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Gaussian Beams and 3-D Bottom Interacting Acoustic Systems

  • Homer P. Bucker
  • Michael B. Porter
Part of the NATO Conference Series book series (NATOCS, volume 16)

Abstract

The analysis of the performance of current array systems requires accurate propagation modeling. In addition, future signal processing algorithms may incorporate a propagation model in order to obtain improved target tracking. The acoustic field received at an array of sensors located on or near the ocean bottom is strongly affected by the local bathymetry and by the physical properties of the ocean subbottom. At very low frequencies, the acoustic field may even be affected by the physical properties of the basement underlying the top sediment layers. This paper describes two techniques based on Gaussian beam tracing for computing the acoustic field in such an environment. The first method employs empirically derived formulas governing the spread of the beams and has the advantage of great simplicity. In the second method the beam curvature and width are obtained formally from an ordinary differential equation along the central ray. This latter method has recently received a lot of attention in the seismological community. Both methods are free of the difficulties at caustics and in shadow zones which afflict standard ray tracing algorithms. Comparisons are presented between the standard ray tracing, simplified beam tracing, formal beam tracing and the exact solution for a difficult negative sound speed gradient problem previously examined by Pedersen and Gordon. Finally, a detection system is proposed that employs Gaussian beam tracing convolved with target tracking.

Keywords

Gaussian Beam Acoustic Field Ocean Bottom Stoneley Wave Shadow Zone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    J. L. Worzel and M. Ewing, Explosion sounds in shallow water, Section I, pp. 1–53 in Geological Society of America, Memoir 27, (1948).Google Scholar
  2. 2.
    C. L. Pekeris, Theory of propagation of explosive sound in shallow water, Sect. II, pp. 1–117 in Geological Society of America, Memoir 27 (1948).Google Scholar
  3. 3.
    H. P. Bucker, J. A. Whitney, G. S. Yee and R. S. Gardner, “Reflection of low frequency sonar signals from a smooth ocean bottom,” J. Acoustic Soc. America, No. 37, pp. 1037–1051 (1965).CrossRefGoogle Scholar
  4. 4.
    E. L. Hamilton, “Geoacoustic modeling of the sea floor,” J. Acoustic. Soc. Am., No. 68, pp. 1313–1340 (1980).CrossRefGoogle Scholar
  5. 5.
    E. L. Hamilton and R. T. Bachman, “Sound velocity and related properties of marine sediments,” J. Acoustic. Soc. Am., No. 72, pp. 1891–1904 (1982).CrossRefGoogle Scholar
  6. 6.
    E. L. Hamilton, R. T. Bachman, R. T. Berger, W. R. Johnson and L. A. Mayer, “Acoustic and related properties of calcareous deep-sea sediments,” J. Sedimentary Petrology, No. 52, pp. 733–753 (1982).Google Scholar
  7. 7.
    O. F. Hastrup, “Some bottom-reflection loss anomalies near grazing and their affect on propagation in shallow water,” pp. 135–152 in Ref. 18.Google Scholar
  8. 8.
    T. Akal, “Sea floor affects on shallow-water acoustic propagation,” pp. 557–575 in Ref. 18.Google Scholar
  9. 9.
    K. E. Hawker, “The existence of Stoneley waves as a loss mechanism in plane wave reflection problems,” J. Acoustic Soc. Am., No. 65, pp. 622–686 (1979).CrossRefGoogle Scholar
  10. 10.
    P. J. Vidmar, “Ray path analysis of sediment shear wave affects in bottom reflection loss,” J. Acoust. Soc. Am., No. 68, pp. 639–648 (1980).CrossRefGoogle Scholar
  11. 11.
    H. Holthusen and P. J. Vidmar, “The affect of near-surface layering on the reflectivity of the ocean bottom,” J. Acoust. Soc. Am., No. 72, pp. 226–234 (1982).CrossRefGoogle Scholar
  12. 12.
    R. A. Koch, P. J. Vidmar, and J. B. Lindberg, “Normal mode identification for impedence boundary conditions,” J. Acoust. Soc. Am., No. 73, pp. 1567–1570 (1983).CrossRefGoogle Scholar
  13. 13.
    F. B. Jensen and W. A. Kuperman, “Sound propagation in a wedge shaped ocean with a penetrable bottom,” J. Acoust. Soc. Am., No. 67, pp. 1564–1566 (1980).CrossRefGoogle Scholar
  14. 14.
    S. T. McDaniel and D. Lee, “A finite-difference treatment of interface conditions for the parabolic equation,” J. Acoust. Soc. Am., No. 71, pp. 855–858 (1982).CrossRefGoogle Scholar
  15. 15.
    H. P. Bucker, “An equivalent bottom for use with the split-stop algorithm,” J. Acoust. Soc. Am., No. 73, pp. 486–491 (1983).CrossRefGoogle Scholar
  16. 16.
    F. D. Tappert, “The parabolic equation method,” Sect. V in Lecture Notes in Physicis, No. 70, Ed. by J. B. Keller and J. S. Papadakis, Springer Verlag, Berlin, 1977.Google Scholar
  17. 17.
    Physics of Sound in Marine Sediments, ed, by Loyd Hampton, Plenum Press, New York, 1974.Google Scholar
  18. 18.
    Bottom Interacting Acoustics, ed. by W. Kuperman and F. Jensen, Plenum Press, New York, 1980.Google Scholar
  19. 19.
    G. A. Deschamps, “Gaussian beams as a bundle of complex rays,” Electronics Letters, No 7, pp. 684–685 (1971).CrossRefGoogle Scholar
  20. 20.
    L. B. Felsen, “Geometrical theory of diffraction, evanescent waves, complex rays and Gaussian beams,” Geophys. J. R. astr. Soc., No. 79, pp. 77–88 (1984).CrossRefGoogle Scholar
  21. 21.
    M. A. Pedersen and D. F. Gordon, “Normal-mode and ray theory applied to underwater acoustic conditions of extreme downward refraction,” J. Acoust. Soc. Am., No. 51, pp. 323–368 (1971).CrossRefGoogle Scholar
  22. 22.
    H. P. Bucker, “Some comments on ray theory with examples from current NUC ray trace models,” pp. 32–36 in SACLANT Conf. Proceed., No. 5, (1971).Google Scholar
  23. 23.
    V. Červeny, M. M. Popov, and I. Pšenčík, “Computation of wave fields in inhomogeneous media-Gaussian beam approach,” Geophys. J. R. astr. Soc., No. 70, pp. 109–128 (1982).CrossRefGoogle Scholar
  24. 24.
    L. Klimes, “Expansion of a high frequency time-harmonic wavefield given on an initial surface into Gaussian beams,” Geophys. J. R. astr. Soc., No. 79, pp. 105–118 (1984).CrossRefGoogle Scholar
  25. 25.
    V. Cerveny and I. Psencik, “Gaussian beams in elastic 2-D laterally varying structures,” Geophys. J. R. astr. Soc., No. 78, pp. 65–91 (1984).CrossRefGoogle Scholar
  26. 26.
    C. T. Tindle, “Ray calculations with beam displacements,” J. Acoust. Soc. Am., No. 73, pp. 1581–1586 (1983).CrossRefGoogle Scholar
  27. 27.
    H. P. Bucker, “Use of calculated fields and matched-field detection to locate sound sources in shallow water,” J. Acoust. Soc. Am., No. 59, pp. 368–373 (1976).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • Homer P. Bucker
    • 1
  • Michael B. Porter
    • 1
  1. 1.U.S. Naval Ocean Systems Center, Code 541San DiegoUSA

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