Elimination of branch cuts from the normal-mode solution using gradient half spaces

Journal of the Acoustical Society of America

Volumn 106, Issue 5, 1999, Pages 2513-2523

  Westwood, Evan K ^a   Koch, Robert A ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTICS; ALGORITHM; ARTICLE; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL; SOUND TRANSMISSION;

EID: 0032716546     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.428083     Document Type: Article

References (24)

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3. D. C. Stickler, "Normal-mode program with both the discrete and branch line contributions," J. Acoust. Soc. Am. 57, 856-861 (1975).
4. C. L. Bartberger, "Comparison of two normal-mode solutions based on different branch cuts," J. Acoust. Soc. Am. 61, 1643 (1977).
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10. Despite the fact that leaky modes are unbounded in the lower half space, leaky modes are certainly useful because they are well-behaved inside the waveguide. Deep in the half space, where the total field must be small, the large field produced by the unbounded leaky modes is counteracted by a large field due to the PBLI. Haddon (Refs. 11 and 12) has developed a method for computing the pulse response of a waveguide using complex frequencies, as well as wave numbers, and has shown that the leaky modes become well-behaved.
11. R. A. W. Haddon, "Exact evaluation of the explosive response of a layered elastic medium to an explosive point source using leaking modes," Bull. Seismol. Soc. Am. 76, 1755-1775 (1986).
12. R. A. W. Haddon, "Response of an oceanic waveguide to an explosive point source using leaking modes," Bull. Seismol. Soc. Am. 77, 1804-1822(1987).
13. C. A. Boyles, Acoustic Waveguides (Wiley, New York, 1984).
14. L. Brekhovskikh, Waves in Layered Media, 2nd ed. (Academic, New York, 1980).
15. M. A. Pedersen and D. F. Gordon, "Normal-mode theory applied to short-range propagation in an underwater acoustic surface duct," J. Acoust. Soc. Am. 37, 105-118 (1965).
16. M. A. Pedersen and D. F. Gordon, "Theoretical investigation of a double family of normal modes in an underwater acoustic surface duct," J. Acoust. Soc. Am. 47, 304-326 (1969).
17. 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. 51, 323-368 (1972).
18. M. Hall, "Normal mode theory: The role of the branch-line integral in Pederson-Gordon type models," J. Acoust. Soc. Am. 72, 1978 (1988).
19. F. B. Jensen, W. A. Kuperman, M. B. Porter, and H. Schmidt, Computational Ocean Acoustics (American Institute of Physics, New York, 1994).
20. E. K. Westwood, C. T. Tindle, and N. R. Chapman, "A normal mode model for acousto-elastic ocean environments,"J. Acoust. Soc. Am, 100, 3631-3645 (1996).
21. For more complicated layering structures the branch culs associated with the vertical wave numbers for the lower half space and reference depth remain in the functional behavior of R1, but those in intermediate layers are cancelled out by intermediate operations.
22. H. Schmidt and F. B. Jensen, "A full wave solution for propagation in multilayered viscoelastic media with application to Gaussian beam reflection at fluid-solid interfaces," J. Acoust. Soc. Am. 77, 813-825 (1985).
23. avg the two definitions are the same. But for a 3-dB difference in a 20-dB null, the new definition results in a 0.35-dB difference.
24. The option in OASES to refrain from using the asymptotic representation for the Bessel function is available in the broadband pulse module OASP, but not in the TL module OAST. Attempts by the authors to extract the correct single-frequency TL from the OASP module were not successful, apparently because of convergence problems. The validity of ORCA at short range was checked by placing the receiver I m from the source and verifying that the TL was approximately O dB, as was done for Fig. 5 of Ref. 20.