Am., 69(4): 1009–1014.MathSciNetCrossRefGoogle Scholar
  17. Xiao, P. and Yang, K., 2015. Experimental results for peak pressure and sound exposure level in deep-sea explosions, Acoust. Aust., 43(2): 175–178.CrossRefGoogle Scholar

Copyright information

© Chinese Ocean Engineering Society and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Peng Xiao (肖 鹏)
    • 1
    • 2
  • Kun-de Yang (杨坤德)
    • 1
    • 2
    Email author
  • Bo Lei (雷 波)
    • 1
    • 2
  1. 1.Key Laboratory of Ocean Acoustics and SensingNorthwestern Polytechnical University, Ministry of Industry and Information TechnologyXi’anChina
  2. 2.School of Marine science and technologyNorthwestern Polytechnical University, Ministry of Industry and Information TechnologyXi’anChina

Personalised recommendations